Understanding Mechanical Behavior of Lunar Soils for The

Home , Direct shear test, Shorty (crater), Sinus Medii

UNDERSTANDING MECHANICAL BEHAVIOR OF LUNAR SOILS FOR THE

STUDY OF VEHICLE MOBILITY

HEATHER ANN ORAVEC

Submitted in partial fulfillment of the requirements

For the degree of Doctor of Philosophy

Dissertation Adviser: Dr. Xiangwu Zeng

Department of Civil Engineering

CASE WESTERN RESERVE UNIVERSITY

May, 2009

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

______

candidate for the ______degree *.

(signed)______(chair of the committee)

______

(date) ______

*We also certify that written approval has been obtained for any proprietary material contained therein.

Dedication:

To my best friend and my greatest supporter, my mother Ruth Marie Hlasko

TABLE OF CONTENTS

List of Tables vii

List of Figures x

Acknowledgements xxii

List of Abbreviations xxiv

Glossary xxvi

Abstract xxix

CHAPTER ONE

INTRODUCTION 1

1.1 History of Lunar Exploration 1

1.2 Future of Lunar Exploration 11

1.2.1 Why the Moon? 12

1.3 Motivation for This Research 15

1.4 Introduction to Surface Mobility 17

1.4.1 Development of Off-Road Vehicles 19

1.4.2 Development of Terramechanics 21

1.5 General Factors Affecting Surface Mobility 22

1.6 Soil Properties Affecting Surface Mobility 25

1.6.1 Bevameter Technique for Determining Soil Strength 28

1.6.1.1 Bearing Capacity 30

1.6.1.2 Shear Strength 43

1.6.2 Other Techniques for Measuring Soil Properties in

Terramechanics 54

1.6.2.1 Direct Shear Test 55

1.6.2.2 Torsional Shear Test 57

1.6.2.3 Triaxial Test 59

1.6.2.4 Cone Penetrometer Test 63

1.6.2.5 Shear Vane, Vane-Cone, and Cohron Sheargraph Tests 70

1.7 Nature of the Lunar Terrain 74

1.7.1 The Lunar Environment 74

1.7.1.1 The Lunar Landscape 76

1.7.2 The Lunar Regolith 81

1.7.2.1 Formation of the Lunar Regolith 82

1.7.2.2 Engineering Properties of the Lunar Regolith 84

1.7.2.3 Trafficability Parameters 94

1.7.3 Important Aspects for Lunar Surface Mobility 97

1.7.3.1 Cohesion 97

1.7.3.2 Friction 99

1.8 Problem Statement and Objectives 100

1.8.1 Scope of Work 103

1.8.2 Basic Assumptions 104

1.9 Organization of the Dissertation 105

CHAPTER TWO

LITERATURE REVIEW 107

2.1 Review of Lunar Soil Investigations 107

2.1.1 Soil Investigations on the Moon 108

2.1.1.1 Robot Interaction 110

2.1.1.2 Spacecraft Interaction 114

2.1.1.3 Footprint Analysis 117

2.1.1.4 Trenching Tests and Boulder Tracks 119

2.1.1.5 Penetrometer Tests 123

2.1.2 Soil Investigations on Returned Lunar Soil 135

2.1.2.1 Apollo Soil Samples 137

2.1.2.2 Laboratory Tests 142

2.2 Review of Lunar Soil Simulants 150

2.2.1 MLS-1 151

2.2.2 JSC-1 155

2.2.3 JSC-1A 159

2.2.4 Other Lunar Soil Simulants 163

2.3 Review of Lunar Vehicle Mobility Studies 166

2.3.1 Lunar Roving Vehicle 166

2.3.1.1 Trafficability and Wheel-Soil Interaction Studies 170

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CHAPTER THREE

DEVELOPMENT OF A NEW LUNAR SOIL SIMULANT: GRC-1 189

3.1 Method for Creating GRC-1 189

3.2 Initial Characterization of GRC-1 197

3.2.1 Particle Size Distribution 198

3.2.2 Specific Gravity 205

3.2.3 Maximum and Minimum Bulk Density with Respect to

Relative Density 209

3.2.4 Porosity and Void Ratio 213

3.2.5 Compressibility 215

3.2.6 Angle of Inclination 221

3.3 Comparison to Lunar Soil and Lunar Soil Simulants 224

CHAPTER FOUR

TRIAXIAL TESTING FOR STRENGTH OF GRC-1 230

4.1 Triaxial Apparatus at NASA Glenn 230

4.2 Experimental Procedure 234

4.3 Test Results and Analysis 240

4.4 Comparison with Lunar Soil 253

4.5 Effect of Strength Properties on Vehicle Mobility 254

CHAPTER FIVE

BEVAMETER TESTING FOR STRENGTH OF GRC-1 261

5.1 Development of NASA Glenn Laboratory Bevameter 261

5.2 Experimental Setup and Limitations 267

5.2.1 Soil Preparation Method 267

5.2.2 Soil Bin Requirements 275

5.2.3 End Effector Requirements 307

5.3 Pressure-Sinkage Test for Vehicle Mobility 312

5.3.1 Experimental Procedure 316

5.3.2 Test Results and Analysis 319

5.4 Shear Test for Vehicle Mobility 332

5.4.1 Experimental Procedure 336

5.4.2 Test Results and Analysis 339

5.5 Comparison with Lunar Soil 350

CHAPTER SIX

CONE PENETROMETER TESTING FOR STRENGTH OF GRC-1 352

6.1 Cone Penetrometer Device at NASA Glenn 352

6.2 Experimental Procedure 354

6.3 Test Results and Analysis 358

6.4 Comparison with Lunar Soil 374

CHAPTER SEVEN

SUMMARY AND CONCLUSIONS 381

7.1 Overview 381

7.2 Conclusions 382

7.3 Suggestions for Practical Use of GRC-1 387

7.4 Suggestions for Future Work 392

APPENDICES

Appendix A: Lunar soil and simulant properties 395

Appendix B: Initial characterization of GRC-1 414

Appendix C: Triaxial test results for GRC-1 416

Appendix D: Table bevameter results for GRC-1 492

Appendix E: Cone penetration test results for GRC-1 604

BIBLIOGRAPHY 616

LIST OF TABLES

Table 1.1 Lunar exploration summary 7

Table 1.2 Lunar exploration themes 13

Table 1.3 Subcategorized objectives for lunar exploration 14

Table 1.4 Comparison of the Moon and Earth 75

Table 1.5 Bulk density of lunar soil 89

Table 1.6 Relative density of the lunar soil 90

Table 1.7 Porosity and void ratio of the lunar soil 92

Table 1.8 Recommended values of lunar soil cohesion and friction angle 94

Table 1.9 Recommended trafficability parameters 96

Table 2.1 In-situ geotechnical properties of lunar soil from Lunokhod

observations 113

Table 2.2 Results of analysis on astronaut footprint depths 119

Table 2.3 Average cone index gradient for lunar soil near the Apollo 15

landing site 134

Table 2.4 Bulk density and void ratio of returned lunar soils 143

Table 2.5 Comparison of friction angle and cohesion of lunar soils and MLS-1 155

Table 2.6 Results of triaxial tests performed on JSC-1 158

Table 2.7 Results of triaxial tests performed on JSC-1A 162

Table 2.8 Comparison of lunar soil and simulated lunar soil 164

Table 2.9 Results of special tests on Yuma sand 178

Table 3.1 Initial target recipe for coarse grained lunar soil simulant 191

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Table 3.2 Histogram by weight for Best Sands compared to the target mixture

for a coarse lunar soil simulant 195

Table 3.3 Sieve sizes used for particle size distribution analysis 198

Table 3.4 Typical values of the temperature correction factor 208

Table 3.5 Results of specific gravity tests on GRC-1 208

Table 3.6 Results of maximum bulk density tests for GRC-1 212

Table 3.7 Results of minimum bulk density tests for GRC-1 212

Table 3.8 Porosity and void ratio of GRC-1 214

Table 3.9 Angle of repose of GRC-1 223

Table 3.10 Comparison of GRC-1 with lunar soil and lunar soil simulants 225

Table 4.1 Sample preparation method and corresponding density 241

Table 4.2 Results of triaxial tests from DS7 242

Table 4.3 Summary of GRC-1 internal angle of friction from triaxial tests 245

Table 4.4 Results of triaxial tests on GRC-1 using alternative analysis 250

Table 4.5 Cohesion and friction angle as determined using q and p 251

Table 4.6 Mohr’s circles compared with q-p method 252

Table 4.7 Friction angle of GRC-1 compared to lunar soil and lunar soil

simulants 253

Table 4.8 Typical properties of different vehicles 258

Table 4.9 Error in thrust caused by variation in cohesion 259

Table 4.10 Acceptable variability in cohesion 261

Table 5.1 Results of calibration for bevameter sensors 267

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Table 5.2 Current design properties of various prospective lunar exploration

vehicles 309

Table 5.3 Typical Bekker parameters for dry sand 325

Table 5.4 Bekker parameters for GRC-1 at various densities 330

Table 5.5 Summary of shear bevameter results for GRC-1 345

Table 5.6 Summary of shear bevameter results for GRC-1 using grousers 349

Table 5.7 Typical shear parameters for dry sand 350

Table 5.8 Comparison of lunar soil parameters to those of GRC-1 as

determined by bevameter testing 351

Table 6.1 Variation of cone index gradient with depth 362

Table 6.2 First test results for large cone 364

Table 6.3 Second test results for large cone 365

Table 6.4 First test results for small cone 366

Table 6.5 Second test results for small cone 367

Table 6.6 Results of cone penetration tests at various densities of GRC-1 371

Table 6.7 Cone index gradient of lunar soil based on Apollo missions 378

LIST OF FIGURES

Figure 1.1 Stonehenge 2

Figure 1.2 Sputnik 1 3

Figure 1.3 JFK calls for a mission to send man to the moon during a joint

session of Congress on May 25, 1961 4

Figure 1.4 Surveyor 6 model on Earth 5

Figure 1.5 Landing sites of the Luna, Ranger, Apollo, and Surveyor missions 10

Figure 1.6 Lunar landing site chart 10

Figure 1.7 President Bush announces plan for man’s return to Moon 11

Figure 1.8 Evolution of land locomotion 19

Figure 1.9 Terramechanics issues flowchart 22

Figure 1.10 Forces acting on a single wheel 25

Figure 1.11 Loading condition on the base of a single wheel 25

Figure 1.12 Schematic of typical bevameter 29

Figure 1.13 Typical pressure-sinkage curves 32

Figure 1.14 Schematic of the method for determining Bekker sinkage moduli and

exponent n 34

Figure 1.15 Typical load-sinkage curves for a dry sandy terrain 39

Figure 1.16 Typical values for Bekker parameters of various terrain type and

condition 40

Figure 1.17 The three phases of soil deformation during a typical plate-sinkage

test 42

Figure 1.18 Typical horizontal stress-strain curves 45

Figure 1.19 Typical horizontal stress-strain curves for a sandy terrain 52

Figure 1.20 Overview of direct shear test 56

Figure 1.21 Typical direct shear test setup 56

Figure 1.22 Typical triaxial test setup 60

Figure 1.23 Typical triaxial test results from Mohr’s circle and Lambe methods 62

Figure 1.24(a) Army Corps of Engineers original laboratory cone penetrometer 66

Figure 1.24(b) Typical hand-held cone penetrometer 66

Figure 1.25 Vane-cone penetrometer 71

Figure 1.26 Shear vane end effector 72

Figure 1.27 Cohron sheargraph 73

Figure 1.28 Lunar highlands and maria 77

Figure 1.29 Hadley rille near the Apollo 15 landing site 78

Figure 1.30 Lunar domes at the Mons Rümker volcanic formation 79

Figure 1.31 King Crater 81

Figure 1.32 Typical lunar soil profile 84

Figure 1.33 Cartoon of lunar space weathering process 85

Figure 1.34 Particle size distribution of lunar soil 87

Figure 1.35 Typical lunar soil agglutinate particle 87

Figure 1.36 Cartoon displaying subgranular porosity of the lunar soil 88

Figure 1.37(a) Honeycomb structure of uncompressed granular soils 92

Figure 1.37(b) Compressed structure of granular soils 92

Figure 1.38(a) USSR Lunokhod 95

Figure 1.38(b) Apollo LRV 95

Figure 1.39 Schematic of objectives for this research 104

Figure 2.1 Famous footprint left on the Moon by Neil Armstrong,

demonstrating the apparent cohesion of the regolith 109

Figure 2.2 Trail of Lunokhod’s 9th wheel 111

Figure 2.3 Frequency distribution of bearing strength of the lunar soil in

kg/cm2 as determined by Lunokhod 1 and Lunokhod 2 113

Figure 2.4 Variation of footprint depth with average porosity and relative

density 118

Figure 2.5 Trench excavated near rim of Shorty Crater of Station 4 during

Apollo 17 121

Figure 2.6 Taurus-Littrow area of the Apollo 17 mission 122

Figure 2.7 Friction angle values from boulder track analysis during Apollo 17 122

Figure 2.8 Lunokhod cone-vane penetrometer 123

Figure 2.9 Lunokhod 1 cone-vane penetrometer data 125

Figure 2.10 Lunokhod 2 cone-vane penetration curves 125

Figure 2.11 Location of Luna 17 landing and Lunokhod 1 traverses 126

Figure 2.12 Cartoon of Apollo SRP 128

Figure 2.13 Cartoon of recording drum 129

Figure 2.14 Apollo 15 EVA traverses 130

Figure 2.15 Stress penetration curve from Apollo 15 SRP Index No. 2 132

Figure 2.16 Original data from Apollo 15 SRP Index No. 2 133

Figure 2.17 Apollo 16 EVA traverses 135

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Figure 2.18 Lunar sampling rake 139

Figure 2.19 Comparison of different Apollo mission core tube sampling bits 141

Figure 2.20 Density as a function of depth for the Apollo 15, 16, and 17 drill

stems 142

Figure 2.21 Compressibility curve represented as a coefficient of porosity versus

loading pressure for Luna 16 returned soil and Luna 20 returned soil 145

Figure 2.22 Shear strength parameters as a function of packing load 146

Figure 2.23 Ultra-high vacuum test chamber and shear box 148

Figure 2.24 Electron microprobe image of grain size and chemical composition

of MLS-1 152

Figure 2.25 Particle size distributions of MLS-1 and JSC-1 153

Figure 2.26 Electron microprobe image of grain size and chemical composition

of JSC-1 156

Figure 2.27 JSC-1 particle size distribution compared to upper and lower range

particle size distributions for the lunar soil 158

Figure 2.28 Particle size distribution of JSC-1A 161

Figure 2.29 Typical dimensions of the LRV 168

Figure 2.30 LRV wheel 169

Figure 2.31 Friction angle versus relative density as determined by various shear

testing methods 174

Figure 2.32 Typical CPT penetration resistance versus depth curves for Yuma

sand 176

Figure 2.33 Soil parameters of LSS1 as determined by WES 181

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Figure 2.34 Soil parameters of LSS4 as determined by WES 181

Figure 2.35 Grain size distribution of Yuma sand, LSS, and Apollo 11 and 12

bounds 183

Figure 2.36 Yuma, LSS4, and LSS5 geotechnical properties 183

Figure 3.1 NASA Glenn lunar vehicle mobility team shown at the SLOPE

facility with the Modular Mobility Technology Demonstrator

shown in the background 188

Figure 3.2 Upper, lower, and average bounds on particle size distribution

of the lunar soil 191

Figure 3.3 Typical silica sand grades from the Best Sands Corp. 192

Figure 3.4 Verification of particle size distribution provided by Best Sands

Corp. 193

Figure 3.5 Coarse lunar average particle size distribution versus Best Sands

ideal mixture particle size distribution 196

Figure 3.6 Histogram representation of particle size distribution 197

Figure 3.7 Humboldt sieve shaker for particle size distribution analysis 199

Figure 3.8 Particle size distribution of initial GRC-1 mixture 201

Figure 3.9 Particle size distributions of 4.5 kg and 45.4 kg GRC-1 samples

compared with coarse lunar regolith average 202

Figure 3.10 Histogram representation of particle size distribution 203

Figure 3.11 Particle size distribution of 317.5 kg GRC-1 sample 205

Figure 3.12 Specific gravity test at CWRU 207

Figure 3.13 Typical standard compaction molds 210

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Figure 3.14 Compaction mold bolted on shake table 211

Figure 3.15 Plot of bulk density versus relative density of GRC-1 213

Figure 3.16 Typical consolidation test setup 217

Figure 3.17 Typical dial reading versus time plot 218

Figure 3.18 Results of one-dimensional consolidation testing on GRC-1 221

Figure 3.19 Homemade Hele-Shaw cell 223

Figure 3.20 GRC-1 particle size distribution versus that of actual lunar soil 226

Figure 3.21 Bulk density versus relative density for GRC-1 and the lunar soil 228

Figure 4.1 Tri-Flex 2/DataSystem triaxial test set from ELE International 232

Figure 4.2 Triaxial cell accessories (base plate, cap, porous stones, sealing rings,

drainage lines) from ELE International 233

Figure 4.3 DS7 DataSystem triaxial software from ELE International 233

Figure 4.4(a) Split mold with rubber membrane folded over the top 238

Figure 4.4(b) Rubber membrane tight against the inner wall of the split mold 238

Figure 4.5 Freestanding triaxial soil sample with internal vacuum applied 239

Figure 4.6 Typical bulge in soil after failure 239

Figure 4.7 Typical plot of corrected deviator stress versus axial strain used to

determine the ultimate strength of the soil sample 243

Figure 4.8 Typical Mohr’s circle plot to determine friction angle and cohesion 243

Figure 4.9 Stress at failure versus confining pressure 244

Figure 4.10 Friction angle versus relative density for GRC-1 246

Figure 4.11 Typical q versus p plot used to determine friction angle and cohesion 251

Figure 4.12 Comparison between Mohr’s circles and q-p friction angle values 252

Figure 5.1(a) Table bevameter shown with plate-sinkage end effector 262

Figure 5.1(b) Portable bevameter shown with shear ring end effector 262

Figure 5.2(a) Soils Design Laboratory 263

Figure 5.2(b) SLOPE facility 263

Figure 5.3 Schematic of table bevameter 265

Figure 5.4 Bevameter data acquisition system 266

Figure 5.5 Typical scatter experienced in pressure-sinkage bevameter tests 268

Figure 5.6(a) Shovel for random soil preparation 269

Figure 5.6(b) Plastic funnel for hopper soil preparation 269

Figure 5.7 Bevameter setup for pressure-sinkage tests 270

Figure 5.8 Plot of load-sinkage data collected from the hopper soil

preparation tests and the random soil preparation tests 273

Figure 5.9 Plot of the raw data and curve-fit for the random soil preparation tests 273

Figure 5.10 Plot of raw data and curve-fit for the hopper soil preparation tests 274

Figure 5.11 Plot of raw data and mean curve-fit for random soil preparation tests

and hopper soil preparation tests 274

Figure 5.12 Standard deviation of the random soil preparation tests and hopper

soil preparation tests 275

Figure 5.13 Pressure bulb for a circular plate 278

Figure 5.14 Large soil hopper for quicker soil preparation 282

Figure 5.15 3 cm, Test 1 286

Figure 5.16 3 cm, Test 2 286

Figure 5.17 3 cm, Test 3 286

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Figure 5.18 6 cm, Test 1 286

Figure 5.19 9 cm, Test 1 287

Figure 5.20 12 cm, Test 1 287

Figure 5.21 18 cm, Test 1 287

Figure 5.22 18 cm, Test 2 287

Figure 5.23 Comparison of mean pressure-sinkage curves tested at various

depths of soil 288

Figure 5.24 Comparison of mean pressure-sinkage curves tested at various

depths of soil (focusing on lunar pressure range) 288

Figure 5.25 Converging pressure-sinkage curves 289

Figure 5.26 3 cm, Test 1 290

Figure 5.27 6 cm, Test 1 290

Figure 5.28 9 cm, Test 1 291

Figure 5.29 Converging pressure-sinkage curves 291

Figure 5.30 3 cm, Test 1 293

Figure 5.31 6 cm, Test 1 293

Figure 5.32 9 cm, Test 1 294

Figure 5.33 12 cm, Test 1 294

Figure 5.34 15 cm, Test 1 294

Figure 5.35 15 cm, Test 2 294

Figure 5.36 18 cm, Test 1 294

Figure 5.37 21 cm, Test 1 294

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Figure 5.38 24 cm, Test 1 295

Figure 5.39 27 cm, Test 1 295

Figure 5.40 Comparison of mean pressure-sinkage curves for various soil depths 296

Figure 5.41 Comparison of mean pressure-sinkage curves for various soil depths

(focusing on the lunar pressure range) 297

Figure 5.42 Schematic for the approximate solution of the settlement of a circular

footing under uniform loading 299

Figure 5.43 For a fixed soil thickness, how does the plate size affect settlement? 302

Figure 5.44 For a fixed radius, how does the soil thickness affect settlement? 304

Figure 5.45 Reformulated data from pressure-sinkage tests performed using

the 10.2 cm diameter penetration plate 305

Figure 5.46 Normalized reformulated data from pressure-sinkage tests performed

using the 10.2 cm diameter penetration plate compared with

theoretical trend for settlement 306

Figure 5.47 ATHLETE robotic vehicle designed by JPL 308

Figure 5.48 Chariot lunar truck vehicle 309

Figure 5.49 Penetration plates used in pressure-sinkage bevameter tests 310

Figure 5.50(a) Bottom view of shear bevameter ring with grousers 312

Figure 5.50(b) Angular view of shear bevameter ring with grousers 312

Figure 5.51 Raw data and mean pressure-sinkage vector for 7.6, 10.2, and 19 cm

penetration plates 321

Figure 5.52 Raw data compared to Bekker curve-fit 322

Figure 5.53 Bekker curve-fits for entire range of data 324

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Figure 5.54(a) Typical amount of sinkage for 19 cm diameter plate 325

Figure 5.54(b) Punching shear failure of 7.6 cm diameter plate 325

Figure 5.55 Comparison of GRC-1 Bekker parameters and parameters derived by

Wong et al. (1984) for a dry sandy terrain 327

Figure 5.56 Clear acrylic soil bin 328

Figure 5.57 Pressure-sinkage curves for GRC-1 at 1.64 g/cc 329

Figure 5.58 Pressure-sinkage curves for GRC-1 at 1.67 g/cc 329

Figure 5.59 Pressure-sinkage curves for GRC-1 at 1.75 g/cc 330

Figure 5.60 New manual rotation system attached to load/torque cell 337

Figure 5.61 Shear bevameter test results for GRC-1 at 14-percent relative density 342

Figure 5.62 Shear bevameter test results for GRC-1 at 24-percent relative density 343

Figure 5.63 Shear bevameter test results for GRC-1 at 52-percent relative density 344

Figure 5.64 Typical failure envelope for determining cohesion and friction angle 345

Figure 5.65 Shear bevameter results for GRC-1 at 1.64 g/cc using grousers 348

Figure 5.66 Shear bevameter results for GRC-1 at 1.75 g/cc using grousers 349

Figure 6.1(a) CP40II Cone Penetrometer form ICT International 353

Figure 6.1(b) CP40II accessories 353

Figure 6.2 Typical readout of CP40II data 354

Figure 6.3(a) Soil hopper 356

Figure 6.3(b) Partially filled soil bin 356

Figure 6.4 Cone penetration test at the NASA Glenn soils lab 358

Figure 6.5 Typical testing grid for 74.2 cm square soil bin 359

Figure 6.6 First test results for large cone 364

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Figure 6.7 Second test results for large cone 365

Figure 6.8 First test results for small cone 366

Figure 6.9 Second test results for small cone 367

Figure 6.10 Comparison between large and small cone 369

Figure 6.11 Cone index gradient versus relative density of GRC-1 371

Figure 6.12 Cone index gradient versus relative density of GRC-1 with respect to

mean cone index values and standard deviation 372

Figure 6.13 Additional cone penetrometer tests performed in conjunction with

bevameter testing on GRC-1 373

Figure 6.14 Apollo 15 data for Test Index 2 in terms of cone index gradient 375

Figure 6.15 Apollo 15 data for Test Index 3 in terms of cone index gradient 375

Figure 6.16 Apollo 15 data for Test Index 4 in terms of cone index gradient 376

Figure 6.17 Apollo 15 data for Test Index 5 in terms of cone index gradient 376

Figure 6.18 Apollo 16 data for Test Index 5 in terms of cone index gradient 377

Figure 6.19 Apollo 16 data for Test Index 10 in terms of cone index gradient 377

Figure 6.20 Comparison of typical lunar cone index gradient values and possible

cone index gradient values of GRC-1 381

Figure 6.21 Comparison of all lunar cone index gradient values and possible

cone index gradient values of GRC-1 381

Figure 7.1 Combination of triaxial, CPT, and bevameter data for GRC-1

compared to lunar soil 388

Figure 7.2 Diagram demonstrating soil preparation for large scale soil bins 389

Figure 7.3 Proper shoveling technique to loosen soil in soil bin 390

Figure 7.4(a) Turn shovel in opposite direction 390

Figure 7.4(b) Loosen soil in opposite direction 390

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ACKNOWLEDGEMENTS

I would like to express my most sincere gratitude to Dr. Xiangwu Zeng and the faculty of the Case Western Reserve University Civil Engineering Department for the opportunity they have given me to accomplish my educational goals. Their guidance, support, and true passion for teaching have been a huge influence in my academic career. They have led me to realize my academic potential and have pushed me to reach beyond that point.

Without their insight I would not be where I am today. The many accomplishments that have been obtained by Dr. Zeng and the rest of the faculty at Case are immeasurable and

I can only dream of accomplishing such success in years to come! I would also like to acknowledge the NASA Glenn Research Center for funding this project and providing outstanding testing facilities without which this research would not have been possible.

Specifically, I would like to thank Mr. Vivake Asnani for mentoring and guiding me throughout this project. He taught me many things throughout the duration of this project including how to approach research from not only an engineer’s point of view, but in an analytical and scientific way as well. In addition, I would like to acknowledge Colin

Creager, Steve Bauman, and Efrain Patino of NASA Glenn as well as Ben Taylor of

Virginia Tech. They played an integral role in minimizing laboratory testing time via assisting in soil preparation and assisting in some of the experimental soil tests as well as fabrication of the testing equipment. I sincerely appreciate all the help they offered to me! Additionally, I would like to acknowledge the support of the Ohio Space Grant

Consortium through the OSGC Fellowship, as well as the Eisenhower Fellowship, and the Saada Family Fellowship. The encouragement and assistance of these groups is

xxii greatly appreciated! Finally, I would like to thank my family, especially my husband

Matt, for all of his support and understanding throughout this portion of my academic career and for never doubting my success.

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LIST OF ABBREVIATIONS

1. ALSD – Apollo Lunar Surface Drill

2. ALSEP – Apollo Lunar Surface Experiments Package

3. ASAE – American Society of Agricultural Engineers

4. ASP – Apollo Simple Penetrometer

5. ASTM - American Society for Testing and Materials

6. ATHLETE - All-Terrain Hex-Legged Extra-Terrestrial Explorer

7. CD – Consolidated Drained (triaxial test)

8. CI – Cone Index

9. CPR – Cone Penetration Resistance

10. CTC – Conventional Triaxial Test

11. CU – Consolidated Undrained (triaxial test)

12. CWRU – Case Western Reserve University

13. CPT - Cone Penetrometer Testing

14. DEM – Discrete Element Model

15. EVA – Extra-Vehicular Activity

16. FEM – Finite Element Model

17. GMC – General Motors Company

18. GRC – Glenn Research Center

19. ISRU – In-Situ Resource Utilization

20. ISTVS – International Society for Terrain-Vehicle Systems

21. JPL – Jet Propulsion Laboratory

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22. JSC – Johnson Space Center

23. LLL – Land Locomotion Laboratory

24. LM – Lunar Module

25. LRL – Lunar Receiving Laboratory

26. LRV – Lunar Roving Vehicle

27. LSS – Lunar Soil Simulant

28. LVDT – Linear Variable Differential Transducer

29. MET – Modular Equipment Transporter

30. MLS – Minnesota Lunar Simulant

31. MRB – Mobility Research Branch

32. MSDS – Material Safety Data Sheet

33. MSFC – Marshall Space Flight Center

34. NASA - National Aeronautics and Space Administration

35. NSSDC – National Space Science Data Center

36. NVB – Napa Valley Basalt

37. RCI – Rating Cone Index

38. RI – Remolding Index

39. SLOPE – Simulated Lunar Operations (facility)

40. SRP – Self-Recording Penetrometer

41. UU – Unconsolidated Undrained (triaxial test)

42. VCI – Vehicle Cone Index

43. VT – Virginia Tech

44. WES – Waterways Experiment Station

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GLOSSARY

Agglutinate – A fragile, irregularly shaped particle composed of lithic, mineral, and glass fragments welded together by glass splashes from micrometeorite impacts.

Angle of internal friction - A measure of the ability of rock or soil to withstand shear stress. It is the angle (φ ), measured between the normal force and resultant force that is attained when failure occurs in response to a shearing stress. Its tangent is the coefficient of sliding friction.

Angle of repose – The maximum angle of slope, measured from horizontal, at which loose, cohesionless material will come to rest on a pile of similar material.

Anorthosite – Igneous rock made up almost entirely of plagioclase feldspar. This rock type forms a major part of the lunar highlands.

Apparent cohesion - In soil mechanics, the resistance of particles to being pulled apart due to the surface tension of the adsorbed moisture film surrounding each particle.

Basalt – Fine-grained, dark-colored rock of volcanic origin composed primarily of plagioclase feldspar, and pyroxene, with other minerals usually including olivine and ilmenite.

Breccia – Rock that consists of coarser fragments or clasts of rock, mineral, or glass, enclosed in a matrix that is of a finer grain size and may be of similar or different material

Bulk density – The mass of a material divided by its volume, including volume of pore spaces.

Chromite – A widely distributed black to brownish-black chromium ore.

Cohesion – Shear strength in a sediment not related to interparticle friction.

Compressibility - Property of a soil pertaining to a decrease in the volume of a soil mass resulting when subjected to load.

Cone index – The force per unit base area required to push the cone penetrometer through a specified small increment of soil.

Cone penetrometer – A device typically used to measure the cone index or penetration resistance of a soil.

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Derivative simulant – Simulant obtained through processing of a root simulant to achieve a simulant of specific properties.

Drawbar pull – In vehicle mobility, it is the difference between the tractive effort and the resisting forces acting on a vehicle, Fd.

End effector – A term used to describe the part of the bevameter that penetrates the terrain, and is mounted at the end of the vertical shaft. Three types of end effectors are typical: penetration plates, shear rings, and cones.

Fidelity – Describes the degree of accuracy with which a simulant material approximates the properties of planetary material.

Illmenite – Iron-black mineral which is the most abundant opaque mineral found in lunar rocks, mostly in mare basalts.

Irradiation - The act of exposing or the condition of being exposed to radiation.

Meteoroid – A naturally occurring solid body traveling through space, which is too small to be referred to as an asteroid or comet.

Micrometeoroids – A meteoroid that has a diameter less than 1 mm and mass less than 10-2 grams.

Olivine – A silicate mineral that displays a solid solution series between Forsterite and Fayalite.

Permeability – The capacity of a porous rock or soil for transmitting a fluid (gas or liquid).

Plagioclase - Silicates of aluminum with calcium and sodium, a member of the feldspar family; an important constituent of many plutonic and volcanic rocks.

Porosity – The percentage of bulk volume of rock or soil occupied by interstices.

Pyroxene – Any of a group of silicate minerals, usually calcium, magnesium and iron silicate, often found in igneous rocks.

Regolith – The layer or mantle of fragmental, incoherent, unconsolidated rocky material that overlies bedrock.

Rolling resistance - The resistance of a tire to free rolling. In other words, it is the force required to keep a tire moving at a constant speed. The lower the rolling resistance, the less energy needed to keep a tire moving.

xxvii

Root simulant – A term used to describe the collection and development of basic materials for the development of simulant materials for the Moon.

Shear strength – The resistance of a body to shear stress.

Slip - The change in distance traveled per tire revolution due to driving or braking conditions; expressed as a percentage of the distance traveled under a free rolling condition.

Solar flare – Nuclei sporadically ejected from the Sun that strike the lunar surface with energies of 1 to 100 MeV (mega electron-volts) per nucleon and penetrate 1 mm into the regolith grains.

Solar wind – Nuclei, mostly protons (hydrogen), with 10% alpha particles (helium), ejected from the Sun that strike the lunar surface at approximately 1 keV (kilo electron- volts) per nucleon and penetrate approximately 100 Å (1 angstrom = 1.0 × 10-10 meters) into the regolith grains.

Lunar soil – The portion of the lunar regolith having grains less than one centimeter in size.

Sputtering - The ejection of material from a solid or liquid surface following the impact of energetic ions, atoms, or molecules.

Stress path – A line that connects a series of points representing a successive stress state experienced by a soil specimen typically during the progression of a triaxial test.

Terramechanics – The study of the interaction between wheeled or tracked vehicles and the terrain upon which they are driven.

Trafficability - The physical ability of a soil to withstand traffic and to provide traction for movement.

Void ratio - The ratio of the volume of void space to the volume of solid substance in any material consisting of void space and solid material, such as a soil sample, a sediment, or a powder.

xxviii

Understanding Mechanical Behavior of Lunar Soils for the Study of Vehicle

Mobility

Abstract

HEATHER ANN ORAVEC

The mechanical properties of the lunar regolith are critical parameters in predicting vehicle performance on the Moon. In preparation for Man’s return to the Moon, surface

exploration vehicles must be tested on terrain that represents the mechanical strength of

the lunar terrain. A soil that simulates the lunar trafficability conditions must have a

similar compaction and shear response underneath the wheel. This dissertation discusses

the development of a new lunar soil simulant, GRC-1, and the soil-preparation method to

emulate the measured compaction and shear characteristics of the Moon’s surface. A

semi-empirical design approach was used incorporating particle sieve and hydrometer

analyses, triaxial strength testing, cone penetrometer testing, and bevameter testing. Soil

preparations were developed to match stress-strain curves resulting from in-situ lunar

experiments. Additionally, results of laboratory strength tests with returned lunar soil

samples and lunar soil simulants were compared to provide insight into the material’s

relative strength properties. Results show that grain size distribution, specific gravity,

relative density, cone index, and strength parameters of GRC-1 are similar to that of the

actual lunar soil. Supplemental recommendations are provided for the use of GRC-1 in

vehicle mobility testing.

xxix

CHAPTER ONE

INTRODUCTION

1.1 HISTORY OF LUNAR EXPLORATION

The Moon has been one of Man’s greatest interests for thousands of years. It has not

only provoked the brilliant minds’ of the scientific community, but has provided an outlet

for the imagination of the general earth-based population in the forms of art and

literature. Throughout the years the Moon has played an integral role in ancient

mythology. Various gods and goddesses have been named in her (the Moon’s) honor,

such as Artemis the Greek goddess of the Moon and Máni the god of the Moon (in Norse mythology). Multiple numbers of shrines and monuments have been built in her honor.

In Knowth, Ireland there exists a 5,000 year old rock carving that is believed to be one of

the earliest representations of the Moon that has been revealed to date (Anonymous

2006). Another famous structure which has been linked to the Moon is Stonehenge. One of the suggested purposes of the notorious Stonehenge creation is based on the combination of both astronomical observation and ritual function (refer to Figure 1.1).

Many believed that the Moon’s orbital movement had a supernatural but gratifying effect on the lives of human beings. Additionally, calendars such as the Islamic calendar have been designed to follow the lunar cycle. Furthermore, many of today’s psychological superstitions and stereotypes have been described by the state of the Moon.

Psychologists once believed that the occurrence of a full Moon had an effect on the mental state of human beings. Similarly, the term “lunatic” derived from the Latin word

“luna” or Moon is used to describe a person with erratic or insane behavior (Anonymous

2001).

Figure 1.1 Stonehenge (Brennan 2007).

It was not until the invention of the telescope by Galileo Galilei in 1609 that the first

distinct observations of the Moon took place and sparked human interest in the study of

the Moon. Galileo’s telescope, comparable to a pair of opera glasses, enabled him to become the first man to view the craters and mountains of the lunar surface (Anonymous

2007). The beginning of the Space Age was then defined in the mid 1940’s by the father of the United States space program, Wernher Von Braun, and his development of the first successful ballistic rocket (Anonymous 1995). During this time, the Cold War had initiated a space race between the United States and the Soviet Union. The goals in mind were to explore outer space with artificial satellites (as distinguished from natural satellites), launch human beings into outer space, and ultimately to land humans on the

Moon. However, the space race was not officially declared until 1957 when the Russians successfully launched Sputnik 1, the first artificial satellite in space (refer to Figure 1.2).

Figure 1.2 Sputnik 1 (credit NASA).

The explicit history of lunar exploration began in 1959 with the Soviet Union’s launch of the Luna satellites. By 1966, the Russians had achieved the first satellite to orbit the

Moon (Luna 1); were the first to impact the Moon (Luna 2); were the first to photograph the far side of the Moon (Luna 3); and were the first to soft-land on the Moon (Luna 9)

(Culp 2007). In addition, they had been the first to put a man and woman, Yuri Gagarin and Valentina Tereshkova, into outer space in 1961 and 1963, respectively (Anonymous

1995). During this time of Russian victory, President John F. Kennedy presented to

Congress a sense of urgency to find some way to stop the success of the Russians who had beaten America in every space milestone. President Kennedy proposed the notion that America would safely land a man on the Moon and return him to earth before the end of the decade (1960). “No single space project in this period will be more impressive to mankind, or more important for the long-range exploration of space, and none will be so difficult or expensive to accomplish,” Kennedy announced (Stenger 2001).

Figure 1.3 JFK calls for a mission to send man to the moon during a joint session of Congress on May 25, 1961 (Stenger 2001).

America had continued to improve rocket technology and lunar landing vehicle design

through the years. This technology included the Saturn rockets, led by Wernher Von

Braun, of which Saturn 1B and Saturn V were the most successful. Wernher Von Braun stated, “We must continually set goals to challenge the human spirit to the utmost”

(Sibille et al. 2005). These rockets were used to power the infamous Apollo missions.

Improved technologies also included the Surveyor series of which Surveyor 6 (launched

November 7, 1967) landed on and successfully off [again] from the lunar surface

(Anonymous 1995). It was these leaps in technology which paved the way for the future of lunar exploration and allowed the dreams of landing a human being on the Moon to become a reality. Indeed, on July 20th, 1969, John F. Kennedy and the United States of

America became the leaders of the space race when Neil Armstrong stepped off the

Apollo 11 and became the first man to walk on the Moon. This feat opened the gate for direct lunar exploration and all subsequent Apollo missions. As Neil Armstrong said, this milestone in space would prove to be, "one small step for man, one giant leap for mankind."

Figure 1.4 Surveyor 6 model on Earth (Anonymous 2004b).

To summarize, in the decade spanning from the mid-1960’s to the mid-1970’s a total of

65 various artificial manned and robotic space crafts reached the Moon. This includes

the ten crafts that reached the Moon in 1971 alone. However, only 18 of these total

missions experienced controlled landings on the Moon, of which nine completed a round

trip from Earth and successfully returned geologic Moon samples (Anonymous 2007).

Table 1.1 provides a complete summary of lunar exploration missions throughout the mid-1970’s. In addition, Figures 1.5 and 1.6 provide a map of the locations of the

various mission’s landing sites on the Moon.

After the United States’ successful attempts in landing humans on the Moon and the several successful missions in returning lunar soil and rock samples to the Earth, the fascination with lunar exploration seemed to dissolve. The Soviet Union and the United

States soon shifted their focus to the planetary exploration of Venus and Mars,

5 respectively. It was not until the Japanese entered the picture and orbited the Moon in

January of 1990 that attention was brought back to the Moon. Shortly after, the U.S. launched the Clementine in 1994 and the Lunar Prospector in 1998, both unmanned missions. However, for nearly four decades the Moon has remained untouched by humans.

Table 1.1 Lunar exploration summary (Vaniman et al. 1991a, Anonymous 2008) Date Mission Country Tasks Results

Oct-58 Pioneer 1 USA lunar orbit failed to obtain lunar trajectory

Nov-58 Pioneer 2 USA lunar orbit failed to orbit Dec-58 Pioneer 3 USA lunar probe launch failure Jan-59 Luna 1 USSR lunar impact 1st lunar flyby, failed to impact passed within 37,300 miles of Mar-59 Pioneer 4 USA lunar probe Moon 1st lunar impact near the Sea of Sep-59 Luna 2 USSR lunar impact Serenity Oct-59 Luna 3 USSR lunar probe 1st photos of lunar farside Nov-59 Pioneer P-3 USA lunar orbit launch failure Aug-61 Ranger 1 USA lunar probe launch failure Nov-61 Ranger 2 USA lunar probe launch failure Jan-62 Ranger 3 USA lunar landing missed the Moon by 22,862 miles Apr-62 Ranger 4 USA lunar landing crashed on lunar farside Oct-62 Ranger 5 USA lunar landing missed Moon by 450 miles Jan-63 Sputnik 25 USSR lunar probe unsuccessful lunar attempt Apr-63 Luna 4 USSR lunar orbit missed Moon by 5,282 miles cameras failed, impacted near Sea Jan-64 Ranger 6 USA lunar photography of Tranquility 1st close-up photos of the Moon, Jul-64 Ranger 7 USA lunar photography impacted near Sea of Clouds high quality photos of the Moon, Feb-65 Ranger 8 USA lunar photography impacted near Sea of Tranquility high quality photos of the Moon, Mar-65 Ranger 9 USA lunar photography impacted in Crater of Alphonsus 1st soft landing attempt, crashed May-65 Luna 5 USSR lunar landing near Sea of Clouds Jun-65 Luna 6 USSR lunar landing missed Moon by 100,041 miles Jul-65 Zond 3 USSR lunar probe photographed lunar farside Oct-65 Luna 7 USSR lunar landing crashed near Ocean of Storms Dec-65 Luna 8 USSR lunar landing crashed near Ocean of Storms 1st lunar soft landing near Ocean Jan-66 Luna 9 USSR lunar landing of Storms, first TV transmission from lunar surface Mar-66 Cosmos 111 USSR lunar probe unsuccessful lunar attempt 1st lunar satellite, studied lunar surface radiation and magnetic Mar-66 Luna 10 USSR lunar orbit field intensity, monitored strength and variation of lunar gravitation 1st soft-landed robotic lab near May-66 Surveyor 1 USA lunar landing Ocean of Storms, high quality images and selenological data lunar satellite, photographed over 2 million square miles of the Aug-66 Lunar Orbiter 1 USA lunar orbit Moon's surface, impacted lunar farside Aug-66 Luna 11 USSR lunar orbit lunar satellite Sep-66 Surveyor 2 USA lunar landing crashed near Crater Copernicus

lunar satellite, large-scale pictures of Sea of Rains and Oct-66 Luna 12 USSR lunar orbit Crater Aristarchus, tested motor for Lunokhod's wheels lunar satellite, photographed Nov-66 Lunar Orbiter 2 USA lunar orbit landing sites, impacted Moon soft landed near Ocean of Storms, Dec-66 Luna 13 USSR lunar landing measured soil density and surface radioactivity lunar satellite, photographed landing sites, provided Feb-67 Lunar Orbiter 3 USA lunar orbit gravitational field and environmental data, impacted Moon soft landed robotic laboratory Apr-67 Surveyor 3 USA lunar landing near Ocean of Storms, returned photos and data on a soil sample lunar satellite, first pictures of May-67 Lunar Orbiter 4 USA lunar orbit lunar south pole, impacted Moon Jul-67 Surveyor 4 USA lunar landing impacted near Sinus Medii lunar satellite, used Moon as an anchor for probing interplanetary Jul-67 Explorer 35 USA lunar orbit magnetic fields, plasma, and meteoroid fluxes Aug-67 Lunar Orbiter 5 USA lunar orbit lunar satellite, impacted Moon soft landed robotic lab near Sea Sep-67 Surveyor 5 USA lunar landing of Tranquility soft landed robotic lab near Sinus Nov-67 Surveyor 6 USA lunar landing Medii soft-landed robotic lab near Jan-68 Surveyor 7 USA lunar landing Crater Tycho lunar satellite, studied Apr-68 Luna 14 USSR lunar orbit gravitational field Sep-68 Zond 5 USSR circumlunar 1st lunar flyby and Earth return Nov-68 Zond 6 USSR circumlunar lunar flyby and Earth return Dec-68 Apollo 8 USA piloted lunar orbital flight first humans to orbit the Moon 1st docking maneuvers in lunar May-69 Apollo 9 USA piloted lunar orbital flight orbit, tested all aspects of a piloted lunar landing Jul-69 Luna 15 USSR lunar sample return crashed near Sea of Crises 1st humans on the Moon, landed near Sea of Tranquility, 2 Jul-69 Apollo 11 USA piloted lunar landing astronauts deployed experiments and collected lunar samples during EVA Aug-69 Zond 7 USSR circumlunar lunar flyby and Earth return Sep-69 Cosmos 300 USSR lunar probe unsuccessful lunar attempt Oct-69 Cosmos 305 USSR lunar probe unsuccessful lunar attempt

2nd group of humans on Moon, landed near Ocean of Storms, 2 astronauts deployed experiments, Nov-69 Apollo 12 USA piloted lunar landing collected lunar samples, and retrieved pieces of Surveyor 3 spacecraft during lunar EVA first robotic sample return, Sep-70 Luna 16 USSR lunar sample return collected lunar samples (100g) in Sea of Fertility area Apr-70 Apollo 13 USA piloted lunar landing aborted human landing attempt Oct-70 Zond 8 USSR circumlunar lunar flyby and Earth return 1st robotic rover (traveled 6.5 Nov-70 Luna 17 USSR lunar rover (Lunokhod 1) miles), landed near Sea of Rains 3rd group of humans on Moon, landed near Fra Mauro area, 2 Jan-71 Apollo 14 USA piloted lunar landing astronauts deployed experiments and collected lunar samples during lunar EVA 4th group of humans on Moon, landed near Hadley Rille area, 2 Jul-71 Apollo 15 USA piloted lunar landing astronauts deployed experiments and collected lunar samples with lunar roving vehicle Sep-71 Luna 18 USSR lunar landing crashed near Sea of Fertility lunar satellite, studied Moon's Sep-71 Luna 19 USSR lunar orbit gravitational field 2nd robotic sample return, Feb-72 Luna 20 USSR lunar sample return collected samples near Sea of Crises fifth group of humans on Moon, landed near Descartes area, 2 Apr-72 Apollo 16 USA piloted lunar landing astronauts deployed experiments and collected lunar samples with lunar roving vehicle 6th group of humans on Moon, landed near Taurus-Littrow area, Dec-72 Apollo 17 USA piloted lunar landing 2 astronauts deployed experiments and collected lunar samples with lunar roving vehicle robotic lunar rover (traveled 23 Jan-73 Luna 21 USSR lunar rover miles), landed near Sea of Serenity May-74 Luna 22 USSR lunar sample return lunar satellite landed on the southern part of the Oct-74 Luna 23 USSR lunar sample return Sea of Crises, failed robot sampler 3rd robotic sample return (170 g), Aug-76 Luna 24 USSR lunar sample return collected near the Sea of Crises

Figure 1.5 Landing sites of the Luna, Ranger, Apollo, and Surveyor missions (Vaniman et al. 1991a)

Figure 1.6 Lunar landing site chart (Sibille et al. 2005).

1.2 FUTURE OF LUNAR EXPLORATION

On January 14th of 2004, President Bush, following in the footsteps of predecessor John

F. Kennedy, announced a plan that would not only put Man back on the Moon by the year 2020, but would establish a permanent outpost on the Moon for future manned deep- space missions.

Figure 1.7 President Bush announces plan for Man's return to Moon (O’Brien and King 2004).

This new program referred to as “Moon, Mars, and Beyond” has committed the United

States to send manned missions to the Moon within the timeframe of 2015 to 2020. This program includes sending a crew of three to four humans to the Moon for several days to several weeks with the goal of constructing permanent bases and test beds for future deeper space missions such as missions to Mars. Bush exclaimed that with the knowledge and experience gained on the Moon, humans would be prepared to take the next steps of space exploration. He stated, "Mankind is drawn to the heavens for the same reason we were once drawn into unknown lands and across the open sea. We

choose to explore space because doing so improves our lives and lifts our national spirit,"

(O’Brien and King 2004). President Bush described this program not as a race, but as a journey in which all nations are invited to participate for the benefit of mankind. Since

then the National Aeronautics and Space Administration (NASA) has put much time and

effort into reorganizing, restructuring, and remotivating space enthusiasts for a successful

trip(s) back to the Moon.

1.2.1 Why the Moon?

As part of the “Global Exploration Strategy,” in 2006 NASA focused on finding the

answers to two very important questions with respect to the future of space exploration.

More than 1,000 people from all over the world with various backgrounds including

scientists, engineers, and academia, as well as the general public were asked: “Why

should we return to the Moon?” and “What do we hope to accomplish through lunar

exploration?” (Wilson 2007). From these questions, six major themes and over 200

subcategorized objectives were developed as justifiable grounds for supporting returned

lunar exploration and as goals to attain during lunar exploration. These themes and

objectives are presented in Tables 1.2 and 1.3, respectively.

Table 1.2 Lunar exploration themes (Wilson 2007).

Topic Details

Human Civilization Extend human presence to the Moon to enable settlement

Pursue scientific activities that address fundamental Scientific Knowledge questions about the history of the Earth, the solar system, and the universe with relation to mankind's role in them

Test technologies, systems, flight operations, and exploration Exploration techniques to reduce risks and increase the productivity of Preparation future missions to Mars and beyond

Provide a challenging, shared and peaceful activity that Global Partnerships unites nations in pursuit of common objectives

Expand the Earth's economic sphere, and conduct lunar Economic Expansion activities with benefits to life on the home planet

Use a vibrant space exploration program to engage the public, encourage students and help develop the high-tech Public Engagement workforce that will be required to address the challenges of tomorrow

The diverse list of themes listed in Table 1.2 above and the considerable list of objectives in Table 1.3 can only begin to portray the importance of Man’s return to the Moon.

Furthermore, the Moon is important in its own right as well. Some believe that the Moon holds the answers to the nature and origin of the solar system as well as the evolution of the planets. Most importantly though, it is envisioned that the Moon can and will be utilized as the ultimate source of resources for all space activity.

Table 1.3 Subcategorized objectives for lunar exploration (Wilson 2007). Topics:

Objectives: Human Civilization Scientific Knowledge Exploration Preparation Global Partnerships Economic Expansion Public Engagement Astronomy and Astrophysics x x x Heliophysics x x x x Earth Observation x x Geology x x x x Materials Science x x x x Human Health x x x x x Environmental Characterization x x x Environmental Hazard Mitigation x x Operational Environmental x x x x Monitoring Life Support & Habitat x x x x General Infrastructure x x x x Operations, Testing, and Verification x x x x x Power x x x Communication x x x x x x Position, Navigation & Timing x x x x Transportation x x x Surface Mobility x x Crew Activity Support x x x x Lunar Resource Utilization x x x x Historic Preservation x x x x Development of Lunar Commerce x x x x Commercial Opportunities x x x x x Global Partnerships x x x x x Public Engagement and Inspiration x x x x x x

1.3 MOTIVATION FOR THIS RESEARCH

Of the aforementioned objectives to be accomplished via returned lunar exploration, this

research is particularly focused on one minute but imperative aspect: surface mobility (as

listed in Table 1.3). More specifically, this research encompasses the investigation of the

mechanical and engineering properties of the lunar soil and lunar soil simulants and their interaction with vehicle traction systems for the study of vehicle mobility on the Moon.

Surface mobility for lunar exploration is currently one of the most pressing issues for

Man’s successful return to the Moon. It is a key asset that not only improves the efficiency of human exploration on the lunar surface, but is essential for in-situ resource utilization (ISRU) and is necessary for construction and transportation purposes.

In order to develop effective lunar vehicles and validate mobility models, it is necessary to test prototypes under simulated terrain conditions. The design of robotic lunar roving vehicles and manned lunar exploration vehicles presents a sizeable challenge as it depends critically on the measurement of the mechanical properties of the lunar soil as well as on the understanding of the behavior of the lunar soil under different loading conditions. Karl Terzaghi commented that, “unfortunately, soils are made by nature and not by man, and the products of nature are always complex” (Sibille et al. 2005). In this case additional difficulty lies in the limited amount and unreliability of geotechnical information currently provided about the lunar soil. Adding to the challenge, only a small quantity (on the order of hundreds of kilograms) of lunar soil was returned to the

Earth from past lunar missions. The current lunar soil sample inventory is insufficient in

quantity to support such projects as vehicle mobility studies. In addition, the scientific

value of the lunar soil samples is too grand to be sacrificed during destructive testing.

The process of obtaining even the smallest quantity of lunar soil is extremely involved

and must go through the lunar sample curator. Access to lunar samples is granted based

on a well defined and peer-reviewed research plan and only after all other possibilities of

material use have been explored (Sibille et al. 2005). Thus, the difficulty in obtaining

lunar soil samples for study leads to the fact that the knowledge obtained through these returned lunar samples is not comprehensive. There are simply too few lunar soil samples which, in addition, only represent a minute fraction of the Moon’s surface.

Various lunar soil simulants have been developed for Earth-based lunar soil studies.

However, most were created from mined and other uncommon materials which are no longer available or are only available in relatively small quantities. These small quantities are insufficient for large-scale laboratory testing such as that necessary for vehicle mobility testing. Other simulants are too costly to obtain in large enough quantities for large-scale vehicle mobility testing. It was discussed at the 2005 Workshop on Lunar Regolith Simulant Materials that the quantities of simulant materials for currently funded projects exceeds 100 metric tons (Schlagheck et al. 2005). Most likely even more will be needed. Thus, it is imperative to produce a lunar soil simulant created from readily-available terrestrial soils which emulates the critical mechanical properties

(relative to vehicle mobility) of the lunar soil. Other soil properties, such as mineral composition and chemistry or mineralogy, are not important for mobility assessment. In addition this simulant must be able to be produced in large quantities at a reasonably

affordable cost. Thus, it is the goal of this research to provide such a lunar soil simulant

for lunar exploration vehicle mobility testing sponsored by the NASA Glenn Research

Center of Cleveland, Ohio.

The following sections provide a comprehensive introduction to the concepts of vehicle mobility with respect to wheel-soil interaction. In addition the nature of the lunar terrain is amply introduced including the major differences between the lunar environment and the Earth’s environment and the effect that these environmental differences have on the corresponding soils. Subsequent to the presentation of this introductory material, the problem statement and objectives for this research are introduced including the complete scope of work and basic initial assumptions.

1.4 INTRODUCTION TO SURFACE MOBILITY

The general idea of surface mobility can be traced back for thousands of years, possibly even dating back to the invention of the wheel around 3500 B.C. However, mobility or transportation in general can be recognized since the beginning of time [on Earth]. A general evolution of mobility can be correlated to the ever changing environment as described by Bekker (1962). Some 300 million years ago amphibians confined to the seas of the Silurian period evolved into the first true land “locomotors”. As such, they began using their bellies for ground support and their legs for paddles when the Earth crust began to crumble, and forced the sea to withdraw from the inland, leaving wetland areas behind. These amphibians continued to evolve during the Mesozoic period when

the marshes and swamps began to dry and form solid terrain. The amphibians’ legs and

arms, which were previously used as paddles, elongated and they gained the ability to

walk, run, and jump (Bekker 1962). At this point a general trend can be seen in the

evolution of mobility. With every change in the Earth’s environment there came a

corresponding evolution in current life forms which served to improve mobility as well as increase mobility speed. As such, Man developed as a result of the change from the

Cenozoic period, characterized by plains and forests, to the Anthropozoic period,

characterized by mountains and eventually paved roads. During this time Man continued

the evolution of mobility in a different way by inventing the wheel. This literally paved

the way for monumental advances in vehicle mobility (both on and off-road) as we know

it today.

Looking back, throughout the evolution of mobility in life forms another general trend

can be observed. This trend is that the amount of mobility or improvement in mobility and mobility speed is directly proportional to the linear dimension of the locomotor or vehicle as implied in Figure 1.8 (Bekker 1962). In addition, mobility is inversely proportional to the vehicle weight (Bekker 1963). These two statements are true for any type of terrain ranging from soft and weak terrain to hard and rocky terrain and are important to keep in mind when considering vehicle mobility studies.

Figure 1.8 Evolution of land locomotion (Bekker 1962).

1.4.1 Development of Off-Road Vehicles

The development of off-road vehicles has become increasingly important throughout the years. It is imperative in such fields of work as agriculture and farming, mining, logging, oil drilling, and many others (Reece 1964a). As the demand for the products from these professions increase it is necessary for companies to expand their resources and begin to

explore and develop in more remote locations and challenging terrain. Thus, there is a

need for improved and more capable vehicles and machines to traverse once inaccessible

regions. This also holds true for military applications. With the development of atomic

weapons and modern warfare, it is required that “armies be able to operate in small units

capable of rapid dispersal in order to avoid an offensive independently of the normal

static means of transport which must be assumed to be destroyed” (Reece 1964a).

Therefore, it is generally implied that the more challenging the mission, the more

challenging the terrain and thus there is a need for enhanced and more reliable forms of transportation. The biggest challenge of all, however, is the development of reliable vehicles with exceptional performance for exploration and eventual construction on the

Moon and other planets.

In past years, the development of [Earth-based] off-road vehicles has been strictly based on empirical data and past experience. This was due in part to the lack of knowledge of soil mechanics and soil behavior; and to the lack of understanding the relationships between vehicle-soil interactions. As time progressed and the economy developed globally, increasing competition between industries deemed the empirical development of off-road vehicles unsatisfactory with respect to cost and efficiency (Wong 2006). Hence, the need for new and complete vehicle-terrain interaction studies for the development of off-road vehicles has become necessary to satisfy requirements such as cost and efficiency as well as to provide a more solid foundation for vehicle design with respect to implementing new development and design guidelines. This is especially necessary when it comes to developing off-road vehicles for military applications as previously mentioned or for space exploration, such as lunar roving vehicles, in which the soil properties are not fully understood or easily accessible for study and there is not much experience or data from past missions in order to develop a vehicle empirically. The cost of such missions can be extremely high in terms of both monetary value and human

safety. Therefore it is not only a necessity, but a demand that the optimum vehicle be

developed to satisfy the given mission requirements and that this development be

accomplished in a timely fashion.

1.4.2 Development of Terramechanics

Interest in the relationship between the vehicle and the soil surface over which it moved

began to increase with the need to explore and traverse more difficult terrain. As a result,

the term “terramechanics” was created by Mieczysław Gregory Bekker (M.G. Bekker) in

the 1960’s (Wong 2006). Terramechanics is currently defined as the study of soil

properties; more specifically with respect to the interaction and performance of wheeled

or tracked vehicles on various terrain surfaces. The physical ability of a soil to withstand

“traffic” is defined as trafficability. In other words, trafficability is the extent to which

the terrain will allow continued movement of a vehicle. The trafficability of a given

terrain is dependent on the mechanical properties of the soil composing the terrain. It should be noted that vehicle properties are important factors in trafficability as well and

that for each terrain or soil condition encountered, trafficability will be different for each different vehicle.

As terramechanics is concerned with the general performance of a vehicle with respect to

the terrain, it encompasses three major issues (Wong 2006). The first issue is

determining the mechanical properties, strength characteristics, and surficial

characteristics (including obstacles, slopes, wetlands, and water) of the terrain. The

second issue involves the modeling of the vehicle-terrain interaction. The final issue is tying everything together and relating vehicle design to terrain characteristics as well as to vehicle performance. In other words, how does the vehicle performance relate to the vehicle design and terrain characteristics (refer to Figure 1.9)? The focus of this research is mainly concerned with the first issue in terramechanics relating to the mechanical properties, strength characteristics, and surficial characteristics of the terrain or soil over

which a vehicle will be traversing. More specifically, it focuses on the lunar soil over

which lunar type roving vehicles will be traversing.

Vehicle Performance

(tractive performance, drawbar pull, etc.)

Vehicle Design Soil Properties

(running-gear, weight, geometry, (strength properties, mechanical power requirements) properties, obstacles, slopes)

Figure 1.9 Terramechanics issues flowchart (Wong 2006).

1.5 GENERAL FACTORS AFFECTING SURFACE MOBILITY

There are several factors which affect the mobility of a wheeled or tracked vehicle on an

off-road type terrain. The most critical factor in vehicle mobility is the tractive

performance of the vehicle over the natural unprocessed terrain. Other factors include:

ride quality, maneuverability, acceleration characteristics, braking characteristics,

obstacle handling (rocks, potholes, craters, fallen trees, etc.), slope handling ability, and

the ability to cross wetland areas. The tractive performance of a vehicle in turn

characterizes the ability of that vehicle to develop drawbar pull, accelerate, climb slopes,

and surmount obstacles (Wong 2006). In other words, the tractive performance of a

vehicle represents the ability of the vehicle to efficiently thrust off the ground and propel

the vehicle. Drawbar pull is defined as the resultant force between the soil thrust and the motion resistance available to pull or push masses. In other words, a vehicle will become

immobilized when the thrust becomes equal to the motion resistance. Drawbar pull is

extremely important when implementing vehicles for excavation, towing, and

construction.

The basic and most general mobility equation for a single wheel can be written as

Fd = F − ∑ R (1)

where Fd is the net traction or drawbar pull available for towing, slope climbing, and acceleration, etc. It is represented as the difference between the gross traction F,

otherwise described as the tractive effort, thrust, or the force required to shear the soil

under the vehicle footprint; and the resultant resisting force, ∑ R . The resultant

resisting force acting on the vehicle consists of the external resistance due to the vehicle

running-gear and terrain interaction Rc, otherwise known as motion resistance or rolling

resistance; the obstacle resistance Ro; the terrain grade or slope resistance Rg; and the

aerodynamic resistance Ra in the case that the vehicle speed is significant. A general

schematic of the forces involved in single wheel-terrain interaction is shown in Figure

1.10. This figure includes both W and T, vehicle weight and torque, respectively, which

are not included in equation (1), but are necessary to incorporate into the schematic.

Vehicle weight affects the normal stress on the contacting surface and in turn affects the

maximum thrust that can be provided by the soil while T is the source of energy provided

by the engine which pushes the vehicle forward. Ignoring Ri which is defined as the sum

of the obstacle, slope, and aerodynamic resistances in Figure 1.10; and assuming for the sake of simplicity that the contacting surface between the wheel and the soil is flat, the loading condition on the contacting surface of a single wheel can be represented as shown in Figure 1.11, where W is the vehicle weight, A is the footprint area or contact patch,

σ is the normal stress under the wheel, and τ is the shear stress developed on the

contacting surface.

*Ri

Fd T

F Rc

*Ri is representative of any other applicable resisting forces, i.e. Ro, Rg, and Ra.

Figure 1.10 Forces acting on a single wheel.

Figure 1.11 Loading condition on the base of a single wheel.

1.6 SOIL PROPERTIES AFFECTING SURFACE MOBILITY

As previously mentioned, for a vehicle to perform well in a given terrain, it is critical to select the appropriate running-gear; i.e. an appropriate size and form (wheels, tracks,

grousers, etc.) of the ground contact area as well as an appropriate loading condition.

The appropriate selection of these parameters is in-turn dependent upon two critical terrain factors. These factors as described by Bekker (1962) are the vertical and horizontal stress-strain characteristics of the terrain along with the geometry of the ground surface (with respect to quality of the ride). More specifically, with respect to the vertical and horizontal stress-strain characteristics, the two most critical terrain factors in surface mobility are whether or not the soil has enough bearing capacity to support the vehicle and whether or not the soil has a sufficient tractive capacity to produce resistance between the soil and the running-gear (wheel or track) to provide the forward thrust that is necessary to overcome motion resistance as described in Trafficability of Soils

(Department of the Army Corps of Engineers Mississippi River Commission 1948).

Both the bearing and tractive capacity of a soil are dependant on the shear strength of the soil. It is important to keep in mind that the bearing capacity referred to in this report is different than the bearing capacity usually employed in engineering, which is entirely based on settlement due to compaction (Department of the Army Corps of Engineers

Mississippi River Commission 1948). Bearing capacity with respect to trafficability depends in part on settlement due to soil compaction under the vehicle weight (especially if the soil is of dry, loose, and granular nature with a large amount of voids), but is more predominantly governed by the settlement that occurs as a result of shear failure

(Department of the Army Corps of Engineers Mississippi River Commission 1948).

Generally speaking, the settlement or “sinkage” of the vehicle running-gear causes motion resistance which in turn opposes the tractive capacity of the vehicle. The tractive

26 capacity of a soil more simply depends on the ability of the running-gear to dig into the soil surface and shear it. In the horizontal direction, this stress-strain relationship is known as soil thrust. The thrust imposed on a vehicle is the result of the terrain surface being sheared by the vehicle running-gear, i.e. thrust is developed by the traction between the soil and the wheel. Thus, the shearing behavior of the terrain is a major factor in determining the tractive performance of an off-road vehicle. Simply put, the interaction between the soil surface and vehicle running-gear affects both the tractive effort and motion resistance of the vehicle, which permits and restricts the movement of the vehicle, respectively (Benoit and Gotteland 2004).

Some vehicle mobility issues that occur are critically dependant on the shearing resistance of soils. These include slip and sinkage. Slip is well defined in Trafficability of Soils (Department of the Army Corps of Engineers Mississippi River Commission

1948) as a condition that is developed when a soft layer of soil overlies a harder layer.

The softer layer of soil acts as a “lubricant” preventing traction from developing since the vehicle wheel or track cannot dig into the hard layer of soil. Sinkage occurs as the result of a soil with low bearing capacity which allows the vehicle to “settle” in the soil. This creates a wall of soil as described in Trafficability of Soils (Department of the Army

Corps of Engineers Mississippi River Commission 1948) which exists in front of the running-gear and increases the motion resistance. In order to overcome the motion resistance, the soil wall must be moved out of the path of the wheel or track. This can easily be done if the soil is very soft with little shearing resistance, but if the soil is harder or stiffer with a lot of shearing resistance it becomes more difficult to move. The vehicle

27 effort to push this soil out of the way thus becomes a function of the shearing resistance of the soil (Department of the Army Corps of Engineers Mississippi River Commission

1948). Therefore, it is important to be able to quantify the vertical and horizontal stress- strain characteristics of a given soil which, in turn, are essential in determining the strength characteristics of the soil.

1.6.1 Bevameter Technique for Determining Soil Strength

Several approaches have been created throughout the years in order to determine the stress-strain or strength characteristics of a soil in relation to vehicle mobility. However, only one technique has been developed which can determine both the vertical and horizontal stress-strain relationships of a soil by simulating the normal and shear loading applied by the vehicle running-gear to the terrain surface. The device capable of this is called a bevameter (short for the Bekker-Value-Meter), formally developed by M.G.

Bekker in the 1950’s. Instruments of this type have been developed and utilized by institutes ranging from the German Research Institute for Agricultural Research in

Germany, to the GM Defense Research Laboratories, as well as the U.S. Army’s Land

Locomotion Laboratory, and the Caterpillar Corporation (Bekker 1969). A schematic of a typical bevameter type device is shown in Figure 1.12. This device is capable of performing two main tests as described by (Wong 2006): a load-penetration test (also referred to as plate-sinkage or pressure-sinkage test throughout this dissertation) to determine the vertical stress-strain relationship of the soil; and an annular shear test to determine the horizontal stress-strain relationship of the soil. During a load-penetration

test, a sinkage plate that simulates the contact area of the vehicle running-gear is pushed

vertically into the terrain (usually with a constant rate of penetration). From this test, the

applied force and resulting sinkage are measured and used to determine the pressure- sinkage relationship of the soil. During a shear test, a shear ring with a predetermined

applied normal pressure is used to simulate the shearing action of the vehicle running-

gear by rotating on the terrain surface. The applied torque and resulting angular

displacement are measured and used to determine the horizontal stress-strain relationship

of the soil. The bevameter is also capable of performing repetitive normal and shear

loading tests which are used to simulate the repetitive loading or shearing of a multi-axel

wheeled vehicle. However, this particular test is outside the scope of work and therefore

will not be described in further detail. More information on this topic can be found in

(Wong 1989).

Figure 3.12 Schematic of typical bevameter (Wong 2006).

1.6.1.1 Bearing Capacity

M.G. Bekker developed the vertical stress-strain relationship supporting the bevameter technique from early attempts by Bernstein and Goriatchkin who basically generalized cases of formulas used in civil engineering soil mechanics and applied them to vehicle mobility (Bekker 1962). Initially, Bernstein, who’s main line of work was in agricultural engineering, experimentally proved that if a plate penetrates soil to a depth z under a given pressure p, then the experimental pressure-sinkage curve obtained in this fashion could be curve-fit with the following equation,

p ≅ kz 0.5 (2)

where k is a modulus of inelastic deformation, and 0.5 is the exponent of sinkage (Bekker

1969, Bernstein 1913). This equation was later modified by Russian investigators, who concluded that the formula could be simplified to the following form,

p = kz n (3)

where n ranged in value from zero to one (Bekker 1969, Goriatchkin et al. 1936). These

equations were found to be very limited in application as the value of k was dependent on

the size and shape of the test plate and was therefore not a true modulus of deformation.

Bekker, while working for the Canadian Army and later for the U.S. Army’s Land

Locomotion Laboratory further developed the Bernstein-Goriatchkin equations to be

applicable to any size or shape of plate. Bekker’s Equation is written as,

⎡kc ⎤ n p = ⎢ + kφ ⎥ ⋅ z (4) ⎣ b ⎦

where p is the pressure and z is the soil depth or sinkage as before, but kc and kφ are moduli of deformation with respect to cohesion and friction (independent of plate shape and size), b is the smaller dimension of the rectangular loading area or the radius of a circular plate, and n is the empirical soil value which defines the shape of the load-

penetration curve (Bekker 1962, 1969). Bekker’s equation for load-penetration is

currently the most commonly used and widely accepted technique applicable to any type

(sand, clay, etc.) of homogeneous soil. Looking more closely at equation (4), it can be recognized that Bekker’s load-penetration equation is nothing more than a generalized form of the well known load-penetration equation for structures in civil engineering, where n is equal to one and b is equal to the length of the structure (Taylor 1948).

Bekker’s load-penetration technique is thus used to predict the sinkage of a vehicle by

use of the bevameter and the interpretation of the resulting plate-sinkage data, which

must take into account the mechanical behavior of the soil (refer to Figure 1.13). The basic concept behind Bekker’s theory is that the normal stress beneath a wheel at a

31 certain depth below the original ground surface equals that obtained in a plate-sinkage test at the same depth.

Figure 1.13 Typical pressure-sinkage curves (Bekker 1969).

However, the accuracy of this prediction is one of the more challenging problems in terramechanics. The general methodology behind its use is as follows (Sela and Ehrlich

1972):

1. An ensemble of plate-sinkage tests are conducted in the specified soil.

2. Parameters of the prediction equation are calculated via curve-fitting techniques.

3. These parameters are then used in the prediction equation to predict load-sinkage

characteristics of other objects.

More specifically, a minimum of two load-penetration tests, each using a different plate size, must be run in order to determine the vertical stress-strain relationship of the soil.

Each test results in two pressure-sinkage curves following the form of equation (4). If plotted on a log p-log z graph the following set of equations are thus defined as,

⎡⎛ k ⎞ ⎤ ⎜ c ⎟ log p1 = log⎢⎜ ⎟ + kφ ⎥ + nlog z (5) ⎣⎝ b1 ⎠ ⎦

⎡⎛ k ⎞ ⎤ ⎜ c ⎟ log p2 = log⎢⎜ ⎟ + kφ ⎥ + nlog z (6) ⎣⎝ b2 ⎠ ⎦

where the subscripts 1 and 2 represent each different bevameter load-penetration test.

These equations define two parallel lines whose slope defines the value n; and the values

of the cohesive modulus of deformation kc and the frictional modulus of deformation kφ are readily determined from the values of pressures acting on the two different plates at a sinkage equal to one (Bekker 1969, Wong 1980). Figure 1.14 depicts this method for determining the sinkage moduli and corresponding exponent (Wong 1980, 2006). This

method for determining kc , kφ , and n experiences a lot of issues due to the fact that experimental data from the load-penetration tests rarely fit equation (4) exactly (Wong

1980). Therefore, there is a lot of user manipulation when plotting the log p-log z curves to approximate the straight lines. In addition, these lines usually are not exactly parallel which requires further manipulation of the data. This method is highly dependent on the experience and judgment of the investigator which means that if two different people are running the same tests, they are likely to get two very different answers.

log z b2 b1

n = tan αs

αs

a2 log p

Figure 1.14 Schematic of the method for determining Bekker sinkage moduli and exponent n. Note that a1 and a2 represent the pressures corresponding to the sinkage of z = 1 for each plate size (Wong 1980, 2006).

Since the development of Bekker’s technique for determining the vertical stress-strain characteristics of terrain, many researchers have added to or modified the method to eliminate the human error or at least provide a measurement of the error involved in the curve-fitting of the load-sinkage data. In 1963, Dewhirst proposed a vertical stress-strain relationship based on a polynomial of two degrees or higher. He claimed that this eliminated size effects that occurred when using a modified form of Bekker’s equation for cohesionless dry soils,

n p = kφ z (7)

Fifty-one sets of random soil data were considered and evaluated using both Bekker’s equation and a third degree polynomial,

2 3 z = a1 p + a2 p + a3 p (8)

where a1, a2, and a3 are constants, z is sinkage, and p is pressure. Out of all 51 cases, 46 cases resulted in a smaller root-mean-square error1 by using the polynomial method than by using the Bekker method. Dewhirst (1963) concluded that any polynomial of degree two or more gives a better fit to the majority of data considered. He also anticipated it would provide a better fit for layered non-homogeneous soils where softer soils overly harder soils, vice versa. The only downfall to this method of curve-fitting pressure- sinkage data was the question of where to truncate the polynomial, which in Dewhirst’s

(1963) words “is a tradeoff between accuracy and complexity.”

In 1964, Reece (Reece 1964a) challenged Bekker’s equation for the vertical stress-strain relationship of a soil stating that it is not applicable to cohesive or incompressible soils such as clay because it does not follow the bearing capacity theory of Terzaghi and

Meyerhof (Terzaghi 1956, Meyerhof 1951). Reece therefore proposed the following pressure-sinkage equation, equation (9), where pressure is a function of both sinkage and plate size instead of just sinkage as in Bekker’s equation.

n p = ck ' + γbk ' z (9) ( c φ )( b)

1/ 2 1 ~ 2 ~ []()z − z / N where z is the measured sinkage, z is the calculated sinkage, and N is the number of data points used in the curve-fit. 35

In this equation c and γ represent the cohesion and weight density of the soil,

' ' respectively, and kc , kφ , and n are parameters of the soil. This equation has been shown to fit the experimental results of both [homogeneous] sand and [homogeneous] clay materials very well. However, this improvement was not significant enough to warrant the rejection of Bekker’s equation (Reece 1964a, Hegedus and Liston 1966).

In addition, during this same time period, Reece developed a minimum error curve-fitting method which was based on the selection of suitable limits for the pressure-sinkage curve

(Reece 1964b). He used the limits of one inch (2.54 cm) of sinkage and 30 pounds per square inch (6.89 kPa) of pressure (corresponding to 10 inches or 25.4 cm of sinkage) and successfully determined the amount of error based on the pressure difference between the actual curve and theoretical curve. Minimizing these limiting error values could thus be accomplished by making the errors equal. The downfall to this method is that it is still a graphical method which relies in part on the experience of the investigator and can still provide two different solutions for two different investigators (Wong 1980).

In both the Bekker and Reece equations for the vertical stress-strain relationship of a soil there is a lot of manipulation, skill, and experience involved in obtaining the soil

' ' parameters n, kc , kφ , and kc and kφ . Wong attempted to correct this issue by imposing a weighted least squares method to obtain unique parameter values (Wong 1980, 2006).

The step-by-step approach to this method is thoroughly described by Wong (1980).

When applied to the Bekker equation for pressure-sinkage, equation (4), Wong’s method

36 for data processing derives the best-fitted values of the pressure-sinkage terrain parameters by minimizing the following function using a weighting factor p2,

2 2 F = ∑ p [ln p − ln(kc / b + kφ )− nln z] (10)

Minimization of equation (10) involves taking the partial derivatives of the function with

respect to n and keq , where keq = (kc /b + kφ ) , and setting them equal to zero. Solving

the resulting equations simultaneously gives rise to the following equations for n and keq .

∑ p 2 ∑ p 2 ln p ln z − ∑ p 2 ln p∑ p 2 ln z n = 2 (11) ∑∑p 2 p 2 ()ln z 2 − () ∑p 2 ln z

p 2 ln p − n p 2 ln z ln k = ∑ ∑ (12) eq ∑ p 2

When using two different plate sizes a unique n is usually obtained for each. Therefore, it is required to use the average n-value resulting from the two different plates when

calculating the natural logarithm of keq in equation (12). However, since

keq = (kc /b + kφ ) there will be two resulting keq -values: one for plate size b1 and another

for plate size b2. Accordingly, the values of kc and kφ can be determined using the

subsequent equations. It should be noted that the value for kc as determined using this analysis is often negative for dry granular soils (Dewhirst 1963).

k − k ( eq )b1 ( eq )b2 kc = b1b2 (13) b2 − b1

⎡(k ) − (k ) ⎤ k = k − eq b1 eq b2 b (14) φ ()eq b1 ⎢ ⎥ 2 ⎣ b2 − b1 ⎦

Wong (1980) also developed a method for defining the error between the experimental and theoretical data. He referred to this as the “goodness-of-fit” equation which defines the ratio of the root mean square error to the mean value of pressure as follows,

2 [∑()pm − pc ] ()N − 2 ε = (15) ∑ pm / N

in which pm is the experimental value of pressure or the measured value, pc is the calculated value of pressure using equation (4) in combination with equations (11) through (14), and N is the number of points used when curve-fitting. The pressure- sinkage curve-fit is defined as “perfect” when the goodness-of-fit value ε is equal to zero

(Wong 1980). A typical pressure-sinkage curve following Wong’s data processing method versus experimental data is shown in Figure 1.15. This technique can also be applied to Reece’s equation, equation (9), in order to eliminate investigator error when defining the corresponding terrain parameters as discussed in (Wong 1980). A chart

38 providing typical terrain parameters based on the equations developed by Bekker is provided in Figure 1.16.

Figure 1.15 Typical load-sinkage curves for a dry sandy terrain (Wong 1980).

With the development of a new mathematical approach to define the terrain parameters in mind, there still exist a few more downfalls to Bekker’s prediction equation for off-road vehicle performance that must be discussed. First of all, equation (4) is only able to predict accurately within the limitations of the plate-sinkage test itself, i.e. within the sinkage range and only for similar plate sizes and shapes. It cannot accurately predict the performance of plates of a much different size or shape (Sela and Ehrlich 1972). Since plate-penetration tests are performed in order to predict vehicle mobility it is acceptable

39 to conclude that the larger the plate size the better, i.e. plate size should be similar to contact area of the wheel footprint; and the larger the difference between the two plate sizes used for the prediction equation the better, i.e. it is acceptable to a certain extent to predict pressure-sinkage relationships for plate sizes or contact areas within the range of plate sizes used for testing.

Figure 1.16 Typical values for Bekker parameters of various terrain type and condition (Wong 2001).

More recent studies have focused on improving these areas where Bekker’s technique for predicting the vertical stress-strain characteristics of a terrain falls short. In 1985,

McKyes and Fan investigated the improvement in variability of the soil parameters n, kc ,

and kφ of sand when multiple [small] circular plate tests (more than the recommended two tests) were utilized. They found that the variability in the value of n was reduced

40 from 82-percent to as low as 16-percent when groups of four tests were run instead of two. They also found that an ensemble of five small plate tests (ranging in size from 4.5 to 6.5 cm in diameter) could be used to accurately predict the sinkage characteristics of a large plate having three times the diameter of the small plates.

In 1987, Holm et al. performed several laboratory tests to determine the influence of plate shape and size on the pressure-sinkage relationship of sand, loam, and clay. Both plates

(round and rectangular) and cones of various sizes and aspect ratios were used in the investigation. Several conclusions were drawn. However, the gist of the investigation showed that small penetrometer bodies were more sensitive to small changes in the soil consistency and laboratory preparation; and that in vehicle mobility studies it is not so important as to what shape of penetration device is used (cones or plates), but to what size of penetration device used, i.e. the larger the penetration device the better.

In 1997, Alexandrou and Earl challenged Bekker’s technique by claiming that plate- sinkage tests do not provide any insight into the deformation process of the soil that occurs below the plate during the test (Alexandrou and Earl 1997, Earl 1997). Earl

(1997) proposed a theoretical model predicting the severity of soil deformation underneath a circular plate. This theory was based on experimental data from both plate- sinkage tests and confined compression tests (Earl 1997). It was suggested that when soil experiences an increasing load below the plate it goes through three different phases of deformation as shown in Figure 1.17. As described by Earl and Alexandrou (Earl and

Alexandrou 2001a), the first phase is accompanied by compaction underneath the plate

41 with a constant lateral stress, σ L . This occurs as a result of the air being forced out of the voids in the soil. The second phase entails compaction with an increase in lateral stress.

This phase continues until the lateral stress becomes larger than the confining stress of the soil otherwise termed the “compaction point” (Earl and Alexandrou 1997) after which the final phase begins and exhibits further compaction with lateral deformation.

Figure 1.17 The three phases of soil deformation during a typical plate-sinkage test, where σL represents the lateral stress (Earl and Alexandou 2001).

Together, Earl and Alexandrou (2001a) derived several mathematical models to predict which mode of failure occurs below the plate and to what extent the soil deforms.

Laboratory plate-sinkage and confined compression tests incorporating long exposure photography were performed on sandy loam in order to observe the deformation processes and to test the capability of the mathematical models (Earl and Alexandrou

2001b). It was found that the predictions made as to the mode of failure and the deformation extents based on the mathematical models were in good agreement with the experimental results.

Most recently, in 2006, Gotteland and Benoit proposed a “New Model of Mobility” otherwise known as N2M which takes into account both the elastic and plastic behavior of a soil experiencing small and large sinkage, respectively (Gotteland and Benoit 2006).

The new model proposes a new pressure-sinkage equation governed by four parameters.

These four parameters representing a defined soil and its “physical state” are determined similarly to Bekker’s parameters by running two plate-sinkage tests, each with a different diameter plate. The benefit of this equation over Bekker’s is that it is completely independent of the plate size which means it could “pave the way for the extrapolation to the scale of full size vehicles” (Gotteland and Benoit 2006). Laboratory tests were conducted on soils including sand, silt, and silty sand. Initial tests showed good comparison between the N2M model and the experimental data for all three soil types. In addition, when compared to Bekker’s model it showed a general improvement in the prediction capability for silt and silty sand.

1.6.1.2 Shear Strength

In 1944, Micklethwaite made a huge breakthrough in terramechanics by modifying

Coulomb’s well known equation to predict the maximum tractive effort of a vehicle

(Micklethwaite 1944). Coulomb’s equation for shear stress is generally defined as follows,

τ max = c + σ tanφ (16)

43 where c and φ are the cohesion and friction angle of the soil, respectively, and σ is the normal stress or ground pressure under the loaded area. It can be seen that the cohesion c, unlike the friction angle φ , is independent of the normal pressure on the loaded or shearing area. Assuming the load on the wheel is uniformly distributed over the contacting surface, Micklethwaite determined that the gross tractive effort or the thrust,

F, can be represented as,

F = Ac +W tanφ (17)

where A is the ground contact area and W is the vehicle weight. This equation is extremely important in determining the effect of the horizontal stress-strain relationship or more specifically the effect of cohesion c and friction angleφ on vehicle mobility.

Bekker soon modified this equation to account for the slip of the vehicle (as discussed previously). The horizontal stress-strain equation that resulted was of the form,

2 2 τ = ()c + σ tanφ (exp[(− K 2 + K 2 −1)K1 j]− exp[(− K 2 − K 2 −1)K1 j]) (18)

in which j is the shear deformation and K1 and K2 are coefficients of slip (Bekker 1969).

This equation is applicable to all soil types including both brittle sand materials and plastic clay materials. Figure 1.18 displays the two typical horizontal stress-strain curves that are commonly seen as a result of shear bevameter testing. Curve 1 in Figure 1.18 exhibits a peak shear stress “hump” followed by a quick drop-off and then linear portion

44 after the soil yields. This linear portion is generally referred to as the residual shear stress

and is labeled as τ r in Figure 1.18 (Wong 1980). This trend is generally seen in brittle soils such as dense compacted sand.

Figure 1.18 Typical horizontal stress-strain curves (Wong 1980).

Following equation (18), Bekker proposed an equation that exclusively represented the shear stress-shear displacement relationship of brittle soils (Bekker 1969, Wong 1989).

The equation is as follows,

⎛ 2 2 ⎞ exp[− K 2 + K 2 −1]K1 j − exp[− K 2 − K 2 −1]K1 j τ = ()c + σ tanφ *⎜ ⎟ (19) ⎜ 2 2 ⎟ ⎝ exp[]− K 2 + K 2 −1 K1 j0 − exp[]− K 2 − K 2 −1 K1 j0 ⎠

where τ is the shear stress, j and j0 are the shear displacement and shear displacement at the maximum shear stress, respectively, and K1 and K2 are empirical constants. Attempts were made by several investigators including Weiss (1955) and Sela (1961) to derive the values of the empirical constants K1 and K2. However, the derivation involved complicated graphical solutions that lead to a great deal of error (Bekker 1969, Wong 45

1989). Bekker (1969) remarked that “accurate definitions of K1 and K2 are difficult without computer methods.” Another downfall to this equation is that when the shear displacement j approaches infinity the value of shear strength approaches zero instead of approaching a residual shear strength value as typically seen in the experimental data for most soils (Wong 1989).

In 1979, Oida improved on Bekker’s equation, equation (19), for brittle soils to eliminate some of its previous limitations (Oida 1979). The new relationship between horizontal shear stress and shear displacement also involved the derivation of two K parameters: Kr and Kw, in which Kr represents the ratio of the shear stress to the maximum shear stress, otherwise known as the normalized shear stress, and Kw represents the shear displacement at which the maximum shear stress occurs. This equation, more thoroughly described by

Oida (1979), satisfies the condition that when the shear displacement is equal to Kw, the shear stress is equal to the maximum shear stress. In addition, when the shear displacement is equal to Kw, the derivative of the shear stress with respect to the shear displacement is equal to zero. In other words, the maximum shear displacement occurs at the peak of the “hump.” Finally, in contrast with Bekker’s equation, when the shear displacement approaches Kw, the shear stress approaches a residual shear stress. The downfall to Oida’s stress-strain relationship is that the value of Kr is not always obvious with experimental data. Therefore, a long and complicated iterative procedure is needed to obtain Kr (Wong 1989). In addition, the shear stress-shear displacement relationship is quite intricate which makes any attempt at predicting the vehicle relationship between

46 thrust and slip difficult (Wong 1989). Wong (1989) presented a solution to these difficulties with the following relationship,

⎡ ⎡ 1 ⎤ ⎛ j ⎞⎤⎡ ⎛ − j ⎞⎤ ⎜ ⎟ ⎜ ⎟ τ = τ max * K r ⎢1+ ⎢ −1⎥ exp⎜1− ⎟⎥⎢1− exp⎜ ⎟⎥ (20) ⎣ ⎣()K r ()1−1/ e ⎦ ⎝ K w ⎠⎦⎣ ⎝ K w ⎠⎦

where Kr and Kw are the same parameters as defined in Oida’s relationship and it satisfies the same conditions as Oida’s excluding the correlation that when the shear displacement is equal to Kw, the derivative of stress with respect to the shear displacement is equal to zero (Wong 1989). In Wong’s relationship, this condition only holds true when Kw is equal to the value 0.66, which means that for all other values of Kw the maximum shear stress will not match that of the experimental data exactly (Wong 1989). However, the value of Kr is now much easier to obtain following a method involving the least squares principal (Wong 1989).

Refocusing attention to the additional curve shown in Figure 1.18, which is the typical stress-strain trend for soils that are plastic in nature, such as loose non-compacted sand or clay; one can see that this relationship typically maintains a maximum stress value. For this type of curve a modification was made to Bekker’s equation, equation (19), which simplified the stress-strain relationship for these types of soil. This new relationship representing the shear stress underneath a wheel was proposed as an exponential form by

Janosi and Hanamoto in 1961 and is written as follows,

⎛ − j ⎞ τ = τ ⎜1− e K ⎟ (21) max ⎜ ⎟ ⎝ ⎠

where τ max is the maximum shearing stress or shear strength of the soil, j is the shear displacement, and K is the shear deformation modulus of the soil which can be considered a measure of the magnitude of the shear displacement required to develop the maximum shear stress in a given soil (Janosi and Hanamoto 1961, Wong 1989). It is important to note that equation (21) is a special case of Wong’s equation, equation (20), when Kr is greater than or equal to one (Asaf et al. 2006).

The general methodology behind the use of equation (19), equation (20), and equation

(21) for the horizontal stress-strain relationship of a terrain is similar to that presented in the previous section for the vertical stress-strain relationship:

1. An ensemble of annular shear bevameter tests are conducted in the specified

soil/terrain.

2. Parameters of the prediction equation are calculated via curve-fitting techniques.

3. These parameters are then used in the prediction equation to predict shear stress-

shear displacement characteristics of similar objects.

More specifically, a minimum of three annular shear tests, but more typically five to seven tests, each using a different applied normal load must be run in order to determine the envelope of Mohr’s circles based on the Coulomb failure criterion of soil (Bekker

1969). Using this procedure along with general soil mechanics procedures, the values of

48 cohesion and friction angle can be determined to define the strength of the soil as well as the type of ground material, i.e. plastic or brittle as previously mentioned.

The evaluation of the coefficients K, K1, and K2 is not a very easy task. As in the Bekker pressure-sinkage equation, equation (4), it involves the curve-fitting of empirical data, which in the case of K1 and K2 turns out to be a very long and complicated process

(Bekker 1969, Wong 1989). Many investigators tried to improve upon the Bekker equation or simplify the process and minimize the error in defining K. One such investigator was Weiss who worked at the Army Tank Automotive Center as part of the

Land Locomotion Laboratory team in Michigan (Weiss 1962). According to Reece

(1964), Weiss’s method was soon forgotten, but was later resurrected by Wills (1966).

Wills proposed that a “family of theoretical curves” with different K-values be plotted against experimental data in order to obtain an optimum K-value corresponding to the experimental data. The downfall to this method as commonly seen is that it relies on the investigator’s judgment and experience, which means that a unique K-value is impossible to obtain. During the same time period, Reece proposed a theory that the deformation parameter K was dependent on the normal pressure resulting in a modification to

Bekker’s equation as shown in the following equation,

τ = (c + σ tanφ)(1− exp − jσ / K ) (22)

where σ is the normal pressure (Reece and Adams 1962). Further experimentation proved that equation (22) could not accurately describe vertical stress-strain relationships.

Later, Reece modified a method of determining K proposed by Janosi and Hanamoto

(1961) where K was determined by drawing the tangent to the experimental stress-strain curve beginning at the origin. However both methods were found to be very difficult and lead to inaccurate K-values.

As before, Wong developed a simpler more reliable data processing methodology to obtain the horizontal stress-strain terrain parameters (Wong 1980). Since most terrain encountered falls under the category of plastic type soils the following methodology will pertain entirely to equation (21). Again, Wong used a weighted least squares method in order to determine the best possible value of K that minimizes error in the curve-fit.

Wong’s procedure as described in Wong (1980) begins with taking the natural logarithm of both sides of equation (21). This leads to the following function,

2 2 ⎛ τ ⎞ ⎡ ⎛ τ ⎞ j ⎤ F = ∑⎜1− ⎟ ⎢ln⎜1− ⎟ + ⎥ (23) ⎝ τ max ⎠ ⎣ ⎝ τ max ⎠ K ⎦

which must be minimized in order to determine the best value of K. It should be noted

2 that this function has an applied weighting factor of (1−τ /τ max ) . In order to minimize equation (23), the first partial derivative of the function with respect to K is taken and set equal to zero. This in turn leads to the final equation, equation (24), which computes the optimum value of K in order to minimize the error from the curve-fit.

2 2 ∑(1−τ /τ max ) j K = − 2 (24) ∑(1−τ /τ max ) j[]ln(1−τ /τ max )

Figure 1.19 shows the results of the curve-fitting method described by Wong as applied to experimental results from shear bevameter testing in a sandy terrain. Again the

“goodness-of-fit” of the predicted or curve-fit stress-strain curve with the experimental data can be determined by the following equation,

2 [∑()τ m −τ c ] ()N − 2 ε = (25) ∑τ m / N

where τm is the experimentally obtained value of shear stress or the measured value and τc is the calculated value of shear stress. Similarly, the shear stress-shear displacement curve-fit is defined as “perfect” when the goodness-of-fit value ε is equal to zero.

Figure 1.19 Typical horizontal stress-strain curves for a sandy terrain (Wong 1980).

In summary, Bekker’s shear bevameter technique in combination with the Janosi-

Hanamoto equation, equation (21), for obtaining the horizontal stress-strain relationship of a soil has proven to be a reasonable model for the tractive performance of a vehicle. It should be noted, however, that this method has certain downfalls which need to be considered. Similar to the plate-sinkage test, equation (21) is only able to predict accurately within the limitations of the annular shear bevameter itself, i.e. within the pressure range and only for similar annular ring sizes (in terms of contact area) and shape

(including number and spacing of grousers, etc.). Since annular shear bevameter tests are performed in order to predict vehicle mobility, it is reasonable to conclude that the larger the annular ring size the better, i.e. annular ring should be similar in contact area to that of the wheel footprint; and the larger the range of normal pressures used for the

52 prediction equation the better. However, it should be noted that the maximum size of the shear ring is limited by the terrain characteristics. If the test is performed in the field, the largest ring size should be used that will viably contact the entire surface area (avoiding lumps, bumps, or furrows, etc.). In the laboratory, the maximum size of the ring is restricted only by the limitations of the instrument in terms of allowable normal load

(Bekker 1969) as well as limitations of the soil bin with respect to boundary conditions.

In either case, the larger the diameter the larger the horizontal shearing area and the better linear shear is approximated, leading to more accurate values of the cohesion and friction angle (Bekker 1969). Additionally, it should be noted that a thin ring (with respect to diameter) has a more uniform or similar stress development from the inner diameter to the outer diameter of the ring.

More recently, investigators have been trying to utilize finite element (FEM) and discrete element models (DEM) to simulate the stress-strain relationships of shear plates in soil.

Asaf et al. (2006) developed a discrete element model for track-soil interaction and compared it to the semi-empirical relationships developed by Bekker (1969), Janosi and

Hanamoto (1961), and Wong (1980). Poor correlation between the Bekker model and

DEM model was obtained. However, a high confidence interval was attained. In addition, the Janosi and Hanamoto (1961) model was found to correlate well with respect to plastic soils, while Wong’s model correlated well with respect to both brittle and plastic soils. Overall, the research by Asaf et al. (2006) provides a solid foundation for the application of DEM in terramechanics and vehicle mobility studies.

In conclusion, the application of the parameters n, kc , kφ , K, c, and φ to the prediction and design of vehicle mobility and vehicle running-gear, respectively, has been proven to be a practical and reliable technique within the limitations and assumptions made (Bekker

1969). Although many attempts have been made in the past and are still currently being made to improve and refine the technique, “no other equally comprehensive concept of a soil value system has yet been proposed” (Bekker 1969).

1.6.2 Other Techniques for Measuring Soil Properties in Terramechanics

Currently there are no standard methods for determining the mechanical properties of the terrain for vehicle mobility studies. However, there are a great number of techniques and testing methods used in the field of civil engineering that are applicable to this issue.

Aside from the bevameter technique previously introduced, there are several other techniques that have been used to determine the mechanical properties of the terrain.

Any investigation involving soil usually necessitates a measurement of the basic soil properties otherwise known as index properties, which are typically used to categorize or classify the soil. These properties include: soil type, grain size distribution, Atterberg limits, specific gravity, bulk density, void ratio, moisture content, and many more. To measure these index properties for mobility studies, the soil is usually sampled from the field and tested in a soils laboratory. These tests to determine the index properties of a soil have all been standardized by the American Society for Testing and Materials

(ASTM). The standard procedures for conducting these tests can be found in any basic geotechnical engineering laboratory manual. In contrast, vehicle mobility studies require

54 more than just the basic properties of the soil composing a terrain. As described in the previous sections of this dissertation, vehicle mobility studies require an in-depth investigation into the strength properties of the soil. As noted by Wills (1966), the tests available to measure the shear strength of a soil can be classified into three major categories. These categories consist of translational, torsional, and triaxial laboratory tests. In addition, the U.S. Army Corps of Engineers typically uses cone penetration tests for trafficability studies. These tests will be described in depth in the following sections of this dissertation.

1.6.2.1 Direct Shear Test

The simplest and most general form of a translational test is known as the direct shear test. It is also the oldest form of shear testing in existence. The direct shear test is basically a “linear two-dimensional” test which “simulates the effects of shear loads acting on a predetermined failure surface” (Wills 1966, Bardet 1997). This test is used to determine the cohesion c, friction angleφ , and undrained shear strengthτ , of the soil.

Results are typically best when direct shear tests are performed on dry sandy materials.

In a direct shear test a soil sample is confined within a rigid square or circular container called a shear box which is split into two horizontal halves. The top of the shear box is subjected to an applied normal load which in turn applies a normal stressσ to the soil specimen. While the normal load is being applied, a shear force is simultaneously applied to the top half of the soil box so that the soil will fail in shear (refer to Figures

1.20 and 1.21). A minimum of three direct shear tests with varying normal loads is suggested to obtain accurate strength parameters. The strength parameters, c andφ , are then determined by plotting the maximum shear stress τ versus the corresponding normal stress σ for the direct shear test ensemble. Using a best-fit line to connect the test points on the resulting plot, the friction angle is defined as the angle of the best-fit line from the horizontal axis; while the cohesion is defined as the intercept of the best-fit line on the vertical axis. The equation for this line follows the coulomb strength criterion defined in equation (16).

Figure 1.20 Overview of direct shear test (Das 2002).

Figure 1.21 Typical direct shear test setup (Bardet 1997).

Direct shear tests have many benefits as well as several shortcomings. The direct shear test is much less complicated and quicker to run than a standard triaxial test and it generally gives fairly reliable strength values (c and φ ) when compared to triaxial test results. For sands with friction angles that are less than 35-degrees the difference between direct shear and triaxial test results are negligible. However, for sands with a friction angle that is greater than 35-degrees the difference between direct shear and triaxial tests range from one to four degrees, with the direct shear overestimating the friction angle (Bowles 1992). This has been attested to the fact that the direct shear test forces a horizontal failure plane instead of allowing the soil to fail along its weakest plane. One downfall to this test is that it utilizes a very small soil sample, which can easily magnify the effects of user or soil preparation errors. It is also more difficult to measure the volume change in a direct shear test since most samples fail at relatively small deformations. In addition, the direct shear test cannot completely define the stress state of the soil as a triaxial test can. This is because the normal and shear stresses are solely being measured in the horizontal direction (Bardet 1997). It is unknown as to what these parameters are on the vertical surfaces.

1.6.2.2 Torsional Shear Test

Torsional shear tests, otherwise known as ring shear tests, have been used for many years in an attempt to measure the strength properties of soil. In this type of test the soil specimen is prepared in a thin solid circular or annular circular shear cell of specified dimensions and is confined between rings. A shear cell lid with bent bars similar to

57 grousers, which are intended to prevent slipping of the soil at the lid, is placed on the sample and a normal load is applied. The specimen is then subjected to torsion and is pre-sheared until a steady-state shear value has been reached, at which point the stress is reduced to zero. At this point, an instantaneous test is performed by reducing the normal load and shearing the sample until a maximum shear value is reached and subsequently reduced. Each shear test provides a single data point that forms part of a yield locus for the specified soil and soil conditions. This yield point is plotted as the yield stress (or the maximum stress before failure) versus the normal stress. Typically a minimum of six shear tests are performed to create a single complete yield locus. Each test is plotted as previously mentioned and the method of least squares is applied to best-fit a straight line through the yield points. The angle of inclination of this line defines the friction angle of the sample, while the y-intercept of the line determines the cohesion.

Some benefits of the torsional shear test over the direct shear test are that the cross- sectional area of the soil specimen does not change during the test and the specimen can be sheared continuously in one rotational direction for any magnitude of displacement, unlike the direct shear test; and that it can be used to measure displacement as well. In addition, the torsional shear test is exempt from the bulldozing effect that is a typical issue of direct shear tests. When the soil gets pushed in front of the rectangular plate in a direct shear test, it usually results in increased shear values which require some correction in order to determine the true yield locus (Bekker 1969). On the contrary, the torsional shear test involves more skill and has a higher difficulty of preparing the soil sample than

58 the direct shear test. Additionally, in torsional shear tests, the shearing is not necessarily linear and there is variation in the stress radially.

1.6.2.3 Triaxial Test

The triaxial test is used to determine the stress-strain strength characteristics of soils under controlled drainage conditions. Although significantly more complicated, this test has the capability of reproducing (in a laboratory) the initial effective stresses and stress changes of soils in-situ in a more realistic way than the direct and torsional shear tests.

The triaxial test offers “the most accurate method for the determination of the maximum shearing resistance [of a soil] and the stress-strain relationship up to failure” (Wills

1966). In a typical triaxial test, a rubber latex membrane encases a cylindrical soil specimen in a cell filled with some relatively incompressible confining medium, typically water or air (refer to Figure 1.22). Within the membrane, the soil sample is sandwiched by porous stones and a top and bottom platen which are connected to the drainage system for saturating and/or draining the soil sample (depending on the type of triaxial test being conducted). Pressurizing the confining medium within the triaxial cell confines the specimen, which is then subjected to loading at a constant strain rate in the axial direction until failure is reached.

Figure 1.22 Typical triaxial test setup (Bardet 1997).

The most common and simplest triaxial test is called the conventional triaxial test or

CTC. Within the CTC there are three major categories of triaxial tests, each dependent on the in-situ stress state of the soil as well as the drainage conditions: the undrained unconsolidated (UU) also called the quick test; the consolidated undrained (CU); and the

consolidated drained (CD). In the conventional triaxial test a constant pressure σ c is maintained within the cell while the soil specimen is loaded in the axial direction at a constant deformation rate until failure. Typically at least three samples are tested, each

with a different cell pressureσ c . Load and deformation readings are taken for each test

so that stress-strain curves can be plotted to obtain the maximum shear stressτ max . The triaxial test data are then used to plot the Mohr’s stress circles using major and minor

principal stresses, σ 1 and σ 3 , respectively. For routine testing the cell pressure σ c is

defined as the minor principal stressσ 3 (which in most cases is identical to the

60 intermediate principal stress σ 2 ), while the major principal stress is the sum of the minor

principal stress σ 3 and the stress from the axial load obtained from the stress-strain curve

Δσ 1 (otherwise known as the deviator stress or principal stress difference). From at least two (but typically three) Mohr’s circles with differing cell pressures, the shear strength parameters c and φ can be obtained by graphically drawing a best-fit tangent to the circles. The intercept of the curve envelope with the ordinate is the cohesion intercept c and its best-fit slope is the angle of internal frictionφ .

Results of triaxial tests can also be represented in terms of stress paths. In 1964, Lambe

(cited Bowles 1992) suggested a type of stress path representative of the top of the

Mohr’s circles. This particular stress path plots q against p where p and q are the x- and y-coordinates of the top of the Mohr’s circles, respectively. The variables p and q are defined by the following expressions described by the major and minor principal stress values,

σ + σ p = 1 3 (26) 2

σ −σ q = 1 3 (27) 2

These coordinates can be from either total or effective stress values of the major and minor principal stresses. A triaxial test series with each test under a different confining pressure provides a locus of points defined by p and q. The best-fit line through these

61 points is defined as the Kf-line. The intercept and slope of the Kf-line are ultimately used to determine the cohesion and friction angle of the soil via the following equations,

a sinφ = tanα and c = (28, 29) cosφ

where α is the angle of the Kf-line from the horizontal and a is the value at which the Kf – line intercepts the q-axis. One advantage of using this method is that it is much simpler than a Mohr’s circle construction, where the circles may overlap or not align perfectly.

The Mohr’s circle method requires a skilled investigator and involves some judgment which may result in a large amount of error. Typical triaxial test results using both

Mohr’s circle method and the Lambe method are shown in Figure 1.23.

Figure 1.23 Typical triaxial test results from Mohr’s circle and Lambe methods (Bowles 1992). There are many advantages of using the triaxial test over the direct shear and torsional shear tests. First, the measurement of the specimen volume change is more accurate in

62 the triaxial test. Second, the complete state of stress is assumed to be known at every stage of the triaxial test. In the direct shear test the stresses at failure are the only ones known. Finally, the triaxial test is more versatile and is adaptable to special testing requirements. Studies performed by Bailey and Webber in 1964 compared the results from triaxial tests and shear annulus tests performed on both sandy and clay type soils

(Bekker 1969). The investigation revealed that the triaxial tests resulted in a straight-line envelope of Mohr’s circles while the shear annular tests resulted in a non-linear curved line that was more representative of vehicles. This was the case for both sand and clay.

However, the triaxial test as well as the direct and torsional shear tests has been questioned as to the applicability of these tests to vehicle mobility. It has been argued that these tests are not similar enough in shearing action to that of a vehicle developing thrust. It is suggested that the most suitable tests for vehicle mobility are those that can simulate the ground contact area of the wheel or track and those that apply normal loads simulating that of the vehicle ground pressure (Bekker 1969).

1.6.2.4 Cone Penetrometer Test

An empirical approach to the prediction of trafficability (more specifically vehicle sinkage and motion resistance) via the measurement of soil strength was developed during the Second World War by the Waterways Experiment Station (WES) of the Army

Corps of Engineers in the early 1940’s (Department of the Army Corps of Engineers

Mississippi River Commission 1948, Wong 1989). The testing device developed, referred to as the cone penetrometer, was intended to provide a convenient way of

63 determining the trafficability of a soil for the mobility of army vehicles. The cone penetrometer was able to combine the mechanical properties of the soil which in mobility are used to characterize soil drag and soil thrust into a single value (Bekker 1969). The

Department of the Army Corps of Engineers believed that this data obtained from the cone penetrometer could be interrelated to the trafficability of the soil (and therefore vehicle mobility) using known military vehicles. They implemented a “go/no go” type analysis which was based on past results of known vehicles, but it was soon discovered that this method was difficult to use on vehicles that had not previously been tested

(Wong 1989, Shoop 1993).

Another intention of the cone penetrometer was to resolve typical issues incurred when measuring soil strength via shear tests. The major issue with shear tests, such as the shear bevameter test, lies in the fact that when applying the test results to predict trafficability there is no knowledge of the stresses that result in the soil underneath the applied load. In the 1940’s accurate stress information was considered to be too difficult to obtain and was not accepted in testing methods for trafficability studies. Therefore, the cone penetrometer was developed and implemented for use as a soil strength indicator. The hand-held cone penetrometer for field testing, shown in Figure 1.24(b), was based off of the original laboratory cone penetrometer as shown in Figure 1.24(a). The standard cone penetrometer developed at the U.S. Army’s Waterways Experiment Station was composed of a 1.59 cm diameter rod, a proving ring with a dial gauge for measuring the applied force, and a 30-degree cone tip with a 323 mm2 base area (Shoop 1997, Wong

1989). Since then, it has been improved upon to include electronic force sensing devices

64 and usually is equipped with an automated data acquisition system. Today cone penetrometers are either hand-held instruments or are integrated onto a vehicle which electrically or hydraulically forces them into the ground (Wong 1989).

There are two standard cone sizes that are used for different soil conditions, both with a

30-degree apex angle. Typically in weaker coarser grained soils like sands, a large cone with a 323 mm2 base area is used. For harder, more compact, and fine grained soils such as clays a smaller cone with base area of 130 mm2 is used. The metric associated with the cone penetrometer is defined as a dimensionless cone index or CI which represents the force per unit base area required to push the cone into the soil. This only provides an index to the penetration resistance or the shearing resistance of the soil being tested. It does not provide an actual physical measurement of the soil strength. In reality, the CI represents a combination of soil properties including shear strength, compressibility, and sidewall friction, but cannot separately define any of these properties (Shoop 1993,

Mulqueen et al. 1977).

(a) (b)

Figure 1.24 (a) Army Corps of Engineers original laboratory cone penetrometer (Department of the Army Corps of Engineers Mississippi River Commission 1948). (b) Typical hand-held cone penetrometer used in the field (Shoop 1993).

In a typical cone penetration test, the cone is pushed into the soil at a constant rate and the first reading is taken when the base of the cone is flush with the soil surface and thereafter at uniformly spaced intervals. The recommended rate of penetration is on the order of 3 cm/s (Wong 1989). The resulting penetration resistance is plotted versus the corresponding soil depth and the cone index is typically taken as the resistance to penetration per unit base area. However, as previously stated, the CI is used as a dimensionless parameter. Another common index of soil penetration resistance is termed the cone index gradient G which is calculated as the slope of the resulting penetration resistance versus depth curve (over the linear portions of the curve). From G one can obtain an idea of the relative strength or density of the soil (through correlation) over a range of soil depth as opposed to the CI which is indicative of the strength at a specific depth. Typically the higher the G-value the stronger the soil. It is generally

66 recommended that a minimum of five cone penetration tests be performed to get a representative average (Shoop 1993). The American Society of Agricultural Engineers provides a thorough document containing the standard method for running a cone penetration test (ASAE 1985).

In addition to the cone index, there are several other indices that can be obtained from the cone penetrometer. These include the remolding index (RI), the rating cone index (RCI), and the vehicle cone index (VCI). The remolding index is used to determine the change in soil strength under repeated load cycles such as that of vehicle traffic. Mathematically, it is the ratio of the CI from the soil state after it has been driven on to that of the natural soil state. The rating cone index is a representation of the actual soil strength under repeated load cycles as opposed to the change in soil strength as represented by the RI.

Mathematically, it is the product of the RI and the original or natural soil state CI value.

Finally, the vehicle cone index is the representation of the trafficability of the soil. The

VCI is based on a critical soil thickness which is dependent on the type and weight of the vehicle. The thickness of this layer increases with increasing vehicle weight. As suggested by Wong (1989), for wheeled vehicles and tracked vehicles up to 22,727 lbs

(10,309 kg) and 45,454 lbs (20,618 kg), respectively, the critical soil thickness ranges from 15.2 to 30.5 cm. The thickness increases to values ranging from 22.9 to 38.1 cm when the vehicles surpass these weights. Now that the critical layer has been defined, the

VCI can be defined as the smallest CI value of a soil within the critical layer which allows a vehicle to make a specified number of passes without becoming immobilized.

In an attempt to expand the use of the cone penetrometer and its ability to define the mechanical properties of soil for mobility studies, several researchers such as Colins

(1971) and Mulqueen et al. (1977) investigated the relationship of the cone penetrometer penetration resistance to other standard engineering properties of soil such as moisture content and soil strength. Mulqueen et al. (1977), who suggested that the CI is an all inclusive parameter representing a combination of shear strength, compressive strength, and skin friction; also showed that these components of the CI from homogeneous soils which experienced repetitive loading changed with the moisture content of the soil.

However, it was discovered that the changes in the shear and compressive strengths were not reflected in the resulting CI values of soils with high moisture contents. In 1981,

Rohani and Baladi were able to develop relationships between the cone penetrometer cone index value and engineering properties such as the shear strength (including friction angle and cohesion), density, and the stiffness of a soil as represented by the shear modulus (Rohani and Baladi 1981). However, these relationships were limited to homogeneous frictional soils only. In addition, it should be mentioned that these relationships between the CI and the mechanical properties of the soil are non-linear

(Wong 1989). Therefore, it is simple to obtain the CI from a soil with known friction angle, cohesion, density, and shear modulus, but extremely difficult to determine these parameters from the CI. In 1982, Ayers and Perumpral investigated the effect of the moisture content and density on the value of the cone index as well (Ayers and Perumpral

1982). On the contrary, several researchers have argued the validity of the cone penetrometer for use in trafficability. Reece and Peca (1981) investigated this issue and determined that the cone penetrometer accurately determined the strength characteristics

68 of remolded clay, but failed to do so for sand. In 1984, Turnage investigated the prediction of wheel performance in sand utilizing the cone penetration resistance gradient. He determined that the gradient needed to be correlated with the original undisturbed properties of the soil such as density and grain size distribution as well as after the wheel had passed over the soil (Turnage 1984). Unfortunately, it has been well accepted that the cone index alone cannot provide all the answers for the prediction of vehicle mobility.

In comparison with the bevameter, which is useful in all types of soil (including snow) and provides several soil parameters, the cone penetrometer was designed specifically for use in fine grained soils or sands that have the potential to behave like fine grained soils, and only provides a single soil parameter (Bekker 1969). The several parameters obtained through plate-sinkage and shear tests via the bevameter technique provide more data than the single cone penetrometer index. The bevameter soil parameters have been related to vehicle mobility through mathematical models that have been experimentally tested, whereas the cone index has been related to vehicle mobility strictly through empirical investigation. This is part of the reason why, as mentioned before, that the cone penetrometer cannot solely be used for the prediction of vehicle mobility.

Interestingly, the value of the cone index was successfully related to the bevameter soil

parameters n, kc , and kφ by Janosi in 1959 (Bekker 1969). The relationship is as follows,

⎧ n+2 n+2 n+1 ⎫ ⎪ kc n+1 n+1 ⎡ ()z +1.5 z ()z +1.5 z ⎤⎪ CI = 1.625⎨ []()z +1.5 − z + 0.517kφ ⎢ + − ⎥⎬ (30) ⎩⎪n +1 ⎣()()n +1 n + 2 n + 2 n +1 ⎦⎭⎪

where z is the amount of cone sinkage. However, this relationship is not commonly used in vehicle mobility studies. Further information on the appropriate use of this equation can be found in Bekker (1969).

1.6.2.5 Shear Vane, Vane-Cone, and Cohron Sheargraph Tests

In another attempt to expand the use of the cone penetrometer and its ability to define the mechanical properties of soil for mobility studies, a vane-cone device as shown in Figure

1.25 was developed by Young et al. in 1975. This device operates in the same fashion as the cone penetrometer developed at the Waterways Experiment Station, but has the additional capability to determine the shear strength of the soil. The device is pressed into the soil and then held at a specific depth while rotated. The vane-cone device, however, does not escape the aforementioned limitations of the cone penetrometer (Wong

1989). It is best used in clay materials and unfortunately is unable to separate the cohesive and frictional components of the shear strength of the material (Wills 1964).

Figure 1.25 Vane-cone penetrometer (Shoop 1993).

A similar device, simpler in application, was designed solely to measure the shear strength of clays (Shoop 1993). This device is known as the shear vane and can be used in either laboratory or field tests. The shear vane typically consists of four thin, equally sized plates that are welded to a steel torque rod (Das 2002). The shear vane operates in a similar fashion to the vane-cone penetrometer. It is pushed into the ground to the desired depth, and then rotated at a uniform speed. A soil cylinder of height h and diameter d, as shown in Figure 1.26, resists the torque until the soil fails in shear. The torque required to rotate the device is recorded and used to determine the shear strength of the soil. However, this device cannot be used to obtain the penetration resistance of soils and is not suitable for sandy soils. In addition, the applicability of this device is limited by the strength of the soil being tested.

Several studies have been carried out to compare the results of the soil strength measurement from the shear vane to that of the triaxial and direct shear devices. Stafford

71 and Tanner (1982) compared the strength measurements of six different soils varying from sand to sandy clay and clay using six different testing devices including the annular torsional shear device, the direct shear box, drained and undrained triaxial tests, and the shear vane instrument. The measurements obtained via the shear vane instrument consistently resulted in the highest values of cohesion. Similar studies performed by

Kogure et al. (1988) resulted in the same conclusion. The shear vane testing device yielded the highest values of shear strength compared to direct shear and triaxial testing devices.

Figure 1.26 Shear vane end effector (Shoop 1993).

Another shear testing device that has been in use for years is the Cohron sheargraph. The

Cohron sheargraph is a device used to measure the in-situ shear strength of soils. It consists of a torsional shear-head with a smooth rubber or metal vane surface. The shear- head is connected to a recording drum by means of a spiral spring. The Cohron sheargraph is operated by setting the shear-head on the terrain surface, applying a desired

72 normal load, and then rotating the device at the wheel-like handle (refer to Figure 1.27).

The drum simultaneously records both the normal and shear forces applied. By applying a combination of normal and torsional loads, a normal stress versus shear stress curve can be produced. By running several tests under different constant normal loads, a yield locus can be obtained from which the cohesion and angle of internal friction of the soil can be determined.

Figure 1.27 Cohron sheargraph (Shoop 1993).

The Cohron sheargraph is one of the simplest shear testing devices. However, it is not widely used or generally accepted. “Its light weight and small size make it a handy field instrument, but at the same time, the readings are less consistent because of the small area sampled and the sensitivity to operator error” (Shoop 1993).

1.7 NATURE OF THE LUNAR TERRAIN

In order to evaluate vehicle mobility on the Moon, it is important to understand the issues that are unique to mobility on the Moon, specifically the behavior of the lunar surface materials. Vehicle mobility studies necessitate the understanding of the engineering properties of the lunar soil. The engineering properties of the lunar soil, or the geotechnical properties of any soil for that matter, are critically dependent upon the environment in which the soil exists. Halajian (2007) states, “Earth soils, unlike Moon soils are a multi-phase system consisting of solid particles, pore fluids (air and water), and an adsorbed film coating each particle and inhibiting their solid-to-solid contact.”

Due to the lunar environment, Moon soils should then be a monophase system of solid particles only. Thus, it is necessary to begin the study of the lunar soil with a general understanding of the lunar environment and its affect on the geology of the Moon.

1.7.1 The Lunar Environment

There are several obvious differences between the Earth and the Moon which make the

Moon’s environment stand out as truly distinctive. Obvious variations include: the

Moon’s almost negligible atmosphere; extreme temperature fluctuations between lunar day and night; hard vacuum on the order of 10-12 Torr; and low gravity compared to that experience on the Earth. Some environmental variations that are not so apparent include ionizing, solar, and cosmic radiations which have a huge impact on the development and state of the lunar surficial materials. For example, the Apollo astronauts noted the

74 electrostatic levitation of lunar dust. Other variations in physical properties between the

Moon and Earth are summarized in Table 1.4 below.

Table 1.4 Comparison of the Moon and Earth (Vaniman et al. 1991b) Property Moon Earth

Mass 7.353 x 1022 kg 5.976 x 1024 kg

Radius 1,738 km 6,371 km 510.1 x 106 km2; Surface Area 37.9 x 106 km2 149.8 x 106 km2 land Mean density 3.34 g/cm3 5.517 g/cm3

Gravity at the equator 1.62 m/sec2 9.81 m/sec2 Escape velocity at the 2.38 km/sec 11.2 km/sec equator Mean surface temperature 107ºC day; -153ºC night 22ºC

Temperature extremes 123ºC to -233ºC 58ºC to -89ºC ~104 molecules/cm3 day; Atmosphere 2.5 x 1019 molecules/cm3 2 x 105 molecules/cm3 night Moment of inertia 0.395 0.3315

Heat flow ~29 mW/m2 63 mW/m2

Seismic energy 2 x 1010 J/yr 1017 to 1018 J/yr

Magnetic field 0 24 to 56 A/m

The lunar environment has a strong influence on the structure of the lunar terrain and surficial materials, i.e. on the geology on the Moon. It is not necessary to present a detailed history of the geology of the Moon. However, it is important to understand that the formation of the lunar soil, including materials ranging from boulders to silt sized particles, has been controlled by two main phenomena including high velocity impacts and volcanism. These external and internal lunar phenomena have resulted in two very distinct land formations on the Moon: the lunar highlands and the maria.

1.7.1.1 The Lunar Landscape

One of the most distinctive aspects of the Moon is the vibrant contrast between light and dark regions on the visible surface as shown in Figure 1.28. These contrasting areas define the landscape that composes the lunar surface. Generally speaking, the bright areas on the Moon are called the lunar highlands, which are characteristically rough and highly cratered regions. The highlands are also commonly referred to as terrae. The darker areas are referred to as the lunar maria and are generally smooth in nature. The lunar maria, appropriately named after the Latin term for “seas”, are the by-products of the volcanic processes on the Moon. One-third of the nearside of the Moon is defined by these “lava-filled plains”, while the farside of the moon has very few areas of mare

(Anonymous 2008). Although described as smooth in nature, it is not refuted that the maria does contain a large number of craters. However, because the mare is younger than the highlands it has a significantly less cratered appearance. In addition, the maria contain basins that are encompassed by high ridged mountains created from high velocity impacts. Basaltic lavas fill these basins which results in its characteristic smooth appearance and low-albedo surface.

Figure 1.28 Lunar highlands and maria (Anonymous 2008).

Chemically, the maria and highlands are quite different as well. Calcium and aluminum dominate the chemical composition of the highlands, while the maria are rich in iron and titanium. Other major differences lie in the mineralogical composition and rock type of the highland and the maria. The highland area is known to contain anorthositic rocks of deep igneous origin or impact-shocked plutonic rocks while the maria have rocks that are of a basaltic lava nature. More specifically, plagioclase feldspar makes up the vast majority of the highlands while the maria are rich in pyroxene (Vaniman et al. 1991a).

In addition to the highlands and maria, the lunar landscape includes many other less prominent features such as rilles, domes, ridges, and impact craters. The term rille comes directly from the German word for “groove”. Rilles are typically described as the long narrow channels that are depressed into the lunar surface. The exact formation of the lunar rilles is unknown. However, most believe that they are related to lava channels, collapsed lava tunnels, or possibly faults resulting from volcanism. Three classifications of rilles have been noted on the lunar surface. These include sinuous or river-like

77 channels; arcuate rilles, or curved rilles found near the perimeter of the lunar maria; and linear or straight rilles (Anonymous 2008). One of the most well known lunar rilles is the

Hadley Rille shown in Figure 1.29, which was explored as part of the Apollo 15 mission in 1971. This rille is approximately 125 kilometers (75 miles) long and nearly 400 meters (0.25 miles) deep. Another notable rille, Schroter’s Valley, exists near the

Oceanus Procellarium mare (Anonymous 2008). This rille is 160 kilometers long (99 miles) and approximately 1300 meters (over 0.75 miles) deep.

Figure 1.29 Hadley rille near the Apollo 15 landing site (credit NASA).

Lunar domes are similar to shield volcanoes, or large volcanoes with shallowly sloped sides, that exist on the Earth. It is believed that lunar domes are formed by viscous lava that after eruption from a “localized vent” tends to cool very slowly (Anonymous 2008).

Typically domes are described as, “wide, rounded, circular features with a gentle slope rising in elevation a few hundred meters to the mid-point” (Anonymous 2008). High populations of lunar domes are found as part of the Mons Rümker volcanic formation

78 within the Oceanus Procellarium mare shown in Figure 1.30. The domes shown in the photograph are nearly eight to 12 kilometers (5 to 7.5 miles) in diameter, but can be up to as large as 20 km (12.5 miles) in diameter (Anonymous 2008).

Wrinkle-ridges typically exist within the lunar maria as surficial winding ridges. Similar to the lunar rilles, wrinkle-ridges can extend up to several hundred kilometers in length.

These ridges represent “tectonic features created when the basaltic lava [of the lunar maria] first cooled and contracted” (Anonymous 2008). These ridges are prominent surrounding structures such as craters that are buried beneath the lunar maria.

Figure 1.30 Lunar domes at the Mons Rümker volcanic formation (Anonymous 2008).

In addition, the lunar terrain is covered with impact craters of various shapes and sizes from slight concavities to massive sharp rimmed basins filled with boulders and rocks

(Hörz et al. 1991). The phenomenon termed “impact cratering” is the most prominent of the geological processes on the Moon. Generally speaking, craters are formed as part of

79 the space weathering process when objects, ranging in size from microscopic dust particles to massive asteroids, impact the lunar surface at high rates of speed (on the order of 17 km per second). The difference in mass of these objects ranges from 10-15 to 1020 grams covering 35 orders of magnitude (Hörz et al. 1991). Such impacts result in the development of kinetic energy creating “compression shockwaves” which propagate away from the point of impact (Anonymous 2008). The response to these compression shockwaves are “rarefaction waves” which cause debris and geological matter to be ejected from the impact site resulting in the formation of craters. Craters can be as small as those occurring on individual particles of soil to large craters and impact basins up to several hundred kilometers in span and several kilometers in depth. Smaller craters typically form a “bowl shape”, whereas craters of larger magnitude generally portray a central peak surrounded by smooth floors, a downward sloping wall, and a raised rim as a result of the ejected material (Anonymous 2008). Overtime, the smaller impacts on the lunar surface by micrometeorites tend to weather the features of craters and give them a more rounded appearance. Impact craters can be used to estimate of the age of the lunar surface by determining the number of craters per unit area. This is due to the fact that impact craters typically accrue at a constant rate and superpose on the lunar surface.

King Crater shown in Figure 1.31 is a prominent lunar impact crater that is located on the farside of the moon. Among the countless number of craters on the Moon some prominent lunar craters include Copernicus, Galileai, Maginus, Littrow, and the South

Pole Aitken basin which is the largest crater on the Moon.

Although it is incorrect to state that the Moon has no atmosphere, the atmosphere on the

Moon is on the order of 14 times less than that experienced on the Earth, but it is distinctly composed of neon, hydrogen, helium, and argon resulting predominately from outgassing and the process of sputtering; it is the negligible atmosphere that allows these craters to maintain their structure. In fact, it is the deficient atmosphere as well as the lack of water, weather, and the presence of life that contribute to the preservation of the lunar landscape and all it encompasses.

Figure 1.31 King Crater (Anonymous 2008).

1.7.2 Lunar Regolith

Regolith is universally defined as “the layer of fragmental or unconsolidated rock material, whether residual or transported, and of highly varied character, that forms the surface of the land and overlies bedrock (McKay et al. 1991). In Greek, the term regolith

81 is literally translated as “blanket rock.” The overwhelming majority of the lunar surface, minus a few crater walls and lava channels, is covered by several meters of this dark to light grey highly fractured and pulverized material. On the Moon, this material is referred to as the lunar regolith or lunar soil. Before proceeding, it is necessary to differentiate between the terms lunar regolith and lunar soil. Although the terms “lunar soil” and “lunar regolith” are synonymously used, the lunar science community presents a physical difference between the two that is solely based on particle size. Lunar soil is defined as the finer grained fraction of the lunar regolith, more specifically, “the sub centimeter fraction of the lunar regolith” (McKay et al. 1991). As a side note, the lunar soil can further be divided into a smaller particle size (sub 50 μm), which is referred to as dust. Dust makes up about 40 to 50-percent of the lunar regolith (Schlagheck et al.

2005). In any case, the term lunar soil will be informally used throughout this dissertation to represent the lunar regolith and all it encompasses.

1.7.2.1 Formation of the Lunar Regolith

Again, the negligible atmosphere and lack of water in combination with weathering and erosional processes unfamiliar to those on the Earth creates a unique environment which has defined the formation of the lunar regolith. The creation of the lunar regolith is owed to the space weathering process dominated by continuous impacts by meteorites and micrometeorites. With these constant bombardments the lunar regolith is continuously fragmented, mixed, and altered or “cultivated”. In addition, there is a continuous combination of destructive and constructive processes occurring when the lunar surface is

82 impacted. Destructively, the impact energy causes fracture or pulverization of soil particles. Constructively, the heat resulting from the high impact energy causes agglutination, or the melting and fusing together of soil particles resulting in impact- produced breccias and impact melt rocks containing minerals, rocks, and glass (McKay et al. 1991). The resulting impact melts are known as agglutinates. It is the glass in these agglutinates which, when continuously fractured and distributed throughout the soil, contribute to the unique geotechnical properties of the lunar soil. As described by

McKay et al. (1991), regolith formation is a two stage process. At locations of any exposed bedrock or bedrock that is exposed by the eruption of a lava flow, the impacts penetrate the minute fraction of regolith that exists on the surface and exhume new bedrock. As more meteors and meteorites impact the surface, the regolith quickly accumulates. With a thicker layer of regolith most impacts are no longer able to penetrate to bedrock. This causes the regolith to be churned and pulverized into smaller particles. At this stage, the development of new regolith is much slower and requires larger impacts to penetrate through the regolith to the bedrock. In addition to the impact process, other space weathering processes which are less influential in the formation of regolith include particle irradiation and sputtering via solar wind, landslides of various degrees, electrostatic particle transportation, and volcanic activity. With the formation processes in mind a general rule of thumb is that the thicker the regolith and the smaller the particle size, the older the lunar surface. Accordingly, the regolith typically varies in thickness from three to five meters in the lunar maria regions and from approximately 10 to 20 meters in the highland regions. Below the surficial layer of finely fractured lunar regolith exists a layer referred to as the megaregolith. This layer, as shown in Figure

1.32, is much thicker and generally consists of fractured bedrock and large-scale ejecta

(typically larger than 1 meter). Currently the properties, characteristics, and the behavior of the megaregolith layer are not well understood.

Figure 1.32 Typical lunar soil profile (Hörz et al. 1991).

1.7.2.2 Engineering Properties of the Lunar Regolith

All the space weathering processes (described in the preceding section and shown Figure

1.33) experienced on the lunar surface combine to “produce a regolith whose structure,

84 stratigraphy, and history may vary widely, even between locations only a few meters apart” (McKay et al. 1991). It has taken a huge effort, including countless analytical investigations and numerous statistical models to even begin to understand the complexity of the lunar regolith. Again, as Karl Terzaghi (1963) stated, “Unfortunately, soils are made by nature and not by man, and the products of nature are always complex.”

This section provides a general summary of the engineering properties of the lunar soil as determined by investigations performed on the lunar soil both on the Moon (by astronauts and robots) and on returned lunar samples, as well as by remote sensing from the Earth.

A tabulated summary of all recommended soil parameters for the lunar soil is provided in

Appendix A. The properties summarized below are generally physical properties of the lunar soil as the chemical properties of the lunar soil are not pertinent to vehicle mobility studies. An in-depth discussion on the chemical composition of the lunar soil can be found in Haskin and Warren (1991). In addition, the information presented below is only a summary. A more formal discussion about the engineering properties of the lunar soil is discussed in the Literature Review in Chapter Two of this dissertation.

Figure 1.33 Cartoon of lunar space weathering process (credit NASA). Particle Size and Shape

The particle size distribution of the lunar soil is an extremely important engineering property which influences the strength and compressibility of the material as well as governs the optical, thermal, and seismic properties (Carrier 1983). The particle size distribution of the lunar soil is determined entirely by the impact processes which are responsible for its formation. More specifically, the grain size distribution is dependent on the comminution, agglutination, and continuous mixing processes previously described. The lunar soil consists of several different particle types. These include crystalline rock fragments, mineral fragments, breccias, agglutinates, and glasses (Carrier et al. 1991). It is important to note that the proportion of these particle types which compose the lunar soil vary from location to location as well as with depth. However, the majority of these lunar soil particles fall in a fairly narrow range of particle size distribution as shown in Figure 1.34. This figure specifically represents the upper and lower bounds of the lunar particle size distribution for all the Apollo mission sites (Sibille et al. 2005). As reported in Carrier et al. (1991), the mean grain size distribution of the lunar soil ranges from 40 to 800 micrometers (μm). However the majority of the grains fall between 45 to 100 μm. The median grain size distribution of the lunar soil ranges from 40 to 130 μm with and average of 70 μm. Approximately half of the lunar soil consists of very fine particles that are much smaller than typical beach sand found on the

Earth (Sibille et al. 2005). In general, the lunar soil is a well-graded, silty sand to sandy silt material otherwise described as SW-SM to ML as determined by the Unified Soil

Classification System (USCS).

Figure 1.34 Particle size distribution of lunar soil (Carter et al. 2004).

The lunar soil particles tend to be irregular in shape, ranging from round to very angular, and can be fairly elongated as shown in Figure 1.35. With these properties the individual particles become highly abrasive and tend to interlock. Though the lunar soil is unique compared to terrestrial soils, it can best be compared with a cobble-bearing silty sand, fine grained slag, or terrestrial volcanic ash (Carrier et al. 1991).

Figure 1.35 Typical lunar soil agglutinate particle (McKay et al. 1991).

Specific Gravity

The specific gravity of the lunar soil ranges from 2.3 to greater than 3.2. This means that the density of the individual soil particles is at least 2.3 times greater than that of water which is approximately 1 g/cc. More specifically, specific gravity is a ratio of the mass of the soil to the mass of the same volume of water at 4º Celsius. It is a function of the proportions of rock and minerals which make up the soil (Sibille et al. 2005). Carrier et al. (1991) suggests a working value of 3.1 to be used for all engineering analyses pertaining to the lunar soil. This is due to the fact that the lunar soil exhibits subgranular porosity which exists as voids enclosed within the interior of the lunar soil particles as shown in Figure 1.36. During specific gravity testing in which a soil sample is submerged in water to determine the volume that it displaces; water cannot fill these subgranular voids. Essentially, this causes the specific gravity of the lunar soil to be underestimated. Other authors such as Carrier et al. (1991) suggest that the specific gravity of lunar soils range from 2.9 to 3.5 which in the author’s opinion may be a more realistic range of specific gravity taking subgranular porosity into account.

Figure 1.36 Cartoon displaying subgranular porosity of the lunar soil (Carrier et al. 1991). Density

The major factors that influence the physical and geotechnical properties of soil are the soil’s bulk density and relative density. The bulk density of the lunar soil is a fundamental property in predicting vehicle mobility as it influences the soil’s bearing capacity and slope stability. In addition, the soil density influences the soil strength, compressibility, and permeability. Carrier et al. (1991) provides the best approximations of the lunar soil bulk density with respect to depth, which are shown in Table 1.5. These estimates come directly from a paper written by Mitchell et al. (1974) as a result of the

Apollo soil mechanics experiment S-200. Generally speaking, the bulk density of the lunar soil tends to increase with increasing depth. It is important to keep in mind that these values represent the best estimates for the bulk density of intercrater areas. The

“best estimates” for bulk density were determined by taking into account the different testing methods and soil sampling techniques including any degree of soil disturbance accompanying the soil sampling techniques (Carrier et al. 1991).

Table 1.5 Bulk density of lunar soil (Carrier et al. 1991). Average Bulk Density (g/cc) Depth (cm) 1.50 ± 0.05 0 – 15 1.58 ± 0.05 0 – 30 1.74 ± 0.05 30 – 60 1.66 ± 0.05 0 – 60

The relative density of the lunar soil is dependent on the sizes and shapes of the individual soil grains, and is determined based on the following relationship:

ρ max ρ − ρ min DR = × ×100% (31) ρ ρ max − ρ min

where ρ max is the maximum bulk density, ρ min is the minimum bulk density, and ρ is the bulk density of the soil sample. The relative density generally refers to the degree of particle packing of the lunar soil. The relative density of the lunar soil is vital to vehicle mobility as it controls the shear strength and compressibility of the soil as well as defines the absolute bulk density. Mitchell et al. (1974) and Houston et al. (1974) estimated the relative density of the lunar soil with respect to depth, corresponding to the best estimates of bulk density previously tabulated. In turn, these values for relative density have been correlated to describe the soil in terms of loose to very dense. The results are summarized in Table 1.6. Generally speaking, the relative density of the lunar soil tends to increase with increasing depth. Again, it is important to note that these values of relative density correspond only to the lunar soil composing intercrater areas.

Table 1.6 Relative density of the lunar soil (Carrier et al. 1991). Soil Description Relative Density (%) Depth (cm) (Lambe and Whitman 1969) 65 ± 3 0 – 15 Medium to Dense 74 ± 3 0 – 30 Dense 92 ± 3 30 – 60 Very Dense 83 ± 3 0 – 60 Dense

Using the best estimates for the specific gravity of the lunar soil in combination with the best estimates for the bulk density of the lunar soil, other engineering properties such as porosity and void ratio of the lunar soil can be estimated. The bulk density, specific gravity, and porosity of a soil are related as:

ρ = Gρ w (1− n) (32)

where ρ is the bulk density of the soil, G is the specific gravity of the soil, ρ w is the density of water (1 g/cc), and n is the porosity of the soil. Rearranging equation (32), the porosity of the soil can expressed as:

ρ n = 1− (33) Gρ w

which is representative of the ratio of the volume of the voids to the total volume of the soil sample. The void ratio of a soil in general is defined as the ratio of the volume of the voids to the volume of the soil solids. Mathematically, it is related to the soil porosity by the following equation,

n e = (34) 1− n

The best estimates of the porosity and void ratio of the lunar soil are presented in Table

1.7. Generally speaking, the porosity and void ratio of the lunar soil tend to decrease with increasing depth.

Table 1.7 Porosity and void ratio of the lunar soil (Carrier et al. 1991).

Depth Range (cm) Average Porosity, n Average Void Ratio, e

0-15 52 ± 2 1.07 ± 0.07 0-30 49 ± 2 0.96 ± 0.07 30-60 44 ± 2 0.78 ± 0.07 0-60 46 ± 2 0.87 ± 0.07

Compressibility

The compressibility of a soil is defined as the change in the volume of the soil when a confining pressure is applied. In other words, it describes the densification of the soil under an applied confining pressure. Generally, compressibility occurs in two phases.

The first phase takes place under low initial confining pressures or when the soil exists in a state of relatively low density. When this happens intergranular slippage occurs and the particles reorient themselves to fill in voids that previously existed in the “honeycomb soil structure” (refer to Figure 1.37). The second phase takes place when the confining pressure is increased or if the initial density of the soil is fairly high. During this phase, the particles themselves are deformed and/or fractured, generally breaking near the points of contact.

(a) (b) Figure 1.37 (a) Honeycomb structure of uncompressed granular soils. (b) Compressed structure of granular soils (Duncan 1998).

The typical metric associated with the compressibility of a soil is termed the compression index Cc and is defined as:

Δe Cc = − (35) Δ logσ v

where e is the void ratio and σ v is the applied vertical stress. The value for Cc is obtained from the straight-line portion past the preconsolidation pressure of the associated semilog plot of void ratio versus log pressure. Typically the compression index of a soil is measured by performing a one-dimensional oedometer test. Carrier et al. (1991) recommends typical values of 0.3 for loose lunar soils and 0.05 for dense lunar soils based on oedometer tests performed by Carrier et al. (1972). In addition, the compression index of lunar soils typically decreases with increasing initial relative density (Carrier et al. 1991).

Strength Properties

The most critical soil properties for the mobility of a wheeled vehicle on the lunar surface are the friction angle and cohesion (as previously described). Together these properties can be combined in the classic Mohr-Coulomb equation to represent the ultimate shear strength of the soil, which directly affects the bearing capacity, slope stability, and potential to thrust against the lunar terrain. The relationship between the ultimate shear strength, friction angle, and cohesion of the soil was previously defined in section 1.6.1.2,

Shear Strength, by equation (16). Some of the best pre-Apollo estimates of the ultimate

93 strength of the lunar soil tend to be under-conservative and near the lower bounds of the actual lunar soil shear strength. For example, Scott and Roberson (1969) approximated values of 0.35 to 0.70 kPa for cohesion and values of 35 to 37-degrees for friction angle of the lunar soil based on the data obtained from the Surveyor soil mechanics surface sampler. Later, Mitchell et al. (1972, 1974) used data from the Apollo missions to determine what they felt were more representative values of the shear strength parameters of the lunar soil. These values ranged from 0.1 to 1 kPa for cohesion and 30 to 50 degrees for friction angle. Carrier et al. (1991) provides a table of recommended shear strength parameters for the lunar soil of inter-crater areas as shown in Table 1.8. These values of cohesion and friction angle generally increase with the increasing density of the soil.

Table 1.8 Recommended values of lunar soil cohesion and friction angle (Carrier et al. 1991). Depth Range Cohesion (kPa) Friction Angle (º) (cm) Average Range Average Range 0-15 0.52 0.44-0.62 42 41-43 0-30 0.9 0.74-1.1 46 44-47 30-60 3 2.4-3.8 54 52-55 0-60 1.6 1.3-1.9 49 48-51

1.7.2.3 Trafficability Parameters

It was once believed that trafficability on the Moon would be very poor and that it would be difficult for vehicles to become mobile (Carrier et al. 1991). However after the launch of the Apollo Lunar Roving Vehicle (LRV), it was demonstrated that vehicles with round wheels can and do perform satisfactorily on the lunar surface. There have been three

94 types of wheeled vehicles, to date, which have successfully operated on the lunar surface.

These include the U.S.S.R. Lunokhod, the Apollo 14 Modular Equipment Transporter

(MET), and the Apollo Lunar Roving Vehicle.

(a) (b) Figure 1.38 (a) USSR Lunokhod. (b) Apollo LRV (Carrier et al. 1991).

Before the development of the LRV there was no actual mobility performance or trafficability data relating to wheel-soil interaction involving extremely light wheel loads and fine-grained granular soils. In order to plan the LRV traverses, trafficability soil

parameters were recommended, i.e. n, kc , kφ , K, c, and φ were estimated. These estimates are shown in Table 1.9. Due to the NASA Request for Proposals being initiated only a month and a half after the Apollo 11 mission, the guidelines for trafficability were based on the soil mechanics data obtained from previous unmanned

Surveyor missions (Costes et al. 1972). Based on a range of recommended trafficability and soil parameters as shown in Table 1.9, five analytical soil models were proposed, representing the lower, mid, and upper range of the recommended total range (Carrier et al. 2006). It is the median design values which are recommended as the “best” values for lunar trafficability parameters in the Lunar Sourcebook (Carrier et al. 1991).

Table 1.9 Recommended trafficability parameters (Costes et al. 1972, Carrier et al. 1991). Recommended Soil Parameter Description Best Value Range of Values 2 2 kc 0 – 0.28 N/cm 0.14 N/cm Bekker pressure-sinkage k 3 3 φ characteristics 0.82 N/cm 0.82 N/cm n 1.0 1 Coefficient of soil/wheel c 0 – 0.035 N/cm2 0.017 N/cm2 cohesion φ Soil/wheel friction angle 35 ± 4º 35º K Coefficient of soil slip 1.78 ± 0.76 cm 1.8 cm

It is important to note that these parameters are general parameters used to design and plan for the LRV mission. According to Carrier et al. (2006), there were no actual soils with the same parameters as the five defined soil models. In addition, it should be kept in mind that the lunar surface materials vary from location to location and that there exist soft soil areas (specifically near craters) which are likely to immobilize a wheeled vehicle. According to the MSFC Lunar Environmental Criteria Document for the development of the LRV (Costes et al. 1972), “these recommendations might be subject to change as a more comprehensive and realistic analysis of data relating to lunar soil- vehicle interaction would become available.” It was not concluded until after the Apollo

15 mission was completed, and the performance of the LRV was evaluated, that the soil parameters listed as “best” values in Table 1.9 were truly the most representative of the performance of the LRV on the lunar soil (Costes et al. 1973 and Mitchell et al. 1974 cited by Carrier et al. 2006). Carrier et al. (1991, 2006) also concluded that, “From the experience of the Apollo and Lunokhod missions, we now know that almost any vehicle with round wheels will perform satisfactorily on the lunar surface provided the ground contact pressure is no greater than about 7 to 10 kPa.” However, it can be argued that

96 this statement is too general and that the empirical data supporting it is too sparse to come to such a bold conclusion.

1.7.3 Important Aspects for Lunar Surface Mobility

It is important to understand the impact of the lunar environment and the nature of the lunar terrain on lunar surface mobility. Soil response to vehicle action is determined by a complex interaction of forces, including body forces due to vehicle weight, inertia of the vehicle, and cohesive and frictional forces from within the soil (Halajian 1963). These forces are heavily influenced by the lunar vacuum and the low lunar gravity and are further discussed in the subsequent sections of this dissertation.

1.7.3.1 Cohesion

Cohesion is defined as the bonding or attraction between particles of certain fine-grained soils that enhances shear strength and is independent of confining pressure. It is the component of the shear strength of a soil that is independent of interparticle friction. On the particulate level, an adsorbed film exists on the surface of the soil particles. “Surface tension and viscosity in the adsorbed phase that separates the particles produce cohesive forces between these particles” (Halajian 1963). When the thickness of the adsorbed film surrounding the soil particles is high, particle to particle contact cannot occur. However, when the adsorbed surface film is non-existent a special case of cohesion occurs which is called adhesion. In this case there is actual particle to particle interaction. Lunar soil in

97 the traditional sense is termed a cohesionless soil because it does not obtain its cohesion from materials like clay which provide inter-particle adhesion after drying (Craig 1992 cited by Sibille et al. 2005). The apparent cohesion of the lunar soil is instead obtained from the angular and re-entrant particles which interlock during settling as well as from an electrostatic surface charge (Sibille et al. 2005). Therefore, the cohesion of lunar soil is not necessarily independent of friction. Other researchers add that the low environmental pressure and hard vacuum experienced on the Moon result in “clean” soil particle surfaces which cause interparticle forces to exist and ultimately increase the apparent cohesion of the soil (Vey and Nelson 1963).

Gross traction of a vehicle interacting with a cohesionless soil is directly proportional to the vehicle weight. In turn, gross traction becomes proportional to the gravitational field.

Essentially, in lower gravity environments, such as experienced on the Moon, the ratio of gross traction to vehicle weight will be increased ultimately improving vehicle mobility.

Any increase in the cohesion of the soil will only add to the gross traction per unit weight. In addition, it is believed (Carrier et al. 1991) that in a low gravity field, such as on the Moon, the interparticle cohesion is “likely to be effective within a wider spectrum of soil grain size.” High temperatures and radiation effects are also believed to cause cold welding of soil particles which also increases the shear strength of the lunar soil

(Vey and Nelson 1963).

1.7.3.2 Friction

Simply defined, friction is the shear force between surfaces in contact. Rather than the interlocking mechanism created by the surface roughness, it is now accepted that the sliding friction between two surfaces is due to chemical bonding or molecular attraction between the asperities of the surfaces (Halajian 1963). The friction force is therefore proportional to the normal force pushing the surfaces together. Greater normal forces result in greater deformation of the surficial asperities which in turn creates a larger contact area increasing adhesion between the two particles (Carrier et al. 1991). With respect to vehicle-soil interaction, friction is the component of the shear strength between soil particles which contributes greatly to the gross traction of the vehicle. The frictional resistance in this case is typically represented by the coefficient of friction or the internal friction angle. A few basic laws of frictional behavior are present during the shearing of soils as described by Lambe and Whitman (1969). These include the aforementioned law that the shear resistance between two bodies is proportional to the normal force between them as well as the law that the shear resistance between two bodies is independent of the dimensions of the bodies. In soil mechanics, there are a number of mechanisms which take place during the shearing of soils which contribute to the frictional resistance between the particles. Some of these processes include: the sliding and rearrangement of particles, resistance to volume change and dilatancy effects, particle interlocking, particle crushing, and strain rate dependent inertia effects. These frictional processes which occur in soil mechanics are far more complicated and much less understood than large masses sliding over one another, such as a wooden block sliding across a wooden surface.

On the Moon, the influence of a hard vacuum on soils results in the absence of adsorbed films on the surface of soil particles, which results in increased particle-to-particle

99 contact. Hinners (1964) states, “No doubt a mineral surface cleaned of lubricating moisture and gases, will have a higher coefficient of static friction than a contaminated surface.” In turn, the adhesion and friction between soil particles is enhanced promoting larger gross traction and drawbar pull (Carrier et al. 1991). An increase in mechanical friction is also promoted by the lack of atmosphere which causes the soil grains to be of increased angularity instead of becoming rounded by abrasion as in terrestrial soils

(Hinners 1964). In addition, the absence of water and other pore fluids in the lunar soil is beneficial to trafficability as it results in a decreased rolling resistance. Typically as these pore fluids are forced out from the soil there is a decrease in the effective stress of the soil which results in greater sinkage of the vehicle applying load. The lunar vacuum in combination with the lack of water on the Moon prevents this type of sinkage and therefore improves the net traction of the vehicle. It is apparent that the “overall effect of the harsh lunar environment would be one of increasing the shear strength of the lunar soil and it’s bearing capacity rather than reducing it” (Vey and Nelson 1963).

1.8 PROBLEM STATEMENT AND OBJECTIVES

As previously stated in section 1.3, Motivation for This Research, lunar exploration vehicle design depends critically on the measurement of the mechanical properties of lunar soils. In order to design vehicles for surface exploration on the Moon, it is essential to understand the mechanical behavior of lunar soils as well as the soil interaction with the vehicle system. One of the first steps in off-road vehicle design is the selection of the vehicle running-gear. Running-gear geometry is the primary consideration for traction

100

(and power consumption) of an off-road vehicle. Traction design relies on an accurate simulation of the geotechnical soil properties including cohesion and angle of internal friction as a function of bulk density. In the case of lunar vehicles it is even more challenging to select the appropriate running-gear as the running-gear must be chosen to meet the requirements of a given mission. This includes minimizing launch mass and volume, meeting the climbing and other work requirements, while keeping within the power limitations of the mission. Thus, it is the goal at the NASA Glenn Research

Center to develop and validate a parametric model that relates running-gear geometry to in-situ tractive performance. The collection of validation data within the lunar environment would be much too costly and impractical. Therefore it is necessary to conduct experiments on Earth, and predict lunar trafficability from the model by extrapolation of the environmental parameters. As such, the first requirement for experimentation under Earth ambient conditions is the development and understanding of a large-scale lunar soil simulant for mobility testing. All trafficability testing must be done in soil that emulates the deformations and shear behavior of the lunar soil when acted on by a wheel. The soil simulant used for laboratory testing will greatly influence the precision and reliability of the mobility model. Therefore, it is imperative to thoroughly investigate and understand the geotechnical behavior of the lunar soil simulant.

1.8.1 Scope of Work

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The focus of this research is on the development of a replica of the lunar soil based on known physical and mechanical properties, with an emphasis on the strength. More specifically, the objective of this research is to develop a soil that emulates the compaction and shear strength of the lunar soil when driven on by wheels in Earth ambient conditions. The research takes into account the results of past lunar missions including, but not limited to: data obtained by astronaut’s observations, in-situ lunar soil tests, returned lunar soil samples, and laboratory lunar soil tests. In addition, the composition and mechanical properties of past lunar soil simulants is taken into consideration in the development of a new lunar soil simulant. These lunar simulants include: MLS-1, JSC-1, and JSC-1a. Such a soil could be prepared to emulate various lunar terrain conditions, in order to validate lunar vehicle trafficability models, and evaluate various lunar vehicle prototypes.

The purpose of this dissertation is to present the development of a new lunar soil simulant, GRC-1; to check and correlate its properties with several semi-empirical models; and to suggest its proper use for vehicle mobility testing at the NASA Glenn

Research Center in Cleveland, Ohio. The sub-objectives of this study are as follows:

1. To review the properties of the actual lunar soil and understand the conditions

under which these properties were determined.

2. To review the properties of current and past lunar soil simulants and understand

the purpose and intent of creation and use.

3. To understand the interaction between soil and the running-gear of off-road

vehicles and the challenges facing lunar vehicle mobility.

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4. To develop a new lunar soil simulant, GRC-1, and determine its geotechnical

properties as well as compare these properties to those of the lunar soil and other

lunar soil simulants.

5. To analyze the cohesion and internal friction angle of GRC-1 using conventional

triaxial testing.

6. To investigate the horizontal and vertical stress-strain relationships of GRC-1

utilizing bevameter testing.

7. To analyze the strength characteristics of GRC-1 using cone penetrometer testing.

8. To compare the strength properties of GRC-1 to the strength properties of the

lunar soil and other lunar soil simulants. To understand the statistical variation of

these properties and how the variation could affect the prediction of vehicle

mobility.

9. To provide general recommendations for the use of this material as a lunar soil

simulant for vehicle mobility testing at the NASA Glenn Research Center. More

specifically, to provide recommendations on the soil preparation of GRC-1 on the

Earth so that vehicles will respond similarly on the Moon.

10. To critically review the results of this study and develop suggestions for future

work in this subject area.

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Basic Soil Properties

Bevameter Plate- Soil Mechanics Cone Sinkage Tests Strength Tests Penetrometer Tests

n, kc , kφ γ, c, φ CI (cone index), G (cone index gradient)

Terrain Terrain Terrain Parameters Parameters Parameters

Stress Stress Stress Distribution Distribution Distribution Underneath Underneath Underneath Wheels Wheels Wheels

Wheel Performance

Figure 1.39 Schematic of objectives for this research (after Karafiath 1970).

1.8.2 Basic Assumptions

There are several general assumptions that are basic to the arguments presented in this dissertation. The first and foremost assumption is that the lunar surface is covered with a layer of unconsolidated, highly fractured or pulverized, silty sand to sandy silt material, with low cohesion; and that the geotechnical properties of this material are best estimated

104 as discussed in section 1.7.2, The Lunar Regolith, and as presented in Table A1 of

Appendix A. In addition, it is assumed that the basic concepts in vehicle mobility and soil mechanics as developed by Bekker and Terzaghi (as described in section 1.5,

General Factors Affecting Surface Mobility and section 1.6, Soil Properties Affecting

Surface Mobility) are applicable to vehicle-soil interaction on the Moon. Finally and equally as important, it is assumed that a dry granular soil that has similar cone penetration resistance to the lunar soil will have similar compaction and shear stress resistance under a wheel.

1.9 ORANIZATION OF THE DISSERTATION

This dissertation presents the development, experimental procedures, testing results, and recommendations for the new lunar soil simulant, GRC-1, created for vehicle mobility studies at the NASA Glenn Research Center. While Chapter One was a brief introduction to terramechanics and the nature of the lunar soil, a more extensive literature review is provided in Chapter Two. This review presents an overview of lunar soil and lunar soil simulant studies as well as a review of vehicle mobility studies for lunar application. Chapter Three includes a detailed description of the development of GRC-1 and initial characterization of GRC-1. In addition, the index properties of GRC-1 are compared to index properties of the lunar soil and other lunar soil simulants. Chapter

Four through Chapter Six present the experimental testing, testing results, and analyses for the strength properties of GRC-1. More specifically, Chapter Four outlines the experimental testing and resulting shear strength properties as determined by triaxial

105 testing. Chapter Five outlines the experimental testing and resulting strength properties as determined by bevameter testing. Chapter Six outlines the experimental testing and resulting strength indices as determined by cone penetrometer testing. Finally, Chapter

Seven provides general conclusions and recommendations for the use of GRC-1 as a lunar soil simulant for vehicle mobility studies as well as outlines suggestions for future research in this subject area.

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CHAPTER TWO

LITERATURE REVIEW

2.1 REVIEW OF LUNAR SOIL INVESTIGATIONS

This literature review begins with the review of lunar soil investigations. According to

Gromov (1999), “the study of the physical and mechanical properties of the lunar soil had been started even before the first flights to the Moon were realized.” Earth based studies were performed using radio-telescope investigations of the lunar surface. Photographs were obtained by the United States Ranger and Orbiter missions (Scott 1975). Soft landings of the Surveyor and Luna spacecrafts provided estimates of the lunar soil properties. However, even after several successful missions to the Moon and with the return of lunar soil and rock materials the existing knowledge about the lunar soil is still lacking in several areas. This is due, in part, to the fact that investigations on the Moon were incomprehensive and investigations on returned lunar soil samples are only representative of a tiny fraction of the materials covering the lunar surface. In addition, the lunar environment and it’s affect on the behavior of lunar soils is not well understood.

The review below provides a general summary of past investigations that have been performed to provide a better understanding of the lunar soil and its typical behavior.

Studies of physical and mechanical properties of lunar soil are grouped as follows: (1) studying the physical and mechanical properties of lunar soil under in-situ conditions; (2) testing of returned lunar soil samples in order to determine the major trends and relation

107 of the physical and mechanical properties with respect to the bulk density; and (3) studying lunar soil simulants for conducting tests on the Earth.

2.1.1 Soil Investigations on the Moon

Measurements of the in-situ soil properties on the Moon were made possible by the successful lunar landings of the Surveyor, Apollo, and Soviet Luna missions to name a few. The in-situ properties of lunar soils were obtained via spacecraft including Luna 9 and 13, rovers including Lunokhod 1 and 2, and astronaut observations from the Apollo missions (Gromov 1999). According to Gromov (1999), “the Lunokhod operations resulted in making 1000 measurements of physical and mechanical properties of the soil surface.” In June of 1966, Surveyor I successfully [soft] landed on the Moon. It was quickly followed in success by Surveyors III, V, VI, and VII (Johnson et al. 1995).

Through experiments performed by the Surveyor Surface Sampler, which was capable of making bearing capacity, impact, and trenching tests; initial estimates of the mechanical properties of the lunar soil could be determined. Based on these results it was approximated that the surficial layer of the lunar surface near the landing site of the

Surveyor missions was comprised of an incompressible, slightly cohesive, silty to fine- grained sand material with a bulk density of 1.5 g/cc, a friction angle ranging from 35 to

37-degrees, and cohesion in the range of 0.35 to 0.7 kPa (Scott 1975, Johnson et al.

1995). In addition, general observations confirmed that the small cohesion existent in the lunar soils contributed immensely to the strength characteristics of the soil due to the low lunar gravity. Calculations based on the results of Surveyor missions indicated that an

108 astronaut’s boots should not sink more than approximately 1 to 2 inches (2.54 to 5.08 cm) into the lunar soil provided that the soil extended to a depth of several feet (Scott 1975).

In addition, surface mobility was anticipated to be very good with problems expected to occur only in traversing crater slopes at angles greater than 15-degrees.

Figure 2.1 Famous footprint left on the Moon by Neil Armstrong, demonstrating the apparent cohesion of the regolith (Sibille et al. 2005).

Lunar soil data from the Surveyor missions was greatly expanded upon by the Apollo missions 11, 12, 14, 15, 16, and 17 during which similar soil experiments were carried out in addition to new and more advanced experiments. According to Scott (1975),

“The main sources from which soil mechanics data could be extracted were as follows: 1. Real-time astronaut observations, descriptions, and comments. 2. Television coverage of the astronaut activities on the lunar surface. (Astronaut activity outside the LM on the lunar surface is referred to as extravehicular activity EVA). 3. Sequence camera, still camera, and close-up stereo camera photography. 4. Spacecraft flight mechanics telemetry data.

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5. Interactions between various objects of known geometry and weight and the lunar surface, such as: (a) The Lunar Module, (b) The Astronauts, (c) The Early Apollo Scientific Experiments Package (EASEP) Instrument Units. 6. The Apollo Lunar Hand Tools (ALHT). 7. Various poles and shafts which were inserted into the lunar surface in the course of the extravehicular activities, including a contingency sampler handle, the Solar Wind Composition Experiment Staff, a flagpole, and core tubes. 8. Astronaut debriefings. 9. Preliminary examination of earth-returned lunar soil and rock samples at the Lunar Receiving Laboratory.”

However, the Apollo 15 mission offered the best opportunity for the study of the lunar soil as a result of an extended stay time, the addition of the Lunar Roving Vehicle, and the addition of new and improved soil testing and collection equipment including the

Self-Recording Penetrometer (Costes et al. 1972). It is important to note that the Apollo missions were limited to investigations in the mare regions and locations in close proximity to the highland terrain. Very little highland material has been investigated.

The lunar soil experiments performed in-situ are categorized and summarized in the following subsections. For convenience, a complete summary of in-situ soil experiments and resulting geotechnical properties has been tabulated in Appendix A as Table A2.

2.1.1.1 Robot Interaction

The in-situ properties of the lunar soil were able to be estimated using the physical distortion of the soil and interaction process as caused by the mover of the self-propelled

Lunokhod chassis (Gromov 1999). According to Leonovich et al. (1976), observations of the soil destruction beneath the chassis mover resulted in cracks, shear planes, and

110 steep trench-like walls typical of fine-grained soil with notable cohesion. Much information was also obtained from the images of wheel tracks left in the soil surface transmitted by television. More specifically, as described in Leonovich et al. (1976),

“The structure of the soil was determined from the visual assessment of the character of the deformation of soil beneath Lunokhod’s mover and 9th wheel while analyzing television images and panoramas of the lunar surface.” He additionally states, “Under the effect of the 9th wheel a clear-cut trail is formed having a lighter tone than undeformed surface which attests to small-grained structure of soil.” Since Lunokhod 1 and 2 identically utilized this technique, the results obtained from both soil investigations can effectively be compared.

Figure 2.2 Trail of Lunokhod's 9th wheel (credit The Planetary Society).

From these observations conclusions were drawn about the classification and physical properties of the lunar soil. As determined by the depth of the 9th wheel’s track, the surficial layer of soil to depths of 2 cm was notably loose with a high bearing strength of

2 to 4 kPa (Leonovich et al. 1976). A more in-depth table of geotechnical properties of the in-situ lunar soil based on the void ratio of the lunar soil is shown in Table 2.1 as well

111 as displayed as a frequency distribution of bearing strength of the soil according to the data from Lunokhod 1 and 2 (Figure 2.3). According to Gromov (1999), “the void ratio for soil in-situ was determined on the basis of experimental measurements of bearing capacity versus void ratio made on simulants chosen according to results of studying physical and mechanical properties of lunar soil samples delivered to Earth.” As can be seen in Table 2.1, the existence of very loose soil (void ratio >1.3) is not typically found in-situ. It is more likely to come across dense lunar soils as a result of the geological processes which create and compact the uppermost layer of the lunar surface materials.

The bearing capacity frequency distribution of Lunokhod 1 is very similar to that of

Lunokhod 2, though the bearing capacity of the soil encountered by Lunokhod 2 is slightly higher than Lunokhod 1.

In comparison, Leonovich et al. (1971) cited by Johnson and Carrier (1971) suggested

2 that the bearing strength of the lunar soil ranged from 0.2 to 1.0 kg/cm with a value of

0.34 kg/cm2 occurring most frequently. These values convert to 19.6 kPa to 98.1 kPa, and 33.3 kPa, respectively, which are slightly higher than those values reported by

Gromov (1999). In addition, the data from Lunokhod 1, according to Costes et al. (1971) as well as Johnson and Carrier (1971), suggest that the density as well as the mechanical strength parameters of the in-situ lunar soil generally increase with increasing depth.

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Table 2.1 In-situ geotechnical properties of lunar soil from Lunokhod observations (Gromov 1999). Void Ratio Soil Parameters >1.3 1.3 – 1.0 1.0 – 0.9 0.9 – 0.8 <0.8 Bearing <7 7 - 25 25 - 36 36 - 55 >55 Capacity, kPa Cohesion, kPa <1.3 1.3 – 2.2 2.2 – 2.7 2.7 – 3.4 >3.4 Angle of Internal <10 10 - 18 18 - 22 22 - 27 >27 Friction, º Relative Frequency of 0.005 0.25 0.3 0.3 0.15 Occurrence (%) Areas of shallow Isolated Fresh crater On depth or re- bumps and Typical Locations edges with elements Inter- worked small beds on the Lunar small of very crater soils; stone of fine- Surface dimensions; eroded areas like grained steep slopes craters formations, material isolated stones

Figure 2.3 Frequency distribution of bearing strength of the lunar soil in kg/cm2 as determined by Lunokhod 1 and Lunokhod 2 (Leonovich et al. 1976).

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Analysis of tracks created by the Modular Equipment Transporter of the Apollo 14 mission were also investigated and analyzed using various methods including bearing capacity theory (Mitchell et al. 1972). Based on the MET tracks, friction angles of the lunar soil were estimated to range from 37 to 47-degrees. It was also noted that soil in the intercrater areas was weaker than soil on the crater rims and slopes.

2.1.1.2 Spacecraft Interaction

The interaction of the Apollo Lunar Module with the lunar surface provided much insight into the characteristics of the lunar soil, especially with respect to various locations on the

Moon. One characteristic immediately noticed during all Apollo missions, as noted during Surveyor missions as well, was that any disturbed areas on the lunar surface appeared darker than the undisturbed areas (Mitchell et al. 1973). The reason for this is not certain. However it has been accounted for by texture-related changes which influence the light reflected off the soil as well as to the differences in scale between views from the lunar surface and views from orbit.

Astronauts’ Neil Armstrong and Buzz Aldrin noted that as the Apollo 11 spacecraft initiated it’s decent to the lunar surface, surficial dust was kicked up via the exhaust gas and visibility was impaired at altitudes of 30.5 m (100 ft) and 73 m (240 ft) above ground surface, respectively. It was concluded that the first observations of surface erosion were visible at altitudes ranging from 70 to 27 m (230 to 90 ft) above ground surface (Scott

1975). It was assumed that the material being eroded was a surficial layer of lunar

114 regolith with lower strength than the underlying remaining layer of soil. However, it was noted that even the surficial layer of lunar soil must consist of some amount of cohesion.

Otherwise erosion and soil disturbance would have been notable at much higher altitudes.

It is not quantitatively known how much soil was eroded upon landing. However, it is estimated that four to six inches (10.16 to 15.24 cm) of erosion is realistic. This is supported by the fact that the footpads on the Lunar Module only penetrated the soil to depths of 8 cm (3 in) as well as the fact that as the astronauts ventured further from the spacecraft, their boot impressions became increasingly deeper.

The astronauts of the Apollo 12 mission also noted a decrease in visibility due to erosion of the soil. However, unlike the Apollo 11 astronauts, they encountered a complete loss of visibility during the final stages of decent. This was accounted for in Scott (1975) by several factors including a different descent profile as the Apollo 11 covered a longer lateral distance upon landing than the Apollo 12 and that there was a higher thrust of the

Apollo 12 Lunar Module (by approximately 5-percent). Footpads of the Apollo 12 LM penetrated the lunar surface on the order of 2.54 cm (1 in), while the depth of astronaut boot prints was similar to those of the Apollo 11 astronauts.

Dust was first observed by the Apollo 14 astronauts at an altitude of 30.5 m (100 ft) above ground surface, but seemed to be less visually disturbing than the dust encountered during Apollo 11 and 12 descents. Scott (1975) points out that it is important to note that the sun angle was different for each of the three missions and therefore the visibility of dust may not be a reliable indication of the amount of material actually removed from the

115 surface of the Moon during landing. However, the behavior of the soil to the landing of the Lunar Module via the penetration of the footpads in the soil reveal that the mechanical properties of the Apollo 14 landing site soil are similar to the mechanical properties of the lunar soil at the previous landing sites.

The astronauts of the Apollo 15 commented that they first observed lunar surface dust erosion at altitudes of 42.5 m (140 ft) above ground surface and stated that there was no visibility during the last 16.5 m (54 ft) of descent. The visibility conditions were reported as being worse than that of the Apollo 12 landing (Scott 1975). However as previously stated this could have been caused by the angle of the sun rather than the amount of soil being eroded by the descent engine. Footpads of the LM penetrated into the soil a couple of centimeters as in the previous missions.

The first visibility of dust erosion was reported by the Apollo 16 astronauts at altitudes ranging from 24 m to 14.5 m (78 to 48 ft) above the lunar ground surface. In addition, they reported absolutely no visibility issues throughout the entire landing process, the first report of this phenomenon out of all previous Apollo missions. Penetration of the

Lunar Module footpads into the lunar soil was again minimal, sinking only a few centimeters into the surface.

Similar to Apollo 16, Apollo 17 astronauts reported visible signs of erosion at altitudes of

18 m (60 ft) above ground surface, but had no difficulty with visibility throughout the landing. The surrounding area to a distance of approximately 50 m from the LM

116 appeared to have been affected by the descent exhaust (Mitchell et al. 1973). Fewer small rock fragments (less than 10 cm in diameter) and soil clumps were seen within the

Lunar Module landing site. Based on the crew members’ observations and comments, the mechanical properties of the lunar soil in this area did not seem to differ greatly from the lunar soil in areas of previous Apollo landings. Thus, it was concluded that the erosion and visibility issues due to dust expelled by the descent engines are dependent on the descent trajectory, descent rate, sun angle, and torque, etc. (Scott 1975).

2.1.1.3 Footprint Analysis

Theoretical analyses were performed on the depth of astronauts’ footprints on the Moon to determine the corresponding porosity and relative density of the surficial layer of lunar soil (Mitchell et al. 1973). After the Apollo 17 mission a total of 144 footprints were analyzed. Results are shown in Figure 2.4 for the first 10 cm of the lunar soil. The estimated contact stress of the lunar footprint is 7 kPa. The relative density estimates were based on previous assumptions that the maximum and minimum porosity of the lunar soil is 58.3 and 31.0-percent as determined from a crushed basalt lunar soil simulant

(Mitchell et al. 1973). This relative density can be calculated using the following equation,

(1− nmin ) (nmax − n) Dr = * (36) ()1− n nmax − nmin

117 where n is the in-situ porosity of the lunar soil, and nmax and nmin are the maximum and minimum porosity of the lunar soil, respectively. It should be noted that based on this estimate of maximum and minimum porosity, there may exist some variability in the in- situ estimates of porosity, especially with respect to different locations on the Moon.

Figure 2.4 Variation of footprint depth with average porosity and relative density (Mitchell et al. 1973).

The mean porosity from all footprint observations in the Taurus-Littrow region is approximately 43.2-percent, corresponding to a relative density of 67-percent. This data agrees well with porosity and relative density estimates from previous Apollo missions as shown in Table 2.2.

Table 2.2 Results of analysis on astronaut footprint depths (Mitchell et al. 1973). Location/Mission Observations Mean Standard Mean Relative

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Porosity Deviation Density (%) (%) Apollo 17/ All Data 144 43.4 2.4 67 Apollo 17/ LM and 80 43.2 2.65 67 ALSEP areas Apollo 17/ All 64 43.65 1.95 66 traverse stations Apollo 11 / Intercrater 30 43.3 1.8 67 areas Apollo 12 / Intercrater 88 42.8 3.1 68 areas Apollo 14 / Intercrater 38 43.3 2.2 67 areas Apollo 15 / Intercrater 117 43.4 2.9 67 areas Apollo 16 / Intercrater 273 45.0 2.8 61.5 areas Apollo 17 / Intercrater 141 43.4 2.4 67 areas

2.1.1.4 Trenching Tests and Boulder Tracks

Trenches were first dug into the lunar surface by the surface sampler of Surveyor III and

VII. Trenches that were dug during the Surveyor III mission were reinvestigated and photographed by the astronauts of the Apollo 12 mission. These trenches standing to vertical depths as great as 17.5 cm were still in very good condition after the lapse of 31 months between missions (Johnson et al. 1995). It was noted that the cohesion which makes these lunar trenches stand vertical is not affected over time by the unique environment and space weathering processes of the Moon. The cohesion of the lunar soil which allows these trench walls to stand nearly vertical is, in part due, to the elongated and angular shape of the soil particles. Observation of the Surveyor VII trench reported a

119 thin layer of soil (2 to 15 cm) overlying a solid foundation of rock material (Johnson et al. 1995).

It was reported that the walls of the Apollo 12 trench, excavated to a depth of 20 cm, remained vertical in nature. It consisted of three general strata of soil including a dark surficial layer, an intermediate agglutinate or glassy layer, and a lighter colored layer. In contrast the walls of the Apollo 14 trench, which was dug near the rim of a crater, were very weak and caved in a very short period of time. It was estimated that the cohesion of the soil in this area was only 10-percent that of the soil in surrounding areas on the Moon

(Johnson et al. 1995). This data is indicative of the fact that the soil on the crater slopes is typically less dense and weaker than the soil overlying flat and level surfaces. A trench excavated into the lunar soil near the rim of Shorty Crater at Station 4 during the Apollo

17 mission revealed a very high cohesion in the material (refer to Figure 2.5). This was observed according to Mitchell et al. (1973) as, “a tendency of the material to break into chunks.” A core tube taken from this location revealed that the upper layer of soil consisted mostly of an orange soil composed of a significant portion of glass or agglutinate particles. The unusually high cohesion is likely a result of the irregular shape and interlocking of these particles.

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Figure 2.5 Trench excavated near rim of Shorty Crater at Station 4 during Apollo 17 (Mitchell et al. 1973).

In summary, results of the trenching tests led investigators to believe that there are definite regional variations and variations with depth in the soil properties on the Moon.

In addition to the trenching tests performed during various lunar missions, the Apollo 17 astronauts investigated the tracks created by lunar boulders rolling or skidding down lunar slopes (Mitchell et al. 1973). Mitchell et al. (1973) stated, “In a qualitative sense, boulder tracks serve as exploratory trenches and can provide information about regolith thickness and history, and the relative sharpness of track features provides some indication of soil movement after track formation.” Additionally, analyses can be performed which relate information collected about the boulder track, such as slope angle and bearing pressure, to the strength and density of the lunar soil in the region of the boulder track (Hovland and Mitchell 1971 cited by Mitchell et al. 1973). Analyses for friction angle values were performed by applying the bearing capacity theory for footings on slopes (Meyerhof 1951 cited by Mitchell et al. 1972). The frequency distribution of friction angle values deduced from several boulder tracks in the Taurus-Littrow area of the Apollo 17 mission are shown in Figure 2.7.

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Figure 2.6 Taurus Littrow area of the Apollo 17 mission (credit NASA).

Figure 2.7 Friction angle values from boulder track analysis during Apollo 17 (Mitchell et al. 1973).

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These friction angle values were determined based on an assumed soil density of 1.6 g/cc and a cohesion of 1 kPa representative of the upper values for cohesion determined on the

Moon (Mitchell et al. 1973). Mitchell et al. (1973) noted that the effect of an error in the estimated cohesion of up to 10 kPa results in an insignificant error in the calculation of friction angle of only one to two degrees. An average friction angle of 37.3-degrees with a standard deviation of 5.6-degrees was estimated for the Taurus Littrow region on the

Moon.

2.1.1.5 Penetrometer Tests

The first type of lunar penetrometer test was performed by the Soviet Union Lunokhod 1 penetrometer as part of the Luna 17 mission in 1970. This device consisted of a cone- vane end effector with a cone base area of 5 cm2, a cone height of 4.4 cm, and as apex angle of 60-degrees. There were four cone vanes each separated by an angular distance of 90-degrees. The diameter of these vanes spanned approximately 7 cm.

Figure 2.8 Lunokhod cone-vane penetrometer (Leonovich et al. 1971)

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Mounted on the chassis of Lunokhod 1, the Lunokhod 1 penetrometer measured the strength of the lunar soil once the vehicle was at rest and the cone-vane was driven into the soil and rotated. A set of sensors was used to measure the depth of penetration and corresponding force required. In addition, the force required to rotate the vanes as well as the rotation angle was recorded. The device was capable of a maximum penetration depth of 10 cm and an applied force greater than 196 N (44 lb). Although the penetration tests were performed regularly every 15 to 30 meters of traverse, data from only four different locations on the lunar surface are provided in the report written by Johnson and

Carrier (1971). This data has been reproduced in excel format and is shown in Figure

2.9. It is important to note that the depth at which the base of the cone is flush with the ground surface is plotted as zero depth. Therefore, all the negative values of penetration shown in the plot are representative of the initial insertion of the cone up to the point where the base of the cone is flush with the soil surface. A similar plot for the cone-vane penetrometer results of Lunokhod 2 is shown in Figure 2.10 as reported by Leonovich et al. (1976). Leonovich et al. (1976) noted that 7.5-percent of all tests accounted for cases in which loose soil overlaid a hard base; 3-percent accounted for cases of hard stony soil; and 4-percent accounted for hard soil overlying loose soil. It was noted from both

Lunokhod missions that the strength of crater rims was generally much higher than in inter-crater locations. In addition, it was observed that the decrease in the size of a crater

(with respect to diameter) corresponded to a decrease in the soil strength of the rim of the crater. This makes sense as the relocation of lunar soil from the interior of the crater to the rim of the crater occurs via ballistic flight paths. Therefore, the rate of settlement of this material on the rim of the crater increases with flight distance and with crater size.

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Stress (N/cm^2)

0 102030405060708090100110 -4.4

-3.2

-2

-0.8

0.4

Penetration (cm) Penetration 1.6

2.8 Horizontal Section Crater Slope 4 Crater Rim Surface Covered by Small Stones

Figure 2.9 Lunokhod 1 cone-vane penetrometer data.

Figure 2.10 Lunokhod 2 cone-vane penetration curves (P = load in kg, h = penetration depth in mm). 1 - destruction of stone; 2 - hard stony soil; 3 - hard cover on loose base; 4 - homogeneous soil; 5 - loose cover on hard base; 6 - loose soil (Leonovich et al.1976).

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The locations on the lunar surface from which these data sets were recorded are not specifically described. Instead, they are generalized as: horizontal section of the lunar surface, crater slope, crater rim, and surface section covered by small stones (Johnson and

Carrier 1971). In general the Lunokhod 1 traversed over 10,000 meters of the lunar mare near the Sea of Rains. So it can be inferred that these four penetrometer tests were recorded at locations within this vicinity (refer to Figure 2.11). The route of motion of

Lunokhod 2 traversed through the region of the Lemonnier crater (located in the Mare

Serenitatis directly east of the Mare Ibrium) in the transitional zone from the sea or mare region to the highland region (Leonovich et al. 1976).

Figure 2.11 Location of Luna 17 landing and Lunokhod 1 traverses (Anonymous 2004a).

The Apollo 14 made use of a device called the Apollo Simple Penetrometer or ASP for short. The ASP consisted of a 30-degree cone tip attached to a shaft approximately 0.95 cm in diameter and 68 cm in length. The purpose of this device was to determine the

126 variation of penetration resistance with respect to location on the Moon. Johnson et al.

(1995) provides a general description of the operation of this device on the Moon. This simple device was manually pushed into the lunar terrain as far as possible with one hand. Upon the maximum penetration, it was manually pushed further into the ground with the use of both hands. This operation was performed by a single astronaut,

Astronaut Mitchell. With the known forces that Mitchell could apply, both single and double-handedly, and the depth of the penetration, it was possible to determine the penetration resistance of the lunar soil. The maximum penetration that was obtained was the limiting depth of 68 cm below lunar ground surface. The results from these tests were related to values of cohesion and internal angle of friction and compared to the results of these values obtained from Surveyor data. It was found that the values of cohesion and friction angle were somewhat higher than the Surveyor data. It is important to note that the results of the ASP are only estimates as precise measurements of applied force were not determined.

The Apollo 15 and 16 astronauts made use of an advanced lunar cone penetrometer called the Self-Recording Penetrometer (SRP). The SRP, developed at the Geotechnical

Research Laboratory at the Marshall Space Flight Center (MSFC) Space Science

Laboratory, was designed to provide a graphical representation of the in-situ penetration resistance of the lunar soil versus depth. Its basic fabrication included a detachable component with a handle, a data recording unit, and probe components. Figure 2.12 shows a cartoon of the SRP in more detail where label 10 is the entire SRP unit, 12 is the handle component, 14 is the data recording component, 16 is part of the probe

127 component, 19 is the astronaut, 20 is the surface pad assembly, and 21 is the upper crossbar.

Figure 2.12 Cartoon of Apollo SRP (Fletcher et al. 1973).

According to Fletcher et al. 1973,

“The handle connects to the upper end of the data recording unit, and the probe connects to the lower end thereof. The data recording component has a metal recording drum on which a stylus scribes a permanent record. A pad assembly is slidably mounted on the probe to serve as a reference plane by resting against the soil surface before the probe is forced into the soil. The pad assembly is connected by a cable to the data recording component so that the movement of the pad assembly relative to the probe as it enters the soil will actuate the scribe to indicate the depth of penetration. Also, the data recording component includes a mechanism to rotate the drum proportionately to the amount of force exerted on the handle to cause penetration of the probe into the soil. The independent motions of the drum and stylus combined to produce a continuous force- penetration diagram on the surface of the recording drum.”

Basically, as the instrument was pushed into the ground with an applied downward force a gold plated cylindrical drum rotated correspondingly and was simultaneously scratched

128 along its height (by a stylus) according to the penetration depth. The cartoon of a typical scribed drum is shown in Figure 2.13 where label 30 represents the recording drum, 130 represents the slotted upper end to allow for expansion within the complete assembly,

132 is the beveled end of the recording drum which prevents damage to the stylus during assembly, 134 corresponds to the curved portion of the trace recording when the penetrometer is being forced into the soil, and 136 and 137 are the result of the end of the test when the probe is removed and the surface pad assembly is returned to its lowest position (also indicating a new test).

Figure 2.13 Cartoon of recording drum (Fletcher et al. 1973).

This device was also equipped with interchangeable end effectors including three different sized cones with base areas of 129, 323, and 645 square mm, respectively, (each with a 30-degree apex angle) and a 2.54 by 12.7 cm flat bearing plate. This device was restricted by a maximum load of 111 N or 25 lbs (applied through a spring-loading mechanism) and a maximum depth of penetration of 75 cm (Johnson et al. 1995). The

SRP had a total Earth weight of 23 N (5 lb).

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During the Apollo 15 mission, the SRP was used for a total of six “runs” or tests: four tests performed with the 323 mm2 cone tip and two tests performed with the 2.54 x 12.7 cm flat bearing plate. The records were scribed on the recording drum, which was returned to Earth for analysis. Each run was performed on August 1, 1971 during the end of the second extra-vehicular activity (EVA). All readings were taken near the Lunar

Module at Station 8 as shown on Figure 2.14. This location is also the site of the Apollo

Lunar Surface Experiments Package or ALSEP, which was comprised of a set of scientific equipment designed to run autonomously and provide long term environmental information about the Moon.

Figure 2.14 Apollo 15 EVA traverses (credit NASA). Each penetrometer test was indexed and performed by Lunar Module pilot James Irwin.

According to Costes et al. (1972), “two of the cone penetration measurements were made within and adjacent to an LRV track, and the other two were made adjacent to and at the bottom of a 30-cm deep trench with a vertical sidewall.” The raw data from these

130 penetration tests was obtained from the National Space Science Data Center as scanned images from microfilm restored as part of the NSSDC’s Lunar Data Project. The soil mechanics data obtained from these documents are in the form of handwritten plots portraying the stress applied at the penetrometer tip as a function of depth of penetration; tables; and general notes from runs using the SRP on the Apollo 15 mission as shown in the following Figures 2.15 and 2.16. Each table provided the mission, date, flight unit, lunar drum, index number, and end effector used, as well as general comments. In addition, the drum load was given in degrees/minutes and decimal degrees, the drum circumference deflection in mm, and finally the load in Newtons and stress in Newtons per square centimeter, which was plotted as stress on the corresponding plots. Additional columns included the initial drum depth/final in cm, the actual drum depth reading from post-flight calibration in cm, and a corrected depth reading in cm which accounted for the additional length of the cone attached to the bottom of the penetrometer rod. A complete graphical set of the Apollo 15 SRP data (index numbers two through seven) is provided in excel format in Appendix A.

It was noted that during these SRP tests, the surface-reference pad tended to ride up the shaft of the device when it was vibrated. This was due to the fact that the friction between the reference-pad busing and the shaft was less than had originally been anticipated. So, although the weight of the reference pad was essentially balanced, by the force on the spring which was designed to retract the pad, it was not enough to keep it from slipping. Therefore, it is difficult to accurately and precisely determine the depth of penetration from the tests. However, the stress-penetration curves provided from these

131 experiments ultimately provide an upper bound on the depth of penetration for the respective applied force. Another possible source of error was noted when placing the

SRP onto the lunar surface while holding it by the housing. This resulted in vertical penetration scribes without any accompanying recorded force. These spikes were also seen when the astronaut leaned on the penetrometer to provide a “steady push” of the penetrometer into the ground and lost balance. This loss of balance, which was a common occurrence, required that the astronaut remove some weight from the penetrometer which caused the instrument to “give” or more specifically allowed the spring to essentially “back off” resulting in spiked readings.

Figure 2.15 Stress-penetration curve from Apollo 15 SRP Index No. 2 (credit NSSDC).

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Figure 2.16 Original data from Apollo 15 SRP Index No. 2 (credit NSSDC).

In relation to the cohesion and internal angle of friction, it was estimated that the SRP encountered soils ranging from 0.25 to 1.0 kPa in cohesion and 46.5 to 51.5-degrees in friction angle (Carrier et al. 1991 cited by Johnson et al. 1995). Mitchell et al. (1972) as cited by Costes et al. (1972) provided a summary of cone penetration resistance test results in terms of average penetration resistance gradient from the Apollo 15 landing site. This summary is provided in Table 2.3 and is specific to data collected using the cone tip with a base area of 323 mm2. Additionally, the comparison of penetration test results with terrestrial simulations resulted in an estimated in-situ lunar soil density (near

133 the trench at Station 8) to range between 1.92 and 2.01 g/cc (Costes et al.1972). Based on a specific gravity estimate of 3.1 the corresponding void ratio of the lunar soil in this area ranges from 0.54 to 0.61.

Table 2.3 Average cone index gradient for lunar soil near the Apollo 15 landing site (Costes et al. 1972). Average Penetration Penetration Location Resistance Gradient Depth (cm) (kPa/mm) Adjacent to trench 8.25 4.06 Bottom of trench <10.25 >3.25 In LRV Track: Upper 2 cm 5.25 5.97 Lower 4 cm 4.36 Adjacent to LRV <11.25 2.98 Track

During the Apollo 16 mission, the SRP was used for a total of ten runs: two tests performed with the 323 mm2 cone tip, six tests performed with the 129 mm2 cone tip, and two tests performed with the 2.54 x 12.7 cm flat bearing plate. Each run was performed on April 22, 1972 during the second extra-vehicular activity. Each penetrometer test was indexed and performed by Lunar Module pilot Charles Duke. All readings were taken either at an astronaut-proclaimed “Bench Crater” or at the ALSEP shown on Figure 2.17.

The first four SRP tests were performed at Station 4, in the side of Stone Mountain near the edge of Bench Crater. The last eight SRP tests were performed at Station 10, the

ALSEP site. During these last tests, index number nine was skipped over before beginning the series and index 14 incurred errors in recording. These two indices are therefore not included in the data set. The raw data from these penetration tests was also obtained from the National Space Science Data Center as scanned images from microfilm restored as part of the NSSDC’s Lunar Data Project. Therefore, the soil mechanics data 134 obtained from these documents are in the same formats as that of the Apollo 15 mission.

However, it is important to note that the penetration depths for the Apollo 16 data were not corrected for the additional length of the cone attached to the bottom of the penetrometer. Again, a complete graphical set of the Apollo 16 SRP data (index numbers five through eight, ten through thirteen, fifteen, and sixteen) is provided in excel format in Appendix A.

Figure 2.17 Apollo 16 EVA traverses (credit NASA).

2.1.2 Soil Investigations on Returned Lunar Soil

Sources for lunar soil investigation on the Earth can be categorized into three major groups. These categories include returned lunar soil from the Apollo missions, returned lunar soil from the Soviet Luna missions, and finally lunar meteorites that have been

135 discovered on the Earth. The most abundant amount of lunar soil was returned from the

Apollo missions. According to Scott (1975), “The Apollo lunar landing missions provided the first opportunity for direct collection of data relating to the physical characteristics and mechanical behavior of the surface materials of an extraterrestrial body by other than remote means.” A total of 381.7 kilograms (841.5 lbs) of lunar soil and rock fragments were collected from the six successful Apollo landings including

Apollo 11, 12, 14, 15, 16, and 17 (Vaniman et al. 1991a). The majority of these samples are representative of the dark basaltic lunar mare material while very little material

(mainly from the Apollo 16 mission) represents the lighter-colored feldspar-rich anorthositic rocks from the lunar highlands. According to Sibille et al. (2005), these

Apollo lunar soil samples were transported to the Earth in containers which were intended to preserve them in their original vacuum environment. However, the seals on the containers failed due to the contamination of the seals by lunar dust and the lunar soil was thus exposed to the Earth’s atmosphere. Currently these geological lunar samples are housed at the Johnson Space Center (JSC) Lunar Reviving Laboratory (LRL) in

Houston Texas. The samples are stored in nitrogen filled cabinets to protect them from further chemical alteration and contamination. A Lunar Sample Curator keeps thorough documentation, both electronic and paper records, on any activity involving the returned lunar materials especially on the state of the sample both before and after any laboratory experimentation has been performed (Vaniman et al. 1991a). A mere 321 grams of lunar surface material was returned to the USSR as a result of Luna missions 16, 20, and 24

(refer to Figure 1.5 from Chapter One of this dissertation). These samples are representative of the lunar mare material. Since 1979, a total of 10 meteorites of lunar

136 origin have been recovered on the Earth (Vaniman et al. 1991a). These meteorites have been found on the Antarctic ice caps. It is believed that these meteorites impacted the

Earth on the order of millions of years ago and were preserved by the ice caps. Studies suggest that these meteorites are of definite lunar origin, but are not similar enough in composition of the lunar materials to be from the different locations where geologic samples had been recovered and returned to the Earth. For convenience a complete summary of returned lunar soil experiments and resulting geotechnical properties has been tabulated in Appendix A as Table A3.

2.1.2.1 Apollo Soil Samples

According to Vaniman et al. (1991a) several types of soil samples were collected during the successful Apollo missions listed above. These samples included contingency samples, bulk samples, documented samples, selected samples, raked samples, and core samples. Contingency samples were taken upon landing of Apollo missions 11, 12, 14, and 15 by the first astronaut to exit the lunar module and set foot on the surface of the

Moon. These samples were collected via the contingency sampler device which is representative of a small rake and scoop. The astronaut would rake, scoop, and bag a small amount of the surficial lunar material. The majority of the material collected consisted of the finer grained fraction of the lunar regolith. However, the sampling astronaut typically made an effort to collect a few small rocks as well. These contingency samples were taken as an “insurance policy” so that some lunar soil would be returned to the Earth in case the mission had to be terminated early and the astronauts

137 could not perform further investigation. It is important to keep in mind that these samples are only representative of a minute fraction of the lunar surface materials taken near the Apollo landing sites. In addition to the smaller contingency samples, a bulk soil sample was collected by Neil Armstrong during the Apollo 11 mission (Vaniman et al.

1991a). The bulk soil sample was representative of a larger sample area including 23 sample locations near the lunar module. A total of 38.3 kilograms (84.5 lbs) of lunar soil and rock material was collected and combined into a single container for return to the

Earth. For laboratory testing purposes these samples were considered “highly disturbed” and it was noted that these samples could not provide a reliable estimate of the bulk density of the in-situ lunar soil (Johnson et al. 1995).

Documented samples as described in Vaniman et al. (1991a) included rock and soil samples that were completely documented with photographs and written observations both before and after sample collection. Each sample was collected and placed in a sample bag which was numbered correspondingly. The corresponding documentation and photographs were used to help determine the “relationship of a sample and its surroundings before astronaut activity disturbed the surface” and “the effects of collection activity on the surface characteristics” after astronaut activity and collection of the sample (Vaniman et al. 1991a). This documentation was useful in identifying and classifying the sample in terms of color, reflectivity, identification of surface features near the sample, and orientation and depth of burial (for rock samples). Similarly, selected samples were documented both before and after collection. However, instead of complete documentation including photographs, these samples only included written

138 documentation of observations made by the astronauts. Though these samples lacked the thorough investigation of documented samples, they were able to be collected in a quicker fashion allowing for a larger number of samples to be collected.

Rake samples were collected during the Apollo 15, 16, and 17 missions to include a larger portion of rock material than soil material. The lunar sampling rake device, similar to the contingency sampler, allowed the astronaut to rake the surface materials of the

Moon while retaining only rocks greater than 1 centimeter in size and allowing all other finer materials to pass through (refer to Figure 2.18). After the rock samples were placed in individual bags a scoop of the lunar soil, taken adjacent to the rake sample location, was collected and added to the bag containing the corresponding rock sample.

Figure 2.18 Lunar sampling rake (Batiste and Sture 2005).

Core samples, as reported by Vaniman et al. (1991a), represent a small fraction of the samples collected on the Moon via the Apollo missions. However, they constitute some of the most valuable samples returned to the Earth for study. Vaniman et al. (1991a) stated, “A returned core is the only type of Apollo sample that permits the detailed study

139 of variations in the physical and chemical properties of the lunar regolith with depth.”

The core tubes consisted of thin-walled hollow aluminum tubes that were 37.5 cm in length with an inner diameter of 4.13 cm and an outer diameter of 4.38 cm. These tubes could be used individually or connected together to form what was called a “double core tube.” A flat disk-like device termed a “keeper” which had the same diameter as the inside of the tube was placed inside the top end of the tube and pushed down to the top of the sample to keep it in place. Upon removal of the tube from the ground, the bottom end was covered with a Teflon cap. A total of 21 hammer driven cores were collected near the landing sites of the six successful Apollo missions (Johnson et al. 1995). Samples ranged from 2 to 4 cm in diameter, depending on the type of drive tube used, and ranged from approximately 10 cm to 3 m in length (Vaniman et al. 1991a, Johnson et al. 1995).

The Apollo 15 mission was the first to make use of new thin-walled aluminum core tubes. These tubes were developed to reduce the amount of sample disturbance, increase the size and amount of sample received, and to create an easier sampling method for the astronauts (Costes et al. 1972). A comparison between the core tube bits for the different

Apollo missions is shown in Figure 2.19. Upon comparison of astronaut observations it was noted that the experience of driving the core tubes into the lunar soil varied for each different location and mission. Observations from the Apollo 11 and 12 missions revealed that the cored tubes were easily driven into the ground. The opposite was reported during the Apollo 14 mission in which the core tubes could only be driven to shallow depths (Johnson et al. 1995). Apollo 17, in which double core tubes were used, resulted in higher density in the lower tube than in the upper tube (Mitchell et al. 1973).

This indicates that the lunar soil density generally increases with increasing depth. The

140 same was found to be true for Apollo 15 and 16 core tube samples (Mitchell et al. 1973).

In general, the soil samples collected with the larger diameter and thinner walled core tubes resulted in less disturbed and more reliable densities.

Figure 2.19 Comparison of different Apollo mission core tube sampling bits (Carrier et al. 1991, Costes et al. 1972).

In addition a battery powered rotary drill, named the Apollo lunar surface drill (ALSD), was used to collect three additional core samples during the Apollo 15, 16, and 17 missions. These drilled samples were 2 cm in diameter and were representative of the first 221 to 292 cm of the lunar regolith (Vaniman et al. 1991a). The density of the soil samples collected with the deep drill near the trench at Station 8 (Apollo 15) was estimated to range from 1.62 to 2.15 g/cc, averaging 1.80 g/cc (Costes et al. 1972). The bulk density as a function of depth for the Apollo 15, 16 and 17 deep drill samples are shown in Figure 2.20. As can be seen, the bulk densities of the Apollo 17 soil are generally higher than that of Apollo 15 and 16. The soil from the Apollo 16 drill stems

141 seemed to be exceptionally softer than the other two missions’ drill samples. According to Mitchell et al. (1973) this suggests that the soil at the Apollo 17 site incurred a

“depositional history” and consists of a composition significantly different from that of the Apollo 15 and 16 sites. In addition, the soft soil conditions for the Apollo 16 site were verified by depth measurements of the astronauts’ footprints as well as impressions left by LRV tracks.

Figure 2.20 Density as a function of depth for the Apollo 15, 16, and 17 drill stems (Carrier et al. 1991, Mitchell et al. 1973). Stippled area represents range of densities for Apollo 16 drill core. Horizontal ruled area represents range of densities for Apollo 17 drill core.

2.1.2.2. Laboratory Tests

The particle size distribution of the lunar soil is the characteristic which greatly influences the physical and mechanical properties of the soil. According to Stacheev

(1979) cited by Gromov (1999), the particle size distribution of the lunar soil samples returned to Earth was determined by dispersion, conductometric method, and by 142 microphotography. It was found that the spatial variation of the lunar soil samples did not significantly influence the overall uniformity of the particle size distribution.

However, investigations performed on the particle size distribution of the lunar soils from

Soviet investigations, Luna 16 and Luna 20, showed that the average particle size generally increased with increasing sample depth. It was observed that the lunar soil samples consisted of “small mineral particles that differ in shape” and that the particles

“easily stick to each other to form separate clods and aggregates” (Gromov 1999).

Another influential property on the physical characteristics of the lunar soil is the “degree of packing” as described by Gromov (1999). The degree of packing is generally estimated in terms of the void ratio of the soil sample. The bulk density and void ratio for loose and dense conditions of returned lunar soil samples are shown in Table 2.4 below.

Table 2.4 Bulk density and void ratio of returned lunar soils (Gromov 1999). Lunar Mission Bulk Density, g/cc Void Ratio Soil Condition Loose Dense Loose Dense Luna 16 1.115 1.793 1.69 0.67 Luna 20 1.040 1.798 1.88 0.67 Apollo 11 1.36 1.8 1.21 0.67 Apollo 12 1.15 1.93 N/A N/A Apollo 14 0.87 – 0.89 1.51 – 1.55 2.37 – 2.26 0.94 – 0.87 Apollo 15 1.1 1.89 1.94 0.71

According to Gromov (1999), the cohesion and friction angle of the returned lunar soil was measured under different packing conditions (via compression under various static pressures) in order to determine the general relationships. In these tests, the average void ratio ranged from less than 0.9 to greater than 1.3. Correspondingly, cohesion ranged from greater than 2.5 kPa to less than 1 kPa, while the angle of internal friction ranged from greater than 20-degrees to less than 10-degrees. Several conclusions were drawn

143 based on the results. It was inferred that the geotechnical properties of the lunar soil are similar no matter the location (of sample collection). It was observed, as is typical of granular soils, that the majority of compression took place during the initial phase of loading. In addition, “the main factors that control the lunar soil packing process are particles sliding and tighter compression of soil particles and aggregates” along with

“distortion of the particles at their points of contact” (Gromov 1999). Failure of the lunar soil due to an applied load was detected as local or punching shear failure when loosely prepared. However, in densely compacted soils, failure was characterized by general shear failure. Finally, Gromov (1999) noted that the Mohr-Coulomb shear strength criterion appropriately described that of the returned lunar soil. It was noted that the angle of internal friction and cohesion of the soil generally increased with increasing soil density.

Much of Gromov’s (1999) work was based on the work performed by Leonovich et al.

(1976) on returned lunar samples from Luna 20. According to Leonovich et al. (1976),

“To study the mechanical properties of the lunar soil delivered to Earth by Luna 20 a sample was chosen corresponding to the uppermost layer of lunar soil in natural bedding with a depth of about 100 mm.” This sample was taken from the highland region of the

Moon and was light gray in color with an average particle size of 70 to 80 microns.

Investigations were performed on the character of soil destruction, the compressibility of the soil, and the shear strength of the soil. Investigations on the character of soil destruction were performed in a Coulomb instrument with a moving partition to induce soil deformation. Deformation of the returned Luna 20 soil resulted in a relative

144 volumetric strain of 0.8 and an increase in bulk density from 1.04 to 1.3 g/cc. The investigators noticed no visible lines of shear or slide and noted that the surface remained horizontal and smooth. A similar experiment on packed soil with an initial bulk density of 1.63 g/cc resulted in a visible shear plane corresponding to an angle of internal friction of 32-degrees. Investigations on the compressibility of the returned lunar soil were conducted in a compression chamber with dimensions of 25.2 mm in diameter and 12 mm in height. Compressive stress was applied in increasing increments of 9.8 kPa ranging from 0 to 98 kPa. As expected of a granular soil, the biggest deformation occurred during the initial pressure increase from 0 to 49 kPa and then significantly tapered off to pressures of 98 kPa as shown in Figure 2.21.

Figure 2.21 Compressibility curve represented as coefficient of porosity versus packing pressure (in kg/cm2) for Luna 16 returned soil (1) and Luna 20 returned soil (2) (Leonovich et al. 1976).

This behavior can be explained by the fact that in granular soils with little cohesion the initial stage of compression results in a decrease in porosity due to the rearrangement or

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“transfer and denser packing” of soil particles (Leonovich et al. 1976). Upon completion of this stage, further compression results in the destruction or fracture of the actual soil particles near their contact surface with other particles. Finally, the investigation of the shear strength of the Luna 20 returned soil was performed as stated in Leonovich et al.

(1976) by a “method of additionally packed soil which made it possible to obtain shear strength graphs with practically constant bulk weight and to trace the change in the parameters of soil’s shear as a function of the degree of soil packing.” This experimental technique was not explained in further detail. Results of the investigation are shown in

Figure 2.22 where, φ is the angle of internal friction in degrees, c is the reduced cohesion

2 2 in kg/cm , and co is the initial cohesion of the soil in kg/cm at the normal pressure equal to zero. The values of internal angle of friction range from 0 to 25-degrees while the values for reduced cohesion and initial cohesion range from 0 to 0.1 kg/cm2 (9.8 kPa) and

0 to 0.04 kg/cm2 (4 kPa), respectively. As can be seen, the increase in packing pressure corresponds to an initial increase in angle of internal friction and initial cohesion which eventually taper off and reach some stable value after pressures greater than 0.5 kg/cm2

(49 kPa). This phenomenon is explained in Leonovich et al. (1976) via the initial increase in particle to particle contact and particles sticking together and then the significant decrease in the increase of particle contact so that the increase of particle contact had become almost negligible. In addition, when there is no packing pressure applied during shearing, the soil tends to become less packed and the inter-particle cohesion tends to decrease. The opposite is experienced when packing pressure is applied during shearing thus explaining the linearity of the reduced cohesion as shown in

Figure 2.22.

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Figure 2.22 Shear strength parameters as a function of packing load (kg/cm2) (Leonovich et al. 1976).

In the early 1970’s, state-of-the-art strength and compressibility tests were performed on a 200 g sample of lunar soil taken from near the Apollo 12 Lunar Module landing site

(Carrier et al. 1972, 1973). A total of two vacuum oedometer or one-dimensional compression tests and three direct shear tests were performed on the material. All tests were prepared in a glove test chamber at the Lunar Receiving Laboratory and placed in a shear box which was ultimately inserted into an ultra-high vacuum test chamber.

Samples were prepared at a pressure of under 2 x 10-6 Torr and were tested at pressures under 5 x 10-8 Torr to avoid any contamination from the Earth’s atmosphere. Previously, upon return of the lunar samples to the Earth, samples had been stored for over a year at pressures of 10-9 Torr. A schematic of the testing device is shown in Figure 2.23.

Results of these tests were intended to provide answers to the following questions as stated in Carrier et al. (1973):

• Does the lunar soil behave notably different than terrestrial simulants?

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• Is the vacuum environment necessary for soil preparation and is it necessary to test

in the vacuum environment as well? How do the results differ?

• Is the sample reusable after testing or do the stresses endured during testing result in

a functional and mechanical change of the material?

Figure 2.23 Ultra-high vacuum test chamber and shear box (Carrier et al. 1972).

Based on previous estimates of in-situ density at the Apollo 12 landing site the two oedometer tests were prepared to densities of 1.67 g/cc and 1.84 g/cc, corresponding to a loose and medium dense condition on the lunar surface, respectively. Assuming a specific gravity of 3.1 as suggested by Carrier (1970) cited by Carrier et al. (1972), these initial densities correspond to void ratios2 of 0.684 and 0.854, respectively. During testing each sample was loaded or compressed in a series of increments and then sheared.

For comparison of the results, similar oedometer tests were performed on a terrestrial basalt sand simulant with similar grain size distribution and initial void ratio. According

2 Void ratio = e = ()()3.1/ ρ −1 ρ 148 to Carrier et al. (1972) it was found that the compressibility of the Apollo 12 returned lunar soil in hard vacuum conditions is equal to or greater than the compressibility of the terrestrial basalt in the same conditions. The lunar soil showed a significantly larger decrease in void ratio during the initial load increment when compared to the terrestrial basalt. However, Carrier et al. (1972) mentioned that this may have been the result of complications in the testing system when applying normal load to the sample. It was noted that further testing was required to validate the results of these initial tests.

The three direct shear tests were performed at void ratios of 0.612, 0.55, and 0.708, respectively. They were consolidated at forces no greater than 70 kPa. Shear failure was reached at a shear displacement of 0.27 cm in all three samples. The cohesion was estimated to range between 0 and 0.7 kPa, while the friction angles were 28-degrees for the loose sample and 34 and 35-degrees for the medium dense samples. These results were compared with strength testing performed on terrestrial basalt simulant measured in ambient conditions via Mitchell and Houston (1970) cited by Carrier et al. (1972).

Carrier et al. (1972) concluded that the frictional strength as represented by tan φ (from the Mohr-Coulomb equation) of the Apollo lunar soil sample was approximately 65 percent of the frictional strength of the terrestrial basalt (at the same void ratio). It was assumed that this was a result of the crushing of fragile particles in the lunar soil such as breccias and glass agglutinate particles.

2.2 REVIEW OF LUNAR SOIL SIMULANTS

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The development of lunar soil simulants stem from the problem that the current availability of lunar soil (on the Earth) is too small to support the lunar technology projects. The value of this lunar soil to the space community is too great to be compromised by destructive laboratory studies. Therefore, lunar soil simulants have been created to replicate the physical and/or chemical properties of the lunar soil and to take the place of the actual lunar soil in scientific investigations. According to Sibille et al. (2005) lunar simulants are defined as “any material manufactured from natural or synthetic terrestrial or meteoritic components for the purpose of simulating one or more physical and/or chemical properties of a lunar rock or soil.” There are two major categories defined for lunar soil simulants. These include root simulants and derivative simulants. Root simulants are composed of terrestrial rock, minerals, and/or synthetic sources. They are designed to represent an end-product with respect to grain size distribution and mineralogical properties (with a minimal degree of processing). Root simulants are typically created to replicate soils from specific regions on the Moon.

Derivative simulants are created by modifying the root simulant with the addition of materials that better define the simulant to meet the needs of specific processes to be tested (such as vehicle mobility). They are created to replicate a specific characteristic of the lunar regolith. The quality of simulants is typically measured in terms of simulant fidelity. The higher the fidelity, the more representative the simulant is of the actual lunar soil. The ability to develop high fidelity simulants is dependent on comparing the characteristics and behavior of the simulant during Earth-based testing to that of the actual lunar soil. Since testing on the actual lunar soil is not realistic in most cases the

150 use of data obtained during past missions is required. Some of the most reliable lunar simulants are presented in the following subsections. However, it should be noted that these simulant used in recent years are either no longer produced or are insufficient in available quantity to meet the needs of current lunar technology projects such as vehicle mobility studies.

2.2.1 MLS-1

MLS-1, otherwise known as Minnesota Lunar Simulant-1, was originally developed at the Space Science Center at the University of Minnesota in the 1970’s. MLS-1 is a standardized simulant that emulates the bulk chemistry of the Apollo 11 soils. It was not designed to represent the geotechnical properties of the lunar soil. MLS-1 is composed of a crushed terrestrial basalt material mined from an abandoned quarry in Duluth,

Minnesota. This material has a very high composition of titanium, which matches the

Apollo 11 basalt material. It also contains minerals such as plagioclase, olivine, ilmenite, titanomagnetite, and clinopyroxene as shown in Figure 2.24. Since the chemical composition of the lunar soil is not pertinent to this research, the chemical composition of the lunar soil simulants will not be discussed in detail.

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Figure 2.24 Electron microprobe image of grain size and chemical composition of MLS-1 (Sibille et al. 2005).

According to Sibille et al. (2005), MLS-1 was crushed and milled in order to produce a particle size distribution and particle size characteristics similar to the Apollo 11 lunar regolith material. The particle size distribution of MLS-1 is shown in Figure 2.25, which includes the particle size distribution of JSC-1 as well. MLS-1 generally has a coarse grain size which is most representative of the coarse lunar basalts. It is important to note that the particle size distribution as shown in Figure 2.25 is representative of MLS-1 that has been “reground” to more accurately represent the particle size distribution of Apollo soils and which classifies it as a silty sand material. It is not representative of the actual distribution MLS-1 simulant. Thus, MLS-1 poorly emulates fine-grained lunar basalts.

This is due to the milling process in which the material is crushed to create the finer fraction or dust component of the simulant. During this process the rock fragments break down and result in the release of large mineral fragments. Lunar soils, in opposition, are composed of lithic or rock fragments even down to the finer dust fraction of the material.

The physical as well as chemical behavior of MLS-1 (especially in melting processes)

152 will vary from that of the lunar soil due to the mineral fragment composition instead of lithic fragment composition. Another shortcoming of MLS-1 is that is does not contain the glassy agglutinate fraction that is prominent in the composition of the lunar regolith.

This again results in melting behavior that varies from the melting behavior of the lunar soil. Although these limitations can be problematic for certain investigations and experiments, MLS-1 has experienced much success as a lunar soil simulant. However, due to the fact that it was mined from an abandoned quarry, it is no longer available for use as a lunar soil simulant. In fact, production of this material ceased more than 10 years ago (Schlagheck et al. 2005). Sibille et al. (2005) points out that it is always beneficial to make use of active quarries which profit due to assistance from current mining operations and the assurance of the availability of fresh rock.

Figure 2.25 Particle size distribution of MLS-1 and JSC-1 (Perkins and Madson 1996 cited by Sibille et al. 2005).

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A large portion of MLS-1 was distributed to the University of Colorado for geotechnical testing as well as for the determination of the engineering properties of the material

(Batiste and Sture 2005). The specific gravity of MLS-1 was found to be 3.2 while the maximum and minimum bulk densities were found to be 2.20 and 1.50 g/cc, respectively.

These values correspond to void ratios of 1.13 and 0.454, respectively (Perkins et al.

1992). It was found that MLS-1 had a lower maximum void ratio than the Apollo lunar soil samples which is believed to be due to the absence of agglutinates in MLS-1.

According to Batiste and Sture (2005), “an increase in maximum void ratios for Apollo

12, Apollo 15, and Apollo 14 samples follows the trend of increasing average agglutinate contents of 15-percent, 33-percent, and 52-percent, respectively.” Essentially, the angular and obtrusive shape of the agglutinate particles allocates a much looser density.

Results of triaxial and compression tests on MLS-1 are summarized and compared to the lunar soil in Table 2.5. The results for angle of internal friction for the lower bound are similar to that of the lunar soil; however MLS-1 shows an increased upper limit on friction. This is most likely due, as explained in Perkins et al. (1992), to differences in testing conditions with respect to confining pressure. It is also noted that the results for cohesion tend to be too low. This is believed to be caused by the absence of agglutinate particles as well as the lack of electrostatic charging in the Earth’s atmosphere.

Table 2.5 Comparison of friction angle and cohesion of lunar soil and MLS-1 (Perkins et al. 1992, Batiste and Sture 2005). Material Density, Confining Stress, Angle of Internal Cohesion,

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g/cc kPa Friction, º kPa 1.89 26.0 48.8 -- Lunar 1.71 52.6 40.7 -- Regolith 1.50 -- 42.0 0.52 1.75 -- 54.0 3.0 1.90 13.8 49.8 -- 1.90 34.5 48.4 -- MLS-1 1.70 34.5 42.9 -- 1.70 68.9 41.4 0 – 0.1 2.17 -- 66.7 1.5

Willman and Boles (1995) conducted conventional triaxial compression tests on MLS-1 as well. The MLS-1 was prepared to a density of 1.92 g/cc and tested at confining pressures of 1.7, 3.44, and 6.89 kPa which are low enough to simulate the low overburden pressures experienced on the Moon. Results of these tests yielded a friction angle of 37-degrees and a cohesion of 0.9 kPa as determined by the Mohr-Coulomb failure criterion. The value of friction angle is much lower than that determined by

Perkins et al. (1992) and Batiste and Sture (2005), but can be attributed to different methods of testing, especially with respect to confining pressure.

2.2.2 JSC-1

The production of JSC-1 resulted from a 1991 workshop on the production and uses of simulated lunar materials. This mare basalt simulant was first developed and produced in

1993 at the Johnson Space Center, hence the name JSC-1. It was developed for use in specific scientific and engineering investigations, specifically extravehicular activity investigations, which required large amounts of soil. JSC-1 is a silty terrestrial soil created from mined volcanic ash deposits located in a cinder ash quarry on the edge of

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Merriam Crater in the San Francisco volcano field near Flagstaff, Arizona. This volcanic ash is of predominately basaltic composition (Chua and Johnson 1998). It simulates the chemical, mineralogical, and textural properties of the lunar mare regolith in the Apollo regions of exploration. More specifically, it matches an average Apollo 14 mare basalt material which is generally low in composition of titanium and high in composition of potassium and phosphorous. The mineralogical composition of JSC-1 includes plagioclase, olivine, pyroxene, ilmenite, and in contrast to MLS-1, it includes basaltic glass as shown in Figure 2.26. Compared to MLS-1, JSC-1 better emulates the texture and mineralogy of the lunar soil. Although JSC-1 represents a root mare simulant because of its composition as an “average” Apollo 14 soil with intermediate compositions of titanium, calcium, aluminum, potassium and phosphorous; JSC-1 can be used in studies that require a simulant that represents both a mare and highland soil (Sibille et al.

2005).

Figure 2.26 Electron microprobe image of grain size and chemical composition of JSC-1 (Sibille et al. 2005).

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Similar to MLS-1, JSC-1 was milled and crushed in order to attain a particle size distribution similar to typical lunar soils. The particle size distribution of JSC-1 is shown in comparison to that of MLS-1 in Figure 2.25. Figure 2.27 shows the particle size distribution of JSC-1 compared to the upper and lower bound particle size distributions of the actual lunar soil. The median particle size distribution for JSC-1, as defined by

McKay et al. (1994), is between 98 and 117 μm. The mean particle size distribution ranges from 81 to 105 μm. JSC-1 is classified as a nonplastic, well graded silty sand with approximately 40-percent passing the number 200 sieve (<75 μm) (Klosky et al. 2000).

The average specific gravity of JSC-1 is 2.9 which falls on the low end of the lunar range suggested by Carrier et al. (1991) cited by McKay et al. (1994). The maximum and minimum bulk densities of JSC-1 are 1.91 and 1.43 g/cc, respectively (Klosky et al.

1996). The angle of internal friction for JSC-1 is approximately 45-degrees and the cohesion is approximately 1.0 kPa providing a “good mechanical analog to lunar soil”

(McKay et al. 1994). These values were determined using the Mohr-Coulomb failure criterion with data from samples tested in a triaxial cell at confining pressures of 34.5, 69, and 103 kPa (Turk 1992 cited by McKay et al. 1994).

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100

50 Lunar Regolith JSC-1 40

20 Accumulative Percent 10

0 1 10 100 1000 10000 Grain Size, Micrometers

Figure 2.27 JSC-1 particle size distribution compared to upper and lower range particle size distributions for the lunar soil (Carter et al. 2004).

Klosky et al. (1996) also performed triaxial tests on JSC-1. These tests were performed at two different densities corresponding to 40 and 60-percent relative density or loose and medium dense consistencies, respectively. The samples were 20 cm in height and 10 cm in diameter and were loaded at a constant rate until 0.75-percent strain was achieved.

The cohesion and internal angle of friction were determined using the standard Mohr-

Coulomb failure criterion. Results of this study are provided in Table 2.6.

Table 2.6 Results of triaxial tests performed on JSC-1 (Klosky et al. 1996). Soil Density, g/cc Relative Density, % φ , º c, kPa 1.62 40 44.43.9 1.72 60 52.713.4

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As can be seen, the values of friction angle and cohesion are directly dependant on the relative density of JSC-1. In addition, these values generally agree with the previous studies of McKay et al. (1994).

JSC-1 has been a very successful simulant for the lunar regolith. According to Sibille et al. (2005), approximately 12,000 kg of JSC-1 was produced in the 1990’s. It has been distributed to a vast number of academic researchers and used in countless NASA sponsored investigations as well as been distributed among the educational outreach community. However, due to poor recordkeeping and unsupervised distribution of this lunar soil simulant, it is not known how much of this material remains or what condition the remaining material is in and as with MLS-1 the production of JSC-1 ceased more than

10 years ago (Schlagheck et al. 2005). Currently, there is no supply of JSC-1 available for distribution to the space exploration community.

2.2.3 JSC-1A

JSC-1A was developed as a replacement simulant for JSC-1 and is produced by Orbital

Technologies Corporation of Madison Wisconsin for widespread use in research projects and to support NASA’s future exploration of the lunar surface (Zeng et al. 2007).

Similarly to JSC-1, it is mined from a volcanic ash deposit in a commercial cinder quarry located in the San Francisco volcano field near the Merriam Crater just outside of

Flagstaff, Arizona. This material emulates a low-titanium mare regolith and contains major crystalline silicate phases of plagioclase, pyroxene, and olivine, with minor oxide

159 phases of ilmenite and chromite, and traces of clay. This material is available in three different forms: JSC-1A, JSC-1AF, and JSC-1AC; which represent JSC-1A as a whole, the fine grained fraction of JSC-1A, and the coarse grained fraction of JSC-1A, respectively. The material safety data sheet (MSDS) provided by Orbital Technologies

Corporation reports JSC-1A as a gray powder similar to sand or dirt with a specific gravity of 2.9, angle of internal friction of 45-degrees, and cohesion of 1.0 kPa.

Several laboratory tests have been conducted recently at Case Western Reserve

University by Dr. Xiangwu Zeng and graduate student Chunmei He to determine and verify the benchmark properties of JSC-1A (Zeng et al. 2007). These laboratory tests included investigations of particle size distribution, specific gravity, bulk density, compaction, shear strength, and compressibility of the material. All testing procedures followed standard testing methods specified by ASTM (1991), commonly used by today’s geotechnical engineering community to ensure comparability of the results. In addition, all tests were repeated multiple times to ensure repeatability of the data. Both sieve and hydrometer tests were run to determine the coarse and fine grained

(respectively) particle size distribution of JSC-1A. Results from repeat tests are shown in

Figure 2.28 and compared with the typical range of lunar soils. As can be seen, the particle size distribution of JSC-1A generally falls between the upper and lower bound of lunar soils, but does not exactly replicate the average range. According to the USCS,

JSC-1A is classified as a poorly graded silty sand (MS) containing 53-percent sand and

47-percent silt. It was also found that JSC-1A has a D10 equal to 0.017 mm, D30 equal to

0.042 mm, and D60 equal to 0.11 mm which represent the particle diameters which are

160 larger than 10, 30, and 60 percent of the particles (by weight), respectively. The coefficient of uniformity, Cu, of JSC-1A is 6.47 and the coefficient of curvature, Cc, is

0.94.

100

70 r 60

50 Percent fine Percent

0 10.000 1.000 0.100 0.010 0.001 0.000

Particle diameter, mm

Lunar soil average Lunar soil average + 1 standard deviation Lunar soil average - 1 standard deviation JSC-1A (1) JSC-1A (2)

Figure 2.28 Particle size distribution of JSC-1A (Zeng et al. 2007).

The specific gravity of JSC-1A was found to be 2.875 which is somewhat lower than the recommended working value for the lunar soil of 3.1 (Carrier et al. 1991). Average maximum and minimum bulk density for JSC-1A were determined as 2028 kg/m3 (2.03 g/cc) and 1566 kg/m3 (1.57 g/cc), respectively. Based on the maximum and minimum densities as well as the specific gravity of JSC-1A the maximum and minimum void ratios were computed as 0.826 and 0.410, respectively. Compaction tests were performed

161 in order to determine the best way to attain compaction for the material in order to simulate extreme conditions possibly encountered on the Moon for engineering related work. It was determined that a maximum dry density of 1746 kg/m3 (1.75 g/cc) could be attained via compaction provided the optimum moisture content was 13.5-percent. In addition, the shear strength of JSC-1A was determined from a total of nine triaxial tests performed at three different dry densities. Following the Mohr-Coulomb failure criterion, the friction angle of the soil was determined as summarized in Table 2.7. As can be seen, the friction angle of JSC-1A tends to increase with increase in density of the soil. In addition, it was concluded that the range of friction angle agrees well with the friction angle reported for the lunar soil (Carrier et al. 1991). It was noted that the measured cohesion was too low to present a meaningful conclusion. The final test performed on JSC-1A determined the compressibility of the material as defined by the compression index which was 0.068 and by the swelling index which was 0.001. These low values indicate that JSC-1A is less compressible with lower swelling than most conventional terrestrial soils. However, Zeng et al. (2007) concluded that this data agrees well with the compressibility data of the lunar soil as provided in the Lunar Sourcebook

(Carrier et al. 1991).

Table 2.7 Results of triaxial tests performed on JSC-1A (Zeng et al. 2007). Average Bulk Relative Peak Friction Density (kg/m3) Density Angle (º) 1659 24.6% 41.87 1789 54.7% 46.48 1940 84.6% 56.70

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2.2.4 Other Lunar Soil Simulants

Besides the aforementioned lunar soil simulants MLS-1, JSC-1, and JSC-1A, there are countless other simulants that have been created. In 1974, the US Army Engineer

Waterways Experiment Station conducted research aimed at predicting the performance of the wheels of the LRV (Melzer 1974). In order to accomplish this task a lunar soil simulant had to be created which replicated the strength characteristics of the actual lunar soil. The simulant created did not have a specific name, but was created by crushing basaltic rocks into small particles of various sizes. The particles were sieved and recombined to match the grain size distribution of the lunar soil representative of that collected on the Apollo 11 and 12 missions. Three different test methods were used to evaluate the strength characteristics of primary importance in vehicle mobility. A total of three complete vacuum triaxial tests were conducted at confining pressures of 3.5, 6.9, and 20.7 kPa in order to determine the friction angle of the material. A trenching test technique similar to the technique used on the Moon during the Surveyor missions was used to evaluate the cohesion. In addition, cone penetration resistance tests were conducted using the standard WES cone penetrometer. Results of all three tests were compared to strength parameters of the lunar soil as determined by Mitchell et al. (1972) and are shown in Table 2.8. It was concluded that the lunar soil strength conditions could successfully be simulated. This simulant is discussed in more detail in section 2.3.1.1,

Trafficability and Wheel-Soil Interaction Studies, of this dissertation.

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Table 2.8 Comparison of lunar soil and simulated lunar soil (Melzer 1974). Lunar Soil Lunar Soil Simulant Bulk Density, g/cc 0.8 – 2.0 1.4 – 1.9 Cohesion, kPa 0.03 – 2.1 0 – 2.9 Friction Angle, º 30 - 50 36 – 49 Penetration Resistance Gradient, MPa/m 0.8 - 30 0.2 - 70

Jensan Scientific, LLC produced a lunar soil simulant called JS-Lunar Simulant which was intended to emulate a lunar mare basalt material (Sibille et al. 2005). This simulant is composed of a mixture of 10-percent aged brecciated basalt from the Colorado Rockies mountain range, 40-percent unweathered vesicular basalt from Hawaii, 40-percent basalt from Pullman Washington, and 5-percent anorthite from the San Gabriel Mountains in

California. This simulant was designed specifically as a geotechnical material.

More recently, a lunar simulant has been produced in Ontario, Canada. Its current design replicates the grain size distribution of the lunar soil for the support of geotechnical work for the RESOLVE project (Schlagheck et al. 2005). In 1995 the Japanese Aerospace

Exploration Agency (JAXA) in conjunction with the Shimizu Corporation developed a lunar soil simulant called FJS-1 which was created from a mixture of Mount Fuji basaltic lava, olivine, and ilmenite. This simulant replicates the bulk mechanical properties and chemical composition of Apollo samples in the mare region of the Moon. FJS-1 is comparable to JSC-1.

Another lunar simulant, CAS-1, developed in China was created from volcanic ash of alkaline basaltic composition from a location called Jinlingdingzi, otherwise known as

164 the Golden Peak, which is in the Jilin Province of Northeast China. Mineralogically this material consists of glass, plagioclase, and olivine. To this point in time, CAS-1 has been ground and sized and placed into storage for later use. Li et al. (2006) created a lunar soil simulant from similar material mined from the Huinan district in the Jilin province of

China. This simulant specifically emulated the Apollo 14 soil samples and was created specifically for use in vehicle-terramechanics investigations. Again, the composition consists of olivine, pyroxene, feldspar, and volcanic glass. Hematite sand was added to the mixture to create a specific gravity more similar to that of the lunar soil, without affecting the mineralogy of the material significantly. Initially five different samples were prepared based on different particle size distributions and the amount of hematite added to the composition. The sample that best correlated with the lunar soil from

Apollo 14, as well as JSC-1, was selected as the appropriate simulant for vehicle mobility testing. This sample contained 6-percent hematite and had a specific gravity of 2.9. The specific gravity is on the low end of the lunar soil specific gravity, but corresponds well to the specific gravity of JSC-1 (McKay et al. 1994). The mean particle diameter was

0.13 mm while the median particle diameter was 0.097 mm. The coefficient of uniformity was 5.16 and the coefficient of curvature was 0.94. The angle of internal friction and cohesion as determined by direct shear testing were 32.75-degrees and 1.79 kPa, respectively. The value for internal angle of friction is within the range of that of the lunar soil; however the cohesion value is slightly higher. In addition, the compressibility coefficient and the relative compaction were 0.19 MPa-1 and 0.66, respectively (as determined via consolidometer tests). Li et al. (2006) concluded that,

“the data indicates that the properties of compounded simulant lunar regolith is close to

165 the real lunar soil, and can be used in the vehicle-terramechanics tests and other related engineering researches.”

2.3 REVIEW OF LUNAR VEHICLE MOBILITY STUDIES

This section provides a general review of the design and developmental procedures of past lunar surface exploration vehicles such as the Lunar Roving Vehicle as well as the development of lunar soil simulants which helped to make the LRV a success. Focus is placed on the physical and mechanical properties of the soils used for soil-wheel interaction studies.

2.3.1 Lunar Roving Vehicle

The Lunar Roving Vehicle (LRV) was developed prior to the Apollo 15 mission in 1971 by the National Aeronautics and Space Administration under the leadership of the

Marshall Space Flight Center in Huntsville, Alabama (Costes et al. 1972). Preliminary design requirements for the LRV were proposed as early as 1969. The purpose of the

LRV was ultimately for a more advanced and a more complete investigation of the lunar surface. According to Costes et al. (1972),

“The LRV [or rover] was the first manned surface vehicle to be used in lunar exploration. It was designed to transport two astronauts with their life support equipment; scientific apparatus and geological tools; lunar soil and rock samples; and television, movie, and still cameras, along geological traverses covering regions that have embraced a much greater

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surface area than that explored and sampled during previous manned and unmanned lunar surface missions.”

The development of the LRV was extremely challenging as it was to be completed in a relatively short time span (17 months), had little information and no past experience to go off of, and had to be developed in such a way that it met the space and loading limitations of the transporting space shuttle. In addition, design requirements for the vehicle had not been finalized until early 1970. The battery powered LRV ultimately weighed a total of

2130 N on the Earth and was designed to carry a payload of 4800 N on the Moon minus the weight of two astronauts, their life support systems, and other scientific equipment which totaled 265 N. It spanned a size of 3.1 m long, 1.83 m wide, and 1.14 m in height

(refer to Figure 2.29). In addition, the LRV was designed to operate at a maximum speed of 14 km/hr (terrain dependent) and was limited to carrying the maximum payload for a total of 120 km. It was operable a minimum of 78 hours per lunar day. With these criteria in mind, the LRV was able to cover an area of 290 square kilometers, which is 10 times the area the astronauts would have been able to cover on foot. The only limiting factor was that the LRV was not permitted to explore more than 9.7 km from the lunar module. This safety factor was imposed as the maximum distance the crew could walk back to the LM in case the vehicle broke down.

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Figure 2.29 Typical dimensions of the LRV (Costes et al. 1971).

The wheels of the LRV, as shown in Figure 2.30, were constructed of zinc-coated piano wires that were intertwined to form a woven mesh. Each wheel had “chevron-shaped” or inverted “V” shaped titanium treads covering approximately 50-percent of the wheel.

The purpose of these treads was to “provide sufficient flotation without degrading traction” (Costes et al. 1972). In addition, each wheel had an aluminum hub and titanium

“bump stop” which prevented excess deformation of the tire upon heavy impacts. The size of each wheel was approximately 81.3 cm in diameter and 22.9 cm in width. The total weight of each wheel was approximately 53.3 N. It is not necessary for this study to provide a complete description of the drive system, operating equipment, navigation system, instrument panel, etc. For the interested audience a thorough description is provided in Costes et al. (1972).

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Figure 2.30 LRV wheel (credit NASA).

The following statements from the Apollo 15 crew summarize the actual performance of the LRV on the lunar surface in the Hadley-Apennine region (as cited by Costes et al.

1972):

“The performance of the vehicle was excellent. The lunar terrain conditions in general were very hummocky, having a smooth texture and only small areas of fragmental debris. A wide variety of craters was encountered. Approximately 90-percent had smooth, subdued rims which were, in general, level with the surrounding surface. Slopes up to approximately 15-percent were encountered. The vehicle could be maneuvered through any region very effectively. The surface material varied from a thin powdered dust (which the boots would penetrate to a depth of 2 to 3 inches on the slope of the Apennine Front) to a very firm rille soil which was penetrated only a quarter inch to a half inch by the boot. In all cases, the rover’s performance was changed very little.”

The depth of wheel tracks on average were approximately 1.25 cm, but varied by as much as 5 cm, with significant wheel sinkage near crater rims (Mitchell et al. 1973). The astronauts observed a clear imprint of the chevron tread which meant that the lunar soil is

169 somewhat cohesive in nature and that the amount of wheel slip was very small (on the order of less than 20-percent). It was noted that the LRV was capable of climbing slopes as steep as 20-degrees without issues although it was recommended not to park the vehicle on steep slopes because the vehicle had a tendency to slide downslope (Mitchell et al. 1973).

In conclusion, the Apollo 15 Lunar Roving Vehicle performed very satisfactorily. It easily met the expectations that were placed on it and served to greatly enhance the scientific aspect of the lunar mission. The following section discusses the investigations and studies that led to the success of the LRV.

2.3.1.1 Trafficability and Wheel-Soil Interaction Studies

The success of the Apollo 15 mission in relation to performance of the LRV was directly dependent on several factors. Most importantly it was dependent on the accuracy of the knowledge on the following topics: topography of the site, lunar soil conditions, and the prediction of the wheel-soil interaction in the lunar environment (1/6th gravity and extreme vacuum conditions). Prior to the Apollo 15 mission, soil mechanics experiments had been included in the Surveyor program and all previous Apollo missions as well as

Soviet missions including the Luna program. Based on the results of these investigations a general idea of the physical and mechanical properties of the lunar soils was defined (as discussed in the previous section 2.1, Review of Lunar Soil Investigations, of this dissertation). It was established that lunar soil parameters representative of the first 15 to

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20 cm in depth would be influential to the performance of the LRV (Costes et al. 1972).

However, prior to the LRV there was no actual vehicle mobility data for the specific case of the behavior of light wheel loads (experienced in low gravity fields) on fine-grained sandy soils. Instead most tests had been conducted on vehicles with pneumatic tires and relatively heavy loads of 1000 N or more. To ensure success of the LRV the U.S. Army

Engineer Waterways Experiment Station performed several single and multi-wheel mobility tests. This testing program was imperative to develop knowledge of vehicle performance incorporating wheels of the type expected to be used on the Moon and carrying light loads similar to those expected to be carried on the Moon. In addition, the vehicle must operate in test conditions utilizing soil with cohesive and frictional or strength components emulating those of the lunar soil.

In 1969, the personnel of the Mobility Research Branch (MRB), Mobility and

Environmental Division, and the U.S. Army WES conducted tests to investigate principles to provide a better understanding of the interaction of lightly loaded, nonpneumatic wheels with soil exhibiting small amounts of cohesion. Their ultimate goal was to evaluate the effectiveness of various types of wheels as traction and transport devices on lunar surfaces (Freitag et al. 1970). Additionally, and more pertinent to the current research, the soil properties of interest were quantified and the effect of soil cohesion on wheel performance was investigated. All tests were conducted on Yuma sand which is a wind-deposited fine dune sand collected from the desert near Yuma,

Arizona. Both single wheel and multi-wheel vehicle tests were conducted in various conditions of Yuma sand ranging from loose to very dense relative density and ranging in

171 cohesions from 0 to 1.8 kPa; as well as various loading conditions corresponding to wheel contact pressures up to 16 kPa simulating lunar conditions. The various soil tests performed included triaxial compression tests, vacuum triaxial tests, direct shear tests, in- situ plate shear tests, rotational shear tests, bevameter shear tests, vane shear tests,

Cohron sheargraph tests, trenching tests, density and moisture content determination, particle size distribution, cone penetrometer tests, and bevameter plate-sinkage tests.

These tests will be discussed in detail as reported by Freitag et al. (1970) in the succeeding paragraphs.

Results of conventional triaxial tests under confining pressures of 48.2 to 289.4 kPa and various relative densities revealed that the friction angle was constant for a given relative density when the initial relative density of the Yuma sand was below 50-percent. When the initial relative density of Yuma sand was above 50-percent, the friction angle appeared to vary according to the confining pressure. It was also determined that the friction angle increased linearly with increasing initial relative density. This type of relationship is expected for a cohesionless soil. The values for internal angle of friction ranged between 35 and 42-degrees for a relative density of zero and 100-percent, respectively. In contrast, vacuum triaxial tests under confining pressures of 3.5 to 20.7 kPa tended to increase nonlinearly with increasing relative density. Internal angle of friction values for vacuum triaxial tests on the same material under different initial relative densities ranged from 35 to greater than 45-degrees. However, a true friction angle was calculated for the vacuum triaxial tests taking into account energy corrections to the deviator stress due to volume change and vertical displacement. The true friction

172 angle was thus found to be 34.3-degrees and was constant with increasing initial relative density. In comparison, results of direct shear tests showed a typically linear increase in friction angle with increasing initial relative density. Friction angles, however, only ranged from 34.6 to 37.4-degrees, but showed a larger amount of scatter than the triaxial tests. This was accounted for by “routine inaccuracy in the test procedure” (Freitag

1970). Similarly to the confining pressures in conventional triaxial tests, normal pressures ranged from 47.5 to 287.0 kPa in the direct shear tests. In-situ plate shear tests under low normal pressures ranging from 0.7 to 10.3 kPa resulted in internal friction angles ranging from 28.1 to 34.4-degrees linearly increasing with increasing initial relative density. Due to the low confining pressure, the energy correction was applied as in the vacuum triaxial tests and the true friction angle was determined to be 33.4-degrees.

Additionally, the maximum shear stress in this test increased directly with increase in normal load for the same soil condition. It was noted that no apparent cohesion was found for the Yuma sand in any of the shear tests. In summary Freitag et al. (1970) stated, “The true friction angle is constant for a certain cohesionless soil and independent of the testing method as verified for the vacuum triaxial and in situ shear tests.”

However, he mentions that the true friction angle should not be relied upon because the angle of friction of a cohesionless material is almost always coupled with a volume change during shear tests. Since the volume change is affected by boundary conditions and stress conditions, the angle of internal friction is in turn affected. Therefore, the angle of internal friction is dependent on the initial relative density as well as the testing method and in Freitag et al.’s (1970) words, “until it has been proven that the stress- deformation mechanism beneath a wheel is at least similar to one of the shear tests” none

173 of the angle of internal friction values can be used to solve the problem of wheel-soil interaction.

Figure 2.31 Friction angle versus relative density as determined by various shear testing methods (Freitag et al. 1970).

Since no apparent cohesion was determined from the shear testing methods, trenching tests were implemented. The sand for trenching tests was prepared at a specific moisture content and density. Moisture contents varied from zero to 2.8-percent while relative density ranged from zero to 100-percent. A vertical wall ranging in lengths from 0.2 to

1.2 meters was excavated into the prepared soil until failure (defined by the wall

174 collapsing). Dimensions of the resulting excavation were recorded and apparent cohesion was determined using both the Coulomb wedge (graphic) method and via slope stability analyses. These procedures are described in detail in Freitag et al. (1970). Results of these analyses confirmed that the apparent cohesion of Yuma sand increased with increasing relative density (for the same moisture content). In addition, apparent cohesion increased with increasing moisture content up to 2-percent at which point apparent cohesion began to decrease. This makes sense as a soil that is fully saturated would exhibit no cohesive properties. Values of apparent cohesion for Yuma sand generally ranged between 0 and 2.0 kPa.

Cone penetration tests were performed to determine the cone index gradient G with respect to relative density and moisture content. A standard WES cone penetrometer was used to penetrate the soil at a constant speed of 0.03 m/sec to a depth of 36 cm using a

30-degree cone tip. Typical results are shown in Figure 2.32 where S1 and S2 are air- dried Yuma sand samples prepared to loose and very dense conditions, respectively; and

C1, C2, and C3 are wet Yuma sand samples prepared to medium dense conditions. It is important to note that the penetration resistance data was recorded as soon as the tip of the cone touched the surface of the soil sample. The cone index gradient was taken over the range of penetration resistance curve where the cone was flush with the soil surface to a depth of approximately 19 cm. As can be seen in Figure 2.32, the Yuma sand preparations were fairly uniform through the first 19 cm of depth and then tended to increase in strength with increasing depth.

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Figure 2.32 Typical CPT penetration resistance versus depth curves for Yuma sand (Freitag et al.1970).

The cone index gradient was also related to the relative density and moisture content of the material. For the same relative density, the cone index gradient increased with increasing moisture content up to 2-percent moisture content. In addition, it was found that at the same moisture content the cone index gradient tended in increase nonlinearly with increasing relative density.

Other tests such as the Cohron sheargraph, shear vane, bevameter ring shear, and bevameter plate-sinkage tests were classified as “special tests” during this investigation

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(Freitag et al. 1970). The purpose of these special tests was not for validation of the aforementioned soil properties, but was for the sole purpose to list the results according to routine soil mechanics tests or special soil mechanics tests. These tests were conducted in conjunction with each wheel test and performed until the characterization of the soil was determined to be sufficient. Plate-sinkage tests were conducted using flat, circular plates with diameters of 5.1, 7.6, and 10.2 cm. Plates were forced to depths of

10.2 cm at a constant speed of 0.0025 m/sec. Bevameter shear ring tests were conducted with a ring having an outer diameter dimension of 17.8 cm and a thickness of 1.9 cm

(corresponding to an inner diameter of 14 cm) and fitted with 0.5 cm tall grousers spaced at 20-degree intervals around the ring. Normal pressure was applied using deadweights and the shear head was rotated via an electric motor to a maximum angular distance of

80-degrees. Results of the shear testing were interpreted graphically via hand drawing the Mohr shear line. This resulted in a large amount of personal interpretation and errors due to personal judgment. Plate-penetration tests were, however, evaluated using computer techniques which did not involve human error. These techniques were not discussed in any detail. Typical results are shown in the following table, Table 2.9,

-n 2 -n 2 where kc is in (kN/m)(cm ), kφ is in (kN/m )(cm ), n is unitless, and sv is in kN/m .

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Table 2.9 Results of special tests on Yuma sand (Freitag et al. 1970).

Soil Condition S1 Soil Condition S2 Soil Condition C1 Soil Condition C2 Soil Condition C3 Max Max Max Max Max Max Avg Avg Avg Avg Avg Min Min Min Min Min

- - k 0.08 0.16 0.07 0.10 0.41 0.16 0.27 0.62 0.17 0.36 0.92 0.51 0.79 c 0.08 0.01

kφ 23.3 4.44 11.4 74.6 58.2 65.1 35.5 19.8 27.8 57.7 42.0 51.0 75.9 52.1 67.0 Bekker Soil Values n 0.96 0.84 0.91 0.51 0.49 0.51 0.70 0.61 0.64 0.79 0.50 0.59 0.49 0.46 0.48

ear 0 0 0 4.9 3.0 4.0 2.8 0.9 2.1 8.5 5.1 7.4 10.7 5.8 8.0 s Sh v Stress

After single wheel and multi-wheeled vehicles were tested under these various conditions, Freitag et al. (1970) proposed several conclusions pertinent to the understanding of vehicle-soil interaction and the study of terramechanics. The following general conclusions were made:

• For single wheel tests, drawbar pull and pull coefficient or pull to vehicle weight

ratio increased with increasing relative density of the Yuma sand.

• The cohesion of the Yuma sand is not influential at loads lighter than 130 N. The

reasoning behind these results is that the drawbar pull at light loads is not affected

by energy losses due to sinkage. The effect of cohesion was seen at higher loads.

• The pull coefficient is independent of the average contact pressure at the soil-wheel

interface for pressures up to 3.5 kPa.

• Most importantly, it was agreed that Yuma sand could be used in various conditions

to emulate the basic lunar soil conditions for vehicle mobility testing.

178

In 1970, another NASA sponsored investigation was conducted by the U.S. Army

Engineer WES (Green and Melzer 1971). The purpose of this investigation was to determine the performance of several different LRV wheel design concepts and tread covers developed by the General Motors Company (GMC) in conjunction with the

Boeing Company under carefully controlled laboratory conditions. In order to satisfy the requirements of this investigation a series of single-wheel slip tests were performed in a crushed basalt material simulating the lunar soil. The investigation performed by WES began with an initial investigation of the lunar soil simulant. It is the simulation, preparation, and soil testing schedule that are of importance to the current research. As described in Green and Melzer (1971), the soil used was a crushed basalt from Napa,

California which was classified as “granular with angular to subangular grains” and exhibiting “a small amount of cohesion when moist or compacted” (Green and Melzer

1971). Four different consistencies of this material were prepared at varying void ratios and moisture contents to simulate a range of cohesive and frictional properties as determined from the Apollo 11 and 12 missions. The four consistencies were labeled as

LSS1 through LSS4 (where LSS is an acronym for lunar soil simulant) which corresponded to very loose and very dense compositions, respectively. In general these lunar soil simulants were referred to as the Napa Valley Basalt Simulants or the NVB.

Soil preparation methods included plowing and air drying, compaction via vibratory compacter, and wetting with water (Sibille et al. 2005). A number of different tests were performed on these soils to determine the geotechnical properties of the four different preparations. These included grain size analyses, vacuum triaxial compression tests, in-situ plate shear strength tests, trenching tests for vertical stability, density, void-

179 ratio, in-place moisture content determinations, cone penetration resistance tests (using the standard WES cone penetrometer), bevameter plate-penetration, and bevameter ring shear tests, as well as a few shear vane tests and Cohron sheargraph tests. Typical soil values of LSS1 and LSS4 are shown in the following Figures 2.33 and 2.34, respectively.

It should be noted that LSS4 was prepared with water and thoroughly mixed to represent a soil with a uniform distribution of water. According to Melzer (1971), “based on the results of the soil mechanics tests following the Apollo 11 and 12 missions LSS4 appeared to have the predominant strength condition of the lunar soil.” A complete set of soil values for all four consistencies can be found in Green and Melzer (1971) as well as

Costes et al. (1972). From the results of these soil tests it was concluded that the crushed basalt material could be effectively used to quantitatively measure the performance of

LRV wheels on a soil similar in range to that of the soil encountered during the Apollo 11 and 12 missions. In addition Costes et al. (1972) stated that, “the effect of soil gradation, packing characteristics, strength, and deformability on the mobility performance of the

LRV wheels was assessed directly.”

180

Figure 2.33 Soil parameters of LSS1 as determined by WES (Green and Melzer 1971).

Figure 2.34 Soil parameters of LSS4 as determined by WES (Green and Melzer 1971).

This material was later used by the WES for additional testing to determine the influence of vehicle velocity, wheel speed and acceleration, wheel load, influence of a fender, travel direction, sloped surfaces, and the effect of soil strength on the LRV wheel

181 performance (Melzer 1971). Again, it is the lunar soil simulant and the effect of the soil strength on the wheel performance that is pertinent to the current research. In addition to

LSS1 through LSS4 a fifth simulant was added based on indications of higher soil strength from the Apollo 12 and 14 missions. The fifth simulant, LSS5, was prepared with water similar to the LSS4, but it was prepared to a slightly higher moisture content. In addition,

Yuma sand from the desert near Yuma, Arizona was used for comparison with the LSS during some of the wheel tests. It was questioned whether or not similar trends would be observed in both the LSS and desert sand. The grain size distribution of LSS, Yuma sand, and the approximate band for Apollo 11 and 12 soils are shown in Figure 2.35. In addition, the geotechnical properties of LSS4, LSS5, and Yuma sand are compared in

Figure 2.36. Cone penetrometer tests were performed through the duration of the study both before and after wheel tests. The standard WES mechanical cone penetrometer was used for these tests and the penetration resistance gradient of each cone insert was recorded. The surface moisture content as well as the density was determined, both before and after conducting wheel tests. In addition, vacuum triaxial and plate shear tests were conducted to determine the shear strength parameters focusing on the angle of internal friction. Cohesion was estimated from trenching tests in which the height at failure was measured and related to known density-friction angle relations (Green and

Melzer 1971).

182

Figure 2.35 Grain size distribution of Yuma sand, LSS, and Apollo 11 and 12 bounds (Melzer 1997).

Figure 2.36 Yuma, LSS4, and LSS5 geotechnical properties (Melzer 1971).

From the results of wheel speed tests on LSS4 and Yuma sand it was concluded that the wheels behaved similarly in the two different soils when the soils were prepared to the same strength and when the wheel speed was 0.9 m/sec. However, contrary to the wheel performance in LSS4, when wheel speed was increased in the Yuma sand the performance (efficiency with respect to power requirements) of the wheel improved. In

LSS4, the efficiency was found to be independent of the wheel speed. It was suggested

183 that this effect could have been caused by the existence of air-pore pressure in the LSS, which resulted from the low permeability of the “silt-to-fine-sand” material (Melzer

1971). As described by Melzer (1971), the existence of air-pore pressure has a weakening effect on the internal friction or shear potential of the soil which ultimately leads to a decrease in pull (or the force causing acceleration of the wheel). Since the magnitude of air-pore pressure is interdependent with the shear velocity, as the wheel speed increases the pull decreases. In addition, the wheel-soil interaction experiences a dynamic force which results as a soil momentum created by the action of the wheel, which is in constant contact with fresh soil (Melzer 1971). This dynamic force ultimately contributes to the pull and to the wheel support. Therefore, as the shear velocity is increased, the efficiency of the system increases as well. In conclusion, it was suspected that this phenomenon in combination with the phenomenon caused by air-pore pressure would cancel each other out and the efficiency would become independent of the wheel speed as verified in the case of LSS4.

Further studies between LSS4 and LSS5 revealed that for a given slip of 20-percent, more pull was developed on LSS5 than on LSS4. This follows suit as the shear potential of the

LSS5 was larger than that of the LSS4 as shown in Figure 2.36. However with this increase in shear potential follows an increase in the torque required to utilize it for a given slip (Melzer 1971). Inversely, for a given pull to vehicle weight ratio, the slip developed in the LSS5 was smaller than the slip developed in the LSS4. Melzer (1971) suggests that this was expected. Typically, in a stronger soil there will be less sinkage.

In supplement, the power requirements (torque required per unit weight per unit distance

184 of travel) for a vehicle with a given pull-to-weight ratio will be larger for weaker soil than for stiffer soil as verified by the slope climbing ability of the same vehicle operating on

LSS4 and LSS5. On LSS5 the maximum slope attained was approximately 23-degrees whereas it was only 19-degrees for the same vehicle on LSS4. Finally, it was determined

3 that the efficiency of the system was higher for LSS5 than for LSS4 with a given power requirement. Overall, these basic vehicle mobility performance characteristics formed a baseline upon which further studies could be evaluated and verified.

In addition to these tests performed in ambient conditions, an additional set of wheel-soil interaction tests were performed under simulated 1/6th gravity conditions on the U.S. Air

Force C-135A aircraft (Mullis 1971 cited by Costes et al. 1972). Scale model LRV wheels without fenders were tested on the same crushed basalt LSS materials used in the

WES tests while inside a vacuum chamber aboard the aircraft. According to Costes et al.

(1972) a complete overview of the test methods and results can be found in Mullis

(1971), though the major variables in these tests were normal load, wheel revolutions per minute, and degree of vacuum. In spite of some questionable data obtained during these tests, there were several general observations that were noted (Costes et al. 1972). One conclusion follows that, in concord with the results of WES testing, under reduced gravity and with negligible pore pressures vehicle mobility performance is improved. In addition the wheel performance and energy requirements were not affected by the accumulation and release of soil within the wire mesh wheel.

3 Efficiency is defined by Melzer (1971) as, “the ratio of recoverable energy to total energy input, reflecting the ratio of the net pull that is developed over and above the pull that allows the wheel or vehicle to propel itself, to the total energy input.” 185

Observations and post-mission power analyses of the operation of the LRV on the lunar surface during the Apollo 15 mission provided several conclusions in relation to these pre-mission wheel-soil interaction investigations. Costes et al. (1972) states that,

“qualitative observations on the interaction of the vehicle with the lunar surface agree with pre-mission estimates on the vehicle’s behavior, based on wheel-soil interaction tests performed on lunar soil simulants under terrestrial and 1/6-g gravity conditions onboard the C-135A aircraft.” In addition it was noted that significant variations in the

soil values prescribed by the U.S. Army WES LLL including n, kc , kφ , K, c, and φ do not notably influence the energy consumption of the LRV. According to Costes et al.

(1972), throughout the entire Apollo 15 mission the energy consumption only varied between 11.4 and 16-percent (in terms of percent deviation of energy consumption per

kilometer traversed). In general though, higher values of n, kc , and kφ are typically associated with lower energy consumption values. It was also verified that based on percent deviation of energy consumption per kilometer for the entire Apollo 15 mission the best values as recommended by the MSFC in section 1.7.2.3, Trafficability

Parameters, were indeed the best soil values. According to Sibille et al. (2005), “The

LSS materials are no longer available and their exact properties are not well documented, but they demonstrated that the use of standard simulant materials by lunar surface hardware development engineers contributed to the historical success of the lunar missions.”

186

CHAPTER THREE

DEVELOPMENT OF A NEW LUNAR SOIL SIMULANT: GRC-1

As can be seen from the literature review of Chapter 2, the mechanical and engineering properties of the lunar soil are not well understood or clearly defined, especially with respect to vehicle-soil interaction. Several different investigations have been performed on lunar soils both in-situ and on returned lunar samples. These investigations resulted in multiple variations of the geotechnical properties of the lunar soil indicating both regional and local variations on the Moon, variations with respect to depth, and variations with respect to testing methods and interpretation of the results. Several different lunar soil simulants have been created for various small and large scale engineering investigations of the lunar soil (when the lunar soil is not available for testing). However, most of these simulants are no longer in production or are too costly for large scale investigations such as vehicle mobility testing. In addition, the properties of these simulants are not clearly defined, as was found for the actual lunar soil, and tend to simulate certain specific aspects of the lunar soil while neglecting others depending on the nature of the investigation. This can greatly affect the reliability of testing results especially with respect to vehicle mobility. In the literature review, several different simulants were used in vehicle mobility testing for development of the lunar rover wheels and performance prediction of the LRV on the Moon. This makes it difficult to compare results and come to meaningful conclusions about the performance of a vehicle. Additionally, none of these simulants matched the lunar soil composition or mechanical properties exactly.

The use of water, an unrealistic component of the actual lunar soil, was even

187 implemented to attain specific strength conditions. Thus, there is a definite need for the development of a standard lunar soil simulant made specifically for vehicle mobility testing. This chapter describes both the development and initial characterization of a lunar soil simulant, GRC-1, which is intended to be used as a standard vehicle mobility lunar simulant at the NASA Glenn Research Center for which it is named after. It should be noted that the development and characterization of GRC-1 is part of a cooperative investigation of vehicle traction for prospective lunar roving vehicles by the NASA

Glenn Research Center Mechanical Components Branch, Case Western Reserve

University, Goodyear Tire and Rubber Company, and Virginia Tech. The common goal is to be able to develop effective lunar vehicles and validate mobility models for future missions to the Moon. Thus, it is necessary to test prototype wheels and vehicles under simulated terrain conditions.

Figure 3.1 NASA Glenn lunar vehicle mobility team shown at the SLOPE facility with the Modular Mobility Technology Demonstrator shown in the background (credit NASA). From left to right: Fred Oswald, Steve Bauman, Tim Krantz, Phil Abel, Heather Oravec, Efrain Patino, Vivake Asnani, Damon Delap.

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3.1 METHOD FOR CREATING GRC-1

According to Schlagheck et al. (2005) as a result of the 2005 Workshop on Lunar

Regolith Simulant Materials, the development of new simulants must be able to support both near term and long term needs; be accurately characterized and evaluated; be based on well defined requirements; and be a material which can be used for comparative research and advancement in technology development. In addition, a new lunar soil simulant must be reproducible and distributable. The critical knowledge obtained by the careful study of in-situ testing and testing on lunar samples returned by past lunar missions, although limited and sometimes inconclusive, enables us to define a lunar simulant material that can be used as a lunar soil analog in vehicle mobility testing. It is important to note that GRC-1 is considered a low fidelity simulant because it does not match both the compositional and textural features of the lunar soil. Additionally, it is most important to recognize the relevance of the material and the fact that it is specifically designed for vehicle mobility studies and may not be suitable for lunar studies in other areas such as in-situ resource utilization. The chemical composition of the lunar soil does not have a significant effect on lunar surface mobility and therefore is not included in the development of GRC-1. Therefore, GRC-1 aims to simulate a subset of features of the lunar soil specifically pertaining to the performance of vehicles and mainly encompassing soil strength.

The particle size distribution of soil is an extremely important engineering property which influences the strength properties and compressibility of the material. According

189 to Sibille et al. (2005), the particle size distribution, “affects the resistance to mechanical action.” High fidelity of the simulation of particle size distribution is one of the most critical factors in creating a lunar soil simulant. The replication of the particle size distribution of the lunar soil is the basis for creating GRC-1. An accurate simulation of the particle size distribution will likely lead to similarities in strength properties and other mechanical properties as well. According to the Lunar Sourcebook (Heiken et al. 1991), there were a wide variety of soils encountered during the early lunar missions. In terms of particle size distribution, a band of soil particle sizes have been identified by Carter et al. (2004) as upper bounds and lower bounds for the particle size distribution of the lunar soil, shown as a cumulative distribution plot in Figure 3.2. The first task for this project is to create a soil mixture that has a particle size distribution similar to that of the average of lunar regolith, which is also shown in Figure 3.2. However, with this first step, a decision was made to omit the finer fraction of soil particles. This decision was imposed as a safety precaution to prevent dust generation during testing. Generally speaking, fine particles allow a granular material to be prepared to a higher density and raise the shear strength of the soil. As such, GRC-1 is expected to have less strength than a soil mixture that includes fines. However, this is acceptable for this investigation because a weaker soil is more conservative for mobility studies. The values estimated from Figure 3.2 representing the coarser fraction (excluding particles finer than 75μm or the #200 sieve) of the average lunar soil particle size distribution are laid out in Table 3.1 along with the corresponding sieve number and particle sizes. The “Histogram by Weight” column gives the percentage of the total mass that would be contained in that particular sieve, but

190 would fall through the sieve above it; i.e. the percentage of the entire sample mass that is larger than the corresponding grain size, but smaller than the previous grain size.

Table 3.1 Initial target recipe for coarse grained lunar soil simulant. Percent Finer by Histogram by Sieve Number Grain Size (mm) Weight (%) Weight (%) 10 4.75 96.2 3.8 20 2.0 83.0 13.2 40 0.425 60.4 22.6 70 0.212 45.3 15.1 100 0.150 28.3 17.0 200 0.075 0.0 28.3

100

Percent Finer 40

0 10 1 0.1 0.01 0.001 Particle Size, mm Lunar Soil Upper Bound Lunar Soil Lower Bound Average Lunar Soil

Figure 3.2 Upper, lower, and average bounds on particle size distribution of the lunar soil.

191

Sands produced by a regional sand manufacturer, Best Sand Corporation of Chardon,

Ohio (affiliated with Fairmount Minerals) were compared to determine possible combinations of sand that would have similar grain-size distributions to the lunar soil.

The various silica sand products of the Best Sand Corporation are shown in Figure 3.3 below.

Figure 3.3 Typical silica sand grades from the Best Sands Corp.

In order to use the commercially available sands from the Best Sands Corporation to obtain the optimum mixture for coarse lunar regolith, it is necessary to ensure the sand samples from the Best Sand Corporation have particle size distributions consistent with the specifications provided by the manufacturer. To do this, tests to determine the particles size distribution of the Best Sands were carried out in the geotechnical laboratory at Case Western Reserve University (CWRU). These tests followed ASTM standards for sieve analysis of coarse particles (ASTM D422) and for hydrometer analysis of fine particles (ASTM D423). Particle size distribution analysis was carried

192 out on four randomly selected types of Best Sand including BS1020, BS565, BS530, and

BS110. The results of sieve and hydrometer analysis are shown in Figure 3.4 below.

100

40 Percent Finer by Weight by Finer Percent 30

0 10 1 0.1 0.01 Particle Size (mm)

BS1020 - Manufacturer BS565 - Manufacturer BS530 - Manufacturer BS110 - Manufacturer BS1020 - CWRU BS565 - CWRU BS530 - CWRU BS110 - CWRU

Figure 3.4 Verification of particle size distribution provided by Best Sands Corp.

As shown in Figure 3.4, the particle size distribution curves obtained from the laboratory at CWRU are close (within 5-percent) to that provided from the manufacturer, suggesting that the process of manufacturing sands at the Best Sands Corporation is reliable.

Therefore, Best Sands silica sand products can confidently be used to obtain the appropriate simulant mixture.

To obtain a sand mixture that has a particle size distribution which closely simulates that of the coarse lunar regolith, while at the same time can be easily produced in large

193 quantities; four types of Best Sands silica sands that have particle sizes encountered in the coarse lunar regolith were chosen. These include BS1635, BS565, BS530, and BS110, the latter three of which were verified in Figure 3.4. The histogram by weight for each of the four sands is provided in Table 3.2 along with the histogram by weight of the coarse lunar regolith target. It is important to note the row labeled “Actual” in Table 3.2 is representative of the percentage of the entire sample mass that is larger than the corresponding grain size, but smaller than the previous grain size, based on a 24 kg (53 lb) soil sample. A careful statistical analysis was conducted to mix the sands at specific proportions so as to achieve an overall particle size distribution closely matching that of the coarse lunar regolith. This was done by first determining the average particle size distribution of the lunar soil and quantifying the amount of soil passing the number 10,

20, 40, 70, 100, and 200 sieves based on an initial 45 kg (100 lb) sample. Barring the finer fraction of material (passing the number 200 sieve or less than 75 μm in diameter) it was determined that 24 kg (53 lb) of material composed the coarser grained average of the lunar soil particle size distribution. Based on this it was determined that 3.8-percent of the lunar soil is greater in diameter than the number 10 sieve; 13.2-percent passed the number 10 sieve; 22.6-percent passed the number 20 sieve; 15.1-percent passed the number 40 sieve; 17.0-percent passed the number 70 sieve; and 28.3-percent passed the number 100 sieve, but was retained by the number 200 sieve. Using the particle size distribution of the sands provided by the Best Sands Corporation (and as reinstated in

Table 3.2), it was easy to determine the percentage of each of the four selected sands that should be combined to match the average coarse-grained fraction of the lunar soil. The total Best Sands mixture is thus composed of approximately 32-percent BS1635, 24-

194 percent BS565, 8-percent BS530, and 36-percent BS110. Figure 3.5 is a cumulative distribution plot comparing the particle size distribution for the coarse lunar regolith average and the actual Best Sands ideal simulant mixture. It is clear that the sand mixture agrees well (within 5-percent) with the coarse lunar regolith particle size distribution.

Another figure, Figure 3.6, is provided to display the histogram grain-size distribution for the coarse lunar regolith and sand mixture. The histogram plot gives a better idea of which size grain particles are more prominent in the sand and of which ones more are required. It can be seen from Figure 3.6 that the coarse lunar soil average is primarily composed of larger grains and is much more heavily weighted in this size region than the

Best Sands ideal or target mixture.

Table 3.2 Histogram by weight for Best Sands compared to the target mixture for a coarse lunar soil simulant. #10 #20 #40 #70 #100 #200

4.75 mm 2.00 mm 0.425 mm 0.212 mm 0.150 mm 0.075 mm BS1635 1% 35% 61% 4% 0% 0% BS565 0% 0% 3% 55% 29% 13% BS530 3% 8% 17% 57% 13% 3% BS110 0% 0% 0% 1% 15% 71% Target 3.8% 13.2% 22.6% 15.1% 17.0% 28.3% Actual 0.56% 11.8% 21.6% 19.4% 13.4% 28.9%

195

100

30 Percent Finer by Weight 20

0 10 1 0.1 0.01 Particle Size (mm)

Coarse Lunar Average Best Sand Target Mixture Coarse Lunar Upper Bound Coarse Lunar Lower Bound

Figure 3.5 Coarse lunar average particle size distribution versus Best Sands ideal mixture particle size distribution.

196

5 Histogram of Percent Finer by Histogram Weight

0 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 Particle Size (mm)

Coarse Lunar Average Best Sands Target Mixture

Figure 3.6 Histogram representation of particle size distribution.

3.2 INITIAL CHARACTERIZATION OF GRC-1

After the proper mixture of Best Sands for the creation of GRC-1 was obtained, the next step was to measure the index and mechanical properties of the simulant and compare them with that of the lunar regolith. A small initial sample of GRC-1 was created in order to first verify that the grain size distribution matched that of the target mixture.

Once verified, larger samples could be created for laboratory experiments to measure the index and mechanical properties. This section discusses the initial characterization of

GRC-1 as provided by particle size distribution, specific gravity, bulk density, porosity and void ratio, relative density, compressibility, and angle of inclination.

197

3.2.1 Particle Size Distribution

A 4.5 kg (10 lb) sample of GRC-1 was initially mixed for verification of particle size distribution. Based on the recipe for GRC-1 provided in the preceding section, a total of

1451.5 g (3.2 lb) of BS1635, 1088.6 g (2.4 lb) of BS565, 362.9 g (0.8 lb) of BS530, and

1632.9 g (3.6 lb) of BS110 were needed for the mixture. The sample was hand mixed and tested for particle size distribution via sieve testing following ASTM Standard D422.

Hydrometer analysis was not needed due to the fact that the finer fraction of the soil was omitted. The sieve test was performed in the soils laboratory at the NASA Glenn

Research Center using a Humboldt H4325 sieve shaker which applies a tapping action at

140 beats per minute to separate the soil particles (as shown in Figure 3.7). Table 3.3 presents the sieve numbers and corresponding particle diameters which were used for testing.

Table 3.3 Sieve sizes used for particle size distribution analysis. Corresponding Sieve Number Grain Size (mm) 4 4.75 10 2 20 0.85 40 0.425 60 0.25 70 0.212 80 0.18 100 0.15 120 0.125 140 0.106 170 0.09 200 0.075

198

Figure 3.7 Humboldt sieve shaker for particle size distribution analysis.

The soil separation test procedure using the standard sieves as listed in Table 3.3 is as follows:

1. Properly clean sieves before conducting a new test. This involves emptying the

sieves of any residual soil from past experiments via tapping the sides of the

sieves to loosen soil particles and using a wire brush to clean the openings of the

sieve mesh.

2. Record the mass of each empty sieve, including the bottom pan, to the most

accurate value possible (in this case 0.001 g).

3. Stack sieves on the sieve shaker in proper order (pan on bottom, then stack by

decreasing sieve numbers) and pour a representative amount of GRC-1 into the

top sieve (approximately 1000 g is sufficient). Record the mass of this initial soil

sample.

199

4. Place lid on top sieve and secure crossbar. Tap sides of sieve stack to help loosen

up any clumps and to even out the soil.

5. Run sieve shaker for approximately 5 to 10 minutes. Typically, the larger the

sample the longer the shake time.

6. Remove the stack of sieves from the shaker, carefully separate the sieves and put

each one on a paper towel. From the top down weigh each sieve with the soil

retained on it (sieve plus retained soil). If the sieving has not been done well

some particles may drop out of the mesh onto the paper towel during handling.

Place this soil into the next lower sieve before it is weighed.

7. Obtain the mass retained on each sieve by subtracting the sieve mass from the

sieve mass plus retained soil mass. Record these values and sum them including

the weight of the pan. Ensure that this mass is not more than 2-percent by weight

of the initial weight of soil that was placed in the top sieve. If it is greater than 2-

percent start over at Step 1.

8. Compute the percent retained on each sieve by dividing the weight retained on

each sieve by the original sample mass.

9. Compute the percent passing or percent finer by beginning with 100-percent and

subtracting the percent retained on each sieve in a cumulative fashion.

The results of the initial 4.5 kg mixture of GRC-1 are displayed as a cumulative distribution plot in Figure 3.8 comparing the particle size distribution of GRC-1 with that of the coarse lunar regolith average and the Best Sands ideal simulant mixture. As can be

200 seen, the initial mixture agrees very well (within 5-percent) with the coarse lunar average particle size distribution, even better than the targeted ideal mixture of Best Sands.

100

40 Percent Finer by Weight Finer Percent 30

0 10 1 0.1 0.01 Particle Size (mm)

4.5 kg GRC-1 Mixture Coarse Lunar Average Best Sands Ideal Mixture

Figure 3.8 Particle size distribution of initial GRC-1 mixture.

In order to ensure repeatability of the results as well as check the homogeneity of the

GRC-1 simulant, a larger quantity totaling 45.4 kg (100 lbs) was created. Based on the recipe for GRC-1 provided in the preceding section, a total of 14.5 kg (32 lb) of BS1635,

10.9 kg (24 lb) of BS565, 3.6 kg (8 lb) of BS530, and 16.3 kg (36 lb) of BS110 was needed for the mixture. The sample was mixed for 10 minutes in a Humboldt Electric

Concrete Mixer and then tested for particle size distribution via sieve testing following

ASTM Standard D422 and the procedure previously outlined. Figure 3.9 displays the particle size distribution of this new mixture compared with the initial mixture of GRC-1

201 as well as the coarse lunar regolith average particle size distribution. A nearly exact replication of the particle size distribution of GRC-1 has been attained, thus, ensuring the reliability of the mixture process. For comparison, a histogram of the coarse lunar regolith average and the mixtures of GRC-1 is provided in Figure 3.10. It can be seen from Figure 3.10 that the coarse lunar soil average is primarily composed of larger grains and is more heavily weighted in this size region than the GRC-1 simulant. This suggests that the addition of the finer fraction of soil particles to GRC-1 in future investigations may not be as imperative or as “large scale” as initially assumed.

100

30 Percent Finer by Weight

0 10 1 0.1 0.01 Particle Size (mm)

45.4 kg Mixture 4.5 kg Mixture Coarse Lunar Average

Figure 3.9 Particle size distribution of 4.5 kg and 45.4 kg GRC-1 samples compared with coarse lunar regolith average.

202

10 Histogram of Percent Finer by Weight 5

0 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 Particle Size (mm)

Coarse Lunar Average 4.5 kg Mixture 45.4 kg Mixture

Figure 3.10 Histogram representation of particle size distribution.

In order to classify GRC-1 using the Unified Soil Classification System it was necessary to determine the grain sizes D10, D30, and D60 where D denotes the size or apparent diameter of the soil particles and the numeric subscripts refer to the percentage that is smaller. For example, D10 is approximately equal to 0.094 mm for GRC-1 in Figure 3.9.

This means that 10-percent of the sample grains are smaller than 0.094 mm. Continuing in this fashion for GRC-1, D30 for GRC-1 is approximately equal to 0.16 mm and D60 is approximately equal to 0.39 mm. These values were used to determine the coefficient of uniformity CU and the coefficient of concavity or curvature CC for GRC-1. The coefficient of uniformity is an indication of the range of particle sizes and is given by the following equation,

203

D60 CU = (37) D10

Typically, a large value of CU is indicative that the D10 and D60 grain sizes differ considerably. The coefficient of concavity is a measure of the shape of the curve between the D60 and D10 grain sizes. It is defined by the following equation:

2 D30 CC = (38) D10 D60

where a CC value much different from 1.0 suggests that there are particle sizes missing between the D60 and D10 grain sizes. The values obtained for the coefficient of uniformity and coefficient of curvature of GRC-1 was approximately 4.15 and 0.698, respectively. Using the USCS this classifies GRC-1 as a poorly graded sand, SP, with little to no fines. A copy of the USCS can be found in Appendix B, Table B1.

In addition to the 45.5 kg quantity of GRC-1, which was used for the initial investigation of the index properties of the material; an even larger quantity of GRC-1 was created for large scale laboratory tests to obtain the strength properties of the material. A total of

317.5 kg (700 lbs) of GRC-1 was created using a total of 101.6 kg (224 lb) of BS1635,

76.2 kg (168 lb) of BS565, 25.4 kg (56 lb) of BS530, and 114.3 kg (252 lb) of BS110.

The particle size distribution was verified and is shown in Figure 3.11. As can be seen, the particle size distribution of this sample does not fit that of the coarse lunar regolith average as well as the last two GRC-1 samples. However, the particle size distribution

204 for the 317.5 kg GRC-1 sample does fall between the upper and lower bounds for the coarse lunar regolith and is acceptable for use in initial strength testing for vehicle mobility studies.

100

30 Percent Finer by Weight Finer Percent

0 10 1 0.1 0.01 Particle Size (mm) Coarse Lunar Average 317.5 kg Mixture Coarse Lunar Upper Bound Coarse Lunar Lower Bound

Figure 3.11 Particle size distribution of 317. 5 kg GRC-1 sample.

3.2.2 Specific Gravity

The specific gravity of a soil is defined as the ratio of the mass density of solid particles to the mass density of pure water at 4ºC. In this study, three samples of GRC-1 were tested in the laboratory at CWRU following ASTM standard D854. The general procedure for testing is as follows:

205

1. Fill a 500 mL volumetric flask with distilled-deaerated water up to the volume

mark (the bottom of the meniscus should be at the calibrated mark). Dry the

neck of the flask above the calibrated mark. Record the mass of the flask and

water to obtain Mw.

2. Obtain a representative sample of oven dried GRC-1 (generally between 100

and 120 g is acceptable). Record the mass of the soil as Ms. Put the sample

into a 500 mL volumetric flask ensuring that no soil is lost. Add deaerated

distilled water until the flask is approximately two-thirds full.

3. Attach the flask to a high vacuum for approximately 10 minutes or until air

bubbles are no longer seen (refer to Figure 3.12). This can take up to several

hours. If the water level drops more than 3 mm when the stopper is pulled to

break the vacuum, deaeration is NOT complete and must be continued. During

vacuum it is important to gently agitate the mixture by carefully shaking and

turning the flask.

4. When the deaerating process is complete, add temperature stabilized deaerated

water to the flask until the bottom of the meniscus is exactly at the volume

mark. Be careful not to reintroduce air into the flask when this water is added.

Carefully dry the neck of the flask above the volume mark.

5. Weigh the flask plus its contents to obtain Mbws. Insert a thermometer and take

the temperature reading to the nearest 1ºC.

206

Figure 3.12 Specific gravity test at CWRU.

The specific gravity, Gs, of the GRC-1 is calculated using the following equation,

αM s Gs = (39) M w + M s − M bws

where α is a temperature correction coefficient to account for temperature effects on the density of water. In this test, the volumetric flask is calibrated to hold a known volume of distilled water at 20ºC. At water temperatures above this value, the volume will be slightly more, while at temperatures below 20ºC the volume will be slightly less. Thus the temperature correction coefficient can be computed as,

ρ α = τ (40) ρ 20° C

207 which is the ratio of the density of water at the test temperature T to the temperature of water at 20ºC formulated so that the value of specific gravity obtained at the test temperature T is appropriately reduced (assuming T is greater than 20ºC). Typical values of the temperature correction factor are listed in Table 3.4 below as listed in Bowles

(1992). The correction factor for values in-between the temperature values listed below can accurately be interpolated as well.

Table 3.4 Typical values of the temperature correction factor (Bowles 1992). T (ºC) α ρw (g/cc) 16 1.0007 0.99897 18 1.0004 0.99862 20 1.0000 0.99823 22 0.9996 0.99780 24 0.9991 0.99732 26 0.9986 0.99681

The results of the three specific gravity tests conducted on GRC-1 are summarized in

Table 3.5 below. As shown, the results of the three tests show very little difference

(within 0.3-percent of each other) in specific gravity which implies good repeatability.

Thus, the average specific gravity of GRC-1 is approximately 2.583 with a standard deviation of ±0.004.

Table 3.5 Results of specific gravity tests on GRC-1. Test Number Ms (g) Mw + Ms + Mbws (g) T (ºC) α Gs 1 100.03 38.69 25 1.00062 2.587 2 101.76 39.43 25 1.00062 2.582 3 100.03 38.81 25 1.00062 2.579 Average ------2.583

208

3.2.3 Maximum and Minimum Bulk Density with Respect to Relative Density

The state of density of a cohesionless soil, such as GRC-1, is typically measured as a relative term with regards to the maximum and minimum densities possible. Therefore it is important to determine the maximum and minimum densities of GRC-1. From the measured in-situ density of the soil, the corresponding relative density can be calculated as previously stated as:

ρ max ρ − ρ min DR = × ×100% (41) ρ ρ max − ρ min

where ρ max is the maximum bulk density, ρ min is the minimum bulk density, and ρ is the in-situ bulk density of the soil sample. As previously explained, the relative density of the soil generally refers to the degree of particle packing. It is one of the most important factors in determining the strength and stiffness of a soil.

A total of six tests were performed in the laboratory at CWRU in order to determine the maximum and minimum bulk density of GRC-1 (three repeat tests for maximum bulk density and three repeat tests for minimum bulk density). These tests followed ASTM standards D4253 and D4254 for maximum and minimum index density, respectively.

The general procedure used is as follows for obtaining the maximum bulk density:

1. Measure and record the inner diameter, height, and mass (not including collar) of

the standard compaction mold (as shown in Figure 3.13). Place the mold on the

vibration table and bolt in place (as shown in Figure 3.14). 209

2. Obtain a representative sample of oven dried GRC-1 (typically 2500 to 5000 g is

sufficient).

3. Using a funnel, place the soil into the mold in three layers. For each layer, place a

confining block on the surface of the soil and vibrate the soil for three minutes.

4. Carefully remove the mold and measure the mass of the soil plus the mold.

5. Calculate the maximum density of the soil sample by dividing the soil weight by

the volume it occupied in the mold.

Figure 3.13 Typical standard compaction molds.

210

Figure 3.14 Compaction mold bolted on shake table.

The general procedure used is as follows for obtaining the minimum bulk density of

GRC-1:

1. Using the same mold as for the maximum bulk density tests, pour the oven dried

GRC-1 into the mold using a funnel. Place the end of the funnel close to the base

of the mold and let the soil evenly deposit into the mold via lifting the bottom of

the funnel throughout the process so that the bottom is always just above the soil

surface. Continue this process until the mold is filled.

2. Remove the compaction mold collar and carefully level the soil surface.

3. Measure the mass of the soil plus the mass of the mold.

4. Calculate the minimum bulk density of GRC-1 by dividing the mass of the soil by

the volume the soil occupied in the compaction mold.

The results of the maximum and minimum bulk density tests on GRC-1 are summarized in Table 3.6 and Table 3.7. As shown, the results of the three tests show very little difference (within 2.7-percent and 0.6-percent of each other for maximum and minimum

211 bulk density, respectively) in bulk density which implies good repeatability. Thus, the average maximum bulk density of GRC-1 is approximately 1.89 g/cc with a standard deviation of ±0.032 g/cc and the average minimum bulk density of GRC-1 is approximately 1.60 g/cc with a standard deviation of ±0.006 g/cc.

Table 3.6 Results of maximum bulk density tests for GRC-1. Volume Maximum Dry Test Number Soil Mass (g) Occupied (cc) Density (g/cc) 1 3910 2118.4 1.85 2 3215 1686.5 1.91 3 3245 1707.5 1.90 Average -- -- 1.89

Table 3.7 Results of minimum bulk density tests for GRC-1. Volume Maximum Dry Test Number Soil Mass (g) Occupied (cc) Density (g/cc) 1 1457 913.3 1.60 2 1464 913.3 1.60 3 1453 913.3 1.59 Average -- -- 1.60

Applying equation (39), these average values for maximum and minimum bulk density correspond to relative densities of 100-percent and 0-percent, respectively. A plot of bulk density versus relative density is displayed in Figure 3.15. This plot is very useful in characterizing the density of GRC-1 during testing and will be referred back to throughout the extent of this dissertation.

212

1.9

1.87

1.84

1.81

1.78 Bulk Density = 0.0029(R d ) + 1.6 1.75

1.72

Bulk Density (g/cc) 1.69

1.66

1.63

1.6 0 20406080100 Relative Density (%)

Very Medium Loose Dense Very Loose Dense Dense

Figure 3.15 Plot of bulk density versus relative density for GRC-1.

3.2.4 Porosity and Void Ratio

Using the average specific gravity of the GRC-1 in combination with the average maximum and minimum bulk density of the soil, other engineering properties such as porosity and void ratio of the GRC-1 can be estimated. The bulk density, specific gravity, and porosity of a soil are related as:

ρ n = 1− (42) Gρ w

213 where ρ is the bulk density of the soil, G is the specific gravity of the soil, ρ w is the density of water (1 g/cc), and n is the porosity of the soil. This equation is representative of the ratio of the volume of the voids to the total volume of the soil sample. The void ratio of a soil, in general, is defined as a ratio of the volume of the voids to the volume of the soil solids. Mathematically, it is related to the soil porosity by the following equation,

n e = (43) 1− n

Using equations (42) and (43) the porosity4 and void ratio of GRC-1 has been determined and is related to bulk density and relative density as shown in Table 3.8. It is important to note that the porosity and void ratio as listed in Table 3.8 actually correspond to minimum values for maximum densities and maximum values for minimum densities. In other words a maximum bulk density means that the soil sample will have as few voids as possible whereas a minimum bulk density means that the soil sample will have the largest amount of voids possible. Therefore, the maximum porosity of GRC-1 is 0.380 while the minimum porosity is 0.263 and the maximum void ratio of GRC-1 is 0.613 wile the minimum void ratio is 0.364.

Table 3.8 Porosity and void ratio of GRC-1.

ρ (g/cc) RD (%) n e Maximum 1.89 100 0.267 0.364 Minimum 1.60 0 0.380 0.613

4 Porosity was calculated using the average specific gravity of 2.58 for GRC-1. 214

3.2.5 Compressibility

For the design of vehicles it is necessary to know the load-settlement relationship for

GRC-1. The soil parameters that are used to describe this relationship can be determined from a consolidation tests conducted in the laboratory following the standard procedures described in ASTM D2435. However since the conditions on the Moon are not likely to include water, GRC-1 can be tested without saturation of the sample. This means that consolidation of the specimen will occur almost instantaneously as expected in dry granular soils. In either case, during a consolidation test, a soil is subjected to a series of one-dimensional loads with a gradual increase in intensity. The corresponding deformation of the material is measured. The results are then plotted as void ratio versus effective stress on a semi-logarithmic scale. From the linear portion of the plotted relationship the compression index CC is determined as:

(e1 − e2 ) CC = (44) ⎛ p2 ⎞ log⎜ ⎟ ⎝ p1 ⎠

where e1 and e2 are the void ratios of the soil sample corresponding to the effective vertical stresses p1 and p2, respectively. After completion of this process, the sample is unloaded by gradually reducing the vertical load in steps, similarly to how it was applied.

The resulting void ratio at these steps is measured and recorded on the same plot. This portion of the curve is referred to as the unloading line. From the unloading line, the

215 swelling index of the soil can be determined similarly to the previous equation, equation

(44), as:

(e1 − e2 ) CS = (45) ⎛ p2 ⎞ log⎜ ⎟ ⎝ p1 ⎠

The following general procedure was used for consolidation tests on GRC-1.

1. Calibrate the equipment to account for compression of the load block, porous

stones, and filter paper under load increments which would ultimately produce

larger dial readings than those solely from the soil compression. Do this by

placing the loading block onto the two porous stones with two pieces of filter

paper between. Adjust the dial gauge and cross-arm assembly and apply the load

sequence to determine the equipment compression for each load increment.

Record these values for later use as ΔH e .

2. Carefully place the soil sample in the consolidometer with one of the porous

stones on each face, making sure that the stones penetrate into the sample ring.

Place the consolidometer into the loading device and attach the dial gauge (refer

to Figure 3.16). Measure and record the mass and height of the soil sample, Ms

and Hi, respectively.

216

Figure 3.16 Typical consolidation test set up.

3. Apply a seating load of approximately 5 kPa and ensure that the porous stones do

not hang on the sample ring. After 5 minutes of this load application, zero the

deformation dial gauge (leaving the seating load on the soil).

4. Apply the first load increment, which should be a sufficient additional load to

develop the first desired load increment. Typically, the load should be applied in

a geometric progression with a load ratio of Δp / p equal to one. This is so that

the soil does not build up internal resistance to the loads. Simultaneously take

deformation readings at pre-determined elapsed times. Typically 0.1, 0.2, 0.5,

1.0, 2.0, 4.0, 8.0, 15.0, and 30.0 minutes; and 1, 2, 4, 8, and 24 hours for each load

are satisfactory.

217

5. When there is little to no change in deformation between two successive readings

of the dial gauge, increase the load to the succeeding value and repeat the elapsed-

time interval readings as in the previous step.

6. Continue this process throughout the desired load range. For each load increment,

plot the dial reading versus the time data on a semi-logarithmic plot. Plot the dial

reading on the arithmetic scale and the corresponding elapsed time on a

logarithmic scale (as shown in Figure 3.17).

Dial Reading 72

80 0.1 1 10 100 Log Time, min Figure 3.17 Typical dial reading versus time plot.

7. Convert this plot to a time-consolidation curve using the theory of consolidation.

a. Determine the end of primary consolidation (D100) and the time at which it

occurs (t100) by fitting a tangent line to the steepest part of the curve. Do

the same at the end portion of the curve. At the intersection of the two

tangent lines draw a horizontal line to the ordinate and read D100. Project

218

this horizontal line to the actual curve and then down to the logarithmic

axis and read t100.

b. To obtain D0, or the dial reading at the beginning of the test, visually

project the initial curve branch to the left towards log 0. If this gives an

initial dial reading close to the actual initial dial reading then this value

can be used as D0.

c. A D50 reading or a dial reading at 50-percent consolidation is also needed

in addition to the corresponding time at which it occurs, t50. D50 is

obtained via the following equation,

D + D D = 0 100 (46) 50 2

Project D50 to the curve and draw a vertical line to the logarithmic axis and

read t50.

8. After the specimen has consolidated under the maximum load, remove the load in

decrements, taking ¾ of the load off successively for each of the first two

decrements and as desired thereafter. Take readings of the dial indicator as each

decrement is removed to determine the rebound of the specimen.

9. Record and plot the dial readings versus time. Again, load should not be removed

until the dial reading versus logarithm of time curve indicates completion of

rebound. When the dial indicator readings indicate no further significant rebound

after the final load is removed, remove the dial indicator and disassemble the

apparatus.

219

10. Compute the height of the soil solids, void ratio before and after the test, and

density before the test.

11. Obtain the final dial reading for each load increment that corresponds to the

selected time interval and record these values. Compute the void ratios of the

specimen corresponding to different load increments. The void ratio is

numerically equal to the height of the voids divided by the height of the solids and

can be calculated via the following equation,

(D100 + ΔH e ) e = e0 − (47) H S

where e0 is the initial void ratio, D100 is the dial reading at the end of 100-percent

consolidation, ΔH e is the equipment calibration correction factor, and HS is the

height of the soil solids.

12. Plot the void ratios obtained in the previous step versus the corresponding

pressure on a semilogarithmic plot where the void ratio is on the arithmetic scale

and the pressure in on the logarithmic scale. Determine the compression index

using equation (44). Determine the swelling index using equation (45).

Two one-dimensional consolidation tests were performed on GRC-1 in the laboratory at

Case Western Reserve University to determine the compression and swelling indices as well as to check the repeatability of the test itself. The results are shown in Figure 3.18 in the form of e versus log p curves. As shown, the test results were very repeatable. From this data it was found that the compression index of GRC-1 is approximately 0.03 and 220 swelling index is approximately 0.008. Both values are pretty low, indicating the soil is less compressible with lower swelling than most conventional soils. A complete data set can be found in Appendix B as Table B2.

0.6

0.55

0.5

0.45 Void Ratio, e

0.4

0.35

0.3 1 10 100 1000 log p, kPa

Figure 3.18 Results of one-dimensional consolidation testing on GRC-1.

3.2.6 Angle of Inclination

Particle size distribution and associated grain shape are the most influential factors in defining the angle of inclination or angle of repose of a soil. These properties affect the ability of particles to interlock and flow. The angle of repose of a soil is defined as the maximum angle at which the unconsolidated material can remain stable without sliding

221 or crumbling. It is an engineering property of granular materials determined by friction, cohesion, and the shapes of the particles.

To observe and measure the angle of repose consistently, a Hele-Shaw cell can be used.

Typically a Hele-Shaw cell is a box with two parallel sheets of rigid transparent material spaced a few millimeters apart. A Hele-Shaw cell can easily be constructed out of a CD case as shown in Figure 3.19. The general procedure for determining the angle of repose of GRC-1 is as follows:

1. Place the Hele-Shaw cell flat on a level surface.

2. Obtain a representative amount of GRC-1 (approximately 50 grams is sufficient).

3. Slowly pour the soil into the funnel at the top of the Hele-Shaw cell. Keep the

Hele-Shaw cell upright and motionless during this process. Observe how the slope

of the pile of granular material is established. Stop pouring when the bottom of

the slope approaches the far side of the cell.

4. Measure the angle of repose of the soil from the horizontal with a protractor.

Ensure that that bottom of the soil slope goes through the center point of the

protractor when measuring the angle.

222

Figure 3.19 Homemade Hele-Shaw cell.

A total of five repeat Hele-Shaw cell tests were performed in the laboratory at Case

Western Reserve University to determine the average angle of repose of GRC-1. The results are shown in Table 3.9 below. As can be seen, the average angle of repose for

GRC-1 is approximately 35.3-degrees with a standard deviation of ±0.711-degrees.

Table 3.9 Angle of repose of GRC-1. Tests Number Angle of Repose (º) 1 34.1 2 35.4 3 35.5 4 36.0 5 35.5 Average 35.3

223

3.3 COMPARISON TO LUNAR SOIL AND LUNAR SOIL SIMULANTS

Several initial laboratory tests were performed, as described in the preceding sections of this dissertation, to determine the index properties of the proposed lunar soil simulant

GRC-1. These measurements form the basis to judge whether this new simulant is effective in simulating the properties of lunar soil which are essential to the study of vehicle mobility. Based on the results of the study, a summary comparing the properties of GRC-1 to the lunar soil and past lunar soil simulants is presented in Table 3.10.

Values for lunar soil properties were determined from the Lunar Sourcebook (Heiken et al. 1991) “best estimates” as provided in Chapter 1 of this dissertation. The properties for the lunar soil simulants were determined as presented in Chapter 2 of this dissertation.

It is important to note that the lunar soil properties as reported in Table 3.10 represent the properties corresponding to the entire composition of the lunar soil, while GRC-1 was designed to represent to coarser grained fraction of the lunar soil. Thus it is expected that

GRC-1 will have geotechnical properties corresponding to a coarser particle size distribution and therefore be weaker than the actual lunar soil.

224

Table 3.10 Comparison of GRC-1 with lunar soil and lunar soil simulants. Lunar Soil Properties GRC-1 MLS-1 JSC-1 JSC-1A Soil Median Particle Size 0.04 - 0.098 – 0.27 0.095 0.085 (mm) 0.13 0.117

D10 (mm) 0.094 0.013 0.019 0.019 0.017

D30 (mm) 0.160 0.034 0.049 0.057 0.042

D60 (mm) 0.390 0.140 0.150 0.150 0.110 Coefficient of Uniformity, 4.150 10.769 7.895 7.895 6.47 CU Coefficient of Curvature, 0.698 0.635 0.842 1.140 0.94 CC

ρmax (g/cc) 1.89 1.81 2.20 1.91 2.03

ρmin (g/cc) 1.60 0.92 1.50 1.43 1.57

Specific Gravity, Gs 2.58 2.3 - >3.2 3.2 2.9 2.875

emax 0.613 32.333 1.130 1.028 0.826

emin 0.364 0.712 0.454 0.517 0.410

nmax 0.380 0.970 0.531 0.507 0.4539

nmin 0.267 0.416 0.313 0.341 0.294 SW-SM USCS Classification SP SP - SM SW - SM SP - SM to ML

Compression Index, CC 0.03 0.3 – 0.05 - - - - 0.068

Swelling Index, Cs 0.008 ------0.001 Angle of Repose (º) 35.3 405 ------

As can be seen from Table 3.10, the particle sizes of GRC-1 are typically greater than that of the lunar soil and lunar soil simulants as expected. This is verified in Figure 3.19 which compares the particle size distribution of the actual lunar soil (including the finer fraction) with GRC-1. Sixty percent of the GRC-1 soil particles have a particle size less than 0.39 mm compared to 60 percent of the lunar soil particles having a particle size less than 0.14 mm. It should be noted that the values of D10, D30, and D60 displayed for the

5 Angle of repose is based on the analysis of data collected from the Lunokhod missions for lunar soil near its landing site. The exact angle is dependent on parameters such as location on the surface, amount of compaction, and presence of stones (R. Zeller personal communication, August 2006). 225 lunar soil were taken from the average particle size distribution as shown in Figure 3.2 and Figure 3.20. Looking at the coarse grained average particle size distribution of the lunar soil as shown in Figure 3.5 it is clear that 60-percent of the particles have a particle size of approximately 0.41 mm or less. This is much closer to that of GRC-1 as expected.

Based on the coefficient of curvature and the coefficient of uniformity, GRC-1 is classified corresponding to Unified Soil Classification System as poorly graded sand. In comparison the lunar soil is a well graded silty sand to silt material. This discrepancy makes sense due to the fact that the actual lunar soil contains a larger amount of fines than GRC-1. In addition, GRC-1 is poorly graded as it focuses on replicating the coarse grained fraction of the lunar soil, whereas the actual lunar soil has a more even distribution of particle sizes.

100

Percent Finer 40

0 10 1 0.1 0.01 0.001 Particle Size, mm

Lunar Soil Upper Bound Lunar Soil Lower Bound Average Lunar Soil GRC-1

Figure 3.20 GRC-1 particle size distribution versus that of actual lunar soil.

226

The maximum and minimum bulk density of the lunar soil was determined by combining

Tables 1.5 and 1.6, which consist of the best estimates for the bulk density and relative density of the lunar soil, respectively; and plotting them as bulk density versus relative density as shown in Figure 3.21. A least squares approach was used to curve-fit the four data points provided in the tables (Tables 1.5 and 1.6). Projecting this trendline through

0-percent and 100-percent relative density makes it possible to interpolate the corresponding minimum and maximum bulk density of the lunar soil, respectively, keeping in mind that these values are based on approximated average densities.

Compared with the relationship of bulk density to relative density for GRC-1, it can be seen that at the same relative density, the bulk density of the lunar soil is much less than that of GRC-1. At 0-percent relative density, the bulk density of the lunar soil is approximately 1.5 g/cc less than that of GRC-1. This difference in bulk density tends to decrease as the relative density increases, until 100-percent relative density where the bulk density of the lunar soil is approximately 0.08 g/cc less than that of GRC-1. One would expect this trend to be opposite, i.e. at the same relative density the lunar soil might be expected to have a higher bulk density due to the increased number of fines in the material. Typically, this should result in more particles per unit volume and therefore more mass per unit volume. However, it is possible that at some point, the size of the soil particles is more influential on the mass per unit volume than the number of particles themselves. If the mass of the larger soil particles in GRC-1 is greater than the mass of all the finer particles in the lunar soil, even though there are more particles per unit volume, the GRC-1 will have a greater density due to the larger mass. This would account for the higher bulk densities of GRC-1 in Figure 3.21.

227

Bulk Density = 0.0029(R d ) + 1.6 1.8

1.6

1.4

Bulk Density = 0.0089(R d ) + 0.9222 1.2 Bulk DensityBulk (g/cc) 1 GRC-1 Lunar Soil 0.8 Linear (GRC-1) Linear (Lunar Soil) 0.6 0 20406080100 Relative Density (%)

Very Medium Very Loose Dense Loose Dense Dense

Figure 3.21 Bulk density versus relative density for GRC-1 and the lunar soil.

The specific gravity of GRC-1 was found to be approximately 2.58 which is toward the low end of the specific gravity range for the lunar soil and much lower than the specific gravity values for the lunar soil simulants. However, it is still considered within the range of the lunar soil as the minimum value of lunar specific gravity has been approximated at 2.3. The maximum void ratio and porosity of GRC-1 are surprisingly low compared to that of the lunar soil and lunar soil simulants. The opposite holds true for the minimum void ratio. In both cases though, one would expect that a coarser grained granular soil would have a larger amount of voids than a finer grained soil.

However, the packing characteristics of soils are highly dependent of the shape of the soil particles. It is well known that the shape of the lunar soil particles, especially the agglutinate particles, is somewhat elongated and angular in nature. Since GRC-1 is a

228 manufactured material the particles are likely to be much more uniform and round in shape. This would allow for the GRC-1 to pack more tightly in spite of the particle size, which would account for the lower void ratio and porosity as compared to that of the lunar soil.

In conclusion, the soil properties of GRC-1 as listed in Table 3.10 show that it is a much coarser grained soil than the lunar soil and lunar soil simulants as expected. This is beneficial to the study of vehicle mobility, because coarser grained soils are generally weaker in nature. Since the properties of the lunar soil are not well known or well understood it is best to represent to worst case scenario when performing vehicle mobility tests. This will ensure that if the vehicle is able to perform well in the worst case, i.e. weakest soil condition, then it is likely to perform even better if the lunar soil is stronger than that of the worst case. Further information is needed on the strength properties of

GRC-1 in order to determine if it can sufficiently emulate the strength conditions of the soil on the Moon for successful vehicle mobility studies. The focus of the subsequent chapters will therefore be on the strength properties of the lunar soil as well as the stress- strain relationships pertinent to vehicle mobility.

CHAPTER FOUR

229

TRIAXIAL TESTING FOR STRENGTH PROPERTIES OF GRC-1

4.1 TRIAXIAL APPARATUS AT NASA GLENN

The most critical soil properties for the mobility of a wheeled vehicle on the lunar surface are the friction angle and cohesion. Together they can be combined in the classic Mohr-

Coulomb equation to represent the ultimate shear strength of the soil, which directly affects the bearing capacity, slope stability, and potential to thrust against the lunar terrain. The equation for shear strength as previously defined is as follows,

τ = c + σ tanφ (48)

where τ is the ultimate shear strength of the soil, c is the cohesion, σ is the normal stress applied to the soil, and φ is the internal angle of friction (Das 1985). Values of cohesion and internal angle of friction for GRC-1 were determined via the most commonly used laboratory test to determine the shear strength and stress-strain relationship of soil: the triaxial test. More specifically, the unconsolidated undrained (UU) triaxial test was used to determine the aforementioned soil parameters. This is the simplest of all triaxial tests as it does not require saturation of the soil sample (compared to the consolidated drained tests and the consolidated undrained tests).

A brand new triaxial testing system was purchased by the NASA Glenn Research Center for strength testing of lunar soil simulants including GRC-1. This equipment was

230 purchased from ELE International6 of Loveland, Colorado. It is specifically designed to follow ASTM D2850-95 standards for the testing of unconsolidated compressive strength of cohesive soils in triaxial compression. The Tri-Flex 2/DataSystem triaxial test set (as shown in Figure 4.1) includes the following equipment:

• A 50 kN capacity Digital Tritest 50 Load Frame with a microprocessor-

controlled stepper motor drive system with speeds ranging from 9.99 mm/min

to 0.00001 mm/min.

• A Triaxial Cell complete with accessories for drained and undrained testing

of 70 mm (2.8 in) diameter specimens to confining pressures of up to 1000

kPa (145 psi). Accessories include the following (as shown in Figure 4.2):

o 70 mm base pedestal and specimen cap

o 70 mm drainage lines

o 70 mm porous stones and filter paper disks

o 70 mm rubber membranes and sealing rings

o 70 mm two-part split mold and suction membrane device

• ADU Data Acquisition Unit with eight channels for automated data

acquisition and recording of test parameters.

• Electronic Measurement Transducers for load, displacement, pressure, and

volume change. The following transducers are included:

o Axial strain transducer

o 1000 kPa pressure transducers

o Volume change transducer

6 http://www.eleusa.com/ 231

o 5 kN submersible load transducer

• DataSystem Triaxial Software (as shown in Figure 4.3) for recording,

analysis and report generation in English or Metric units. Software programs

include:

o Quick Undrained triaxial software

o CU\CD effective stress triaxial software

• Tri-Flex 2 Master Control Panel and De-Aired Water Tank System for

precise applications of confining, back, and saturation pressures.

Figure 4.1 Tri-Flex 2/Data System triaxial test set from ELE International.

232

Figure 4.2 Triaxial cell accessories (base plate, cap, porous stones, sealing rings, drainage lines) from ELE International.

Figure 4.3 DS7 DataSystem triaxial software form ELE International.

233

4.2 EXPERIMENTAL PROCEDURE

The procedure outlined below was generally followed for determining the shear strength of GRC-1 via UU triaxial tests.

1. In a glass beaker weigh a representative amount of GRC-1 slightly larger than the

amount to be used for the test specimen (typically 1000 g is acceptable).

2. Place the rubber membrane over the bottom platen or base plate and seal with two

o-rings. Insert a porous stone and filter paper into the membrane so they enclose

the bottom of the soil sample. Assemble and mount the split mold. Fold back the

membrane on the top rim of the mold as shown in Figure 4.4(a).

3. Evacuate the air between the rubber membrane and the membrane stretcher using

a vacuum pump. The membrane should be tight to the inside wall of the mold as

shown in Figure 4.4(b).

4. Pour the sand inside the membrane by means of a funnel. The desired density

may be achieved by tapping, tamping, or vibrating the specimen. It is important

to note that a specimen which is properly formed will deform in a symmetric

fashion upon loading.

5. Weigh the unused GRC-1 to calculate the dry sample weight.

6. Once the membrane is filled to the desired height, place a filter disk and porous

stone on the top of the specimen (ensuring not to compress the specimen). Next,

plate the specimen cap on top of the porous stone and roll the membrane over the

specimen cap, sealing it with o-rings.

234

7. Simultaneously apply vacuum to the inside of the soil specimen while removing

vacuum from the outside of the soil specimen. Keep the intensity of the vacuum

relatively small to avoid consolidation of the specimen (approximately 200 to 250

mm of mercury). Remove the split mold from the sample. It should now be free-

standing as shown in Figure 4.5.

8. Determine the dimensions of the sample using calipers. Typically three height

measurements should be made at intervals approximately 120-degrees apart. The

average value should be recorded. In addition, three diameter readings at

intervals approximately 120-degrees apart at the top, near the middle, and at the

base of the sample should be taken. Make sure to correct the diameters for the

membrane thickness (typically 0.35 mm thick). The average diameter is typically

determined using the following equation,

d + 2d + d d = top middle base (49) avg 4

where, dtop, dmiddle, and dbase correspond to the sample diameters at the top, middle,

and base of the soil sample, respectively. This equation allows more weight to be

placed on the middle diameter of the sample.

9. Calculate the initial density of the soil sample.

10. Assemble the triaxial cell ensuring an airtight seal is created and place the cell in

the loading device or compression machine. Adjust the machine (raise or lower

the cell) so that the loading piston just barely comes in contact with the specimen

cap. Ensure that the piston is directly in the center of the sample.

235

11. Simultaneously increase the confining pressure in the triaxial cell to the desired

value while removing the vacuum from inside the sample. Typically water is

used as the confining medium, however, in this case, compressed air is used to

better simulate the environment that exists on the Moon, which does not include

any free water source. The only advantages to using water as a confining medium

is that it typically provides a more uniform pressure on the sample (Bowles 1992).

In addition, it is more viscous than air and is not as sensitive to membrane leaks.

The sample is now held together by the external confining pressure and no longer

by the internal vacuum.

12. Zero the load transducer and the axial displacement transducer.

13. Select a loading rate of approximately 0.5-percent of the axial strain per minute

(the appropriate loading rate is predetermined by the DS7 DataSystem triaxial

software).

14. Begin loading the sample. The applied axial load and piston displacement is

simultaneously recorded and plotted via the DS7 DataSystem triaxial software.

Be sure to monitor the cell pressure continually. If the cell pressure varies by

more than 5 kPa there is a leak in the cell and the test must be redone. This slight

change in cell pressure is enough to significantly alter the deviator stress which

defines the failure of the sample.

15. After having completed the axial loading (until visible sample failure: typically

the sample will bulge outward at the center as shown in Figure 4.6; until 20 to 25-

percent axial strain; or until the load peaks and then fall or holds constant for

236

three or four successive readings), remove the confining pressure, reverse the

compression machine, and disassemble the triaxial cell and soil sample.

16. Repeat steps 1 through 15 for a total of three different confining pressures (at the

same sample density7 within 0.02 to 0.05 g/cc). Typically confining pressures of

50, 100, and 200 kPa are used.

17. For each test a plot of deviator stress versus unit strain is automatically compiled

by the DS7 DataSystem triaxial software. The peak stress or ultimate stress is

manually selected and entered into the program.

18. Using the maximum deviator stress the software automatically computes the

major principal stress for each test as:

σ 1 = σ 3 + Δσ 1 (50)

where σ 1 is the major principal stress, σ 3 is the corresponding cell pressure, and

Δσ 1 is the maximum deviator stress.

19. Using σ 1 and σ 3 , the DS7 DataSystem triaxial software automatically plots the three

resulting Mohr’s circles. The program manually allows the user to create a best-fit

tangent line to all three circles. Once the line has been created, the program measures

the ordinate intercept for the cohesion c and the slope angle for the angle of internal

friction φ . If the curve envelope does not fit reasonably well to all three Mohr’s

7 It is important to note that the density of the soil sample is only as accurate as the measurements of diameter and height. For a more accurate density additional values for height and diameter should be carefully measured. 237

circles either one or more of the tests may be bad and additional tests will need to be

performed.

(a) (b) Figure 4.4 (a) Split mold with rubber membrane folded over the top. (b) Rubber membrane tight against the inner wall of the split mold.

238

Figure 4.5 Freestanding triaxial soil sample with internal vacuum applied.

Figure 4.6 Typical bulge in soil after failure.

239

4.3 TEST RESULTS AND ANALYSIS

A total of 10 unconsolidated undrained triaxial test sets were performed at the NASA

Glenn Research Center. Each test set consisted of three individual triaxial tests (indexed as A, B, and C) at confining pressures of 50, 100, and 200 kPa, respectively; for a total of

30 individual triaxial tests. All three tests were prepared to approximately the same density. Ten different soil preparation methods were used to achieve an increased density for each complete triaxial test set. The sample preparation methods and corresponding densities are listed in Table 4.1. The results of the triaxial testing in terms of angle of internal friction and cohesion are summarized in Table 4.2 as determined by the DS7

DataSystem triaxial software for UU triaxial tests following ASTM D2850-95. Figure

4.7 and 4.8 correspond to typical deviator stress versus axial strain and Mohr’s circle plots as produced by DS7. Complete triaxial test result reports from DS7 are provided for each of the ten complete triaxial tests in Appendix C.

240

Table 4.1 Sample preparation method and corresponding density. Average Standard Test Density Sample Preparation Density Deviation Index (g/cc) (g/cc) (g/cc) Test 1 A 1.60 Funnel pour (bottom of funnel just touching B 1.61 1.60 ±0.010 top of soil layer as soil pours out) C 1.59 Test 2 A Funnel pour (bottom of funnel slightly 1.63 B elevated from top of soil layer as soil pours 1.59 1.62 ±0.023 C out) 1.63 Test 3 A 1.64 Funnel pour in 3 layers (tap 2 sides of split B 1.63 1.64 ±0.006 mold 10 times per layer with metal rod) C 1.64 Test 4 A 1.65 Funnel pour in 5 layers (tap 2 sides of split B 1.66 1.66 ±0.006 mold 10 times per layer with metal rod) C 1.66 Test 5 A 1.70 Funnel pour in 3 layers (tap 2 sides of split B 1.70 1.71 ±0.017 mold 20 times per layer with metal rod) C 1.73 Test 6 A 1.73 Funnel pour in 5 layers (tap 2 sides of split B 1.72 1.73 ±0.015 mold 20 times per layer with metal rod) C 1.75 Test 7 A Funnel pour in 5 layers (shake each layer 30 1.77 B seconds with shake table at medium 1.76 1.76 ±0.006 C intensity) 1.76 Test 8 A 1.79 Funnel pour in 3 layers (shake each layer 1 B 1.82 1.78 ±0.046 minute with shake table at medium intensity) C 1.73 Test 9 A Funnel pour in 3 layers (shake each layer 30 1.80 B seconds with shake table at medium 1.78 1.79 ±0.010 C intensity) 1.79 Test 10 A Funnel pour in 3 layers (shake each layer 1 1.83 B minute with shake table at medium intensity 1.80 1.82 ±0.017 C while applying 1 kg weight to top of sample) 1.83

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Table 4.2 Results of triaxial tests from DS7 (void ratio is calculated assuming Gs = 2.58). Internal Cell Compressive Axial Test Density Void Angle of Cohesion Pressure Strength Strain Index (g/cc) Ratio Friction (kPa) (kPa) (kPa) (%) (º) Test 1 A 1.60 0.61 50.7 125.8 7.26 B 1.61 0.60 100.3 244.2 8.29 29.84 8.71 C 1.59 0.62 200.1 417.7 10.44 Test 2 A 1.63 0.58 51.7 139.2 9.61 B 1.59 0.62 99.2 238.1 8.72 30.40 9.92 C 1.63 0.58 199.0 440.3 12.99 Test 3 A 1.64 0.57 49.6 102.4 5.51 B 1.63 0.58 101.0 278.4 6.92 33.28 0.00 C 1.64 0.57 200.1 556.7 7.27 Test 4 A 1.65 0.56 50.2 85.2 2.80 B 1.66 0.55 100.3 243.1 4.09 33.38 0.00 C 1.66 0.55 200.1 488.0 5.13 Test 5 A 1.70 0.52 50.2 152.7 6.51 B 1.70 0.52 100.3 257.4 6.39 33.83 7.17 C 1.73 0.49 199.6 527.1 5.39 Test 6 A 1.73 0.49 44.8 136.6 2.57 B 1.72 0.50 100.7 329.9 3.92 37.18 0.00 C 1.75 0.47 200.5 605.5 4.61 Test 7 A 1.77 0.46 50.9 172.1 2.44 B 1.76 0.47 99.8 386.6 2.72 38.43 4.85 C 1.76 0.47 200.6 658.7 4.04 Test 8 A 1.79 0.44 50.6 224.2 3.10 B 1.82 0.42 100.0 456.2 3.23 42.06 4.30 C 1.73 0.49 200.0 817.3 3.29 Test 9 A 1.80 0.43 49.3 253.2 2.70 B 1.78 0.45 100.9 460.4 3.38 42.43 9.04 C 1.79 0.44 200.1 868.3 3.18 Test 10 A 1.83 0.41 49.8 260.0 2.81 B 1.80 0.43 99.8 452.4 2.99 44.38 1.64 C 1.83 0.41 199.6 965.5 3.44

242

Shearing Stage (Stress Vs Axial Strain %)

433.4

383.4

333.4

283.4

233.4

183.4

133.4

83.4 Corrected Deviator Stress kPa

33.4 0246810121416 Axial Strain %

Figure 4.7 Typical plot of corrected deviator stress versus axial strain used to determine the ultimate strength of the soil sample.

Figure 4.8 Typical Mohr’s circle plot to determine friction angle and cohesion.

243

1000

900

800

700

600

500

400

Stressat Failure (kPa) 300

200

100

0 0 50 100 150 200 250 Confining Pressure (kPa)

Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10 Linear (Test 10) Linear (Test 9) Linear (Test 8) Linear (Test 7) Linear (Test 6) Linear (Test 3) Linear (Test 5) Linear (Test 4) Linear (Test 2) Linear (Test 1)

Figure 4.9 Stress at failure versus confining pressure.

It is clear from Figure 4.7 that GRC-1 exhibits the typical stress-strain trend for soils that are plastic in nature, such as loose non-compacted sand or clay. One can see that this relationship typically maintains a maximum stress value. Figure 4.9 above depicts the general relationship between the stress at failure and the corresponding confining pressure. In general, the stress at failure linearly increases with increasing confining pressure. In addition, this relationship appears to shift upward on the plot with increasing density. Thus, as the confining pressure and density of the sample increase, the soil can withstand higher stresses before failure. Based on this ultimate stress value and the

Mohr’s circles, the internal angle of friction of the material is more clearly summarized in

Table 4.3. It is clear that the angle of internal friction of GRC-1 generally increases with

244 increasing density. Figure 4.10 displays the internal angle of friction versus the relative density of GRC-1. Relative density is used instead of bulk density because it indicates the consistency of the soil and affords a qualitative means for comparing different soil conditions. The data points have been curve-fit using a least-squares approach. The trend is clearly linear and is accurate within ±2.5-percent error as shown. The maximum and minimum internal angle of friction of GRC-1 can therefore be interpolated as 29.31- degrees and 48.16-degrees, respectively.

Table 4.3 Summary of GRC-1 internal angle of friction from triaxial tests. Average Density (g/cc) Relative Density (%) Friction Angle (º) 1.60 0.00 29.84 1.62 6.90 30.40 1.64 13.79 33.28 1.66 20.69 33.38 1.71 37.93 33.83 1.73 44.83 37.18 1.76 55.17 38.43 1.78 62.07 42.06 1.79 65.52 42.43 1.82 75.86 44.38

245

Friction Angle = 0.1885(R d ) + 29.305

35 Internal Angle ofFriction (degrees)

25 0 102030405060708090100 Relative Density (%)

Figure 4.10 Friction angle versus relative density for GRC-1 (as shown with 2.5-percent error bars).

The cohesion values are significantly more difficult to accurately predict. As shown in

Table 4.2, the cohesion values for GRC-1 range from 0 to 9.92 kPa with no observable trend. Typically for granular cohesionless soils, such as GRC-1, the cohesion intercept should be very small (unless the soil is damp in which case surface tension becomes measured as cohesion). Bowles (1992) attributes cohesion values up to 14 kPa that are obtained from triaxial tests on dry granular soils to the rubber membrane used to surround the sample. He states that, “values of 7 to 14 kPa are generally neglected.” As this may partially account for the erroneous cohesion values, it is more likely that the current method of evaluating cohesion is not very accurate. More specifically, the triaxial tests performed herein were conducted with considerably high effective confining pressures.

However, in order to measure cohesion accurately it is necessary to use very low

246 effective confining pressures. In addition, as pointed out by Das (1985), the determination of cohesion from triaxial tests may be difficult as a straight line extrapolation of the failure envelope back to the normal stress of zero. It is more likely that the strength envelope is curved in the region of small confining pressures. However, due to the fact that there is neither an easy way to perform tensile tests on a soil nor a reliable way to conduct triaxial tests at a low effective confining pressure (Mitchell

1993); the task of accurately determining the cohesion of a soil remains a challenge.

Willman et al. (1995) also poses the question of uncertainty of cohesion associated with the actual causes of cohesion or reason for the cohesion.

Additionally, it is important to evaluate these data to determine the influence of normal

stress σ n and relative density Dr on the friction angleφ as well as to verify the results as determine by the Mohr’s circle method. These results are plotted using stress paths in a q versus p relation shown in equations (51) and (52) below and as previously described in section 1.6.2.3 of this dissertation entitled Triaxial Test.

σ −σ σ + σ q = 1 3 and p = 1 3 (51, 52) 2 2

In this plot each Mohr’s circle appears as a single point. The best-fit line through the locus of points obtained from a test series is called the Kf-line. For a given relative density,

247

σ −σ tanα = sinφ = 1 3 (53) σ 1 + σ 3

Where σ 1 is the major principal stress or the minor principal stress plus the deviator

stress, σ 3 is the minor principal stress equal to the cell pressure or confining pressure, φ is the internal angle of friction, and α is the angle of the Kf-line. This line, projected back to the p or horizontal axis cuts the q or vertical axis with an intercept a. From the plot geometry one can obtain c the cohesion as:

a c = (54) cosφ

One advantage of this procedure as pointed out by Bowles (1992) is that it poses a graphical presentation of the possible path traced by an increase in stress. In addition, it is much simpler to use than Mohr’s circles. The values of p and q as determined by equations (51) and (52) are summarized in Table 4.4 below. A typical q versus p plot is displayed in Figure 4.11 from which cohesion and angle of internal friction of GRC-1 can be determined. A complete set of q-p plots can be found in Appendix C. The data points have been curve-fit using a least squares approach. The results of this analysis in terms of internal friction angle and cohesion are listed in Table 4.5. As can be seen, overall the angle of internal friction generally increases with increasing density of the material.

However, there is a discrepancy between a relative density of 13.79-percent and 37.93- percent (corresponding to tests three, four, and five), which was not observed in the

Mohr’s circles analysis. In addition, the cohesion values now range from -10.14 kPa to

248

10.74 kPa in no logical order. It should be noted that in the DS7 DataSystems triaxial program cohesion values below zero are not permitted. Therefore, when using this program and applying a tangent line to the three Mohr’s circles, it is possible that this line is not actually the best-fit line with respect to the circles. However, it is the best-fit line assuming that the cohesion is zero. This leads to the difference in friction angle and cohesion values between the Mohr’s circle and q-p analyses as shown in Table 4.6. From

Table 4.6 it can be more clearly seen that the most likely cause of the discrepancy with increasing friction angle is the forcing of zero cohesion in tests three and four when using the Mohr’s circles method. It is possible that one or more of these tests may have had some internal source of error and ultimately should have been redone to obtain more accurate values. However, it can be seen from Figure 4.12 that this discrepancy does not significantly affect the friction angle. More specifically it can be interpolated that from the q-p method at a relative density of zero-percent the friction angle is approximately

30.30-degrees. Similarly for a relative density of 100-percent the friction angle is approximately 47.48-degrees. This is a change of less than ±0.7-degrees from the Mohr’s circles approximations for the friction angle of GRC-1. The issue of accurately determining the cohesion of GRC-1 is not clarified using the q-p procedure. This task still remains a challenge.

249

Table 4.4 Results of triaxial tests on GRC-1 using alternative analysis. Test Density Void σ σ 3 Δσ (kPa) 1 p (kPa) q (kPa) Index (g/cc) Ratio (kPa) 1 (kPa) Test 1 A 1.60 0.61 50.7 125.8 176.5 113.6 62.9 B 1.61 0.60 100.3 244.2 344.5 222.4 122.1 C 1.59 0.62 200.1 417.7 617.8 409.0 208.9 Test 2 A 1.63 0.58 51.7 139.2 190.9 121.3 69.6 B 1.59 0.62 99.2 238.1 337.3 218.3 119.1 C 1.63 0.58 199.0 440.3 639.3 419.2 220.2 Test 3 A 1.64 0.57 49.6 102.4 152.0 100.8 51.2 B 1.63 0.58 101.0 278.4 379.4 240.2 139.2 C 1.64 0.57 200.1 556.7 756.8 478.5 278.4 Test 4 A 1.65 0.56 50.2 85.2 135.4 92.8 42.6 B 1.66 0.55 100.3 243.1 343.4 221.9 121.6 C 1.66 0.55 200.1 488.0 688.1 444.1 244.0 Test 5 A 1.70 0.52 50.2 152.7 202.9 126.6 76.4 B 1.70 0.52 100.3 257.4 357.7 229.0 128.7 C 1.73 0.49 199.6 527.1 726.7 463.2 263.6 Test 6 A 1.73 0.49 44.8 136.6 181.4 113.1 68.3 B 1.72 0.50 100.7 329.9 430.6 265.7 165.0 C 1.75 0.47 200.5 605.5 806.0 503.3 302.8 Test 7 A 1.77 0.46 50.9 172.1 223.0 137.0 86.1 B 1.76 0.47 99.8 386.6 486.4 293.1 193.3 C 1.76 0.47 200.6 658.7 859.3 530.0 329.4 Test 8 A 1.79 0.44 50.6 224.2 274.8 162.7 112.1 B 1.82 0.42 100.0 456.2 556.2 328.1 228.1 C 1.73 0.49 200.0 817.3 1017.3 608.7 408.7 Test 9 A 1.80 0.43 49.3 253.2 302.5 175.9 126.6 B 1.78 0.45 100.9 460.4 561.3 331.1 230.2 C 1.79 0.44 200.1 868.3 1068.4 634.3 434.2 Test 10 A 1.83 0.41 49.8 260.0 309.8 179.8 130.0 B 1.80 0.43 99.8 452.4 552.2 326.0 226.2 C 1.83 0.41 199.6 965.5 1165.1 682.4 482.8

250

450 q = 0.491(p) + 9.3592 400

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa) Figure 4.11 Typical q versus p plot used to determine friction angle and cohesion.

Table 4.5 Cohesion and friction angle as determined using q and p. Average Density Relative Density Friction Angle (º) Cohesion (kPa) (g/cc) (%) 1.60 0.00 29.41 10.74 1.62 6.90 30.34 9.84 1.64 13.79 36.84 -9.39 1.66 20.69 34.81 -10.14 1.71 37.93 34.02 4.23 1.73 44.83 36.81 3.16 1.76 55.17 37.98 7.56 1.78 62.07 41.51 9.00 1.79 65.52 42.16 11.19 1.82 75.86 44.85 0.44

Table 4.6 Mohr's circles compared with q-p method. Mohr’s Circles q-p

251

Relative Friction Cohesion Friction Cohesion Density (%) Angle (º) (kPa) Angle (º) (kPa) 0.00 29.84 8.71 29.41 10.74 6.90 30.40 9.92 30.34 9.84 13.79 33.28 0.00 36.84 -9.39 20.69 33.38 0.00 34.81 -10.14 37.93 33.83 7.17 34.02 4.23 44.83 37.18 0.00 36.81 3.16 55.17 38.43 4.85 37.98 7.56 62.07 42.06 4.30 41.51 9.00 65.52 42.43 9.04 42.16 11.19 75.86 44.38 1.64 44.85 0.44

Friction Angle = 0.1885(R d ) + 29.305

Friction Angle = 0.1718(Rd ) + 30.296 45

Internal Angle of Friction (degrees) of Friction Internal Angle 30

25 0 102030405060708090100 Relative Density (%)

Mohr's Circles q-p method Linear (Mohr's Circles) Linear (q-p method)

Figure 4.12 Comparison between Mohr's circles and q-p friction angle values.

4.4 COMPARISON WITH LUNAR SOIL

252

The purpose of these unconsolidated undrained triaxial tests was to determine the stress- strain strength characteristics of GRC-1 under Earth ambient conditions and to compare them to the accepted values of the lunar soil stress-strain strength characteristics from previous studies. The goal is to determine whether GRC-1 will properly simulate the strength conditions of the lunar soils and if this material can legitimately be used for

Earth-based lunar mobility studies. With that in mind, the results of the triaxial tests on

GRC-1 show very good comparison with the best estimates of the friction angle for the actual lunar soil as provided in the Lunar Sourcebook (Heiken et al. 1991). Table 4.7 summarizes the friction angle of GRC-1 as compared to the lunar soil and lunar soil simulants. It is clear that GRC-1 covers almost the full range of internal angle of friction expected for the soils on the Moon. It also appears to cover the lower range of friction angles much better than any other lunar soil simulant. This is a beneficial characteristic for a lunar soil simulant for lunar exploration vehicle mobility studies. More specifically,

GRC-1 is able to simulate the worst case scenario for mobility on the Moon in terms of soil friction angle based on triaxial testing.

Table 4.7 Friction angle of GRC-1 compared with lunar soil and lunar soil simulants. Friction Angle (º)

Minimum Maximum Average GRC-1 29.31 48.16 38.74 Lunar Soil 30 50 40 MLS-1 <41.4 >66.7 - - JSC-1 <44.4 >52.7 45 JSC-1A <41.87 >56.70 - -

253

Unfortunately, a meaningful conclusion could not be drawn based on the measured values of cohesion from the triaxial tests. It is safe to assume, however, that dry GRC-1 has very low cohesion values (less than 10 kPa), but no accurate comparison can be made with that of the lunar soil or lunar soil simulants at this point.

4.5 EFFECT OF STRENGTH PROPERTIES ON VEHICLE MOBILITY

For vehicle mobility studies it is important to reflect the magnitude of possible error in cohesion and/or internal angle of friction upon the tractive performance of the vehicle. In other words it is important to understand how thrust is affected by errors in the soil parameters obtained from conventional triaxial test methods. The following analysis on the results of the unconsolidated undrained triaxial tests performed on GRC-1 attempt to clarify this issue.

One major issue seen in the results of the triaxial tests on GRC-1 is that the cohesion values of the material show a lot of scatter and a high amount of variability and inconsistency. From the Mohr’s circles analysis it was shown that the cohesion values for GRC-1 ranged from 0.0 kPa to approximately 10 kPa in no logical order. For dry granular soils these high values of cohesion seem unreasonable. Thus, it is important to understand how these values of cohesion affect the predicted thrust of a wheeled vehicle.

The thrust of a vehicle is the result of the terrain surface being sheared by the vehicle running-gear, e.g. wheels. Thus, the shearing behavior of the terrain is a major factor in determining the tractive performance of an off-road vehicle. Following Janosi and

254

Hanamoto’s (1961) theory, the shear stress underneath a wheel is given by the following equation,

⎛ − j ⎞ τ = τ ⎜1− e K ⎟ (54) max ⎜ ⎟ ⎝ ⎠

The maximum shear strength of the soil is commonly defined using the Mohr-Coulomb strength criterion as shown in equation (55) below.

τ max = c + σ tanφ (55)

where c and φ are the cohesion and friction angle of the soil, respectively, as typically determined via triaxial testing. The shearing behavior of the soil, applicable for plastic soils following equation (54), can be characterized by an exponential equation resulting from the combination of equations (54) and (55) as follows,

⎛ − j ⎞ ⎜ K ⎟ τ = ()c + σ tanφ ⎜1− e ⎟ (56) ⎝ ⎠

255

Assuming that σ ()j is equal to σ 0 and assuming that K is much smaller than the contact length of the wheel, equation (56) simplifies to the following equation:

τ ≅ c + σ 0 tanφ (57)

Assuming that the load on the wheel is uniformly distributed over the contacting surface, the thrust can be represented as:

F = τA (58)

where τ is the shear strength and A is the contact area of the wheel on the soil surface.

Integrating equation (58) over the length of the contacting surface (of the wheel) leads to the following progression of equations,

l0 F ≅ b0 ⋅ τ ⋅ ∂x (59) ∫0

F ≅ b0 ⋅l0 (c + σ 0 tanφ) (60)

F ≅ A(c + σ 0 tanφ) (61)

F ≅ cA +W tanφ (62)

256 where b0 is the width (or radius) of the contacting surface, l0 is the length of the

contacting surface, σ 0 is the applied normal pressure, and W is the vehicle weight.

Assuming that the friction angles obtained in the UU triaxial tests are with minimal error and that the cohesion varies from some minimum value cmin to some maximum value cmax, the following error equation is developed,

ΔF Error = *100% (63) thrust F

(c A +W tanφ)− (c A +W tanφ) Error = max min *100% (64) thrust F

(c − c )A Error = max min *100% (65) thrust ()cA +W tanφ

Thus, applying equation (65) to the triaxial test data from the Mohr’s circles analysis in

Table 4.6 the effect of the variation of cohesion on thrust can be determined. Choosing the test set with the lowest friction angle projects the maximum possible error in thrust out of all ten tests. In contrast, choosing the test set with the highest friction angle provides the minimum possible error in thrust out of all ten tests. Test number one has the lowest friction angle of 29.84º (0.5028 radians). Looking at all ten test sets, the maximum value for cohesion is 9.92 kPa and the minimum value is 0.00 kPa.

257

Substituting these values into equation (65) the following equation for error in thrust is determined as:

(9.92kPa − 0.00kPa)A Error = *100% (66) thrust ()cA +W tan()0.5208

(9.92kpa)A Error = *100% (67) thrust cA +W ()0.5736

where A and W are vehicle specific parameters corresponding to the ground contact area of the wheel and the vehicle weight, respectively. Table 4.8 provides wheel contact areas and vehicle weights of three different lunar vehicle cases or prototypes, of which the first case represents the lunar roving vehicle8.

Table 4.8 Typical properties of different vehicles (Case 1 represents the lunar roving vehicle). Wheel Contact Vehicle Weight Vehicle Area (m2) (kN) Case 1 0.0353 0.254 Case 2 0.08 2.18 Case 3 0.08 0.55

The error in thrust as determined for cases one through three in Table 4.8 and using the cohesion values obtained from the Mohr’s circles evaluation of the triaxial data as shown in Table 4.6 is shown in the subsequent table, Table 4.9. As can be seen, the errors associated with the variation in cohesion are extremely high.

8 Cases 2 and 3 in Table 4.8 represent the current design parameters of two prospective lunar roving vehicles: the Athlete and the Chariot, respectively. It is important to note that these values are subject to change. 258

Table 4.9 Error in thrust caused by variation in cohesion. c (kPa) Errorthrust Case 1 (%) Errorthrust Case 2 (%) Errorthrust Case 3 (%) 8.71 77.27 40.75 78.40 9.92 70.62 38.82 71.55 0.00 240.36 63.47 251.55 0.00 240.35 63.47 251.55 7.17 87.81 43.51 89.26 0.00 240.35 63.47 251.55 4.85 110.50 48.44 112.81 4.30 117.71 49.77 120.34 9.04 75.33 40.21 76.41 1.64 172.00 57.44 177.67

The allowable variability in the values of cohesion for the triaxial tests can be determined by assuming that a 10-percent error in thrust is acceptable via back calculating the values for ΔF in equation (67) as follows,

(c − c )A 10% = max min *100% (68) cA +W ()0.5736

The acceptable variability in cohesion for a 10-percent error in thrust is shown in Table

4.10 and is based on the cohesion and internal angle of friction values used in the preceding calculations. It is important to note that this variability in cohesion is only acceptable provided that the values for cohesion and friction angle used in the evaluation are accurate values. As can be seen, the acceptable variability in cohesion is relatively small. For this specific case the variability appears to be on the order of 2.6 kPa or less.

However, it is observed that the magnitude of the cohesion affects the acceptable variability of this parameter. Generally speaking, it appears that the larger the cohesion the larger the acceptable variability. This means that for dry granular soils such as those

259 encountered on the Moon, the small cohesion values of 1 kPa and less have significant influence on the thrust and must be considerably accurate.

Table 4.10 Acceptable variability in cohesion. Errorthrust Acceptable Errorthrust Acceptable Errorthrust Acceptable c (kPa) Case 1 (cmax-cmin) Case 2 (cmax-cmin) Case 3 (cmax-cmin) (%) (kPa) (%) (kPa) (%) (kPa) 8.71 77.27 1.28 40.75 2.43 78.40 1.27 9.92 70.62 1.40 38.82 2.56 71.55 1.39 0.00 240.36 0.41 63.47 1.56 251.55 0.39 0.00 240.35 0.41 63.47 1.56 251.55 0.39 7.17 87.81 1.13 43.51 2.28 89.26 1.11 0.00 240.35 0.41 63.47 1.56 251.55 0.39 4.85 110.50 0.90 48.44 2.05 112.81 0.88 4.30 117.71 0.84 49.77 1.99 120.34 0.82 9.04 75.33 1.32 40.21 2.47 76.41 1.30 1.64 172.00 0.58 57.44 1.73 177.67 0.56

In summary, it can be concluded that the values of cohesion below 1 kPa have a significant effect on the thrust or gross traction of a lunar wheeled vehicle (which has a relatively low weight and large ground contact area compared to typical Earth vehicles) if not accurately predicted or determined. A high range of variability in cohesion resulting from errors or limitations of triaxial testing can have a significant impact on the thrust or gross traction of a wheeled vehicle. This error can be reduced by decreasing the error in cohesion and by increasing the vehicle weight (as shown from Case 2 and Case 3).

260

CHAPTER FIVE

BEVAMETER TESTING FOR STRENGTH PROPERTIES OF GRC-1

5.1 DEVELOPMENT OF NASA GLENN LABORATORY BEVAMETER

Current vehicle mobility models are based on the semi-empirical equations presented by the father of terramechanics, M.G. Bekker. In off-road operations, such as lunar surface exploration, a variety of terrain is expected to be encountered. The soil properties of the various terrains have a significant influence on the performance of the off-road vehicles selected to traverse the terrain. As such, vehicle mobility performance models are dependent on the soil or terrain parameters as determined by the plate-sinkage and torsional shear bevameter tests. Thus, it was deemed necessary to perform bevameter testing, which is known to best measure the terrain properties most influential to vehicle mobility under the loading conditions similar to those exerted on off-road vehicles; on

GRC-1 in order to determine the stress-strain or strength characteristics of this soil in relation to lunar exploration vehicle mobility. More specifically, it is necessary to measure the mechanical properties of GRC-1 as they relate directly to the compaction and shear under a wheel or track and in this case under a lunar exploration vehicle wheel.

However, there is no standard bevameter testing device in existence as there are standard testing devices for other tests such as the triaxial test and cone penetration test, etc.

Therefore, it was necessary to manufacture a bevameter at the NASA Glenn Research

Center in order to perform the necessary tests.

261

Two different bevameter testing devices were constructed for use in the GRC soils laboratories. The first bevameter designated here on out as the “table bevameter” was designed for use in the Soils Design Laboratory at NASA Glenn to perform small scale laboratory tests for the characterization of various lunar soil simulants including GRC-1.

The second bevameter designated here on out as the “portable bevameter” was designed for use in the SLOPE facility (Simulated Lunar Operations facility) at NASA Glenn to perform large scale laboratory tests for the measurement of terrain properties during vehicle mobility tests. These two bevameters are shown in Figure 5.1(a) and 5.1(b), respectively. Figure 5.2(a) and 5.2(b) show the Soils Design Laboratory and SLOPE facility in which each of the respective bevameters are be used. All bevameter tests on

GRC-1 were carried out with the table bevameter which will therefore be the focus of this chapter. More specifically, in this chapter, the bevameter technique and the methodologies for processing the test data measured using the table bevameter and for characterizing the behavior of GRC-1 are presented.

(a) (b) Figure 5.1 (a) Table bevameter shown with plate-sinkage end effector. (b) Portable bevameter shown with shear ring end effector.

262

(a)

(b) Figure 5.2 (a) Soils Design Laboratory. (b) SLOPE facility.

The basic design behind the table bevameter consists of a table mounted structure supporting a vertical shaft, at the bottom of which various end effectors are mounted.

The shaft and end effectors can be driven into the soil with a known force while the corresponding sinkage is measured. They can also be rotated with a known angular

263 velocity while the corresponding torque is measured. The schematic of the table bevameter is shown in Figure 5.3. It consists of the pressure-sinkage test component including load cell and linear variable differential transformer (LVDT) for measuring normal load and sinkage, respectively; the shear test component including torque cell and potentiometer for measuring torque and angular displacement, respectively; and the data acquisition system. The load/torque cell is a single unit which was purchased from

SensorData Technologies, Inc.9 of Sterling Heights, Michigan. The manufacturer specifications of this device are provided in Appendix D. This device is limited to a maximum of 113 N-m of torque (1000 lb-in) and a maximum of 907 kg of thrust (2000 lb). In the pressure-sinkage test, the sinkage plate or end effector is attached to the end effector mount, which is attached to the base of the load/torque cell. The load/torque cell is attached to a shaft to which a platform for placement of the dead weights is mounted.

In the shear tests, the shear head or end effector is manually rotated via the wheel type structure mounted at the top of the shaft. The shear head is directly attached to the base of the load/torque cell, which is in-turn attached to the shaft. A potentiometer is connected directly to the torque cell through a system of gears to measure the rotational displacement of the shear head.

9 www.sensordata.com 264

Figure 5.3 Schematic of table bevameter.

265

The pressure-sinkage test and the shear test are each performed separately. The test data is collected using the data acquisition system as outlined in Figure 5.4. The methods for processing the test data are described in the following respective pressure-sinkage and shear testing sections. It is important to note that after the complete construction of the bevameter and before performing any pressure-sinkage or shear tests, the load cell, torque cell, LVDT, and potentiometer had to be calibrated. The results of the calibration are summarized in Table 5.1. These include a second calibration which was performed after some minor modifications were made to the bevameter system.

AC Power Power AC Agilent E3620A Source Conditioner DC Power Supply

AC Voltage Preston 830XWB Source Amplifier (Isolators, Filters, Gains) LVDT Voltage 1 Yokogawa Module 1 Pot. DL708E Voltage 2 Module 2 Oscilloscope Voltage Signals Strain 3 Torque Module 3 Strain 4 Thrust Module 4

Bridge Excitation

Figure 5.4 Bevameter data acquisition system.

266

Table 5.1 Results of calibration for bevameter sensors. Calibration September 2007 February 2008 Load Cell 1170.2 N/(mV/V) 1155.1 N/(mV/V) Torque Cell 53.6255 Nm/(mV/V) 56.4216 Nm/(mV/V) Potentiometer 2389.9 deg*V 2389.9 deg*V LVDT 1126.3 mm*V 1139.8 mm*V

5.2 EXPERIMENTAL SETUP AND LIMITATIONS

In the performance of bevameter tests there are several requirements which need to be met and techniques which need to be followed in order to ensure reliability and repeatability of the results. This section discusses the effects of the soil preparation method, soil bin size, and end effector size and geometry on the results of pressure- sinkage and shear bevameter testing. Recommendations for proper soil preparation method, optimum soil bin size, and optimum end effector sizes and geometries are also presented.

5.2.1 Soil Preparation Method

Simulation of the geotechnical properties of the lunar regolith in experimental tests requires the proper choice of simulant material as well as the proper preparation of the test bin or test bed. According to Sibille et al. (2005) preparation of the lunar soil simulant (in this case GRC-1) in a test bin should effectively reproduce the range of bulk density, cohesion, and frictional properties of the lunar soil. In the case of pressure- sinkage bevameter testing, Bekker (1969) points out that, “even the best laboratory methods applied to the easiest soil, dry sand, to reproduce its original condition cannot

267 prevent the scatter of measured data.” Figure 5.5 shows typical scatter in plate-sinkage data for a 5 cm diameter (2 in) penetration plate in moist sand. In other words, it is essentially impossible to reprocess soil to the same exact condition in order to repeat pressure-sinkage experiments. Some degree of scatter will always exist in the measured data provided that all external factors are constant (i.e. bin size, method of soil preparation, environmental conditions, plate size, etc.).

Figure 5.5 Typical scatter experienced in pressure-sinkage bevameter tests (Bekker 1969).

Therefore, it is necessary to determine the most efficient and most repeatable method of preparing and reprocessing GRC-1 for each new pressure-sinkage bevameter test. In this investigation two different methods of soil preparation were used as shown in Figure

5.6(a) and Figure 5.6(b). These included a random shoveling process and a hopper pour process. In the random shoveling process, the soil was randomly poured into the soil bin by a scoop similar to the one shown in Figure 5.6(a). In the hopper process, the soil was

268 poured into the soil bin through a plastic funnel similar to the one shown in Figure 5.6(b).

The funnel was held no more than an inch (2.54 cm) above the soil surface at all times

(the higher the funnel the more dense the soil) and was moved around the soil bin in a sweeping fashion to evenly layer the soil as it was poured.

(a) (b) Figure 5.6 (a) Shovel for random soil preparation. (b) Plastic funnel for hopper soil preparation.

Each method was used to create seven 12 cm deep GRC-1 soil samples of minimum bulk density10. The soil samples were prepared in a rigid polypropylene bin with an approximate diameter of 55.3 cm. A 19 cm penetration plate was mounted to the table bevameter load/torque cell and was used for all plate-penetration tests (for both methods of soil preparation). Results were curve-fit using a decaying exponential model and a least squares approach. A statistical analysis was additionally performed to show the effect of the soil preparation method on the pressure-sinkage tests. The general methodology of the testing procedure and analysis is as follows:

1. Data from each pressure-sinkage test was collected via the Yokogawa data

acquisition linked to the LVDT and load cell as shown in Figure 5.4. The LVDT

10 Since each test is being conducted under the same conditions, the bottom boundary conditions of the soil bin will have the same affect on each of the test results. Therefore, the depth of the soil sample is not significant. A height of 12 cm was selected as a conservative value based on time constraints with respect to soil preparation. The same holds true for sidewall boundary effects. 269

data was recorded in units of V/V while the load cell data was recorded in units of

mV/V.

2. As shown in Figure 5.7, the penetration plate was physically balanced and then

lowered until it became flush with the surface of the soil. The load cell was

electrically balanced. The LVDT data was offset so its output was zero (or close

to zero); indicating zero sinkage at this stage.

3. Weights were placed on the bevameter platform, as shown in Figure 5.3, in

increments of 2 kg until a total of 10 kg was reached (to get good resolution at

small loads and small sinkages) and then in increments of 5 kg until the maximum

load of 55 kg was reached. After each load increment the LVDT and load cell

data was recorded. Thus, a total of 15 data points were collected for each sensor.

Figure 5.7 Bevameter setup for pressure-sinkage tests.

270

In the data processing steps, the variable i represents the soil preparation method

(i ∈[]1,2 ) where 1 is representative of the random shovel method and 2 is representative of the hopper method; and j represents the test number index ( j ∈[]1,7 ). For each of the seven tests performed with the ith soil preparation method, the same loads were applied.

However, the resulting force varied slightly because of friction in the bevameter system.

To compensate for this minor variation, a least squares method was employed to fit the data to the following decaying exponential function using a uniformly spaced force vector fi.

z(f ) = a ⋅ (e − f −1)+ b ⋅ f ⋅ e− f + c ⋅ f 2 ⋅ e − f (69)

Here, z is the sinkage in mm, f is the load in N, and {a, b, c} are dimensionless constants that control the relationship. The resulting sinkage data was stored in vectors zij. Using these vectors, the ensemble mean and ensemble deviations were calculated as follows, respectively:

1 n z i = ∑ z ij (70) n j=1

1 n ˆ z i = ⋅ ∑ z ij − z i (71) n −1 j=1

271 where n is the total number of observations. The corresponding MATLAB code for the data processing is provided in Appendix D. The results of the analysis are as shown in

Figure 5.8 thorough Figure 5.12. As can be seen, in Figure 5.8 and Figure 5.12, the use of the hopper method for soil preparation generally results in less scatter of the repeat pressure-sinkage tests. Also, in using the hopper method for soil preparation, a looser soil consistency seems to be achieved as shown by the consistently lower load-sinkage curves shown in Figure 5.8 and Figure 5.11. One final observation is that the scatter of the load-sinkage in both methods of soil preparation seems to be worse at increasingly higher loads as shown in Figure 5.12. The reason for this is not clear at this point. One possible explanation is that under the initial loading of the system the soil tends to compact by rearrangement of the soil structure so that the voids are filled. Upon increase in load, compaction occurs by the actual compression and eventual breakage and fracturing of individual soil particles usually are their points of contact. Since the soil is re-prepared for each pressure-sinkage test it is impossible for the soil particles to be arranged in the exact same structure as that of the previous test. Therefore, where the initial compression or minimization of the voids may be similar in all tests, the secondary compression or fracturing of the soil particles may not be similar which may result in greater scatter of the data at increased loads.

272

0 ο Hopper Data + Random Data -10

-20

-30

-40 Depth (mm)

-50

-60

-70 0 100 200 300 400 500 600 Load (N)

Figure 5.8 Plot of load-sinkage data collected from the hopper soil preparation tests and the random soil preparation tests.

0 + Raw Data - Curve Fit -10

-20

-30

-40 Depth (mm)

-50

-60

-70 0 100 200 300 400 500 600 Load (N)

Figure 5.9 Plot of the raw data and curve-fit for the random soil preparation tests.

273

0 o Raw Data - Curve Fit -10

-20

-30

-40 Depth (mm) Depth

-50

-60

-70 0 100 200 300 400 500 600 Load (N)

Figure 5.10 Plot of raw data and curve-fit for hopper soil preparation tests.

0 ο Hopper Data - Mean of Hopper Data -10 + Random Data -- Mean of Random Data

-20

-30

-40 Depth (mm)

-50

-60

-70 0 100 200 300 400 500 600 Load (N)

Figure 5.11 Plot of raw data and mean curve-fit for random soil preparation tests and hopper soil preparation tests.

274

8 + Random 7 ο Hopper

2 Standard Deviation of Depth (mm)

0 0 50 100 150 200 250 300 350 400 450 500 Load (N)

Figure 5.12 Standard deviation of the random soil preparation tests and hopper soil preparation tests.

5.2.2 Soil Bin Requirements

There are several requirements to consider when selecting the appropriate soil bin for pressure-sinkage and shear bevameter testing. These requirements include boundary effects caused by both the sidewalls and bottom of the soil bin, as well as time constraints as far as the size of the bin and corresponding soil preparation time is concerned, and feasibility of the system, i.e. can the soil bin be managed by a single person? From experience, Bekker (1969) suggested that to avoid any sidewall effect, the soil bin should be at least five times the diameter of the largest penetration plate or shear ring in width

(or diameter). He also suggested that to avoid any bottom boundary effect the height of the soil bin should be five times the diameter of the largest penetration plate or shear ring.

275

Jo Wong suggested that the soil bin should be able to support soil to a depth of at least five times deeper than the anticipated sinkage in order to avoid bottom boundary effects

(personal communication, 18 Sept 2007). Ference Pavlics who worked with M.G.

Bekker at General Motors developing the original bevameter based terramechanics work also agreed that the “rule of five” (five times the diameter of the plate in width and depth) was sufficient to overcome boundary effects during testing (personal communication, 19

Aug 2008).

Looking at classical soil mechanics theory, settlement is generally defined as the action by which a footing pushes into the soil in response to the load to which it is subjected

(Duncan 1998). In terms of bevameter testing, it is a function of the size of the plate, the load to which the plate is subjected, and the geotechnical characteristics of the soil beneath the plate. Granular materials that have no cohesion, such as pure dry sands similar to GRC-1, rely on the particle-to-particle contact and interlocking of particles to resist plate penetration or settlement. In an undisturbed state sand typically takes on a honeycomb structure due to the various shapes and sizes of the particles. In this type of soil arrangement the larger particles tend to brace the gap over the voids as the smaller particles tend to settle out. This is a highly unstable soil arrangement. As load is applied to the soil surface, the particles shift and rearrange to minimize the voids and create a more solid and stable structure. This phenomenon is generally referred to as intergranular slippage. The quantitative amount of settlement is directly dependent on the degree of intergranular slippage. The amount of settlement is also dependent on lateral yielding of the soil as the pressure from the plate dissipates into the ground in all

276 directions. In addition, each individual soil particle is compressible to a certain extent.

However, the amount of settlement that results from this elastic type deformation is almost negligible compared to the settlement from both intergranular slippage and lateral yielding.

Looking more closely at the lateral yielding of the soil as the pressure from the plate dissipates; circular plates under an applied load are known to distribute pressure to the soil underlying the plate as well as to the soil surrounding the plate, i.e. the pressure varies both laterally and vertically. Pressure is generally greatest at the point directly below the center of the plate and diminishes with increasing horizontal distance and depth from the center of the plate. This phenomenon has been termed the pressure bulb effect (Duncan 1998). The pressure bulb for a circular footing or plate is shown in Figure

5.13. Generally speaking, bearing pressure has negligible influence in the soil beyond the

10-percent gradient line of the pressure bulb. The pressure gradient at 0.10 (10-percent) of contact pressure has a conservative depth and width of 2D and 1D, respectively, where

D is the diameter of the circular plate. Therefore, it can be expected that two different plate sizes (experiencing the same contact pressure) will have two very different pressure bulbs. Obviously, the larger plate will have an equally larger pressure bulb. This would mean that in order to avoid any effects of the sidewalls of the soil bin on the pressure bulb created underneath and surrounding the penetration plate a bin diameter greater than two times the diameter of the plate should be sufficient. Correspondingly, in order to avoid any effects of the bottom boundary of the soil bin on the pressure bulb created

277 underneath the penetration plate a bin depth (or soil depth) greater than 2 times the diameter of the plate should be sufficient.

Figure 5.13 Pressure bulb for a circular plate (Duncan 1998).

With respect to the size of the soil bin, the largest plate size used for pressure-sinkage bevameter testing, as discussed in the subsequent section, is 19 cm in diameter (which is larger than the shear ring used for shear bevameter testing as well). Assuming that a conservative approach would be to follow the advice of Bekker and employ the rule of five, a conservative bin size would have a minimum diameter and depth of 95 cm. Based on the minimum bulk density of GRC-1 (1.60 g/cc) to fill a soil bin of this size would require approximately 1,077,409 g (2375 lbs) of soil. This amount of soil is not feasible for one person to manually fill and empty the soil bin for each new bevameter test and would cost too much time in soil preparation. It is more feasible to choose a bin less conservatively in the eyes of Bekker, but more conservative than classic soil mechanics

278 theory and choose a bin that has a diameter and depth at least three times the diameter of the largest penetration plate. This results in a minimum bin diameter of 57 cm as well as a bin depth of 57 cm. In this case a soil mass of approximately 232,720 g (513 lbs) is required to fill the soil bin, which is more feasible for a single person to handle, but still costs a lot of time in soil preparation.

Therefore, in order to verify the minimum soil depth to which the soil should be prepared

(which will ultimately govern the height of the soil bin) a simple experiment was conducted. The idea was to repeatedly perform pressure-sinkage tests on GRC-1 prepared to various increasing depths in a rigid soil bin. It was hypothesized that this process would reveal the minimum depth at which the pressure-sinkage data starts to converge (meaning that the bottom boundary effects have become negligible). In other words, the bearing strength of the soil, as represented by corresponding pressure-sinkage curves will become weaker as the prepared soil depth increases, until a limiting soil depth is reached where the bottom of the bin adds negligible strength to the soil. At this soil depth and each increasing soil depth thereafter, the corresponding load-sinkage curves should converge and remain constant, assuming that the soil has been prepared to the same relative density and in a repeatable uniform fashion. It was also assumed that for the specific plate sizes11 used in this experiment (7.6 cm and 19 cm diameter), the soil bin is large enough to ignore the sidewall boundary effects of the soil bin. Since the pressure-sinkage test results are related to vehicle testing by assuming that the compaction pressure and resulting sinkage that occurs underneath a wheel may be

11 Various penetration plate sizes were used to better understand the size effect of the plate with respect to bottom boundary conditions. 279 represented by an equivalent pressure underneath a flat plate; the ultimate goal of this investigation was to determine the minimum soil depth in the vehicle testing facility of the SLOPE Lab, so that the bottom boundary conditions will not have an effect on the performance of the vehicle. The general procedure followed for this investigation is as follows:

1. Measure and record the soil bin geometry such that the soil density may later be

calculated.

2. Measure and record the bevameter penetration plate geometry such that the

applied ground pressure may later be calculated.

3. Prepare GRC-1 in the designated rigid soil bin to approximately 50-percent of the

maximum bulk density or to a density of 1.75 g/cc using the hopper method

discussed in the preceding section. In an attempt to decrease the preparation time

a much larger soil hopper was created as shown in Figure 5.14. This new soil

hopper has a single 2.54 cm diameter orifice from which soil can flow at a

maximum rate of 350 g/sec. It was created using an aluminum funnel with a

flexible 91 cm (3 ft) hose attached to the bottom to mitigate the creation of dust

when the soil falls through the funnel orifice as well as to direct the location of

soil fall so that the soil can be dispersed in even layers in the respective soil bin.

This funnel is seated in a five gallon pail lift which can easily be raised and

lowered for optimum height of soil fall.

a. Back-calculate the mass of GRC-1 needed to fill the soil bin to the

predetermined soil depth at a bulk density of 1.75 g/cc using the following

equation,

280

g ms 1.75 = 2 (72) cc π ⋅ r ⋅ H s

where ms is the mass of the soil in g, r is the inner radius of the soil bin in

cm (or in the case of a rectangular soil bin r2 can be replaced with the

length and width of the soil bin in cm), and Hs is the known depth of the

soil in the soil bin in cm.

b. Measure and mark or scribe the inside of the soil bin to indicate the

predetermined soil depth.

c. Pour the soil into the soil bin in uniform layers using the hopper, keeping

the height of fall of the soil approximately 2.54 cm (1 in) or less from the

surface of the soil in the bin. Upon completion of pouring the soil, the

level of the soil should be slightly higher than the predetermined soil depth

scribed in the wall of the soil bin.

d. Use the Syntron 76.2 cm (30 in) square vibrating table at an intensity level

of two to compact the soil in the soil bin down to the predetermined soil

depth as scribed in the wall of the soil bin. This is the most accurate

method (investigated in this dissertation) of preparing the soil to a density

of 1.75 g/cc (ensuring that the soil surface is level and as close to the

predetermined height as possible12).

12 It should be noted that depending on the dimensions of the soil bin, especially in soil bins that have larger diameters than heights, a variation in depth of the soil from the predetermined height by as little as 0.5 cm can lead to significant errors in density. For a square soil bin with a width of 74.2 cm and predetermined soil height of 18 cm, it was found that for an error of 0.5 cm, the density could vary by as much as 0.04 g/cc, which is a significant difference. 281

Figure 5.14 Large soil hopper for quicker soil preparation.

4. Perform pressure-sinkage bevameter tests as described in the preceding section

(for the determination of the best soil preparation method).

a. Data from each pressure-sinkage test was collected via the Yokogawa data

acquisition linked to the LVDT and load cell as shown in Figure 5.4. The

LVDT data was recorded in units of V/V while the load cell data was

recorded in units of mV/V.

b. As shown in Figure 5.7, the penetration plate was physically balanced and

then lowered until it became flush with the surface of the soil. The load

cell was electrically balanced. The LVDT data was offset so its output

was zero (or close to zero); indicating zero sinkage at this stage.

c. Weights were placed on the bevameter platform, as shown in Figure 5.3,

in increments of 1 kg until a total of 5 kg was reached (to get good

resolution at small loads and small sinkages), then in increments of 2 kg

until 15 kg was reached, and finally in increments of 5 kg until the

282

maximum load of 55 kg was reached. After each load increment the

LVDT and load cell data was recorded. Thus, a total of 19 data points

were collected for each sensor.

5. After completion of each bevameter test, remove the soil from the soil bin, and

repeat steps 3 and 4, using the same soil bin, the same soil depth, the same soil

density, and the same penetration plate size. Follow this procedure for a total of

five repeat pressure-sinkage tests. Bekker (1969) suggests that in optimum

laboratory conditions, typically two or three repeat tests are sufficient for

averaging the scatter that is unavoidable in pressure-sinkage data. Therefore, a

total of five should be more than sufficient to obtain a representative average

pressure-sinkage curve for determining the minimum soil depth in the soil bin.

6. Repeat steps 3 through 5 for increasing predetermined soil depths until pressure-

sinkage curves converge. Typical soil depths used include 3 cm, 6 cm, 9 cm, 12

cm, etc., and in some cases up to 24 cm soil depth.

7. Repeats steps 3 through 6 for additional penetration plate size to account for plate

size effects with respect to bottom boundary conditions.

In the data processing steps, the variable i represents the plate number (i ∈[1, 2]) and j represents the test number index ( j ∈[1, 5]). For each of the five tests done with the ith plate size, the same loads were applied. However, the resulting plate pressure varied slightly because of friction in the bevameter system. To compensate for this minor variation, a least squares method was employed to fit the data to the following decaying exponential function using a uniformly spaced pressure vector pi.

283

z(p) = a ⋅ (e − p −1)+ b ⋅ p ⋅ e − p + c ⋅ p 2 ⋅ e− p (69)

Here, z is the sinkage in mm, p is the pressure in N/mm2, and {a, b, c} are dimensionless constants that control the relationship. The resulting sinkage data was stored in vectors, zij. Using these vectors, the ensemble mean and ensemble deviations were calculated as follows, respectively:

1 n z i = ∑ z ij (73) n j=1

1 n ˆ z i = ⋅ ∑ z ij − z i (74) n −1 j=1

where n is the total number of observations. The corresponding MATLAB code for the data processing is provided in Appendix D.

All tests were performed in a rigid polypropylene bin with manufacturer dimensions of

74.2 cm in width (29 in), 74.2 cm in length (29 in), and 50 cm in height (20 in) as shown in Figure 5.7. A total of eight test sets or 40 individual pressure-sinkage tests were performed using the 7.6 cm penetration plate. Five repeat tests were performed for predetermined soil depths of 3 cm, 6 cm, 9 cm, 12 cm, and 18 cm. Testing at 3 cm soil depth was repeated a total of three times (for a total of 15 individual tests or five tests per each of the three repetitions). This was to evaluate the repeatability of the mean pressure-

284 sinkage curves. Testing at 18 cm was repeated twice (for a total of 10 individual tests or five tests per each of the two repetitions). This again, was to evaluate the repeatability of the mean pressure-sinkage curves. The results are shown in Figure 5.15 though Figure

5.25 below. Figures 5.15 through 5.22 show the raw data and mean curve-fit for each of the test sets conducted at various predetermined soil depths. As can be seen, the scatter of the data is relatively low excluding that of Figure 5.16, Figure 5.19, and Figure 5.22, for 3 cm, 9 cm, and 18 cm soil depths, respectively. Figures 5.23 and 5.24 display a comparison of the mean pressure-sinkage curves from each of the eight test sets shown in

Figures 5.15 through 5.22 over two different pressure ranges. The pressure range in

Figure 5.24 represents the maximum ground pressure expected from lunar exploration vehicle wheels on the lunar terrain. At first glance, the pressure-sinkage curves do not tend to converge at any particular soil depth. However, if the second test at 3 cm is neglected, the test at 9 cm is neglected, and the second test at 18 cm is neglected (based on the increased amounts of scatter associated with these data sets), it becomes clear that the pressure-sinkage curves tend to converge at depths greater than 6 cm as shown in

Figure 5.25. The reason that some data sets tend to have more scatter than others is not clear, but could have to do with the random nature of soil and the fact that the tests results are only as good as the test method itself. It is possible that in these cases the soil was not as uniformly prepared as in the other cases. In addition, it is clear from the first and third test sets at 3 cm soil depth, shown in Figure 5.23, that the mean pressure-sinkage curves for those data sets with minimal scatter are fairly repeatable. Based on the subjective judgment call to discard those data sets which showed an increased amount of scatter, it is reasonable to assume that for a 7.6 cm diameter penetration plate and GRC-1

285 prepared to a density of 1.75 g/cc, the minimum depth of soil preparation should be 6 cm to neglect bottom boundary effects from the soil bin. This seems to be shallow compared to soil depths following the “rule of five” or classic soil mechanics theory, in which a 7.6 cm plate should no longer experience boundary effects at soil depths of 38 cm and 15.2 cm, respectively.

0 0 ο Raw Data ο Raw Data -1 - Mean -1 - Mean

-2 -2

-3 -3

-4 -4

-5 -5

Depth (mm) -6 Depth (mm) -6

-7 -7

-8 -8

-9 -9

-10 -10 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure (kPa) Pressure (kPa) Figure 5.15 3cm, Test 1. Figure 5.16 3cm, Test 2.

0 0 ο Raw Data ο Raw Data -1 - Mean -1 - Mean

-2 -2

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-8 -8

-9 -9

-10 -10 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure (kPa) Pressure (kPa) Figure 5.17 3cm, Test 3. Figure 5.18 6cm, Test 1.

286

0 0 ο Raw Data ο Raw Data -1 - Mean -1 - Mean

-2 -2

-3 -3

-4 -4

-5 -5

Depth (mm) -6 Depth (mm) -6

-7 -7

-8 -8

-9 -9

-10 -10 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure (kPa) Pressure (kPa) Figure 5.19 9cm, Test 1. Figure 5.20 12cm, Test 1.

0 0 ο Raw Data ο Raw Data -1 - Mean -1 - Mean

-2 -2

-3 -3

-4 -4

-5 -5

Depth (mm) -6 Depth (mm) -6

-7 -7

-8 -8

-9 -9

-10 -10 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure (kPa) Pressure (kPa) Figure 5.21 18cm, Test 1. Figure 5.22 18cm, Test 2.

287

-1

-2

-3

-4

-5 3cm Test 1 Depth(mm) -6 3cm Test 2 3 Test 3 -7 6cm Test 1 -8 9cm Test 1 12cm Test 1 -9 18cm Test 1 18cm Test 2 -10 0 20 40 60 80 100 120 Pressure(kPa)

Figure 5.23 Comparison of mean pressure-sinkage curves tested at various depths of soil.

-0.5

-1

-1.5

-2

-2.5 3cm Test 1 Depth(mm) -3 3cm Test 2 3cm Test 3 -3.5 6cm Test 1 -4 9cm Test 1 12cm Test 1 -4.5 18cm Test 1 18cm Test 2 -5 0 5 10 15 20 25 30 35 40 Pressure(kPa)

Figure 5.24 Comparison of mean pressure-sinkage curves tested at various depths of soil (focusing on lunar pressure range).

288

-1

-2

-3

-4

-5

Depth(mm) -6

-7 3cm Test 1 -8 3cm Test 3 6cm Test 1 -9 12cm Test 1 18cm Test 1 -10 0 20 40 60 80 100 120 Pressure(kPa)

Figure 5.25 Converging pressure-sinkage curves.

A second set of tests to determine the minimum soil depth was conducted using a 19 cm diameter penetration plate. In this case, a total of three tests sets or 15 individual pressure-sinkage tests were conducted. Five repeat tests were performed for predetermined soil depths of 3 cm, 6 cm, and 9 cm. No repeat test sets were performed for the 19 cm diameter plate13. The same rigid polypropylene soil bin was used that was used for the previous tests. The results of these tests are shown in Figure 5.26 through

Figure 5.29 below. Figures 5.26 through 5.28 show the raw data and mean curve-fit for each of the test sets conducted at various predetermined soil depths. No repeat test sets were performed for any of the soil depths tested, so it is difficult to subjectively judge the amount of scatter in the data sets. The results in Figure 5.29 clearly show converging pressure-sinkage curves for soil depths greater than 3 cm. This suggests that for a 19 cm

13 Typically the larger the penetration plate, the less scatter in the resulting pressure-sinkage data (Bekker 1969). 289 diameter penetration plate and GRC-1 prepared to a density of 1.75 g/cc, the minimum depth of soil preparation should be 3 cm to neglect bottom boundary effects from the soil bin. This is surprising compared to soil depths following the “rule of five” or classic soil mechanics theory, in which a 19 cm plate should no longer experience boundary effects as soil depths of 95 cm and 38 cm, respectively. Clearly, the smaller 7.6 cm diameter penetration plate should experience convergence at shallower soil depths than the larger

19 cm diameter penetration plate. It is possible that the decision to stop testing at 9 cm soil depth based upon convergence of the data was premature and that at deeper soil preparations the pressure-sinkage curves may diverge and then eventually converge again. At these shallow depths, due to the large size of the plate and the large pressure bulb created in the soil underneath the penetration plate it is possible that similar pressure-sinkage relationships were experienced, but that at deeper soil depths the pressure-sinkage relationships will diverge due to the diminishing effect of the pressure bulb.

0 0

-0.5 -0.5 ο Raw Data ο Raw Data -1 - Mean -1 - Mean

-1.5 -1.5

-2 -2

-2.5 -2.5

Depth (mm) -3 Depth (mm) -3

-3.5 -3.5

-4 -4

-4.5 -4.5

-5 -5 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Pressure (kPa) Pressure (kPa) Figure 5.26 3cm, Test 1. Figure 5.27 6cm, Test 1.

290

-0.5 ο Raw Data -1 - Mean

-1.5

-2

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Depth (mm) -3

-3.5

-4

-4.5

-5 0 2 4 6 8 10 12 14 16 18 20 Pressure (kPa) Figure 5.28 9cm, Test 1.

0 3cm Test 1 -0.5 6cm Test 1 9cm Test 1 -1

-1.5

-2

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Depth (mm) Depth -3

-3.5

-4

-4.5

-5 0 2 4 6 8 10 12 14 16 18 20 Pressure (kPa)

Figure 5.29 Converging pressure-sinkage curves.

In order to test this theory a third set of plate penetration tests were conducted using an intermediate penetration plate size of 10.2 cm in diameter. In this case, a total of 10 test sets or 50 individual pressure-sinkage tests were conducted. Five repeat tests were performed for predetermined soil depths of 3 cm, 6 cm, 9 cm, 12 cm, 15 cm, 18, cm, 21

291 cm, 24 cm, and 27 cm. One repeat test set was performed for the 10.2 cm diameter plate at a soil depth of 15 cm to evaluate the repeatability of the resulting mean pressure- sinkage curve. The same rigid polypropylene soil bin was used that was used for the previous two tests. As for the previous two investigations, the MATLAB code for data processing can be found in Appendix D14.

The results of these tests are shown in Figure 5.30 through Figure 5.41 below. Figures

5.30 through 5.39 show the raw data and mean curve-fit for each of the test sets conducted at various predetermined soil depths. From a subjective point of view, little scatter is seen in all of the ten test sets. Additionally, Figures 5.34 and 5.35 in conjunction with Figure 5.40 show good repeatability of the mean pressure-sinkage curve for a soil depth of 15 cm. The results of Figure 5.40 are difficult to analyze. It appears that the mean pressure-sinkage follows a general trend of becoming weaker with increasing soil depth. However there are a few obvious anomalies to this trend, the most obvious of which is the mean pressure-sinkage curve for the 21 cm soil depth. Toward the higher pressure ranges (greater than 80 kPa) there appears to be some convergence of mean pressure-sinkage curves for 12 cm, 15 cm, and, 18 cm soil depths. However, this is followed by a divergence of the mean pressure-sinkage curves at 21 cm, 24 cm, and 27 cm soil depths. Looking only at the pressure range that is expected to be experienced on the Moon, Figure 5.41 does not clearly show the general trend expected of weakening pressure-sinkage curves with increasing soil depth. Several anomalies are apparent including the mean pressure-sinkage curves for the 12 cm, 15 cm, and 18 cm soil depths,

14 It should be noted that for the data processing of these test in an effort to save processing time the application of the curve-fit was eliminated. It was found that the curve-fit had little effect on the outcome of the data except to smooth out the pressure-sinkage curves. 292 respectively. There appears to be a convergence of mean pressure-sinkage curves at soil depths of 21 cm and 24 cm, however this is again followed by a divergent mean pressure- sinkage curve at the 27 cm soil depth. For a 10.2 cm diameter penetration plate, following the “rule of five” or classic soil mechanics theory, boundary effects should no longer be experienced at soil depths of 51 cm or 20.4 cm, respectively. Therefore, clear convergence of mean pressure-sinkage curves should have been apparent at minimum soil depths of 21 cm. As a result of the aforementioned observations, no meaningful conclusion can be drawn as to the minimum soil depth needed to eliminate bottom boundary effects from the soil bin. However, it can be concluded that the results from the previous tests using 7.6 cm diameter plates and 19 cm diameter plates are probably based on soil depths that are too shallow to completely ignore bottom boundary effects.

0 0

0.5 0.5 Sinkage, cm Sinkage, cm 1 1

ο Raw Data ο Raw Data - Mean - Mean

1.5 1.5 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure, kPa Pressure, kPa Figure 5.30 3cm, Test 1. Figure 5.31 6cm, Test 1.

293

0 0

0.5 0.5 Sinkage, cm Sinkage, cm 1 1

ο Raw Data ο Raw Data - Mean - Mean

1.5 1.5 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure, kPa Pressure, kPa Figure 5.32 9cm, Test 1. Figure 5.33 12cm, Test 1.

0 0

0.5 0.5 Sinkage, cm Sinkage, cm 1 1

ο Raw Data ο Raw Data - Mean - Mean

1.5 1.5 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure, kPa Pressure, kPa Figure 5.34 15cm, Test 1. Figure 5.35 15cm, Test 2.

0 0

0.5 0.5 Sinkage, cm Sinkage, cm 1 1

ο Raw Data ο Raw Data - Mean - Mean

1.5 1.5 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure, kPa Pressure, kPa Figure 5.36 18cm, Test 1. Figure 5.37 21cm, Test 1.

294

0 0

0.5 0.5 Sinkage, cm Sinkage, cm 1 1

ο Raw Data ο Raw Data - Mean - Mean

1.5 1.5 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Pressure, kPa Pressure, kPa Figure 5.38 24cm, Test 1. Figure 5.39 27cm, Test 1.

295

120 100 80 60 Pressure, kPa Pressure, 40 20 3cm 6cm 9cm 12cm 15cm 15 cm 18cm 21cm 24cm 27cm

0 0 1

0.5 1.5 Sinkage, cm Sinkage,

Figure 5.40 Comparison of mean pressure-sinkage curves for various soil depths.

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40 35 30 25 20 Pressure, kPa Pressure, 15 10 3cm 6cm 9cm 12cm 15cm 15 cm 18cm 21cm 24cm 27cm 5

0 0

0.1 0.2 0.3

0.05 0.15 0.25 Sinkage, cm Sinkage,

Figure 5.41 Comparison of mean pressure-sinkage curves for various soil depths (focusing on the lunar pressure range).

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In an effort to better understand the effect of plate size and depth of soil on settlement of and stress distribution underneath a circular plate a theoretical analysis for the settlement of circular footings in sand was performed. This analysis was based on the Boussinesq stress distribution within a soil mass resulting from vertical surface loading and settlement based on linear-elastic theory and the Schmertmann method for sandy soil. An in depth discussion on these topics can be found in McCarthy (2002) and Das (2004).

The initial assumptions made in this analysis are as follows. A schematic of the problem statement is displayed in Figure 5.42 below.

• The soil behaves elastically and experiences uniform soil properties throughout the

sample, i.e. is a homogeneous isotropic material.

• The influence of the rigid base on the stress distribution is ignored so that

Boussinesq’s equation for vertical stress underneath the center of a flexible circular

foundation is applicable.

• The settlement at the center of the footing is calculated and is treated as a one-

dimensional problem.

• r is the radius of the footing, Ho is the thickness of the soil layer, q is the applied

pressure or load intensity, z is the respective coordinate under the centerline of the

circular foundation, and S is the settlement of the footing.

298

r r

Soil Ho

Rigid Foundation z

Figure 5.42 Schematic for the approximate solution of the settlement of a circular footing under uniform loading.

Following Boussinesq’s formulation, the stress increase at a depth z (in the center of the footing) is,

⎧ ⎫ ⎪ ⎪ ⎪ 1 ⎪ ⎡ z 3 ⎤ ⎢ ⎥ Δσ = q⎨1− 3 ⎬ = q 1− 3 (75) 2 2 ⎢ 2 2 2 ⎥ ⎪ ⎡ ⎛ r ⎞ ⎤ ⎪ ⎣ ()r + z ⎦ ⎪ ⎢1+ ⎜ ⎟ ⎥ ⎪ ⎩⎪ ⎣⎢ ⎝ z ⎠ ⎦⎥ ⎭⎪

Following linear elastic theory, for a small thickness of soil ∂z at depth z, the settlement due to Δσ is,

Δσ ∂S = ⋅ ∂z (76) E

299 where E is the elastic modulus or Young’s modulus of the soil. The settlement of the entire soil layer can thus be determined by integrating equation (76) over the thickness of the soil layer, Ho, as follows,

Ho Δσ S = ∫ ∂S (77) 0 E

⎡ 2 ⎤ q 2 2 r S = ⎢H 0 + 2r − r + H 0 − ⎥ (78) E ⎢ 2 2 ⎥ ⎣ r + H 0 ⎦

From equation (78), relationships between the depth of the soil (or soil thickness), the radius of the footing (or penetration plate), and settlement can be determined. More specifically, the following questions can be answered:

1. For a fixed soil depth, how does the plate size (radius) affect the settlement?

2. For a fixed plate size (radius), how is the settlement affected by the thickness of

the soil layer (soil depth)?

Normalizing the plate radius r with the soil thickness H0 the following relationships can be determined and plotted as shown in Figure 5.43:

r c = (79) H 0

300

S c 2 = 1+ 2c − c 2 +1 − (80) q 2 H ⋅ c +1 0 E

Several conclusions can be drawn based on Figure 5.43. First, it can be seen that the larger the plate radius the larger the settlement for a certain contact stress q. More specifically, as the plate radius increases, settlement increases trending towards a maximum potential settlement at which point the increase in the size of the plate no longer has an affect on the settlement. Secondly, as the soil thickness increases, the size of the plate radius needed to reach maximum potential settlement increases. This makes sense based on the theory of the pressure bulb for which a larger plate is required to create stress deeper in the soil. Also, for a fixed value of c, settlement is proportional to the soil thickness. This implies that settlement increases by a factor of x when r and H0 are simultaneously increased by x. Additionally, it can be estimated that for a fixed value of soil thickness, the plate radius must be approximately 2.2 times the soil thickness in order to achieve 98-percent of the maximum potential settlement. However, it should be noted that in order for these relationships to hold true, the value of q/E must be much less than unity.

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100%

90%

80%

70%

60%

50%

40%

30% Settlement / (q/E * Soil Thickness) 20%

10%

0% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Plate Radius / Soil Thickness

Figure 5.43 For a fixed soil thickness, how does the plate size affect settlement?

Similarly, normalizing the soil thickness H0 with the plate radius r the following relationships can be determined and plotted as shown in Figure 5.44:

H d = 0 (81) r

S − (d 2 + 2) = d + 2 + (82) q 2 r ⋅ 1+ d E

Several conclusions can be drawn based on Figure 5.44. First, it is obvious that the larger the soil thickness the larger the settlement for a certain contact stress q. More specifically, as the soil thickness increases, the settlement increases trending toward a maximum potential settlement at which point the increase in soil thickness has no affect

302 on the settlement. Secondly, as the size of the plate increases, the soil thickness needed to achieve the maximum potential settlement increases. This again makes sense based on the pressure bulb theory. Additionally, for a fixed value of d, the settlement is proportional to the plate radius. This implies that the settlement increases by a factor of y, when r and H0 are simultaneously increased by y. This also implies that increased settlement is always possible for a given soil type and contact stress, i.e. settlement can always be increased by simultaneously increasing the plate size and soil depth. Finally, it can be observed that for a fixed radius, in order to achieve 98-percent of the maximum potential settlement, the soil thickness must be approximately 37-times the plate radius.

This means that for the rigid polypropylene soil bin used for plate-sinkage testing at

NASA Glenn, which has the capability of supporting a maximum soil thickness of 30 cm, the maximum penetration plate size that can be used in order to achieve 98-percent of the maximum potential settlement is approximately 1.6 cm in diameter. This is an extremely small plate size and is smaller than the smallest penetration plate available for use in bevameter testing at GRC which has a diameter of 5.1 cm.

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100%

90%

80%

70%

60%

50%

40%

30%

Settlement / (q/E * Plate Diameter) 20%

10%

0% 0 20406080100120140 Soil Thickness / Plate Radius Figure 5.44 For a fixed radius, how does the soil thickness affect settlement?

Comparing the test results from the 10.2 cm diameter pressure-sinkage bevameter tests to the theoretical curves of Figure 5.43 and 5.44, it is clear that the test results do not necessarily follow the general trends expected from theory. Re-plotting the data from

Figure 5.40 in terms of soil thickness (soil depth) and settlement (sinkage) for various applied pressures, as shown in Figure 5.45, clarifies the previous statement. It can be seen in Figure 5.45 that as the soil thickness is increased, the settlement does not increase in the general trend expected as shown in Figure 5.44. Instead, there exist several undulations in the trend in which the settlement increases and then decreases and then increases and decreases again, with increasing soil depth. These undulations appear to be more intense for higher pressures. Figure 5.46 shows the same data normalized with plate radius (as well as with the ratio of stress to elastic modulus) and compared to the theoretical trend as shown in Figure 5.44. It is important to note that a value of 645 kPa was used for the elastic modulus of GRC-1 as estimated from the stress-strain curves of

304 previous triaxial tests on this material15. With the normalization, the data from the pressure-sinkage tests using the 10.2 cm diameter penetration plate should have converged and formed a similar trend as shown by the theoretical line in Figure 5.45.

Clearly the experimental data does not follow the theoretical expectations.

1.40

1.20

1.00

0.80

0.60 Settlement, cm Settlement,

0.40

0.20

0.00 3 6 9 12 15 18 21 24 27 Soil Thickness, cm

10 kPa 20 kPa 30 kPa 40 kPa 60 kPa 70 kPa 80 kPa 90 kPa 100 kPa 110 kPa

Figure 5.45 Reformulated data from pressure-sinkage tests performed using the 10.2 cm diameter penetration plate.

15 It should be noted that this value for elastic modulus of a medium dense sandy soil is much lower than suggested by the CRC Handbook of Engineering Tables (Dorf 2004), which suggests a range of 17 to 28 MPa for medium dense sandy soil. 305

100%

90%

80%

70%

60%

50%

40%

30%

Settlement / (q/E * Diameter) Settlement Plate 20%

10%

0% 01234567 Soil Thickness / Plate Radius

10 kPa 20 kPa 30 kPa 40 kPa 60 kPa 70 kPa 80 kPa 90 kPa 100 kPa 110 kPa Theory

Figure 5.46 Normalized reformulated data from pressure-sinkage tests preformed using the 10.2 cm diameter penetration plate compared with theoretical trend for settlement.

In conclusion, it can be stated that the behavior of GRC-1 under pressure-sinkage tests is not appropriately described by the semi-empirical theory of linear-elastic deformation. It is possible that the behavior of GRC-1 under pressure-sinkage tests could better be described using plastic theory for deformation. This however is not in the scope of work and will not be covered. Thus, even though the relationships between soil thickness, plate size, and settlement are better understood, no clear assessment can be made as to the minimum soil depth required to eliminate bottom boundary effects. Therefore, a judgment call was made, based on a combination of soil preparation time and recommendations from Bekker, Wong, and Pavlics (as previously discussed) and traditional soil mechanics theory; that a conservative soil depth for all future bevameter

306 testing should be no less than 24 cm (for a maximum penetration plate size of 19 cm in diameter).

5.2.3 End Effector Requirements

As previously discussed, the term end effector is used to describe the part of the bevameter that penetrates the terrain or soil. The end effectors of the table bevameter are mounted either directly to the base of the load/torque cell or to the end effector mount which is attached to the base of the load/torque cell. There are three major categories of end effectors that can be used with the table bevameter, two of which are solely used for pressure-sinkage and shear tests. The first category of end effectors are cones such as the type used in cone penetration tests. This type is not used for testing of GRC-1 and will therefore not be discussed in further detail. The second category of end effectors is penetration plates. Penetration plates are rigid metal discs that connect to the end effector mount as shown in Figure 5.3. These plates are pushed into the ground during pressure- sinkage tests in order to measure the ground compaction resistance. In order to minimize the shearing resistance caused by the sidewall of the plate, the outer edge of all plates should be a maximum of 5 mm thick. In addition, the plates should be rigid enough so as not to deflect more than a few millimeters in the worst case scenario. The diameter of the penetration plates are determined based on the ground contact area that bounds the wheel sizes of the prospective lunar exploration vehicles being considered. Currently three different lunar exploration vehicles are being considered for operation in future missions to the Moon. The first is a replica of the original lunar roving vehicle. The second is the

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Mobile Lander with ATHLETE (All-Terrain Hex-Legged Extra-Terrestrial Explorer) robotic vehicle mobility system designed by the Jet Propulsion Laboratory (JPL) in

California. The ATHLETE, as shown in Figure 5.47, is designed with the capabilities of rolling over Apollo-like undulating terrain and "walking" over exceptionally rough or steep terrain so that robotic or human missions on the surface of the Moon can load, transport, manipulate, and deposit payloads to essentially any desired sites of interest.

Figure 5.47 ATHLETE robotic vehicle designed by JPL (credit NASA).

The third exploration vehicle being considered for operation in future missions to the

Moon is the Chariot “lunar truck” as shown in Figure 5.48. Developed by NASA’s

Exploration Technology Development Program's Human-Robotics Systems Project, the

Chariot features 12 wheels driven by two electric motors through a two-speed transmission. The modular design consists of a steel alloy frame which can be fitted with several different crew/payload combinations, including a small pressurized cabin and a

308 sample collector. The current estimated nominal tire load and ground contact area of these prospective vehicle are summarized in Table 5.2 below16.

Figure 5.48 Chariot lunar truck vehicle (credit NASA).

Table 5.2 Current design properties of various prospective lunar exploration vehicles. LRV17 ATHLETE Chariot

(NASA) (JPL) (NASA) Contact Area, cm2 353 800 800 Design Load, kN 0.254 2.18 0.55 Design Pressure, kPa 7.2 27.25 6.88

Based on these current design parameters three different penetration plate sizes were chosen for pressure-sinkage testing. These plate sizes include a 7.6 cm diameter plate corresponding to a contact area of 45.36 cm2; a 10.2 cm diameter plate corresponding to a

16 These design parameters are not absolute and are subject to change at any time. The parameters listed are the most current parameters to date. 17 It is important to note that these values as listed in Table 5.2 for the LRV are based on the design load and contact area. However, after operation of the LRV during the Apollo 15 mission, it was learned that the nominal wheel load was actually 0.2885 kN which was supported by only 43.3 cm2 of the wheel contact area (Personal communication with Vivake Asnani, 19 Feb 2008). 309 contact area of 81.71 cm2; and a 19 cm diameter plate corresponding to a contact area of

283.53 cm2. These plates are shown in Figure 5.49 below. This approximately covers the range of contact areas experienced by the LRV (as noted in Footnote 17). However the upper range of contact areas expected to be experienced by the ATHLETE and

Chariot could not be met due to limitations imposed by the size of the soil bin as discussed in the preceding section as well as loading limitations of the table bevameter

(in order to meet the maximum expected contact pressure).

Figure 5.49 Penetration plates used in pressure-sinkage bevameter tests.

The third and final category of end effectors includes the shear rings for shear bevameter testing. The shear ring is a metal annulus shaped plate that may or may not have evenly spaced, radially oriented grousers. During the shear test, a constant normal load is applied and the shear ring is rotated at a constant velocity. During the test, the grousers move or shear the soil, so that the internal soil shear resistance is measured. If the shear ring does not have grousers, then the metal-soil (or material-soil) shear resistance is measured. Typically, grousers are implemented to determine the internal shear strength

310 of the soil whereas shear rings lined with rubber, sandpaper, or various other materials are implemented to determine the shearing characteristics between the material

(representative of the material composing the exterior of the wheel) and the soil or terrain. Due to the fact that the soil “flows” during shear testing, the shear ring will ultimately sink. Therefore the shear rings are designed to be mounted on a “cup” which has ample clearance so as not to impede the sinkage. The dimensions of the shear rings selected for shear bevameter testing were based on four main considerations. These include: soil bin boundary effects which ultimately limited the size of the penetration plates as previously described; the ground pressure range that bounds the vehicles being considered; shear ring geometry effects that occur due to forcing the failure to shear in a rotational rather than linear fashion and cause the soil failure to occur outside the direction of motion (typically larger shear rings eliminate this effect); and the ground contact area that bounds the vehicles being considered. Based on the size of the soil bin as discussed in the previous section, as well as the loading limitations of the table bevameter, a shear ring with outer diameter of 17.9 cm and inner diameter of 14.0 cm was selected with corresponding normal loads ranging from 5 to 30 kg. This provides a contact area of 97.71 cm2 with contact pressures ranging from 5.02 to 30.1 kPa.

Although this size ring does not correspond to the contact areas of any of the above proposed lunar vehicles, it is more important to simulate the range of ground pressures, as shown in Table 5.2, which is successfully achieved with this shear ring. Two different finishes were used on this shear ring for shear bevameter testing. The first finish consisted of the shear ring lined with a low grit sandpaper to simulate the material-terrain shear interaction of several prototype wheels currently being tested at the NASA Glenn

311

Research Center. The second finish consisted of the shear ring with attached grousers having a height of 0.5 cm, a width equal to that of the annular shear ring (1.95 cm), and a thickness of 0.2 mm, spaced equally around the shear ring at intervals of 20-degrees.

This was used to determine the internal shear strength of GRC-1. The shear ring with grousers is shown in Figure 5.50(a) and Figure 5.50(b) below.

(a) (b) Figure 5.50 (a) Bottom view of shear bevameter ring with grousers. (b) Angular view of shear bevameter ring with grousers.

5.3 PRESSURE-SINKAGE TEST FOR VEHICLE MOBILITY

The bevameter test designated to simulate the normal loads exerted by a vehicle on the terrain surface is the pressure-sinkage or plate-sinkage test (used interchangeably throughout this dissertation). The results of the pressure-sinkage test allow for the prediction of vehicle sinkage and motion resistance to the compaction of the terrain. In the pressure-sinkage test, various sizes of plates are used to simulate the range of possible contact area of a vehicle wheel or track on the soil surface, and both the penetration force and the corresponding sinkage are recorded. Typically, penetration speed is kept at low 312 rates of approximately 1 cm/s in order to reduce dynamic effects of the system (Chen

1993). However, the table bevameter is designed to operate in a static type fashion as the penetration is manually controlled as dead weights are incrementally placed on the shaft of the bevameter by the operator. The pressure on the penetration plate is obtained by dividing the penetration force by the contact area of the plate as shown in the following equation,

L p = (83) π ⋅ r 2

where p is the normal pressure, L is the penetration force, and r is the radius of the penetration plate. Contact pressure is more or less closely related to deflection and load.

Thus, it is extremely important to ensure that the entire surface area of the penetration plate is in contact with the soil.

A single bevameter test is not generally reliable for extrapolative purposes. Multiple penetration tests are needed due to the small chance of a given measurement being reliable. In the case of bevameter tests on actual terrain, multiple measurements are needed over a large area of the terrain for the reason previously mentioned and to ensure representative results of the entire terrain. However, a single bevameter plate-sinkage test is useful in the case that it is used in conjunction with other experiments. For example, if it is known that the soil is homogeneous via additional testing methods (such as the cone penetrometer test), then the quantitative data from the single bevameter test would enable the establishment of reasonable limits for the soil constants (Hinners 1964).

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Bekker (1969) recommends a minimum of two to three pressure-sinkage curves produced by plates of two or three sizes for soil characterization. Bekker states that this amount of testing is appropriate for a practical evaluation of the error caused by differences in penetration plate size and the vehicle’s ground contact areas as well as errors due to instrumentation and random nonhomogeneities of the soil.

The pressure-sinkage relationship used in this dissertation is the equation proposed by

Bekker (1969), which was defined in equation (4). For clarity the Bekker equation takes the following form:

⎡kc ⎤ n p = ⎢ + kφ ⎥ ⋅ z (84) ⎣ b ⎦

where p is the pressure and z is the sinkage, kc and kφ are moduli of deformation with respect to cohesion and friction, b is the contact width of a rectangular plate or the radius of a circular plate, and n is the empirical soil value which defines the shape of the load-

penetration curve (Bekker 1962, 1969). kc , kφ , and n are otherwise known as the terrain constants. In order to process the experimental data, namely the pressure p and sinkage z curves, obtained from the plate-sinkage bevameter tests to determined the terrain constants, Wong’s (1980) weighted least squares method is employed. This method was originally derived as reflected in equations (10) through (14) of section 1.6.1.1, Bearing

Capacity, for bevameter tests using two different plate sizes. Again for clarity, Wong’s

314 method for data processing derives the best fitted values of the pressure-sinkage terrain parameters by minimizing the following function using a weighting factor p2,

2 2 F = ∑ p [ln p − ln(kc / b + kφ )− nln z] (85)

Minimization of equation (85) involves taking the partial derivatives of the function with

respect to n and keq , where keq = (kc /b + kφ ) , and setting them equal to zero. Solving

the resulting equations simultaneously gives rise to the following equations for n and keq .

∑ p 2 ∑ p 2 ln p ln z − ∑ p 2 ln p∑ p 2 ln z n = 2 (86) ∑∑p 2 p 2 ()ln z 2 − () ∑p 2 ln z

p 2 ln p − n p 2 ln z ln k = ∑ ∑ (87) eq ∑ p 2

When using two different plate sizes a unique n is usually obtained for each. Therefore, it is required to use the average n-value resulting from the two different plates when

calculating lnkeq in equation (87). However, since keq = (kc /b + kφ ) there will be two

resulting keq -values, one for plate size b1 and another for plate size b2. Accordingly, the

values of kc and kφ can be determined using the following equations, equations (88) and

(89). It should be noted that these equations were derived based on two plate sizes, but can easily be modified to account for a third plate size using a lest squares approach.

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k − k ( eq )b1 ( eq )b2 kc = b1b2 (88) b2 − b1

⎡(k ) − (k ) ⎤ k = k − eq b1 eq b2 b (89) φ ()eq b1 ⎢ ⎥ 2 ⎣ b2 − b1 ⎦

The initial characterization of GRC-1 was determined by performing a total of 15 pressure-sinkage tests. Five repeat tests were conducted using a penetration plate size of

7.6 cm in diameter. Five repeat tests were conducted using a penetration plate size of

10.2 cm in diameter. The final five repeat tests were conducted using a penetration plate size of 19 cm in diameter. All tests were conducted in the 74.2 cm square polypropylene soil bin at a soil depth of 24 cm. The test procedure followed for all pressure-sinkage tests for the determination of the soil parameters for GRC-1 is discussed in the following section.

5.3.1 Experimental Procedure

The following experimental procedure was used for pressure-sinkage bevameter testing to determine the Bekker soil parameters of GRC-1:

1. Prepare GRC-1 to a depth of 24 cm in the 74.2 cm square rigid polypropylene soil

bin (using the hopper method) to a density of 1.67 g/cc (24-percent relative

density).

2. Collect plate-load and sinkage data as usual, using a load cell and LVDT,

respectively.

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3. Physically balance the penetration plate (using the counter balance platform as

shown in Figure 5.3) and then lower the penetration plate until it just touches the

soil surface (ensuring that the penetration plate is near the center of the soil bin).

Electrically balance the load cell and offset the LVDT data so that the output now

corresponds to zero load and zero sinkage.

4. Place weights on the bevameter load platform (as shown in Figure 5.3) in

increments of 1 kg until 10 kg (to get good resolution at small loads and

sinkages), then in increments of 2 kg until 20 kg, and 5 kg until 65 kg is reached.

If additional load is necessary continue in increments of 9 kg (20 lb weights) until

failure, which occurs when the plate “punches” through the soil.

5. Repeat steps 1 through 4 a total of 5 times for each penetration plate size, using

penetration plate sizes of 7.6 cm, 10.2 cm, and 19 cm diameters.

In the data processing steps, the variable i represents the penetration plate number

(i ∈[]1,3 ) where 1 is representative of the 7.6 cm diameter plate, 2 is representative of the

10.2 cm diameter plate, and 3 is representative of the 19 cm diameter plate; and j represents the test number index ( j ∈[1,5]). For each of the five repeat tests performed with the ith penetration plate, the same loads were applied. However, the resulting force varied slightly because of friction in the bevameter system. To correct for this minor variation, a cubic spline18 was used to resample the sinkage data for each plate size to a common and uniformly spaced pressure vector pi. The resulting sinkage data was stored

18 In MATLAB, the cubic spline is constructed of piecewise third-order polynomials which pass through a set of control points. The second derivative of each polynomial is commonly set to zero at the endpoints to provide a boundary condition that completes the system of equations. This creates a cubic spline which leads to a simple tridiagonal system that can be solved easily to give the coefficients of the polynomials. 317

19 in vectors zij. Using these vectors , the ensemble mean and ensemble deviations were calculated as follows, respectively:

1 n z i = ∑ z ij (90) n j=1

1 n ˆ z i = ⋅ ∑ z ij − z i (91) n −1 j=1

where n is the total number of observations. Using the new pressure vectors pi and the

mean sinkage vectors zi , equations (86) through (89) are employed to determine ni and k for each corresponding plate size. Following a least squares approach20, k and eqi c

kφ are determined as follows (using navg including all three plates):

A⋅ x = b (92)

x = A \ b (93)

Where,

1 b 1 ⎡k ⎤ ⎡ 1 ⎤ eq1 ⎢ ⎥ ⎢ ⎥ ⎡kc ⎤ A = 1 b2 1 , b = keq , and x = ⎢ ⎥ ⎢ ⎥ ⎢ 2 ⎥ k ⎢1 b 1⎥ ⎢k ⎥ ⎣ φ ⎦ ⎣ 3 ⎦ ⎣ eq3 ⎦

19 In this sense the term “vector” is intended to represent a column array. 20 As implemented in MATLAB. 318

Finally, with the values of values of kc , kφ , navg, and bi, the Bekker curve-fit was applied to each corresponding data set following equation (84) and the goodness-of-fit of this curve-fit to the data set was calculated using equation (15). The corresponding

MATLAB code for the data processing is provided in Appendix D.

5.3.2 Test Results and Analysis

Initial pressure-sinkage tests for the determination of the Bekker soil parameters of GRC-

1 were performed using three plate sizes as previously stated; 7.6 cm diameter, 10.2 cm diameter, and 19 cm diameter. The results of these tests on GRC-1 prepared to a density of 1.67 g/cc or 24-percent relative density are shown in Figures 5.51 and 5.52 below. It is important to note that although data was collected to pressures exceeding those shown in the plots below (for the small and medium sized penetration plates), the pressure range over which the data was evaluated was selected to represent the range of expected ground pressures from lunar exploration vehicles on the Moon. Figure 5.51 displays the raw data collected from each of the five repeat tests for each penetration plate; as well as the mean pressure-sinkage curve for each data set. The maximum standard deviations of these pressure-sinkage curves are 0.5 mm, 0.4 mm, and 0.8 mm, for the 7.6 cm, 10.2 cm, and

19 cm plate, respectively. Figure 5.52 displays the results of Bekker curve-fit and soil parameters. As can be seen, the Bekker curve-fit corresponds to the experimental data very well. The “goodness-of-fit” as determined by equation (15) was 0.069 for the 7.6 cm diameter plate, 0.143 for the 10.2 cm diameter plate, and 0.249 for the 19 cm

319 diameter plate. The closer these values are to zero the better the fit. In all three cases the curve-fits were fairly accurate. Initial observations reveal that for similar pressures, the larger plate sizes sink more than the smaller plate sizes, which makes sense based on general soil mechanics theory. However, it can also be seen that for small changes in plate sizes such as the small change between the 7.6 cm diameter plate and the 10.2 cm diameter plate, the pressure-sinkage curves are very close to each other. This means that the size effect is very small in this case. In addition, for GRC-1 prepared to a density of

1.67 g/cc (24-percent relative density) and pressures up to 50 kPa, the value of n is approximately 1.23. Since this value is greater than one it suggests a “soil strengthening” behavior which is clearly shown by the Bekker curve-fits in Figure 1.52. The values for

n+1 n+2 kc and kφ were determined to be 4096 kN/m and -22,285 kN/m , respectively. The

negative value determined for kφ is not an issue because kc and kφ do not explicitly represent physical soil parameters and correlate with n. Therefore, as the value of n

changes, the values of kc and kφ change correspondingly.

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50 45 7.6 cm Plate 40 10.2 cm Plate cm 10.2 35 19 cm Plate 30 2 25 Pressure, kN/m Pressure, 20 15 10 5 0

0 1 2 3 4 5 6 7 8 9

10 Sinkage, mm Sinkage,

Figure 5.51 Raw data and mean pressure-sinkage vector for 7.6, 10.2, and 19 cm penetration plates.

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50 45 7.6 cm Plate 40 10.2 cmPlate 10.2 35 19 cm Plate 30 2 25 Pressure, kN/m Pressure, n+2 20 15 , kphi = -22284.5786 kN/m = -22284.5786 , kphi n+1 10 5 n = 1.232, kc= 4096.3537 kN/m 0 0 1 2 3 4 5 6 7 8 9 10

Sinkage, mm Sinkage,

Figure 5.52 Raw data compared to Bekker curve-fit.

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For comparison with the Bekker curve-fits over the entire range of data (not just the lunar range) collected for the three penetration plates, Figure 5.53 is shown below. As can be seen, the Bekker curve-fits are not as good as for the lunar pressure range. The

“goodness-of-fit” now ranges from 0.466 to 0.794 which is much greater than the goodness-of-fit for the lunar range and is significantly higher than zero. This is most likely due to the large amount of scatter in the data that is seen in the higher pressure ranges, especially for the 7.6 cm plate. The maximum standard deviation for the pressure-sinkage curves over the entire pressure range were 12 mm, 1.6 mm, and 1.7 mm for the 7.6 cm, 10.2 cm, and 19 cm plate, respectively. These values are much larger than experienced over the lunar pressure range. During the repeat tests for the 7.6 cm diameter plate a few tests actually experienced soil failure, where the plate “punched” through the soil as shown in Figure 5.54(b). Punching shear is typical for compressible soil such as sands having low relative density and being subjected to significant bearing pressure. The other tests experienced general shear failure and therefore did not sink to such great extents. As a result, the scatter in the data is very large and the mean pressure- sinkage curve may not have been truly representative of a 7.6 cm plate bearing on GRC-1 at 24-percent relative density. As such, the Bekker parameters show a “soil weakening” condition where n is less than one as compared to the soil strengthening condition over the lunar pressure range. For the complete pressure range tested, the n value of GRC-1 is

approximately 0.81. The values for kc and kφ were determined to be approximately 97 kN/mn+1 and 1744 kN/mn+2, respectively.

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160 140 7.6 cmPlate 120 100 2 80 Pressure, kN/m Pressure, 60 n+2 10.2 cm Plate cm 10.2 40 , kphi = 1744.2495 kN/m n+1 20 19 cm Plate n = 0.80563, kc = 97.06 kN/m 0 0 5 10 15 20 25

Sinkage, mm Sinkage,

Figure 5.53 Bekker curve-fits for entire range of data.

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(a) (b) Figure 5.54 (a) Typical amount of sinkage for 19 cm diameter plate (as shown by resulting impression in GRC-1). (b) Punching shear failure of 7.6 cm diameter plate (plate is completely submerged in GRC-1, just the end effector mount is visible).

It is difficult to directly compare these soil parameters for GRC-1 with typical values for dry sandy soil found in the literature. This is because most cases of pressure-sinkage bevameter tests were conducted in the field on “terrain” instead of in laboratory conditions of manually prepared “soil”. Therefore, the density corresponding to these sandy terrains were not determined or not reported and the Bekker parameters presented are representative of that specific type of terrain, not a specific density of a soil.

Nevertheless, typical Bekker parameters for dry sandy terrains are presented in Table 5.3.

As can be seen, the value of n obtained for GRC-1 is definitely comparable to typical sandy terrain parameters determined by previous investigators.

Table 5.3 Typical Bekker parameters for dry sand.

kc, k φ , n n+1 Source kN/m kN/mn+2 0.6 0 624.6 NASA 1970 0.793 102 5301 Wong et al. 1984 0.8 0 520.8 NASA 1970 0.93 118 8501 Wong 1980 1.1 0.99 1528.43 Wong 2001 1.29 -27.83 3579.8 Sela and Ehrlich 1972 1.68 29.31 8378.5 Chen 1993

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In order to compare the general trend of the pressure-sinkage curves obtained for GRC-1 with those from the previous researchers listed in Table 5.3, i.e. the Bekker parameters determined by these investigators were used to derive pressure-sinkage curves following the experimental parameters of the tests performed on GRC-1 (7.6 cm , 10.2 cm, and 19 cm plate diameters). The closest parameters to those of the parameters obtained for

GRC-1 over the entire pressure range21 were Wong et al.’s (1984). Thus, these parameters were selected to directly compare to GRC-1. The results are shown in Figure

5.55. As can be seen, the general trends are very similar, i.e. for similar pressure, the larger plates sink more than the smaller plates; and both show the general trend of “soil weakening”. However, GRC-1 appears to be weaker than the dry sandy terrain as tested by Wong et al. (1984). It is difficult to make a definite conclusion as to why, but most likely the terrain was more compact and therefore denser than GRC-1 prepared to a density of 1.67 g/cc or 24-percent relative density.

21 The Bekker parameters for the entire pressure range of GRC-1 were selected for this analysis (over those for the lunar pressure range) because typical pressure-sinkage tests in terrestrial terrain were evaluated over much larger pressure ranges. Thus, it was felt that parameters over this pressure range would be more comparable to parameters obtained from previous investigations on dry sandy terrain. 326

15 Wong et al. 1984

Sinkage, mm 25 GRC-1

40 0 100 200 300 400 500 600 Pressure, kN/m2

Figure 5.55 Comparison of GRC-1 Bekker parameters and parameters derived by Wong et al. (1984) for a dry sandy terrain.

Additional plate-sinkage tests were performed on GRC-1 prepared to various densities so that a general relationship or better understanding of the relationship between the Bekker parameters and relative density of GRC-1 could be determined. A total of nine new tests were completed. These tests were performed following the same procedure as the previous pressure-sinkage tests on GRC-1. However, only a single test was performed for each plate size rather than the five repeat tests. Although Bekker recommends a minimum of at least two repeat tests, Hinners (1964) as previously stated, suggests that a single bevameter plate-sinkage test is useful in the case that it is used in conjunction with other experiments. The results from a single bevameter test on GRC-1 can be compared to the results of cone-penetration tests on GRC-1 to establish reasonable limits for the soil parameters as will be discussed in subsequent chapters. Additionally, as a measure to

327 save time and increase reliability of the soil density a new soil bin was used. This soil bin was a clear acrylic soil bin with a wall thickness of 1.27 cm (0.5 in). It is extremely rigid compared to the previous soil bin. Thus, it ensures that no bowing out of the bin walls will take place during soil preparation or testing (which could affect the soil density). Additionally, since the bin is clear, it has the advantage of visually ensuring a level soil surface at the desired height. This bin, as shown in Figure 5.56, has an inner diameter of 59.7 cm (23.5 in), which is over three times the diameter of the largest plate

(19 cm), and has a height of 30.5 cm (12 in). GRC-1 was again prepared to a depth of 24 cm, but was prepared to densities of 1.64 g/cc, 1.67 g/cc, and 1.75 g/cc or 14, 24, and 52- percent relative density, respectively. It was found to be increasingly difficult to uniformly prepare GRC-1 to densities greater than 1.75 g/cc. Test results are shown in

Figure 5.57 through Figure 5.59 together with the corresponding Bekker curve-fits over the lunar pressure range. The soil parameters are summarized in Table 5.4.

Figure 5.56 Clear acrylic soil bin.

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7.6 cm Plate 3

5 19 cm Plate

Sinkage, mm 6 10.2 cm Plate

9 n = 0.95024, kc = 221.2618 kN/mn+1, kphi =1957.5095 kN/mn+2 10 0 5 10 15 20 25 30 35 40 45 50 Pressure, kN/m2

Figure 5.57 Pressure-sinkage curves for GRC-1 at 1.64 g/cc.

1 7.6 cm Plate 2

4 10.2 cm Plate 5 19 cm Plate

Sinkage, mm 6

9 n = 1.0119, kc = 649.6448 kN/mn+1, kphi =-1199.1232 kN/mn+2 10 0 5 10 15 20 25 30 35 40 45 50 Pressure, kN/m2

Figure 5.58 Pressure-sinkage curves for GRC-1 at 1.67 g/cc.

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1 7.6 cm Plate 2

10.2 cm Plate 4

5 19 cm Plate

Sinkage, mm 6

9 n = 1.1107, kc = 1581.1504 kN/mn+1, kphi =-5139.1398 kN/mn+2 10 0 5 10 15 20 25 30 35 40 45 50 Pressure, kN/m2

Figure 5.59 Pressure-sinkage curves for GRC-1 at 1.75 g/cc.

Table 5.4 Bekker parameters for GRC-1 at various densities. Average Density Relative k, n k , kN/mn+1 φ Goodness (g/cc) Density (%) c n+2 kN/m of Fit 1.64 14 0.95 221.26 1957.51 0.238 1.67 24 1.01 649.64 -1199.12 0.598 1.75 52 1.11 97.06 1744.15 0.282

As shown, the goodness-of-fit for the Bekker curve-fits to the raw pressure-sinkage data for GRC-1 are relatively good. The n-values tend to increase with increasing density going from a soil weakening condition at a low relative density to a soil strengthening

condition at mid relative densities. The kc and kφ values show no obvious trends with respect to density. However, these parameters are difficult to analyze as they are dependent on the pressure, sinkage, and n. To check the validity of this data since it was

330 determined based on a single test, the test results for GRC-1 at 1.67 g/cc can be compared to previous test results for GRC-1 at 1.67 g/cc based on multiple repeat tests. Recall that for the lunar pressure range the Bekker parameters were 1.23, 4096 kN/mn+1, and -22,285

n+2 kN/m for n, kc , and kφ , respectively, with an average goodness-of-fit of 0.154.

Compared to the new results for GRC-1 (1.01, 649.64 kN/mn+1, and -1199.12 kN/mn+2, respectively, with an average goodness of fit of 0.598), the n value is much higher

therefore forcing kc and kφ to be higher and lower, respectively; and the goodness-of- fit is much better. This however, does not invalidate the new data. It simply suggests two things: that the density of the material may have varied from test to test and may not have been 1.67 g/cc in both cases; and that based on the goodness-of-fit, the Bekker parameters from the repeat tests are more reliable than those from the single test. It has been shown that the value of n is extremely sensitive to the soil density (Bekker, 1969).

Unfortunately, soil density is one of the most difficult soil parameters to control.

Based on the scatter naturally associated with bevameter plate-sinkage tests, it is difficult to make a definite conclusion about the Bekker parameters of GRC-1. However, from the results of the data collected over the lunar pressure range it is reasonable to assume that the value of n is slightly greater than or equal to one for a loose to medium dense soil preparation. Thus, GRC-1 is generally a strong soil and tends to “strengthen” as it compacts. Additionally, under low pressures (up to 50 kPa) sinkage is expected to be less than 10 mm (0.4 in) for contact areas ranging from 45 cm2 to 284 cm2. Therefore, wheels operating in GRC-1 under very light loads produce relatively flat contact patches and such small sinkage that, for practical purposes, that latter might be neglected.

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Therefore, the “soil potential” available for the wheel to produce forward pull would be equal to the horizontal force given by the Coulomb relationship and modified by

Micklethwait (1944) cited by Freitag et al. (2007), as described in section 1.6.1.2 of this dissertation entitled Shear Strength. For clarity the equation is repeated as,

F = Ac +W tanφ (94)

Where A is the contact area of the wheel and W is the vehicle weight or load. Thus, the bevameter shear test is extremely important for the characterization of GRC-1 with respect to lunar exploration vehicle mobility. The bevameter shear tests on GRC-1 are discussed in the subsequent section.

5.4 SHEAR TEST FOR VEHICLE MOBILITY

The bevameter test designated to simulate the shear loads exerted by a vehicle on the terrain surface is the shear test. The results of the bevameter shear test provide the basis for the prediction of vehicle traction in a specific terrain. According to Bekker (1969),

“since one of the basic conditions for predicting vehicle performance is that the vehicle’s shear action be simulated by instrument-predictor, the values of devices like the triaxial shear apparatus has been questioned, inasmuch as their operation is too dissimilar to actual conditions for developing vehicle thrust.” In the bevameter shear test, two different types of shear rings are used. The first shear ring used is for measuring the internal shear strength of the soil. It consists of a shear ring with grousers. The second

332 shear ring is used to measure the wheel material-terrain shearing characteristics. This shear ring surface is covered with low grit sandpaper. For each different shear test, various normal loads are applied on the shear ring to represent the range of normal pressures expected to be experienced by the vehicle. During each test, the shear displacement or the rotational distance traveled by the shear ring and the torque are recorded. Additional information such as sinkage (slip-sinkage) and variation of the normal load can be recorded as well. The shear stress of the soil according to Chen

(1993) is obtained by dividing the torque by the product of the contact area of the shear ring and the average radius of the shear ring as shown in the following equation,

T τ = (95) π ()r + r ()r 2 − r 2 2 o i o i

where τ is the shear stress, T is the torque measured, and ro and ri are the outer and inner radii of the shear ring, respectively. The shear stress (strength) of soil is heavily dependent on the bulk properties of the soil such as the grain size distribution, bulk density, cohesion, angle of friction, and grain shape and hardness. The shape of the soil grains affects their ability to interlock which increases friction and shear strength. More specifically, round or spherical particles typically flow easily while angular soil particles or glass particles such as lunar agglutinates typically interlock and obstruct soil flow.

The shear strength of soils under load is directly related to friction between grains and provides a measure of aggregate interlock and soil structure as well.

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According to Bekker (1969), a minimum of three shear tests at different normal pressures

(within the range of ground pressure expected to be exerted from the wheels of a vehicle) is necessary to accurately determine the terrain parameters from stress-deformation curves produced by shear bevameter tests. Moreover, he recommends a total of five tests at various normal pressures, especially for investigations conducted in the field. It is suggested to perform two repetitive tests in order to determine the size of discrepancy between the two. Based on this information, the minimum number of tests can be determined subjectively by the investigator. Generally, in a laboratory environment five tests is sufficient to accurately determine the soil parameters. Since shear tests are less sensitive to variation in density than pressure-sinkage tests, repeat tests usually show a negligible scatter of data.

The stress-deformation or stress-displacement (used interchangeably) relationship used in this dissertation is the exponential equation previously defined by equation (21), proposed by Janosi and Hanamoto (1961). For clarity, the equation is as follows,

⎛ − j ⎞ τ = τ ⎜1− e K ⎟ (96) max ⎜ ⎟ ⎝ ⎠

where τ max is the maximum shearing stress or shear strength of the soil, j is the shear displacement, and K is the shear deformation modulus of the soil which can be considered a measure of the magnitude of the shear displacement required to develop the maximum shear stress in a given soil. In order to obtain the shear parameters of the soil,

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Wong’s (1980) weighted least squares principle is applied as previously described by equations (23) through (25). Again, for clarity, Wong’s procedure as previously described begins with taking the natural logarithm of both sides of equation (21). This leads to the following function,

2 2 ⎛ τ ⎞ ⎡ ⎛ τ ⎞ j ⎤ F = ∑⎜1− ⎟ ⎢ln⎜1− ⎟ + ⎥ (97) ⎝ τ max ⎠ ⎣ ⎝ τ max ⎠ K ⎦

which must be minimized in order to determine the best value of K. Note that this

2 function has an applied weighting factor of (1−τ /τ max ) . In order to minimize equation

(97), the first partial derivative of the function with respect to K is taken and set equal to zero. This in-turn leads to the final equation which computes the optimum value of K in order to minimize the error from the curve-fit.

2 2 ∑(1−τ /τ max ) j K = − 2 (98) ∑(1−τ /τ max ) j[]ln(1−τ /τ max )

The initial characterization of GRC-1 was determined by performing a total of 18 shear bevameter tests. Five shear tests at various normal pressures ranging from 5 kPa to 30 kPa (within the expected lunar pressure range and within limitations of the table bevameter shear system) in order to determine the shear parameters of GRC-1 at a specified density. A total of three complete test sets were performed: one at a density of

1.64 g/cc, a second at a density of 1.67 g/cc, and a final at a density of 1.75 g/cc, or 14,

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24, and 52-percent relative density, respectively. Again, it was difficult to uniformly prepare GRC-1 to densities greater than 1.75 g/cc. One repeat test set was performed for a density of 1.67 g/cc at three various normal loads to check the repeatability of the tests.

All tests were conducted in the 59.7 cm diameter acrylic soil bin at a soil depth of 24 cm.

The shear ring used for these tests was an annular ring with an inner diameter of 14 cm and an outer diameter of 17.9 cm, with the bottom surface covered with a low grit sandpaper. The test procedure followed for all shear bevameter tests for the determination of the soil parameters of GRC-1 is discussed in the following section.

5.4.1 Experimental Procedure

The following experimental procedure was used for shear bevameter testing to determine the Bekker soil parameters of GRC-1:

1. Prepare GRC-1 to a depth of 24 cm in the 59.7 cm diameter rigid acrylic soil bin

(using the hopper method) to a predetermined density of 1.64, 1.67, or 1.75 g/cc.

2. Collect plate-load and sinkage data as usual, using a load cell and LVDT,

respectively. In addition, collect torque and angular displacement data using a

torque cell and potentiometer, respectively.

3. Physically balance the shear ring (using the counter balance platform as shown in

Figure 5.3) and then lower the shear ring until it just touches the soil surface

(ensuring that the shear ring is near the center of the soil bin). Electrically

balance the load/torque cell and offset the LVDT and potentiometer data so that

the output now corresponds to zero sinkage and zero displacement.

336

4. Place weights on the bevameter load platform (as shown in Figure 5.3) to obtain a

normal pressure of approximately 5 kPa. For the size shear ring used this

corresponds to 5 kg of normal force.

5. Shear the soil by rotating the shear ring using the new moment arms22 attached to

the top of the load/torque cell as shown in Figure 5.60. According to Bekker

(1969), the rate of deformation has little effect on the resulting soil strength.

Therefore, the rate of rotation is not critical as long as it is kept at a nearly

constant rate.

6. Repeat steps 1 through 4 a total of five times for increasing normal pressures of 5,

7, 10, 20, and 30 kPa (5, 7, 10, 20, 30 kg).

Moment Arms

Figure 5.60 New manual rotation system attached to load/torque cell.

22 Originally the table bevameter was designed to be rotated manually using the shear wheel as shown in Figure 5.3. However through preliminary shear testing it was discovered that there was a significant amount of elasticity in the system which led to a slip-stick phenomenon. Essentially, the end effector or shear ring “sticks” in place until enough torque is generated to move it. The shaft and moment arm act like a spring coil, winding and then unwinding each time the end effector “sticks” in the soil. Therefore, the shaft, which was assumed to have the most elasticity, was bypassed and new moment arms were designed to be placed directly on the load/torque cell as shown in Figure 5.60. This new design eliminated the dynamic effects from the slip-stick phenomenon. 337

In the data processing steps, the variable i represents the normal pressure number

(i ∈[]1,5 ) where 1 is representative of the 5 kPa normal pressure, 2 is representative of the 7 kPa normal pressure, and so on. The resulting K values were stored in vectors Ki.

Using these vectors, the mean and standard deviations of K were calculated as follows, respectively:

1 n K = ∑ K i (99) n i=1

n ˆ 1 K = ⋅ ∑ K − K i (100) n −1 i=1

where n is the total number of observations, in this case five. Although equation (98) provides the value of K that minimizes the error in curve-fitting, the optimum value of

τ max is still unknown (τ max is not necessarily the maximum value of τ experimentally

obtained). Therefore, to obtain the optimum value of τ max , an iterative procedure was

implemented. In this procedure a value for τ max is approximated from the experimental data. The value of K is obtained as previously described. The goodness-of-fit is then evaluated using equation (25). If the goodness-of-fit is at its minimum possible value

(zero is a perfect fit) then the process is completed. However, if the goodness-of-fit is not

at its minimum value then a newτ max is estimated based on the current information, and the process is repeated and continued until the minimum goodness-of-fit is reached. The resulting τ values are then stored in vectors τ , while the corresponding normal max maxi

338 pressures are stored in vectors pi. Using the pressure vectors pi and the maximum shear stress vectors τ , the cohesion and friction angle of the soil at the specified density can maxi be obtained following the Mohr-Coulomb failure criterion (as described in equation (16)) and implementing a least squares approach. In this case,

A⋅ x = b (101)

x = A \ b (102)

Where,

τ ⎡ p1 1⎤ ⎡ max1 ⎤ ⎢ ⎥ ⎢ ⎥ p 1 τ max ⎢ 2 ⎥ ⎢ 2 ⎥ ⎡tanφ⎤ A = ⎢ p 1⎥ , b = ⎢τ ⎥ , and x = 3 max3 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ c p 1 τ ⎣ ⎦ ⎢ 4 ⎥ ⎢ max4 ⎥ ⎢ p 1⎥ ⎢τ ⎥ ⎣ 5 ⎦ ⎣ max5 ⎦

All data processing was performed in Microsoft Excel, the raw data for all shear tests is provided in Appendix D.

5.4.2 Test Results and Analysis

Results of the initial shear tests performed on GRC-1 at relative densities of 14, 24, and

52-percent are shown in Figures 5.61 through 5.63. A typical failure envelope for

339 determining cohesion and friction angle is shown in Figure 5.64. It is important to note that the curve-fits in Figure 5.61 through 5.63 were based on a K-value determined for only the first 5 cm of the data. It was important to determine K so that curve-fits fit the first 5 cm of data as best as possible. This distance was based on a maximum expected slip for lunar exploration vehicles of 20-percent which directly affects the traction or drawbar pull of a vehicle. Given the three prospective lunar vehicles: the LRV,

ATHLETE, and Chariot; the maximum contact length of the wheel on the ground surface currently is approximately 27 cm. This corresponds to a shear displacement of approximately 5 cm (under 20-percent slip). Therefore, it is important to best-fit the data in this given range of shear displacement and extrapolate the curve-fit to shear displacements beyond 5 cm. The resulting soil parameters are summarized in Table 5.5.

As shown, the average value of K tends to increase with increasing density of GRC-1.

This makes physical sense because when the density of a soil is higher, there will be fewer voids to fill and it will therefore take a shorter shear displacement for the soil particles to rearrange themselves and fill in the voids to ultimately reach a point where the soil reaches its maximum shear strength. In addition, the increase in density tends to have very little effect on the friction angle and cohesion of the soil. The friction angle ranged from 33 to 34-degrees and the cohesion held steady near 0 kPa. Because the friction angle and cohesion in this case are based on the interaction between the sandpaper and the soil, these properties of friction angle and cohesion are not as sensitive to the change in density. The negative values in cohesion are again a result of the difficulties experienced in measuring cohesion when using the Mohr-Coulomb failure criterion. As previously stated for the triaxial results, the determination of cohesion may

340 be difficult as a straight line extrapolation of the failure envelope back to the normal stress of zero. It is more likely that the strength envelope is curved in the region of small confining pressures. None-the-less, it is reasonable to assume, based on the results, that the cohesion for GRC-1 is very small (on the order of 1 kPa or less). One final observation is that the repeatability of the shear bevameter tests is very good as shown by the repeat tests at 1.67 g/cc in Table 5.5. The average K-values varied by only 0.01 cm while the friction angles varied by only 0.1-degree. This is especially good for the variation in applied pressure experienced with the table bevameter system. It was found that during the shear bevameter tests it was very difficult to control the normal load when applying torque. In some cases the normal pressure varied by as much as 0.8 kPa

(typically it varied more for larger loads than for smaller loads) which is why some of the resulting stress-displacement curves are not as smooth as they could or theoretically should be. However, it is assumed that the overall trend is correct. Therefore, an average value of normal load was used in the determination of the cohesion and friction angle values. In an ideal situation, a shear bevameter should have a normal load controlled by dead weights and a rotation controlled by a motor to avoid the variation of load due to additional load or removal of load by manual rotation. However, it is not known if bevameters of this type are better at controlling the normal load as the results of shear tests found in the literature (by these types of bevameters) did not report on the normal load or in most cases did not even have a load cell incorporated into the system to monitor the normal load. The portable bevameter at NASA Glenn, which operated with hydraulic load and motor controlled rotation, encountered many problems in holding a

341 constant normal load. In any case, this seems to be a common issue in shear bevameter tests and would be a viable issue to look into in future research.

20000

15000

10000 Shear Stress, Pa

5000

0 0.00 0.05 0.10 0.15 0.20 0.25 Shear Displacement, m

4.80 kPa Fitted 7.03 kPa Fitted 10.87 kPa

Fitted 19.89 kPa Fitted 29.01 kPa Fitted

Figure 5.61 Shear bevameter results for GRC-1 at 14-percent relative density.

342

20000

18000

16000

14000

12000

10000

8000 Shear Stress, Pa Shear 6000

4000

2000

0 0.00 0.05 0.10 0.15 0.20 0.25 Shear Displacement, m

4.94 kPa Fitted 7.10 kPa Fitted 10.22 kPa

Fitted 19.85 kPa Fitted 29.14 kPa Fitted

Figure 5.62 Shear bevameter results for GRC-1 at 24-percent relative density.

343

20000

18000

16000

14000

12000

10000

8000 Shear Stress, Shear Pa 6000

4000

2000

0 0.00 0.05 0.10 0.15 0.20 0.25 Shear Displacement, m

5.13 kPa Fitted 7.08 kPa Fitted 10.30 kPa Fitted 19.72 kPa Fitted 29.61 kPa Fitted

Figure 5.63 Shear bevameter results for GRC-1 at 52-percent relative density.

344

20000

18000 phi = 33.3 degrees c = 0.01 kPa 16000

14000

12000

10000

8000

6000 Max Shear Strength, Pa Strength, Shear Max 4000

2000

0 0 5000 10000 15000 20000 25000 30000 Normal Load, Pa

Figure 5.64 Typical failure envelope for determining cohesion and friction angle (result for 1.64 g/cc GRC-1).

Table 5.5 Summary of shear bevameter results for GRC-1. Standard Density Relative Average K Deviation c (kPa) φ (º) (g/cc) Density (%) (cm) (cm) 1.64 14 2.55 ±0.92 0.01 33.3 1.67 24 2.42 ±0.82 -0.10 33.7 1.67 24 2.43 ±1.29 -0.03 33.6 1.75 52 1.81 ±0.85 -0.48 34.0

In the bevameter shear tests, lateral failure limits the magnitude of applicable shear stresses, just as in the case of wheels. Therefore, bevameter tests as reported above (apart from effects of geometry) are representative of the strength that may be developed at the wheel-soil interface rather than of the internal friction of the soil (Karafiath 1970). The addition of grousers to wheels adds more vehicle thrust due to the forces produced by the vertical shear surfaces. Furthermore, the addition of grousers to shear bevameter tests

345 results in cohesion and friction angles more representative of the internal angle of friction of the soil rather than the surficial friction between the soil and the material of the wheel.

Therefore, a total of six additional tests were performed on GRC-1 in order to determine the internal friction angle of the soil and to evaluate any difference in the K-values obtained by using grousers. These tests were performed in the same rigid acrylic soil bin as the previous tests. Additionally, the same shear annulus was used; however the sandpaper was replaced by grousers as shown in Figure 5.50. GRC-1 was prepared to two different densities including 1.64 g/cc and 1.75 g/cc or 14 and 52-percent relative density, respectively. Three tests shear tests were performed for each density at normal pressures of 5 kPa, 10 kPa, and 30 kPa, respectively. The results of these tests are shown in Figure 5.65 and Figure 5.66. Table 5.6 provides a summary of the soil parameters obtained.

As shown, the average value of K tends to decrease with increasing density of GRC-1 as previously experienced. Again, the increase in density tends to have very little effect on the friction angle and cohesion of the soil. The friction angle ranged from 33.5 to 35- degrees and the cohesion again held steady near 0 kPa. None-the-less it is reasonable to assume that the cohesion for GRC-1 is very small (on the order of 1 kPa or less). It was initially expected that the internal angle of friction would increase with increasing density. However this is not what the results show. The results show the opposite, but vary in friction angle by only 1.5-degrees. This is most likely due to errors caused by the variation in normal pressure. For the shear ring with grousers the normal pressure seemed even more difficult to control than previously experienced. In some cases it

346 varied by as much as 3.2 kPa (again, typically it varied more for larger loads than for smaller loads). Therefore an average value of normal load was used in the determination of the cohesion and friction angle values, which could have easily thrown off the results by a couple degrees. In comparison to the data for the shear ring lined with sandpaper, the results generally agree very well. For a density of 1.64 g/cc the K-values varied by

0.23 cm and for a density of 1.75 g/cc the K-values varied by 0.19 cm. The cohesion remained small and is still assumed to be in the range of 1 kPa or less and the friction angles agreed well, remaining in the range of 33 to 35-degrees. From this it can be determined that the addition of grousers to prospective wheels for the lunar exploration vehicles is not necessary to gain vehicle thrust. The sandpaper appears to be sufficient.

347

20000

15000

10000 Shear Stress, Pa

5000

0 0.00 0.05 0.10 0.15 0.20 0.25 Shear Displacement, m

5.14 kPa Fitted 9.79 kPa Fitted 27.70 kPa Fitted

Figure 5.65 Shear bevameter results for GRC-1 at 1.64 g/cc using grousers.

348

20000

15000

10000 Shear Stress, Pa

5000

0 0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 Shear Displacement, m

4.99 kPa Fitted 9.28 kPa Fitted 28.04 kPa Fitted

Figure 5.66 Shear bevameter results for GRC-1 at 1.75 g/cc using grousers.

Table 5.6 Summary of shear bevameter results for GRC-1 using grousers. Standard Density Relative Average K Deviation c (kPa) φ (º) (g/cc) Density (%) (cm) (cm) 1.64 14 2.32 ±0.53 0.28 35.0 1.75 52 2.00 ±0.32 0.41 33.5

As with the pressure-sinkage bevameter tests, it is difficult to compare the results obtained for GRC-1 with results for sandy soil as reported in the literature, due to the fact that the resulting parameters were typically determined for a specific terrain type and not a soil tested in laboratory conditions. Therefore, the density and moisture content of the soil corresponding to the terrain tested were typically not reported. In addition, these

349 tests were typically conducted under much higher normal pressures than attainable in the soils lab at NASA Glenn. None-the-less, the typical parameters for dry sandy terrains as determined by previous investigators are reported in Table 5.7 below.

Table 5.7 Typical shear parameters for dry sand. Shear Ring Average K c (kPa) φ (º) Source Type (cm) Grousers 1.9 1.08 25 Chen 1993 Rubber 1.9 0.22 27.7 Rubber 3.3 0 27.6 Wong 1980 - - - - 1.04 28 Wong 2001 - - 1.02 0 34 ± 3 NASA 197023 - - 0.89 0 34 ± 3

As shown, the results for GRC-1 tend to agree fairly well with typical results for dry sand terrain. Typical results for K-values range from 0.89 to 3.3 cm, whereas GRC-1 ranged from 1.81 to 2.55 cm. Typical results for the friction angle of dry sand terrain ranged from 25 to 34-degrees whereas GRC-1 was on the higher end ranging from 33 to 35- degrees. The cohesion values typically reported for dry sandy terrain are near 1 kPa or less as suggested for GRC-1. Thus, it can be concluded that the soil shear parameters obtained for GRC-1 are reasonable values for a dry sandy soil.

5.5 COMPARISON WITH LUNAR SOIL

There are no available terrain parameters directly measured for the lunar soil. The closest soil parameters available for comparison are those recommended in the Lunar

Sourcebook (Heiken et al.1991) which were empirically determined based on a proposal

23 The first listing in table 5.7 is for uncompacted dry sand. The second listing is for the same compacted dry sand. 350 for the LRV as previously described in section1.7.2.3, Trafficability Parameters, of this dissertation. These values are listed in Table 5.8 compared to those obtained for GRC-1.

Table 5.8 Comparison of lunar soil parameters to those of GRC-1 as determined by bevameter testing. Lunar Soil GRC-1 n 1.0 .95 – 1.23 n+1 kc, kN/m 1.4 97 – 4096 n+2 k,φ kN/m 820 -22285 – 1958 K (cm) 1.8 1.81 – 2.55 c (kPa) 0.17 0 – 1.0 φ (º) 35 33 – 35

As shown, the soil parameters generally agree very well between the lunar soil and that of

GRC-1, excluding the kc and kφ values. Based on the results of GRC-1, it appears that a loose to medium dense preparation more accurately simulates the stress-strain relationships and terrain parameters of the lunar soil. However, it is important to remember that these are not actual terrain parameters for the lunar soil and are only best estimates based on laboratory testing of lunar soil simulants compared to the actual performance of the LRV after Apollo 15.

CHAPTER SIX

351

CONE PENETROMETER TESTING FOR STRENGHT PROPERTIES OF GRC-1

6.1 CONE PENETROMETER DEVICE AT NASA GLENN

Prior to conducting lunar exploration vehicle mobility tests on large specimens of dry sand, specifically GRC-1, it was necessary to develop procedures and techniques for controlled preparation of these specimens. This preparation requirement generated a need for a non-destructive test that could be used to determine a characteristic physical property of the specimen and also to assess the uniformity of the specimen construction and its similarity in strength to the actual lunar soil. The cone penetrometer test was selected as the device having the greatest potential for this test, as a result of the instrument’s capabilities and the available cone penetrometer data from the Apollo missions. The cone penetrometer has the ability to quickly and easily provide cone penetration resistance (CPR) as a function of depth for in-situ material, while creating little disturbance of the soil specimen. It is important to note that the CPR represents an indirect measurement of soil properties (and is unitless), but can be correlated with more basic properties such as relative density as will be discussed later in this chapter.

All cone penetration tests on GRC-1 were performed at the NASA Glenn Research

Center using the CP40II Cone Penetrometer from ICT International24 of Australia.

Figures 6.1(a) and 6.1(b) show the device and its accessories, respectively. This device was designed to follow ASAE standard S313.3 for soil cone penetrometers. It consists of two interchangeable 30-degree cone tips with base areas of 130 mm2 for harder soils and

24 www.ictinternational.com.au 352

323 mm2 for softer soils. The shaft size is approximately 9.53 mm in diameter. Using the small cone, a maximum pressure of 5600 kPa can be applied. Using the large cone, a maximum pressure of 2200 kPa can be applied. Both of these pressure ratings correspond to 75 kg of mass pushing the cone into the soil.

(a) (b) Figure 6.1 (a) CP40II Cone Penetrometer from ICT International. (b) CP40II accessories.

Via load cell and ultrasonic transducer, respectively, the CP40II measures and records cone index values of the load required to insert the cone through the soil. The device automatically plots the cone index values against the depth in a graphical representation of the hardness of the soil as shown in Figure 6.2. These results can be downloaded to a

PC from the CP40II retrieval software provided. The penetrometer can record up to 2047 insertions (individual penetration tests) with depths of up to 750 mm25. During each insertion the CP40II takes readings from both the load cell and ultrasonic transducer at the rate of 40 readings per second. The device then averages those results and stores the average as the data for that interval. The interval can be set to 10, 15, 20, or 25 mm depending on the total depth of the penetration test. So, if the interval was set to 10 mm,

25 The device is designed to record zero depth as the point at which the base of the cone is flush with the soil surface, i.e. the point of burial of the cone. 353 the CP40II would take readings from 0 to 10 mm depth and average them for the first interval. Then it would take readings from 10 to 20 mm depth and average them for the second interval and so on, until the last interval is recorded at the end of the insertion.

The company claims that this method of processing data minimizes errors caused by

“jittering” of the CP40II by small pockets of air, stones, sticks, roots, etc.

Figure 6.2 Typical readout of CP40II data.

6.2 EXPERIMENTAL PROCEDURE

The procedure outlined below was generally followed in accordance with ASAE standards S313.3 and ASAE EP542 to determine the cone penetration resistance as well as the cone index gradient of GRC-1 with respect to depth and density.

1. Prepare GRC-1 to a predetermined density in a designated rigid soil bin26.

26 Three different soil bins were used throughout the duration of CPT testing. Initial tests were performed in a rigid 74.2 cm square polypropylene bin. Later tests were conducted in a circular polypropylene bin with approximate diameter of 55.3 cm, as well as a circular acrylic bin with approximate diameter of 58.4cm. 354 a. Begin with a specified density of GRC-1. b. Back calculate the mass of GRC-1 needed to obtain this density, using the

known bin dimensions and a soil height of 18 cm. For example, to obtain

a soil density of 1.60 g/cc the following steps would be taken to determine

the mass of the soil needed:

g mass 1.60 = cc volume

g mass 1.60 = cc 74.2cm*74.2cm *18cm

mass = 158562.43g ≅ 349.57lb

c. Measure the appropriate amount of GRC-1 and fill the bin in uniform

layers using the single-orifice soil hopper with an average flow rate of 350

g/sec and a maximum fall height (the height at which soil falls out of the

hopper and into the soil bin) of no more than 2.54 cm (1 inch). Figures

6.3(a) and 6.3(b) show the soil hopper and partially filled soil bin,

respectively. It should be noted that the larger the fall height the more

dense the soil will be. d. Place the bin on the Syntron 76.2 cm (30 in) square vibrating table and

shake at a power level of three until the soil is compacted to the desired

height of 18 cm. The power level may need to be increased to six in order

355

to obtain very dense soil samples. In the case of minimum density this

step may not be necessary.

(a) (b) Figure 6.3 (a) Soil hopper. (b) Partially filled soil bin.

2. Place the cone penetrometer target over the desired testing location, ensuring that

the target is level. Be careful not to test too close to the sidewalls of the soil bin

as boundary effects will ultimately increase the strength of the soil.

3. Keeping the target on the ground, hold the weight of the CP40II to stop the cone

from sinking into the soil. The cone needs to be above the ground to start the

insertion. Once the insertion is started, push the cone through the soil vertically,

putting no sideways/lateral force against the shaft, following the hole made by the

cone smoothly and at a constant speed (aiming for 2 cm per second or less) until

the insertion is finished and the maximum depth27 is attained (refer to Figure 6.4).

4. Save the data, remove the cone from the soil, and repeat steps 2 through 3

ensuring ample space between test location so that the test is not performed on an

27 To avoid influence of bottom boundary conditions from the soil bin, measurements were only taken to a depth of 120 mm (not the full 180 mm of soil). 356

area of previously disturbed soil. Perform a minimum of sixteen tests per soil

preparation (depending on the size of the soil bin) in order to obtain a

representative average of the cone penetration resistance of GRC-1 throughout the

soil bin. ASAE standard EP542 recommends a minimum of 20 cone penetration

tests be performed to provide a reliable estimate of the mean CI. However, this

standard is for in-situ conditions. Since the GRC-1 is prepared in a controlled

laboratory environment the results are likely to be more repeatable. In addition

GRC-1 is a dry material. Therefore, moisture content will have no impact on the

cone index results. Statistical analyses of similar cone penetration tests performed

on dry sand by Poplin (1965) showed that four penetration tests produced a

computed mean value of CPR that should be within 10-percent of the true mean

value; the average of eight observations should be within 6-percent of the true

value; and the average of 25 observations should be within 2.5-percent of the true

mean value; i.e. the more penetration tests within a given area of soil sample, the

more statistically sound the evaluation.

5. Repeat steps one through three for various soil densities to determine the

relationship between penetration resistance and density.

357

Figure 6.4 Cone penetration test at the NASA Glenn soils lab.

6.3 TEST RESULTS AND ANALYSIS

Initially, four complete tests of 16 insertions each (for a total of 64 CPT tests) were performed in ambient conditions at the NASA Glenn Research Center to determine the effect of cone size on penetration resistance as well as to determine the repeatability of testing. Four different samples of GRC-1 were prepared in the 74.2 cm square polypropylene soil bin to a density of 1.69 g/cc (relative density of approximately 31- percent). Two of the samples were tested with the large cone (323 mm2) and the other two were tested with the small cone (130 mm2). Each test was inserted to a depth of 120 mm with the averaging interval set to 10 mm. For each soil preparation, a testing grid

358 was mapped out so that each of the 16 individual tests would be approximately 150 mm

(6 inches) apart from each other (from center to center) and from the sidewalls of the bin.

This ensured a minimum distance of at least seven times the diameter of the large cone between testing locations. The typical testing grid is shown in Figure 6.5 below which is numbered corresponding to the test index.

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16 150 mm

150 mm

Figure 6.5 Typical testing grid for 74.2 cm square soil bin.

For each test the cone penetration resistance was recorded in kPa with the corresponding depth in mm28. A plot of cone penetration resistance versus depth was created. The corresponding cone index gradient G was determined for each test via determining the slope of the linear regression line through the data points for each set of penetration resistance curves as follows,

28 Since the CP40II takes an average cone penetration resistance over a specified depth interval, the corresponding depth is taken as the median value of that interval. For example, if the interval is 10 mm, the cone penetration resistance would be recorded with a corresponding depth of 5 mm for the first interval, 15 mm for the second interval, and so on. 359

n ∑()xi − x ()yi − y i=1 G = n (103) 2 ∑()xi − x i=1

where yi is the value of measurement of a single cone penetration resistance observation in kPa for corresponding depth xi in mm, x and y are the arithmetical mean or average depths and penetration resistance values in mm and kPa, respectively, i is the test index, and n is the total number of observations in the set of data. These mean values are determined as,

n n ∑ xi ∑ yi x = i=1 and y = i=1 (104, 105) n n

where xi is the value of measurement of a single observation of soil depth in mm, i is the test index, and n is the total number of observations in the data set (in this case 16).

Similarly, yi is the value of measurement of a single observation of cone penetration resistance in kPa, i is the test index, and n is the total number of observations in the data set. The standard deviation of the cone index gradient was determined using the following equation,

n 2 ∑()Gi − G σ = i=1 (106) G ()n −1

360 where Gi is the value of measurement of a single observation of the cone index gradient in kPa/mm, G is the arithmetic mean or average cone index gradient in kPa/mm determined using the format of equations (104) and (105), i is the test index, and n is the total number of observations in the data set.

The results of the first four tests are shown in Table 6.2 through Table 6.5 as well as

Figure 6.6 through Figure 6.9. As can be seen, throughout all four tests the cone penetration resistance generally increases linearly with increasing depth. The linearity of the cone penetration resistance versus depth curve reflects the homogeneity of the soil with depth, i.e. the more linear the curve, the more homogeneous the soil sample. The homogeneity of the soil can be evaluated by applying a second order polynomial curve-fit to the mean penetration resistance versus depth curve for each complete test and determining the linearity of the equation via inspecting the coefficient of the second order term (as shown in Figures 6.6 through 6.9). The closer this coefficient is to zero, the more linear the curve and the more homogeneous the soil. If the coefficient is slightly positive, this suggests a general increase in soil strength with increasing depth. The opposite is true for slightly negative values. As can be seen, all four tests show coefficients representing nearly linear curves. All are slightly positive which suggests that the soil increases in strength with increasing depth. This behavior is expected as dry granular soils tend to compress under load and gain strength.

Another important note is that the cone index gradient for all four tests was determined by evaluating the slope of the penetration resistance versus depth curve over the entire

361 testing depth, i.e. over 120 mm. If the penetration resistance versus depth curve is not linear as determined by the first coefficient of the second order polynomial curve-fit as previously described, then the cone index gradient will vary at different points along the penetration resistance versus depth curve. The magnitude of the variation is dependent on the magnitude (absolute value) of the linearity coefficient; the larger the magnitude of the linearity coefficient, the more significant the variation of cone index gradient. Out of all four tests, the worst case had a linearity coefficient of 0.0126 as shown in Figure 6.7.

This case corresponds to a cone index value of 5.0 kPa/mm. Dividing this mean penetration resistance versus depth curve into sections of 10 mm the variation in the cone index gradient can be determined, i.e. evaluate the slope at an interval of 5 to 15 mm depth, 15 to 25 mm depth, 25 to 35, mm depth, and so on. The results are as shown in

Table 6.1.

Table 6.1 Variation of cone index gradient with depth. Soil Depth, mm Cone Index Gradient, kPa/mm 5 – 15 4.03 15 – 25 4.01 25 – 35 4.56 35 – 45 4.09 45 – 55 5.06 55 – 65 4.93 65 – 75 5.08 75 – 85 5.79 85 – 95 5.78 95 – 105 5.74 105 – 115 6.91

As seen, the value of the cone index gradient can vary significantly with respect to depth.

In this worst case it varies from 4.01 kPa/mm to 6.91 kPa/mm which is a difference of 2.9 kPa/mm. Compared with the cone index gradient of 5.0 that was determined over the entire depth (0 to 120 mm) range, the fact that the penetration resistance versus depth

362 curve is not linear can cause a significant difference in cone index gradient. Therefore, it is important to note the range of depth over which the cone index gradient was determined. For all cone penetration tests presented in this chapter (performed on GRC-

1) the cone index gradient is determined over the entire depth range. Additional observations of the test results show that the uniformity of the soil is fairly consistent throughout the soil bin and that there is no notable increase in strength for those tests conducted nearest the sidewalls of the soil bin (tests 1, 2, 3, 4, 5, 8, 9, 12, 13, 14, 15, 16).

Therefore, boundary conditions are negligible. In all four tests there exists a notable increase in scatter of the cone penetration resistance data with increasing depth. The reason for this is not clear but could be caused by human error induced when applying greater pressure to the CP40II to push the cone deeper into the soil. The more force required to push the cone into the ground, the more likely the operator is to “lean” on the

CP40II device causing the cone to veer from vertical when being pushed into the soil. It is also likely that the operator pushes on the CP40II in a “jerking” fashion when it becomes more difficult to penetrate the soil. This is likely to cause variation in penetration rate which could also be a likely source of error. One final observation is that the penetration resistance curves shown in Figures 6.6 through 6.9 tend to be shifted on the vertical axis and do not necessarily intersect the plot at the origin as expected. This is due to the limitations of the ultrasonic sensor in determining the depth of the cone. It was observed during testing that the device had trouble determining the zero ground reference

(when the base of the cone was flush with the soil surface). This limitation does not, however, influence the cone index gradient upon which the analyses are made.

363

Table 6.2 First test results for large cone. C.I. Gradient, Depth, mm5152535455565758595105115 kPa/mm Test 1 15 46 95 150 199 238 279 308 330 360 408 461 3.9 2 40 84 132 177 215 242 271 311 333 368 435 480 3.8 3 52 84 122 161 197 243 285 309 358 391 407 451 3.7 4 52 83 124 169 205 239 271 309 353 362 384 464 3.6 5 78 123 166 211 258 305 359 407 455 528 589 632 5.1 6 96 162 178 229 324 338 426 467 545 672 741 793 6.4 7 65 105 152 204 254 310 372 435 505 575 639 686 5.8 8 76 112 162 200 242 298 345 388 428 490 539 601 4.7 9 68 114 156 201 246 306 377 435 583 636 663 726 6.3 ±kPa/mm 10 76 124 169 262 294 357 421 491 598 657 721 698 6.3 11 54 89 132 182 230 278 315 371 423 464 484 525 4.4 12 46 82 123 168 217 245 276 352 347 382 444 500 4.0 13 49 83 127 170 214 266 316 362 404 433 491 558 4.6 14 kPa Resistance, Penetration 82 130 183 241 287 338 380 476 492 580 601 674 5.4

15 51 84 125 170 223 273 330 382 437 510 525 589 5.1 Gradient, Index of Cone Deviation Standard 16 86 107 146 191 235 297 339 389 438 508 519 574 4.7 mean, kPa 62 101 143 193 240 286 335 387 439 495 537 588 4.9 1.0

900

800 y = 0.0041x2 + 4.3634x + 35.483

700

600

500

400

300 Penetration Resistance, kPa Resistance, Penetration 200

100

0 0 20406080100120140 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10 Test 11 Test 12 Test 13 Test 14 Test 15 Test 16 Mean Poly. (Mean)

Figure 6.6 First test results for large cone.

364

Table 6.3 Second test results for large cone. C.I. Gradient, Depth, mm5152535455565758595105115 kPa/mm Test 1 81 120 138 174 207 245 265 302 352 426 477 528 4.0 2 82 120 156 226 232 272 313 358 412 453 495 547 4.2 3 70 103 141 193 225 276 302 341 395 406 457 3.9 4 51 78 105 132 154 180 223 239 281 298 351 365 2.9 5 65 95 122 156 191 246 299 346 407 444 509 582 4.7 6 101 154 210 259 307 359 419 478 539 597 670 755 5.8 7 80 135 185 232 282 331 397 476 566 665 682 747 6.3 8 73 110 149 200 248 297 347 410 466 583 619 692 5.7 9 71 122 171 217 273 335 442 506 557 633 710 845 6.8 ±kPa/mm 10 52 90 128 178 222 266 297 316 381 410 448 510 4.0 11 32 86 99 170 201 243 288 344 365 420 493 519 4.4 12 83 128 179 223 278 331 363 409 465 540 632 683 5.3 13 66 101 173 196 241 295 367 440 486 544 611 679 5.6 14 kPa Resistance, Penetration 54 95 143 185 241 295 349 400 460 499 556 573 5.0

15 44 75 112 156 204 287 315 371 442 513 580 677 5.7 Gradient, of Index Cone Deviation Standard 16 60 97 139 182 228 286 346 408 496 564 624 692 5.9 mean, kPa 67 107 147 192 233 284 333 384 442 500 557 626 5.0 1.0

900

800 y = 0.0126x2 + 3.5282x + 50.446

700

600

500

400

300 Penetration Resistance, kPa Resistance, Penetration 200

100

0 0 20406080100120140 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10 Test 11 Test 12 Test 13 Test 14 Test 15 Test 16 Mean Poly. (Mean)

Figure 6.7 Second test results for large cone.

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Table 6.4 First test results for small cone. C.I. Gradient, Depth, mm5152535455565758595105115 kPa/mm Test 1 8 37 69 95 129 151 195 214 271 287 337 388 3.4 2 16 56 94 121 168 228 266 312 366 422 499 494 4.6 3 45 71 143 199 243 298 366 383 449 446 448 462 4.1 4 20 67 112 147 183 227 269 309 354 422 489 527 4.5 5 20 57 97 138 172 228 255 279 333 348 419 474 4.0 6 46 90 148 217 306 323 392 455 510 582 590 721 5.9 7 60 121 187 244 299 372 442 542 620 696 803 938 7.7

8 32 87 145 203 245 326 429 504 573 634 726 813 7.2 ±kPa/mm 9 21 67 116 157 201 241 281 308 401 537 514 484 4.8 10 39 101 166 231 290 370 444 501 558 667 691 6.7 11 47 114 173 234 297 369 448 545 636 719 806 893 7.8 12 34 83 142 183 288 365 381 441 484 545 568 657 5.6 13 12 46 78 128 198 256 304 355 413 478 549 570 5.4 14 kPa Resistance, Penetration 29 83 140 196 235 287 337 448 427 459 468 522 4.5 15 8 46 93 149 183 246 297 330 372 405 439 479 4.4 Gradient, Index Cone of Deviation Standard 16 15 52 90 136 176 229 275 334 391 410 469 4.6 mean, kPa 28 74 125 174 226 282 336 391 447 504 551 602 5.3 1.4

1000

900 y = 0.002x2 + 5.0717x - 2.0543

800

700

600

500

400

300 Penetration Resistance, kPa

200

100

0 0 20 40 60 80 100 120 140 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10 Test 11 Test 12 Test 13 Test 14 Test 15 Test 16 Mean Poly. (Mean)

Figure 6.8 First test results for small cone.

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Table 6.5 Second test results for small cone. C.I. Gradient, Depth, mm5152535455565758595105115 kPa/mm Test 1 16 45 75 101 141 175 221 257 293 324 358 415 3.6 2 43 79 130 180 236 306 349 403 482 498 579 609 5.4 3 35 86 159 205 267 339 406 463 526 581 593 676 5.9 4 27 80 138 192 253 302 365 420 562 616 705 807 7.0 5 8 44 90 126 155 216 259 311 374 459 491 565 5.1 6 43 107 184 258 345 435 477 578 636 705 796 967 7.9 7 56 128 207 269 401 432 539 666 716 830 1076 1132 9.7

8 39 99 150 217 311 407 481 549 653 773 868 969 8.6 ±kPa/mm 9 2 39 88 134 177 214 252 292 327 383 403 483 4.2 10 15 60 126 208 311 374 471 572 670 778 885 993 9.1 11 42 93 173 247 332 426 528 551 629 777 813 897 8.0 12 25 78 131 191 266 327 386 465 524 584 658 689 6.3 13 14 53 104 147 183 250 282 412 402 470 507 550 5.1 14 kPa Resistance, Penetration 30 83 135 192 261 307 359 414 486 534 571 691 5.7 15 31 87 145 202 289 336 377 429 444 512 534 603 5.1 Gradient, Index Cone of Deviation Standard 16 21 67 124 173 223 281 342 404 457 590 560 624 5.7 mean, kPa 28 77 135 190 259 320 381 449 511 588 650 729 6.4 1.8

1200

1000 y = 0.0041x2 + 4.3634x + 35.483

800

600

400 Penetration Resistance, kPa

200

0 0 20 40 60 80 100 120 140 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10 Test 11 Test 12 Test 13 Test 14 Test 15 Test 16 Mean Poly. (Mean)

Figure 6.9 Second test results for small cone.

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A direct comparison between the mean of the repeat tests of the cones and between the mean of the large cone and small cone is shown in Figure 6.10 below. As can be seen, the results of Test 1 and Test 2 (the repeat tests for the large cones) are very repeatable.

This is also suggested by the cone index gradient determined in Tables 6.2 and 6.3. The cone index gradient for Test 1 was 4.9 kPa/mm and the cone index gradient for Test 2 was 5.0 kPa/mm, both with standard deviations of ±1.0 kPa/mm. The results for the two small cone tests were not as repeatable. The first small cone test, Test 3, agrees well with the large cone results; having a cone index gradient of 5.3 kPa/mm with a standard deviation of ±1.4 kPa/mm as shown in Table 6.4. However Test 4 has a much higher cone index gradient of 6.4 kPa/mm and a corresponding standard deviation of ±1.8 kPa/mm. It is difficult to tell whether the uniformity of the soil was better in one test preparation over another or if local variations in the soil sample truly existed or were the result of boundary conditions or lateral pressure; however these test results suggests several general conclusions. First, the results of the cone penetration tests indicate some significant differences in cone index gradient over the area of the specimens. However, the statistical analysis indicated the average cone index gradient value expected and standard deviation of that value. Secondly, it seems that the size of the cone does not have a significant effect on the cone index gradient or penetration resistance of GRC-1.

However, the higher standard deviations of the small cones as compared to that of the large cones suggest that the repeatability of the cone penetration tests with the small cone is not as good. This is most likely due to area effects being accounted for better with the larger cone than the smaller cone. It is believed that the observed variations in cone index gradient were probably due to minor variations in density not detectable by

368 standard methods of measurement (although other factors could have contributed to the variations). The variations are believed to have been induced largely by the method of placement of the soil. Modification of the placement technique to reduce operator- induced bias is anticipated to reduce some scatter in the data. However, since it seems that the large cone is not as sensitive to these variations as the small cone; the large 323 mm2 cone will be used for all further cone penetration testing in GRC-1. This selection of cone use is also beneficial for the comparison of GRC-1 to the actual lunar soil as the majority of the Apollo SRP tests were performed using a cone of the same dimensions.

800

700

600

500

400

300

Penetration Resistance,kPa 200

100

0 0 20 40 60 80 100 120 140 Depth, mm

Test 1 - Large Cone Test 2 - Large Cone Test 3 - Small Cone Test 4 - Small Cone

Figure 6.10 Comparison between large and small cones.

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Additional cone penetration tests were performed in a rigid circular polypropylene soil bin with approximate diameter of 55.3 cm in order to determine the relationship between cone index gradient and relative density of GRC-1. GRC-1 was prepared to a total of 11 different densities following the method outlined in step one of section 6.2, Experimental

Procedure. Due to the smaller size of the soil bin and in an effort to save time a total of nine cone penetration tests were performed for each soil preparation (corresponding to a single density). The large 323 mm2 cone tip was used for all tests. In an effort to characterize a larger range of the soil, testing was performed to a depth of 170 mm (out of

180 mm total soil depth). Data was processed similarly to the initial tests performed on

GRC-1 described above. All corresponding data tables and penetration resistance versus depth plots can be found in Appendix E. The results of cone index gradient versus bulk density and relative density are summarized in Table 6.6. As can be seen, the mean cone index gradient typically increases with increasing relative density of GRC-1. To determine the general trend, all data points, including those data points from the large cone tests previously run on GRC-1, were plotted on a cone index gradient versus relative density graph. A least squares approach was used to determine the linear curve-fit for the data. This approach was used instead of plotting the mean cone index gradient values versus the standard deviation because a larger number of tests were performed at a density of 1.69 g/cc (31.03-percent relative density) than at any other density. This method gives an equal weight to all data points when curve-fitting (no matter the amount of tests conducted at a specific density). The results are displayed in Figure 6.11.

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Table 6.6 Results of cone penetration tests at various densities of GRC-1. Mean Cone Index Standard Bulk Density Relative Density Gradient Deviation (g/cc) (%) (kPa/mm) (±kPa/mm) 1.60 0.00 1.59 0.21 1.63 10.34 2.32 0.14 1.65 17.24 3.21 0.31 1.68 27.59 4.21 0.41 1.70 34.48 4.03 0.60 1.71 37.93 4.73 0.47 1.73 44.83 5.96 0.92 1.75 51.72 5.85 0.67 1.76 55.17 5.92 0.63 1.78 62.07 5.86 0.73 1.80 68.97 8.98 0.74

10 y = 0.086x + 1.7858

6 G, kPa/mm

0 0 20406080100 Relative Density, %

Figure 6.11 Cone index gradient versus relative density of GRC-1.

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The accuracy of this data as displayed in Figure 6.11 is better portrayed as shown in

Figure 6.12, where the linear trendline, as determined above, is plotted with the mean values of the cone index gradient and their corresponding standard deviations. The fit is fairly accurate with just a few data points towards the higher relative density range falling outside the error bounds. It should be noted that at higher relative densities, the deviation or scatter in the cone penetration data seems to be consistently higher than at lower relative densities (less than 30-percent). This may suggest that using the shake table for a longer duration to compact the soil to higher densities may not do so uniformly throughout the soil sample. It is probably more likely that there will be pockets of higher and lower densities throughout the soil sample as compared to a soil sample with minimum vibration applied. Therefore, the cone penetration results at higher densities may not be as accurate as those at lower densities, i.e. may not be representative of a single specific density.

6 G, kpa/mm

0 0 20406080100 Relative Density, % Figure 6.12 Cone index gradient versus relative density of GRC-1 with respect to mean cone index values and standard deviation.

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A total of 49 additional cone penetration tests were performed throughout bevameter testing to check the accuracy of the soil density as well as the accuracy of the cone index gradient versus relative density of GRC-1 as determined above in Figures 6.11 and 6.12.

These tests were conducted in the rigid circular acrylic soil bin following the same procedures as all previous cone penetration tests. However, in these tests the soil was prepared (following the requirements of the bevameter tests) to a depth of 24 cm and the cone penetration tests were conducted to a depth of 19 cm. The data was again analyzed in terms of cone index gradient and relative density as shown in Figure 6.13. A complete summary of the data for these tests is provided in Appendix E. As shown, the results agree well with the previous cone penetration test results, thus verifying the density of the soil preparation for bevameter testing.

6 G, kPa/mm

0 0 20406080100 Relative Density, %

Old Tests Bevameter Tests Linear (Old Tests)

Figure 6.13 Additional cone penetrometer tests performed in conjunction with bevameter testing on GRC-1.

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6.4 COMPARISON WITH LUNAR SOIL

As previously discussed in Chapter 2, section 2.1.1.5, Penetrometer Tests, the actual data from the Apollo 15 and 16 Self-Recording Penetrometer tests is available for comparison with the results of cone penetrometer testing on GRC-1. All Apollo 15 and 16 data taken with the 323 mm2 cone has been reanalyzed in terms of cone index gradient for direct comparison with the data from testing with GRC-1. This includes the first four tests

(Test Index 2 through 5) of the Apollo 15 mission and the first and fifth test (Test Index 5 and 10) of the Apollo 16 mission (as shown in Appendix A). It is important to note that for this analysis all likely anomalies caused by the friction in the surface pad assembly, operator error, and the scribe marking the end of a test were removed from the data sets so that a more accurate linear trendline could be fit to the data in the determination of the cone index gradient. It is also important to note that due to the errors caused by the surface pad assembly as described in section 2.1.1.5, Penetrometer Tests, the zero ground reference was difficult to determine. Therefore, the penetration resistance versus depth curves may seem shifted on the depth axis and the actual depth may not be correct.

However, this does not affect the value of the cone index gradient as it represents the slope of the data points. The cone index gradient is determined in the same fashion as it was determined for GRC-1, following equation (103). The results of the analyses are shown in Figures 6.14 through 6.19 and are summarized in Table 6.7.

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400

350 G = 4.803 kPa/mm

300

250

200

150

Penetration Resistance, kPa 100

0 0 50 100 150 200

Depth, mm

First Run, Index 2 Linear (First Run, Index 2)

Figure 6.14 Apollo 15 SRP data for Test Index 2 in terms of cone index gradient.

400

350 G = 13.01 kPa/mm

300

250

200

150

Penetration Resistance, Penetration Resistance, kPa 100

0 0 50 100 150 200

Depth, mm

Second Run, Index 3 Linear (Second Run, Index 3)

Figure 6.15 Apollo 15 SRP data for Test Index 3 in terms of cone index gradient.

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400

350 G = 5.08 kPa/mm

300

250

200

150

Penetration Resistance, kPa 100

0 0 50 100 150 200

Depth, mm

Third Run, Index 4 Linear (Third Run, Index 4)

Figure 6.16 Apollo 15 data for Test Index 4 in terms of cone index gradient.

400

350 G = 11.306 kPa/mm

300

250

200

150

Penetration Resistance, kPa Penetration Resistance, 100

0 0 50 100 150 200

Depth, mm

Fourth Run, Index 5 Linear (Fourth Run, Index 5)

Figure 6.17 Apollo 15 data for Test Index 5 in terms of cone index gradient.

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700

600 G= 3.32 kPa/mm

500

400

300

200 Penetration Resistance, kPa

100

0 0 50 100 150 200 250 300

Depth, mm

First Run, Index 5 Linear (First Run, Index 5)

Figure 6.18 Apollo 16 data for Test Index 5 in terms of cone index gradient.

700

600

500

400

300

200 Penetration Resistance, kPa Penetration Resistance,

100 G = 2.22 kPa

0 0 50 100 150 200 250 300

Depth, mm

Fifth Run, Index 10 Linear (Fifth Run, Index 10)

Figure 6.19 Apollo 16 data for Test Index 10 in terms of cone index gradient.

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Table 6.7 Cone index gradient of lunar soil based on Apollo missions. Cone Index Mission Landing Site Test Index Test Location Gradient (kPa/mm) Station 8, Hadley-Apennine First Run, Apollo 15 adjacent to 4.80 Region Index 2 trench Hadley-Apennine Second Run, Station 8, Apollo 15 13.01 Region Index 3 trench bottom Hadley-Apennine Third Run, Station 8, in Apollo 15 5.08 Region Index 4 rover track Station 8, Hadley-Apennine Fourth Run, Apollo 15 adjacent to 11.31 Region Index 5 rover track Descartes First Run, Station 4, top Apollo 16 3.32 Highlands Region Index 5 part of crater Station 10 near Descartes Fifth Run, Apollo 16 ALSEP, near 2.22 Highlands Region Index 10 rover track

As can be seen from Table 6.7, the cone index gradient of the lunar soil varies greatly from location to location. It makes sense that the gradient would be much higher for the

Apollo 15 test taken at Station 8 at the bottom of the 30 cm deep trench, as the top layer of soil has been excavated and is not included in the data set. It was previously noted in

Chapter 1, section 1.7.2.2, Engineering Properties of the Lunar Regolith, that the lunar soil typically increases in density with increasing depth. It is not clear as to why the fourth Apollo test (Index 5) cone index gradient is so high compared to the other values and is assumed to be the result of regional variation of the lunar regolith. As shown, the lower end of cone index gradients for the lunar soil ranges from values of 2.22 to 5.08 kPa/mm. Mitchell et al. (1972) as cited by Costes et al. (1972) suggested values of 4.06,

>3.25, 5.97, and 2.98 kPa/mm for the average cone index gradient values corresponding to the first four Apollo 15 SRP data sets. It is important to recognize that the lower the cone index gradient, the weaker the soil; which corresponds to a worst case scenario for

378 vehicle mobility. This is important to keep in mind when comparing the lunar soil with

GRC-1. Although it is difficult to directly compare these cone index gradient values for the lunar soil with that of GRC-1 due to the lack of knowledge of soil density in the areas in which the penetration data was recorded, several differences in the experimentation method between the SRP on the Moon and the CPT on the Earth can be expected to lead to variation in data. These differences and their possible effects include the following:

• A stronger gravitational pull on the Earth will likely cause a greater compaction of

the GRC-1 soil samples and therefore results in stronger cone penetrometer readings

than those experienced on the Moon.

• Due to the limitations of the NASA Glenn soils lab as well as time constraints with

respect to soil preparation, samples of GRC-1 were tested in various plastic

containers which may have caused boundary constraints and lateral compression

leading to stronger cone penetrometer readings.

• The dense samples of GRC-1 were artificially consolidated using a shake table.

Apollo data, however, was taken from unconsolidated lunar soil in low gravity

which was compacted only via processes of space weathering and settlement over

extended periods of time. This would likely lead to different strength values as

determined by cone penetration testing.

• Although GRC-1 is a dry granular material, trace amounts of water vapor and the

humidity experienced in ambient testing conditions may result in more cohesive

properties of the samples as well as stronger cone penetrometer readings. In

addition, all tests on GRC-1 were performed at room temperature, in contrast with

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tests performed on the lunar soil at the extreme temperatures of the lunar surface.

This difference in temperature is likely to have some affect on the soil properties.

In summary, it can be stated that many differences exist; most notably the material and atmosphere. However, it was our primary assumption that these differences do not matter, as long as the same cone penetration terrain response can be achieved. Therefore, despite these differences, a general recommendation for the preparation of GRC-1 to simulate the strength of the lunar soil can be provided. Assuming that the lower bounds of the lunar soil cone index gradient values range from approximately 2.22 kPa/mm to

5.08 kPa/mm the following Figure 6.20 provides a visual analysis of the possible cone index gradients of GRC-1 and the relative densities at which they fall within the lower lunar bounds (corresponding to a conservative case for vehicle mobility studies). As shown the minimum and maximum assumed values of G for the lunar soil intersect the cone index gradient versus relative density curve for GRC-1 at values of 5.05 and 38.30- percent relative density, respectively. This suggests that a preparation of GRC-1 within this range of relative densities will simulate the worst case scenario of the lunar soil strength with respect to cone index gradient. For comparison, Figure 6.21 shows the full range of measured values for the lunar soil. It can be concluded that based on the analysis of cone penetration tests, GRC-1 can be used to successfully simulate the strength conditions of the lunar soil for vehicle mobility testing; and since the range of G- values for GRC-1 matches the range of G-values for the lunar soil GRC-1 may be applicable for use in studies other than just vehicle mobility. However, this is not included in the scope of work and will not be discussed in further detail.

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Suitable Relative Density Range for Preparing GRC-1 10 to Lunar-Like Conditions

6 Apollo 15, Index 4 : In LRV Track G, kPa/mm

Apollo 16, Index 10 : Near LRV 2

0 0 102030405060708090100 Relative Density, %

Figure 6.20 Comparison of typical lunar cone index gradient values and possible cone index gradient values of GRC-1.

14 Apollo 15, Index 3 : Trench Bottom

12 Apollo 15, Index 5 : Near LRV Track

G, kPa/mm 6 Apollo 15, Index 4 : In LRV Track

Apollo 15, Index 2 : Near Trench 4

Apollo 16, Index 5 : Crater Top 2 Apollo 16, Index 10 : Near LRV

0 0 102030405060708090100 Relative Density, % Figure 6.21 Comparison of all lunar cone index gradient values and possible cone index gradient values of GRC-1.

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CHAPTER SEVEN

SUMMARY AND CONCLUSIONS

7.1 OVERVIEW

A comprehensive investigation was performed on the geotechnical properties of the lunar soil and lunar soil simulants with respect to those properties most important to the prediction of vehicle mobility performance. In order to develop vehicles for surface exploration on the Moon, it is necessary to perform large scale laboratory tests under simulated lunar conditions. As such, a new lunar soil simulant, GRC-1, was developed from industrially manufactured sands by emulating the particle size distribution of the coarse grained fraction of the lunar soil in order to simulate the stress-strain properties of the lunar soil and those properties most critical to vehicle mobility. This material was developed based on the requirements of being cost efficient and being available to be reproduced in massive quantities for a long period of time.

A comprehensive laboratory testing program was conducted in ambient conditions to determine the geotechnical properties of this new lunar simulant, GRC-1. These measurements were used to form the basis to judge whether the simulant is effective in simulating the critical properties of lunar soil with respect to vehicle mobility as well as to determine the proper preparation of GRC-1 to best simulate the worst case conditions on the Moon which have the highest potential to immobilize an exploration vehicle. The

382 following sections provide recommendations for use of this material as well as conclusions based on the results of the laboratory tests.

7.2 CONCLUSIONS

Founded on the results of the analyses performed throughout this investigation it can be concluded that GRC-1 is a useful lunar soil simulant for lunar exploration vehicle mobility studies. As GRC-1 is created from industrially produced silica sand products from the Best Sand Corporation of Chardon, Ohio; it can be easily reproduced in large quantities for large scale laboratory testing at a relatively low cost. Based on the results of this investigation, the following additional conclusions can be drawn:

1. The particle size distribution of GRC-1 simulant falls within the upper and lower

bounds for the coarse grained fraction of the lunar soil. Over the majority of the

particle size ranges, it closely simulates the average of the coarse grained lunar

soil particle size distribution. Without the finer fraction of the lunar soil (sub 75

μm) GRC-1 can be used for large scale laboratory tests with a lesser amount of

dust generation. The simulant is classified as a poorly-graded sand.

2. The average specific gravity was found to be 2.583, which is slightly lower than

that of typical lunar regolith. However it is still within the recommended lunar

range of 2.3 to 3.2.

3. The bulk density of GRC-1 ranges from 1.60 to 1.89 g/cc which correspond to a

maximum void ratio of 0.613 and a minimum void ratio of 0.364. This range in

bulk density that can be achieved by GRC-1 is slightly higher than that observed

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for the lunar soil, which typically ranges form 0.92 to 1.81 g/cc. This is most

likely attributed to the round particle shapes of GRC-1 versus the angular particle

shapes of the lunar soil which allow for greater voids in the lunar soil and thus

lower density. In addition, it can be concluded for this study, that a good way to

achieve a uniformly dense compaction of GRC-1 is by vibration with a vertical

surcharge.

4. The compressibility and swelling index of GRC-1 are considerably lower than

typical soils. The compression index of GRC-1 is approximately 0.03 while that

of the lunar soil is estimated to be between 0.3 and 0.05.

5. The angle of internal friction of GRC-1 increases with increasing density as

determined by results of triaxial testing. It was found that the angle of internal

friction of GRC-1 ranges from 29.31-degrees to 48.16-degrees which is almost

identical to the range of the lunar soil from 30 to 50-degrees.

6. It is quite difficult to measure the cohesion of the dry simulant accurately as the

cohesion is relatively low. However, it is reasonable to assume that GRC-1 has

cohesion in the range of 1 kPa and lower which agrees with that of the lunar soil.

Additionally, it was determined that an error in the estimate of cohesion

especially for lower ranges of cohesion (1 kPa and less) can lead to significant

errors in the predicted thrust or gross traction of a lunar exploration wheeled

vehicle which is lower in weight and has a higher ground contact area than typical

Earth vehicles.

384

7. Using a hopper and shake table to prepare GRC-1 to the desired density is one of

the more reliable ways to ensure homogeneity of the sample and repeatability of

the density.

8. The soil parameters as determined by Bekker and the pressure-sinkage bevameter

test are typically influenced by a significant amount of scatter in the pressure-

sinkage data. Despite this scatter reasonable values for n, kc, and kφ can be

determined for use in vehicle modeling. The value of n derived for GRC-1 varied

from 0.95 to 1.23 for the soil densities tested, typically increasing slightly with

increasing soil density. This suggests that GRC-1 is typically a “soil

strengthening” material and generally increases in strength with compaction. The

value for n suggested for the lunar soil is 1.0 which can definitely be achieved by

GRC-1. The values of kc and kφ were more difficult to evaluate and compare to

recommended soil parameters for GRC-1 because they do not represent any

specific physical soil property and are only moduli of deformation. As the values

of kc and kφ are coupled with n, they are subject to change accordingly with a

change in n. However, it has been shown that the typical deformation curve of

GRC-1 is comparable to that of similar dry sandy terrains.

9. The soil parameters obtained from shear bevameter testing agree well with similar

sandy terrains as well as the lunar soil. The value of K obtained for GRC-1

ranged from 1.81 to 2.55 cm while the recommended value for the lunar soil is 1.8

cm. Additionally, the friction angle ranged from 33 to 35-degrees which

compares to a recommended value of 35-degrees for the lunar soil. The cohesion

for GRC-1 was more difficult to evaluate, but is assumed to range between 0 and

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1 kPa, while the recommended value for lunar soil is 0.17 kPa. It was also

determined that there was very little difference between using a shear ring with

grousers or a shear ring with sandpaper for shear bevameter tests on GRC-1.

10. Common issues with the shear bevameter encountered during testing include slip-

stick phenomenon and variation of the normal load during testing. These issues

can result in unreliable cohesion and friction angle values. The dynamic response

from slip-stick phenomenon is avoidable by removing all sources of elasticity

from the system, i.e. making the system completely rigid as well as placing the

source of rotation as close to the end effector as possible.

11. The cone index gradient for GRC-1 ranges from 1.79 kPa/mm to 10.39 kPa/mm.

Based on SRP data from the Apollo 15 and 16 missions, a preparation of GRC-1

in the range of 5 and 38-percent relative density most closely simulates the lower

bound strength of the lunar soil. However, the cone index gradients for GRC-1

correspond well to all the measurements from Apollo 15 and 16 missions.

Therefore, GRC-1 may be used for additional studies beyond the realm of vehicle

mobility which may necessitate a stronger preparation of the soil.

In summary, the majority of the geotechnical properties of GRC-1 are similar to that of lunar soils excluding the cohesion, which is difficult to measure. A better understanding of and the development of a reliable way to measure the small amount of cohesion experienced in dry granular soils needs further study. Additional suggestions for future work can be found in section 7.4, Suggestions for Future Work, of this dissertation. The

386 following section provides recommendations as to the proper use and preparation of

GRC-1 in vehicle mobility testing.

7.3 SUGGESTIONS FOR PRACTICAL USE OF GRC-1

Based on the results of laboratory testing performed on GRC-1 several recommendations can be made as to the proper preparation of the material for use in lunar exploration vehicle mobility studies. Figure 7.1 is extremely useful in comparing the range of properties attainable by GRC-1 to the range of properties reported and recommended for the actual lunar soil. This plot is based on data results from triaxial, bevameter, and cone penetration testing on GRC-1 as well as the SRP results from the Apollo 15 and 16 missions. As shown, to be within the typical lower bound strength range of lunar soil,

GRC-1 must be prepared to relatively loose densities. In order to replicate a worst case scenario on the Moon in which the soil is fairly weak, GRC-1 should be prepared to a relative density of no greater than 10-percent. However, anywhere from approximately 5 to 35-percent relative density should be sufficient for vehicle mobility testing, though it is possible to achieve less conservative preparations as well. It is important to note that in

Figure 7.1 the friction angle scale only applies to the triaxial data and the shear bevameter data and is not intended to correspond to the cone penetrometer data. Additionally, it is important to note that the friction angle obtained from the triaxial tests and the shear bevameter tests are not (necessarily) directly comparable as the friction angle from triaxial tests is obtained under confined conditions, while the friction angle from bevameter tests is obtained under unconfined conditions.

387

14 55

12 50

10 45

8 40 6 Apollo 15, Index 4 : In LRV Track 35

4 (degrees) Angle Friction ConeIndex Gradient (kPa/mm) Apollo 16, Index 10 : Near LRV 30 2

0 25 0 20406080100 Relative Density (%)

CPT Tests Apollo 15 Data Apollo 16 Data Triaxial Tests Shear Bevameter Tests Linear (Triaxial Tests) Linear (Shear Bevameter Tests) Linear (CPT Tests)

Figure 7.1 Combination of triaxial, CPT, and bevameter data for GRC-1 compared to lunar soil.

It is recommended that all soil preparations be prepared via hopper for small scale laboratory tests. However, this will not work for large scale testing in which several tons of soil is being prepared. Therefore, it is necessary to develop a time efficient and repeatable manner of preparing the soil before vehicle mobility testing. A trial procedure was tested in the large soil bin at the Virginia Tech Vehicle Dynamics Laboratory and it was found that this procedure provided repeatable cone index gradients within 0.3 kPa/mm with relatively linear penetration resistance curves (ensuring homogeneity to the bottom of the soil bin). The suggested method for preparation in the soil bin at the

388

SLOPE facility at the NASA Glenn Research Center based on experimentation at

Virginia Tech is as follows:

1. To initially return the soil to an uncompacted state a flat blade shovel is

implemented. With force, thrust the shovel perpendicular to the soil surface

starting close to wall A as shown in Figure 7.2. It is important that the shovel

reach the bottom of the bin. Push the shovel in with the bottom of the foot,

similar to digging a hole.

SIDE “C”

WALL “B”

WALL “A”

SIDE “D”

Figure 7.2 Diagram demonstrating soil preparation for large-scale soil bins.

2. Pull down on shovel handle so that soil is lifted slightly from the bin. Lift the

handle up and slowly remove the shovel, allowing the soil to fall back into place

gently as shown in Figure 7.3.

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Figure 7.3 Proper shoveling technique to loosen soil in soil bin.

3. Repeat steps 1 and 2 every three to four inches from wall A to wall B.

4. Turn the shovel around and repeat steps 1 through 3 starting from wall B and

going to wall A (the opposite direction of step 3) as shown in Figure 7.4(a) and

7.4(b).

(a) (b)

Figure 7.4 (a) Turn shovel in opposite direction. (b) Loosen soil in opposite direction.

5. Repeat this complete method for the entire test bed length, overlapping shovel

paths by one to two inches (2.54 to 5.08 cm).

390

6. Pull a leveling tool (a simple aluminum or steel blade attached to a shovel handle)

across the soil surface beginning at side C of the test area and progressing to side

D of the test area (as shown in Figure 7.2).

7. Compact the soil to the desired density using a tamper. Begin by holding the

tamper approximately three to eight centimeters off the soil surface starting in the

lower left corner (corner C-B) of the soil test area.

8. Release the tamper, ensuring no external force has been applied to the tamper.

Make sure that the tamper is released when it is at a level position so that it hits

the soil surface with full/solid contact (there should be little to no rocking motion

when it hits the soil surface). Lift the tamper from the soil straight up so as not to

disturb the soil.

9. Repeat steps 7 and 8 moving from wall B to wall A (along side C). Make sure to

overlap at least half of the area that was previously tamped.

10. Repeat steps 7 through 9 until the entire surface area has been tamped from side C

to side D ensuring to overlap at least half of the area that was previously tamped.

Repeat this procedure until the desired density is achieved as determined by cone

penetration testing. In lieu of a tamp which can take a significant amount of time

to compact soil in large soil bins, a roller filled with sand may be pulled across the

surface of the soil instead.

391

7.4 SUGGESTIONS FOR FUTURE WORK

Recommendations for future work in this area of study may include but not be limited to:

• Investigation and analysis of the primary assumption proving that matching the cone

penetration curves of GRC-1 and the lunar soil will yield similar compaction and

shear responses.

• Since the gravity on the Moon is 1/6th that on the Earth and the mechanical properties

of soils are critically dependent on the effective confining pressure, which is gravity

dependent, it is necessary to develop relevant simulation rules and scaling laws so

that the results of studies conducted on the Earth can be properly related to the

conditions expected on the Moon.

• It may prove more useful, for vehicle mobility studies, to perform UU triaxial tests

using an internal vacuum as the confining pressure on the soil instead of the typical

external confining pressure. The current triaxial test setup at NASA Glenn can be

modified into a new vacuum triaxial test with the capability to place the soil sample

under lower confining pressures. The vacuum triaxial test would feature internal

confining pressures ranging from approximately 6 to 50 kPa. These lower confining

pressures should better represent the vehicle-terrain pressures of prototype Moon

vehicles (wheels in particular). Additionally, the low confining pressures should also

provide more reliable values of cohesion for GRC-1.

• In order to better validate simulation models of soil strength, such as finite element

or discrete element models of triaxial testing, it is important to determine the triaxial

lateral bulge profile versus vertical displacement, i.e. lateral extension distribution at

392

discrete points throughout the length of the triaxial specimen per vertical

displacement. This is a challenge as the volume change of the material under the

applied normal load cannot physically be measured at NASA Glenn due to

limitations of the equipment. In addition, if the limitations to the equipment were not

an issue, it is often-times very difficult to completely saturate a triaxial soil sample in

order to accurately determine the volume change. This test procedure is very

difficult and extremely sensitive. Other methods such as directly measuring the

dimensions of the soil sample at regular intervals throughout the application of the

normal load are not feasible as the sample must be enclosed within the triaxial

chamber to maintain the external confining pressure. One plausible method however

would be to place a sheet of graph paper behind the sample and take high quality

digital photographs over time to develop the general volume change trend. Although

plausible, this method proves challenging as it requires the development of scaling

laws to account for refraction errors imposed on the digital image by the triaxial

chamber walls.

• Further study should be conducted on the minimum depth to which soil can be

prepared in a soil bin without being influenced by bottom boundary conditions.

• It would be of great benefit to lunar vehicle mobility studies to develop relationships

between the relative density of GRC-1 and the corresponding Bekker parameters kc ,

kφ , and n, as well as K for the complete range of bulk density of the material.

• Small scale vacuum bevameter testing would be useful for testing soil simulants

under the environmental conditions of the lunar surface for vehicle mobility studies.

393

This would be functional for estimating the lunar terrain strength where there are no

in-situ measurements.

• An investigation on the rheology or flow of GRC-1 over a range of mobility speeds

and surface loads would be beneficial to understanding the dynamic interaction

between the soil and traction systems. This understanding can assist in the

determination of the amount of wheel slippage and the amount of regolith retained in

open mesh wheels, among other things.

• The development of GRC-1 including the finer fraction of lunar regolith would be

beneficial for vehicle mobility studies as well as other studies such as in-situ resource

utilization. It would provide the ability to prepare a more dense or stronger simulant

which would be extremely useful in ISRU studies where the worst case scenario

would be an extremely strong soil as opposed to the weak soil necessary for vehicle

mobility.

394

APPENDIX A LUNAR SOIL AND SIMULANT PROPERTIES ______

Table A1: Recommended Lunar Soil Parameters (Carrier et al. 1991).

Relative Average Average Average Average Bulk Density, ρ Soil Depth (cm) Density, Rd Porosity, n Void Cohesion, c Friction (g/cc) Description (%) (%) Ratio, e (kPa) Angle, Φ (º) Medium to 1.07 ± 0-15 1.50 ± 0.05 65 ± 3 52 ± 2 0.52 42 Dense 0.07 0.96 ± 0-30 1.58 ± 0.05 74 ± 3 Dense 49 ± 2 0.9 46 0.07 0.78 ± 30-60 1.74 ± 0.05 92 ± 3 Very Dense 44 ± 2 354 0.07 0.87 ± 0-60 1.66 ± 0.05 83 ± 3 Dense 46 ± 2 1.6 49 0.07

Specific Gravity, G = 2.3 to >3.2, with a recommended value of 3.1 for engineering analyses

USCS = SW-SM to ML

Mean Particle Size = 40 to 800 μm

Average Median Particle Size = 70 μm

395

Figure A1. Apollo 15 SRP stress-penetration curve (first run, index 2) adjacent to trench using 323 mm2 cone tip (credit NSSDC).

First Run, Index First2 Run, Index Stress, N/cm^2 Stress, 0 10203040

0 5

10 15 20 25 Penetration, cm Penetration,

396

Figure A2. Apollo 15 SRP stress-penetration curve (second run, index 3) from trench bottom using 323 mm2 cone tip (credit NSSDC).

Second Run, Index 3 Run, Second Stress, N/cm^2 010203040

0 5

10 15 20 25 Penetration, cm Penetration,

397

Figure A3. Apollo 15 SRP stress-penetration curve (third run, index 4) from rover track using 323 mm2 cone tip (credit NSSDC).

Third Run, Index 4 Third Run, Stress, N/cm^2 0 10203040

0 5

10 15 20 25 Penetration, cm Penetration,

398

Figure A4. Apollo 15 SRP stress-penetration curve (fourth run, index 5) adjacent to rover track using 323 mm2 cone tip (credit NSSDC).

Fourth Run, Index 5 Stress, N/cm^2 Stress, 0 10203040

0 5

10 15 20 25 Penetration, cm Penetration,

399

Figure A5. Apollo 15 SRP stress-penetration curve (fifth run, index 6) from trench bottom using bearing plate tip (credit NSSDC).

Fifth Run, Index 6 Stress, N/cm^2 Stress, 01234

0 5

10 Penetration, cm Penetration,

400

Figure A6. Apollo 15 SRP stress-penetration curve (sixth run, index 7) from top of trench wall using bearing plate tip (credit NSSDC).

Sixth Run, Run, Sixth Index 7 Stress, N/cm^2 Stress, 01234

0 5

10 Penetration, cm Penetration,

401

Figure A7. Apollo 16 SRP stress-penetration curve (first run, index 5) uphill on top part of crater using 323 mm2 cone tip (credit NSSDC). First 5 Run, index Stress, N/cm^2 Stress, 0 10203040506070

0 5

10 15 20 25 Penetration, cm Penetration,

402

Figure A8. Apollo 16 SRP stress-penetration curve (second run, index 6) from edge of crater using 129 mm2 cone tip (credit NSSDC).

Second Run, Second Index 6 Stress, N/cm^2 0 50 100 150

10 20 30 40 50 60 70 80 Penetration, cm Penetration,

403

Figure A9. Apollo 16 SRP stress-penetration curve (third run, index 7) from edge of crater using 129 mm2 cone tip (credit NSSDC). Third Run, Index 7 Stress, N/cm^2 0 50 100 150 200

10 20 30 40 50 60 70 80 Penetration, cm Penetration,

404

Figure A10. Apollo 16 SRP stress-penetration curve (fourth run, index 8) downhill on crater using 129 mm2 cone tip (credit NSSDC).

Fourth 8 Index Run, Fourth Stress, N/cm^2 0 50 100 150 200

10 20 30 40 50 60 70 80 Penetration, cm Penetration,

405

Figure A11. Apollo 16 SRP stress-penetration curve (fifth run, index 10) from near rover using 323 mm2 cone tip (credit NSSDC). Fifth Run, Index 10 Stress, N/cm^2 0 10203040506070

0 5

10 15 20 25 Penetration, cm Penetration,

406

Figure A12. Apollo 16 SRP stress-penetration curve (sixth run, index 11) from near rover next to index 10 using 129 mm2 cone tip (credit NSSDC). Sixth Run, Run, Sixth Index 11 Stress, N/cm^2 0 50 100 150 200

10 20 30 40 50 60 70 80 Penetration, cm Penetration,

407

Figure A13. Apollo 16 SRP stress-penetration curve (seventh run, index 12) from southwest of rover using 129 mm2 cone tip (credit NSSDC).

y Seventh Run,Index 12 go to below 40 40 cmgo to below depth. *Only half of the data is available from half of available is the data *Only the resource.the This actuall should plot Stress, N/cm^2 Stress, 0 50 100 150 200

10 20 30 40 50 60 70 80 Penetration, cm Penetration,

408

Figure A14. Apollo 16 SRP stress-penetration curve (eighth run, index 13) from southwest of rover using 129 mm2 cone tip (credit NSSDC). Eigth Run, IndexEigth 13 Stress, N/cm^2 0 50 100 150 200

10 20 30 40 50 60 70 80 Penetration, cm Penetration,

409

Figure A15. Apollo 16 SRP stress-penetration curve (tenth run, index 15) from near rover using bearing plate (credit NSSDC). Tenth Run, Index 15 Stress, N/cm^2 Stress, 01234567

0 1 2 3 4 5 6 7 8 9

10 Penetration, cm Penetration,

410

Figure A16. Apollo 16 SRP stress-penetration curve (eleventh run, index 16) from near rover using bearing plate (credit NSSDC). Eleventh Run, Index 16 Eleventh Stress, N/cm^2 01234567

0 1 2 3 4 5 6 7 8 9

10 Penetration, cm Penetration,

411

Table A2: In-Situ Lunar Soil Properties

Mission Evaluation Method Soil Parameter Value Soil Depth Source Lunokhod 1 vane-cone penetrometer shear strength 2.9 - 8.8 kPa - - Cherkasov and Shvarev 1973

distortion from Lunokhod Luna 17,21 chassis bearing capacity <7 - >55 kPa - - Gromov 1999 distortion from Lunokhod Luna 17,21 chassis bearing capacity 19.6 - 98.1 kPa - - Leonovich et al. 1971 cited by Johnson and Carrier 1971 Lunokhod II ninth wheel bearing capacity 2-4 kPa 1 to 2 cm Leonovich et al. 1976

Russian probe / gamma-ray Luna 13 device density 0.8 g/cc - - Cherkasov et al. 1968 cited by Costes et al. 1972 Luna 16 rotary drill sample density 1.2 g/cc - - Vinogradov 1971 cited by Costes et al. 1972 Luna 16 - - p density 1.5 - 1.7 g/cc - - Leonovich et al. 1971 cited by Mitchell et al. 1972 Surveyor I interactions density 1.5 g/cc - - Christensen et al. 1967 cited by Costes et al. 1972 Surveyor V - - density 1.1 g/cc - - Christensen et al. 1968 cited by Costes et al. 1972 soil mechanics surface Surveyor III & VIII sample experiments density 1.5 g/cc - - Scott and Roberson 1968 cited by Costes et al. 1972 footpad interactions and Surface Sampler Surveyor I, III, V, VI, VII experiments density 1.5 g/cc lunar surface layer Johnson et al 1995 Apollo 11 core tube density 0.75 - 1.75 g/cc - - Scott et al. 1971 cited by Mitchell et al. 1972 Apollo 11 penetration resistance density 1.81 - 1.94 g/cc - - Costes et al. 1972 cited by Mitchell et al. 1972 Apollo 12 penetration resistance density 1.81 - 1.84 g/cc - - Costes et al. 1972 cited by Mitchell et al. 1972 Apollo 12 core tube density 1.6 - 2.0 g/cc - - Scott et al. 1971 cited by Carrier et al. 1972 Apollo 12 core tube simulation density 1.55 - 1.9 g/cc - - Houston and Mitchell 1971 cited by Mitchell et al. 1972 Apollo 12 core tube simulation density 1.7 - 1.9 g/cc - - Carrier et al. 1971 cited by Carrier et al. 1972 Apollo 14 core tube samples density 1.45 - 1.6 g/cc - - Carrier et al. 1972 cited by Mitchell et al. 1972 SRP test results and Apollo 15 terrestrial simulations density 1.92 - 2.01 g/cc - - Mitchell et al. 1972 cited by Costes et al. 1972 Apollo 15 deep drill stem density 1.62 - 1.93 g/cc - - Carrier et al. 1972 cited by Mitchell et al.1972 Apollo 17 double core tube density 1.60 - 1.73 g/cc - - Mitchell et al. 1973 Apollo 17 double core tube density 2.03 - 2.29 g/cc up to 70 cm Mitchell et al. 1973 Apollo 17 double core tube density 1.57 g/cc 16.2 cm Mitchell et al. 1973 Apollo 17 double core tube density 1.67 - 1.74 g/cc - - Mitchell et al. 1973 Apollo 17 double core tube density 1.77 g/cc 28 cm Mitchell et al. 1973

penetration resistance and Apollo 15 simulation studies void ratio 0.54 - 0.61 - - Mitchell et al. 1972

penetration resistance and Apollo 15 simulation studies porosity 35 - 38% - - Mitchell et al. 1972

soil mechanics trench cohesion <0.03 - 0.3 kPa - - Mitchell et al . 1971 cited by Costes et al. 1972 Lunar Orbiter boulder track analysis cohesion 0.35 kPa - - Nordmeyer 1967 cited by Costes et al. 1972 Lunar Orbiter boulder track records cohesion 0.1 kPa - - Moore 1970 cited by Costes et al. 1972 Lunar Orbiter boulder track records cohesion 1.0 kPa - - Hovland and Mitchell 1971 cited by Costes et al. 1972 distortion from Lunokhod Luna 17,21 chassis cohesion <1.3 - >3.4 kPa - - Gromov 1999 Surveyor I strain gage and TV data cohesion 0.15 - 15 kPa - - Jaffe 1967 cited by Costes et al. 1972 Surveyor I cohesion 0.13 - 0.4 kPa - - Christensen et al. 1967 cited by Costes et al. 1972 Surveyor III landing data cohesion 0 kPa - - Christensen et al. 1968 cited by Costes et al. 1972 Surveyor III landing data cohesion 10 kPa - - Christensen et al. 1968 cited by Costes et al. 1972 Surveyor VI vernier engine firing cohesion >0.07 kPa - - Christensen et al. 1968 cited by Costes et al. 1972 Surveyor VI altitude control jets cohesion 0.5 - 1.7 kPa - - Christensen et al. 1968 cited by Costes et al. 1972 footpad interactions and Surface Sampler Surveyor I, III, V, VI, VII experiments cohesion 0.35 - 0.7 kPa lunar surface layer Johnson et al 1995 penetration of core tubes, Apollo 11 flagpole shaft cohesion 0.8 - 2.1 kPa - - Costes et al. 1971 cited by Costes et al. 1972 penetration of core tubes, Apollo 12 flagpole shaft cohesion 0.6 - 0.8 kPa - - Costes et al. 1971 cited by Costes et al. 1972

Apollo 15 and 16 Self Recording Penetrometer cohesion 0.25 - 1.0 kPa up to 75 cm deep Carrier et al . 1991 cited by Johnson et al . 1995 SRP and slope stability Apollo 15 analysis cohesion 1.0 kPa - - Costes et al. 1972 cohesion 0.52 0 - 15 cm Carrier et al . 1991 cited by Perkins et al. 1992 cohesion 3 30 - 60 cm Carrier et al . 1991 cited by Perkins et al. 1992

soil mechanics trench friction angle 35 - 45º - - Mitchell et al . 1971 cited by Costes et al. 1972 MET tracks friction angle 37 - 47º - - Mitchell et al . 1971 cited by Costes et al . 1972 Lunar Orbiter boulder track analysis friction angle 33º - - Nordmeyer 1967 cited by Costes et al. 1972 Lunar Orbiter boulder track records friction angle 10 - 30º - - Moore 1970 cited by Costes et al. 1972 Lunar Orbiter boulder track records friction angle 19 - 53º - - Hovland and Mitchell 1971 cited by Costes et al. 1972

Table A3: Returned Lunar Soil Properties

412

Mission Evaluation Method Soil Parameter Value Soil Depth Source dispersion, conductometric Luna 16 method, microphotography average particle size .085 mm - - Gromov 1999 dispersion, conductometric Luna 20 method, microphotography average particle size .077 mm - - Gromov 1999 Luna 20 - - average particle size .07 to .08 mm - - Leonovich et al. 1976 dispersion, conductometric Apollo 11 method, microphotography average particle size .098 mm - - Gromov 1999 dispersion, conductometric Apollo 12 method, microphotography average particle size 0.118 mm - - Gromov 1999 dispersion, conductometric Apollo 14 method, microphotography average particle size 0.138 mm - - Gromov 1999 dispersion, conductometric Apollo 15 method, microphotography average particle size 0.061 mm - - Gromov 1999 dispersion, conductometric Apollo 16 method, microphotography average particle size 0.153 mm - - Gromov 1999 Apollo 16 - - average particle size 0.101 - 0.268 mm - - McKay et al. 1991 cited by McKay et al. 1994 dispersion, conductometric Apollo 17 method, microphotography average particle size 0.079 mm - - Gromov 1999 Apollo 17 average particle size 0.042 - 0.166 mm - - McKay et al. 1991 cited by McKay et al. 1994

Apollo 11 - - median particle size 48 - 105 μm - - McKay et al. 1991 cited by McKay et al. 1994 Apollo 12 - - median particle size 42 - 94 μm - - McKay et al. 1991 cited by McKay et al. 1994 Apollo 14 - - median particle size 75 - 802 μm - - McKay et al. 1991 cited by McKay et al. 1994 Apollo 15 - - median particle size 51 - 108 μm - - McKay et al. 1991 cited by McKay et al. 1994

Luna 16 - - loose bulk density 1.115 g/cc - - Gromov 1999 Luna 16 - - compact bulk density 1.793 g/cc - - Gromov 1999 Luna 20 - - loose bulk density 1.04 g/cc - - Gromov 1999 Luna 20 - - compact bulk density 1.798 g/cc - - Gromov 1999 achieved in a nitrogen Apollo 11 atmosphere density 1.36 g/cc - - Costes et al. 1970 cited by Carrier et al. 1972 Apollo 11 - - loose bulk density 1.36 g/cc - - Gromov 1999 Apollo 11 - - compact bulk density 1.8 g/cc - - Gromov 1999 Apollo 11 - - density 1.54 - 1.66 g/cc - - Costes et al. 1969 cited by Costes et al. 1972 Apollo 11 core tube density 1.59 - 1.71 g/cc - - Costes et al. 1969 cited by Mitchell et al. 1972 Apollo 11 core tube density 1.54 - 1.75 g/cc - - Costes and Mitchell 1970 cited by Costes et al. 1972 Apollo 11 - - density 0.74 - >1.75 g/cc - - Scott et al. 1971 cited by Costes et al. 1972 Apollo 11 - - density 1.81 - 1.92 - - Costes et al. 1972 Apollo 12 - - loose bulk density 1.15 g/cc - - Gromov 1999 Apollo 12 - - compact bulk density 1.93 g/cc - - Gromov 1999 Apollo 12 - - density 1.6 - 2.0 g/cc - - Scott et al. 1971 cited by Costes et al. 1971 Apollo 12 - - density 1.80 - 1.84 g/cc - - Costes et al. 1971 cited by Costes et al. 1972 Apollo 12 - - density 1.55 - 1.90 g/cc - - Houston and Mitchell 1971 cited by Costes et al. 1972 Apollo 12 - - density 1.7 - 1.9 g/cc - - Carrier et al. 1971 cited by Costes et al. 1972 Apollo 14 - - loose bulk density 0.89 g/cc - - Gromov 1999 Apollo 14 - - compact bulk density 1.55 g/cc - - Gromov 1999 Apollo 14 - - loose bulk density 0.87 g/cc - - Gromov 1999 Apollo 14 - - compact bulk density 1.51 g/cc - - Gromov 1999 Apollo 14 - - density 1.45 - 1.6 g/cc - - Carrier et al. 1972 cited by Costes et al. 1972 Apollo 15 - - loose bulk density 1.1 g/cc - - Gromov 1999 Apollo 15 - - compact bulk density 1.89 g/cc - - Gromov 1999 Apollo 15 - - density 1.35 - 2.15 g/cc - - Mitchell et al. 1972 cited by Costes et al. 1972 Apollo 15 - - density 1.92 - 2.01 g/cc - - Mitchell et al. 1972 cited by Costes et al. 1972 Apollo 11 - - density 1.36 - 1.8 g/cc - - Johnson et al 1995 Apollo 12 - - density 1.7 - 2.0 g/cc - - Johnson et al 1995 Apollo 15 - - density 1.62 - 2.15 g/cc - - Costes et al. 1972 - - - - density 1.4 - 2.2 g/cc - - Carrier 1971 cited by Sibille et al . 2005 Apollo 17 - - density 1.76 g/cc - - Mitchell et al. 1973 Apollo 17 - - density 2.11 g/cc - - Mitchell et al. 1973 Apollo 17 - - density 1.62 g/cc - - Mitchell et al. 1973 Apollo 17 - - density 1.80 g/cc - - Mitchell et al. 1973 Apollo 17 - - density 1.85 g/cc - - Mitchell et al. 1973 Apollo 17 - - density 1.84 g/cc - - Mitchell et al. 1973 Apollo 17 - - density 1.83 g/cc - - Mitchell et al. 1973 Apollo 17 - - density 1.71 g/cc - - Mitchell et al. 1973

- - - - relative density 65% 0-15 cm Carrier 1971 cited by Sibille et al . 2005 - - - - relative density 90% >30cm Carrier 1971 cited by Sibille et al . 2005

loose void ratio 1.69 - - Gromov 1999 Luna 16 - - compact void ratio 0.67 - - Gromov 1999 Luna 16 - - loose void ratio 1.88 - - Gromov 1999 Luna 20 - - compact void ratio 0.67 - - Gromov 1999 Luna 20 - - loose void ratio 1.21 - - Gromov 1999

APPENDIX B INITIAL CHARACTERIZATION OF GRC-1

413

______

Table B1: Unified Soil Classification System (Bowles 1991)

Table B2: One-Dimensional Consolidation Tests on GRC-1

414

One Dimensional Consolidation Test #1: Initial Height = 20.13 mm Dial readings = .0001 inches per unit (200 total units per revolution) Initial Void Ratio = 0.525

1 psi 2 psi 4 psi 8 psi 16 psi 32 psi 8 psi 2 psi Time (min) Dial Readings Dial Readings Dial Readings Dial Readings Dial Readings Dial Readings Dial Readings Dial Readings 0 0 28 44.5 71 99.5 143 189.5 169 0.1 26.5 44 69.5 97.5 140.5 185.5 169.5 147 0.2 26.5 44.5 69.5 97.5 141 186 169 147 0.5 26.5 44.5 69.5 98 141.5 186.5 169 147 1 26.5 44.5 70 98.5 141.5 187 169 147 2 28 44.5 70.5 98.5 142 188 169 147 4 28 44.5 71 99.5 142.5 188.5 169 147 8 28 44.5 71 99.5 142.5 189 169 147 15 28 44.5 71 99.5 143 189.5 169 147

One Dimensional Consolidation Test #2: Initial Height = 18.42 mm Dial readings = .0001 inches per unit (200 total units per revolution) Initial Void Ratio = 0.406

1 psi 2 psi 4 psi 8 psi 16 psi 32 psi 8 psi 2 psi Time (min) Dial Readings Dial Readings Dial Readings Dial Readings Dial Readings Dial Readings Dial Readings Dial Readings 0 0 3 39.5 52 89 131.2 181.5 156.5 0.1 2 37 49 86 128 177.5 156.5 131 0.2 2 38 50 86 128.5 178 156.5 131 0.5 3 38.5 50.5 87 129 179 156.5 131 1 3 38.5 51 87 129.5 179.5 156.5 131 2 3 39 51 88 130 180 156.5 131 4 3 39.5 51.5 89 130.5 180.5 156.5 131 8 3 39.5 52 89 131.2 181 156.5 131 15 3 39.5 52 89 131.2 181.5 156.5 131

One Dimensional Consolidation Test #1: ep (kPa) 0.406 0 0.4 6.89 0.397 13.79 0.392 27.58 0.387 55.16 0.378 110.32 0.37 220.63 0.371 55.16 0.378 13.79

One Dimensional Consolidation Test #2: ep (kPa) 0.525 0 0.524 6.89 0.517 13.79 0.515 27.58 0.508 55.16 0.5 110.32 0.49 220.63 0.495 55.16 0.5 13.79

APPENDIX C

415

TRIAXIAL TEST RESULTS FOR GRC-1 ______

It is important to note for the following reports that the “Specimen Reference Letter” does not necessarily correspond to the test index provided in Tables 4.1 and 4.2 of

Chapter 4. In addition, the initial diameters, initial dry unit weights, and void ratios provided in these reports have not been corrected for membrane thickness. The appropriate values (after correction) are as listed in Tables 4.1 and 4.2 of Chapter 4.

416

Report C1: Triaxial Test 1 Results

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421

422

423

Report C2: Triaxial Test 2 Results

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425

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427

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429

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Report C3: Triaxial Test 3 Results

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436

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Report C4: Triaxial Test 4 Results

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Report C5: Triaxial Test 5 Results

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448

449

450

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Report C6: Triaxial Test 6 Results

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455

456

457

458

Report C7: Triaxial Test 7 Results

459

460

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Report C8: Triaxial Test 8 Results

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469

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Report C9: Triaxial Test 9 Results

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Report C10: Triaxial Test 10 Results

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486

Figure C1: q versus p analysis of triaxial test 1 on GRC-1.

450 q = 0.491(p) + 9.3592 400

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

Figure C2: q versus p analysis of triaxial test 2 on GRC-1.

450

400 q = 0.5052(p) + 8.4954

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

487

Figure C3: q versus p analysis of triaxial test 3 on GRC-1.

450

400 q = 0.5996(p) - 7.5126

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

Figure C4: q versus p analysis of triaxial test 4 on GRC-1.

450

400 q = 0.5709(p) - 8.3291

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

488

Figure C5: q versus p analysis of triaxial test 5 on GRC-1.

450

400 q = 0.5595(p) + 3.5081

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

Figure C6: q versus p analysis of triaxial test 6 on GRC-1.

450

400 q = 0.5991(p) + 2.5322

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

489

Figure C7: q versus p analysis of triaxial test 7 on GRC-1.

450

400 q = 0.6154(p) + 5.9561

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

Figure C8: q versus p analysis of triaxial test 8 on GRC-1.

450

400 q = 0.6627(p) + 6.7427

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

Figure C9: q versus p analysis of triaxial test 9 on GRC-1.

490

450

400 q = 0.6712(p) + 8.2915

350

300

250

q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

Figure C10: q versus p analysis of triaxial test 10 on GRC-1.

500

450 q = 0.7053(p) + 0.313

400

350

300

250 q (kPa) 200

150

100

0 0 100 200 300 400 500 600 700 800 p (kPa)

APPENDIX D TABLE BEVAMETER RESULTS FOR GRC-1 ______

491

Table D1: Specifications of Load/Torque Cell (from www.sensordata.com)

492

493

Code D1: Determination of Best Soil Preparation Method

%Soil Depth experiment (10/8/07): Oravec. %Experiment to check the effects of soil preparation on plate sinkage. %Weights were applied to the 19cm plate with a soil depth of 12cm %prepared by funnel pour and compared to results from random soil %preparation %Sinkage tests were repeated seven times, removing and replacing the %soil after each one.

%Load cell sensitivity -1170.2 N / (mV/V) %LVDT sensitivity -1091.1 mm / (Vout/Vin) clear;clc;close all

%Random Soil Preparation

%Test #1: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_1 = [0 2 4 6 8 10 15 20 25 30 35 40 45 50 55]; %applied weights %(kg) z_1 = -10^-3*[.6001 6.6001 10.29 13.1 16 17.3 20.9 23.5 26.5 28.2 29.7 31.3 33.1 34.8 37.5]'; %LVDT Output (V/V) f_1 = [-.0014 .0085 .0192 .0338 .0447 .0575 .0986 .1339 .1705 .2084 .2456 .2846 .3232 .3642 .4037]'; %Negative Load Cell (mV/V)

%Offset Correction to 0-intercept z_1 = [(z_1+(-10^-3*-.6001))]; f_1 = [(f_1+.0014)];

%curve-fit the data with the exponential equation: z(f) = a*((e^-f)-%1)+b*f*e^- f+c*f^2*e^-f M_1 = [(exp(-(f_1))-1) f_1.*exp(-(f_1)) f_1.^2.*exp(-(f_1))]; C_1 = M_1\z_1; N = 15; F_1 = (linspace(0,max(f_1),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_1 = ([(exp(-F_1)-1) F_1.*exp(-F_1) F_1.^2.*exp(-(F_1))]*C_1); %Curve-%fit LVDT Ouput (V/V)

F_1 = F_1*1170.2; %Converting (mV/V) to N Z_1 = Z_1*1091.1; %Converting (V/V) to mm f_1 = f_1*1170.2; z_1 = z_1*1091.1;

%Test #2: depth = 12cm, plate diam = 19cm, soil freshly prepared %LVDT WENT OUT OF RANGE AT 20KG LOAD %Load_2 = [0 2 4 6 8 10 15]; %applied weights (kg) %z_2 = -10^-3*[1.3901 3.4 5.69 8.5001 10.79 12.09 14.8]'; %LVDT output %(V/V) %f_2 = [.0001 .0147 .0311 .0478 .064 .0799 .1200]'; %load cell %compression (mV/V)

%Test #3: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_3 = [0 2 4 6 8 10 15 20 25 30 35 40 45 50 55]; %applied weights %(kg) z_3 = -10^-3*[.090003 2.5901 4.9001 6.4001 8.1 9.6 13.1 16.2 19.5 21.6 24.1 26.4 29 31.69 34.59]'; %LVDT output (V/V) f_3 = [-.0004 .0146 .0314 .0471 .064 .0791 .1181 .1590 .2009 .2404 .2841 .3214 .3619 .402 .4414]'; %load cell compression (mV/V)

%Offset Correction to 0-intercept z_3 = [(z_3+(-10^-3*-.090003))]; f_3 = [(f_3+.0004)];

%curve-fit the data with the exponential equation: M_3 = [(exp(-f_3)-1) f_3.*exp(-f_3) f_3.^2.*exp(-(f_3))]; C_3 = M_3\z_3; N = 15; F_3 = (linspace(0,max(f_3),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_3 = ([(exp(-F_3)-1) F_3.*exp(-F_3) F_3.^2.*exp(-(F_3))]*C_3); %Curve-%fit LVDT Ouput (V/V)

F_3 = F_3*1170.2; %Converting (mV/V) to N

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Z_3 = Z_3*1091.1; %Converting (V/V) to mm f_3 = f_3*1170.2; z_3 = z_3*1091.1;

%Test #4: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_4 = [0 2 4 6 8 10 15 20 25 30 35 40 45 50 55]; %applied weights %(kg) z_4 = -10^-3*[.23842 3.4 6.0003 9.4001 12 15.2 19.79 23.4 27.1 30.3 33.39 35.8 38.89 41.09 46.19]'; %LVDT output (V/V) f_4 = [-.0004 .0147 .0292 .0447 .0598 .0759 .1168 .1562 .1963 .2375 .2798 .3213 .3576 .3983 .443]'; %load cell compression (mV/V)

%Offset Correction to 0-intercept z_4 = [(z_4+(-10^-3*-.23842))]; f_4 = [(f_4+.0004)];

%curve-fit the data with the exponential equation: M_4 = [(exp(-f_4)-1) f_4.*exp(-f_4) f_4.^2.*exp(-(f_4))]; C_4 = M_4\z_4; N = 15; F_4 = (linspace(0,max(f_4),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_4 = ([(exp(-F_4)-1) F_4.*exp(-F_4) F_4.^2.*exp(-(F_4))]*C_4); %Curve-%fit LVDT Ouput (V/V)

F_4 = F_4*1170.2; %Converting (mV/V) to N Z_4 = Z_4*1091.1; %Converting (V/V) to mm f_4 = f_4*1170.2; z_4 = z_4*1091.1;

%Test #5: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_5 = [0 2 4 6 8 10 15 20 25 30 35 40 45 50 55]; %applied weights %(kg) z_5 = -10^-3*[.20003 4.7001 9.6 11.59 13.69 15.49 19.69 23.7 27.39 30.3 34 37.4 41.09 44.49 49.19]'; %LVDT output (V) f_5 = [0 .0152 .0327 .048 .0641 .0815 .1219 .1639 .2039 .2451 .2890 .3268 .3675 .4076 .4494]'; %load cell compression (mV/V)

%Offset Correction to 0-intercept z_5 = [(z_5+(-10^-3*-.20003))]; f_5 = [(f_5+0)];

%curve-fit the data with the exponential equation: M_5 = [(exp(-f_5)-1) f_5.*exp(-f_5) f_5.^2.*exp(-(f_5))]; C_5 = M_5\z_5; N = 15; F_5 = (linspace(0,max(f_5),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_5 = ([(exp(-F_5)-1) F_5.*exp(-F_5) F_5.^2.*exp(-(F_5))]*C_5); %Curve-%fit LVDT Ouput (V/V)

F_5 = F_5*1170.2; %Converting (mV/V) to N Z_5 = Z_5*1091.1; %Converting (V/V) to mm f_5 = f_5*1170.2; z_5 = z_5*1091.1;

%Test #6: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_6 = [0 2 4 6 8 10 15 20 25 30 35 40 45 50 55]; %applied weights %(kg) z_6 = -10^-3*[.6001 5.4902 9.7901 12.1 14.49 16.7 20.89 24.2 27.5 30.3 33.4 36.5 40.2 43.8 47]'; %LVDT output (V/V) f_6 = [.0005 .017 .0343 .051 .0671 .0841 .1264 .1671 .2076 .2478 .2877 .3301 .3694 .4106 .4508]'; %load cell compression (mV/V)

%Offset Correction to 0-intercept z_6 = [(z_6+(-10^-3*-.6001))]; f_6 = [(f_6+-.0005)];

%curve-fit the data with the exponential equation: M_6 = [(exp(-f_6)-1) f_6.*exp(-f_6) f_6.^2.*exp(-(f_6))]; C_6 = M_6\z_6; N = 15; F_6 = (linspace(0,max(f_6),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_6 = ([(exp(-F_6)-1) F_6.*exp(-F_6) F_6.^2.*exp(-(F_6))]*C_6); %Curve-%fit LVDT Ouput (V/V)

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F_6 = F_6*1170.2; %Converting (mV/V) to N Z_6 = Z_6*1091.1; %Converting (V/V) to mm f_6 = f_6*1170.2; z_6 = z_6*1091.1;

%Test #7: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_7 = [0 2 4 6 8 10 15 20 25 30 35 40 45 50 55]; %applied weights %(kg) z_7 = -10^-3*[1.1902 6.2902 10.8 14.49 19.3 21.2 26.9 30.9 35.4 38.2 40.7 44.29 46.89 50.1 54.4]'; %LVDT output (V/V) f_7 = [.0007 .0173 .0345 .0511 .0678 .084 .1257 .1666 .2074 .2489 .2881 .3311 .3711 .4108 .4528]'; %load cell compression (mV/V)

%Offset Correction to 0-intercept z_7 = [(z_7+(-10^-3*-1.1902))]; f_7 = [(f_7+-.0007)];

%curve-fit the data with the exponential equation: M_7 = [(exp(-f_7)-1) f_7.*exp(-f_7) f_7.^2.*exp(-(f_7))]; C_7 = M_7\z_7; N = 15; F_7 = (linspace(0,max(f_7),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_7 = ([(exp(-F_7)-1) F_7.*exp(-F_7) F_7.^2.*exp(-(F_7))]*C_7); %Curve-%fit LVDT Ouput (V/V)

F_7 = F_7*1170.2; %Converting (mV/V) to N Z_7 = Z_7*1091.1; %Converting (V/V) to mm f_7 = f_7*1170.2; z_7 = z_7*1091.1;

%Mean value of old Data Matrix_old_F = (cat(2,F_1,F_3,F_4,F_5,F_6,F_7))'; Mean_old_F = mean(Matrix_old_F); Matrix_old_Z = (cat(2,Z_1,Z_3,Z_4,Z_5,Z_6,Z_7))'; Mean_old_Z = mean(Matrix_old_Z);

%Hopper Soil Preparation

%Test #1: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_1a = [0 2 4 6 8 10 15 20 25 30 35 40 45 50]; %applied weights (kg) z_1a = -10^-3*[0.10014 5.7001 13.4 18.4 22.2 24.6 29.2 32.79 35.7 37.49 39.8 42.7 45.19 47.2]'; %LVDT output (V/V) f_1a = 1*[0 .0136 .0283 .043 .0604 .0747 .1157 .1619 .1975 .2427 .2795 .322 .3616 .4008]'; %Load cell compression (mV/V)

%Offset correction to 0-intercept z_1a = [(z_1a+(-10^-3*-.10014))]; f_1a = [(f_1a+0)];

%curve-fit the data with the exponential equation: M_1a = [(exp(-f_1a)-1) f_1a.*exp(-f_1a) f_1a.^2.*exp(-(f_1a))]; C_1a = M_1a\z_1a; N = 14; F_1a = (linspace(0,max(f_1a),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_1a = ([(exp(-F_1a)-1) F_1a.*exp(-F_1a) F_1a.^2.*exp(-(F_1a))]*C_1a); %Curve-fit LVDT Ouput (V/V)

F_1a = F_1a*1170.2; %Converting (mV/V) to N Z_1a = Z_1a*1091.1; %Converting (V/V) to mm\ f_1a = f_1a*1170.2; z_1a = z_1a*1091.1;

%Test #2: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_2a = [0 2 4 6 8 10 15 20 25 30 35 40 45 50]; %applied weights (kg) z_2a = -10^-3*[.40019 4.4 9.3002 13.6 16.2 18.4 24 29.2 32.69 37.6 41.7 45 48.4 50.99]'; %LVDT output (V/V) f_2a = 1*[-.0011 .0133 .0286 .0443 .0601 .0765 .1177 .16 .2007 .2413 .2825 .3227 .3646 .404]'; %Load cell compression (mV/V)

%Offset correction to 0-intercept z_2a = [(z_2a+(-10^-3*-.40019))]; f_2a = [(f_2a+.0011)];

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%curve-fit the data with the exponential equation: M_2a = [(exp(-f_2a)-1) f_2a.*exp(-f_2a) f_2a.^2.*exp(-(f_2a))]; C_2a = M_2a\z_2a; N = 14; F_2a = (linspace(0,max(f_2a),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_2a = ([(exp(-F_2a)-1) F_2a.*exp(-F_2a) F_2a.^2.*exp(-(F_2a))]*C_2a); %Curve-fit LVDT Ouput (V/V)

F_2a = F_2a*1170.2; %Converting (mV/V) to N Z_2a = Z_2a*1091.1; %Converting (V/V) to mm f_2a = f_2a*1170.2; z_2a = z_2a*1091.1;

%Test #3: depth = 12cm, plate diam = 19cm, soil freshly prepared %DATA NOT USED DUE TO SLIGHT VARIATION IN SOIL PREPARATION %Load_3a = [0 2 4 6 8 10 15 20 25 30 35 40 45 50]; %applied weights %(kg) %z_3a = -10^-3*[.40019 4.1901 7.9001 11.3 12.29 13.99 18.3 21.1 23.6 %26.79 29.2 31.4 33.8 37.6]; %LVDT output (V/V) %f_3a = 1*[-.0011 .0117 .027 .0424 .0565 .0727 .1136 .1522 .1924 .2332 %.2731 .3126 .3523 .3925]; %Load cell compression (mV/V)

%Test #4: depth = 12cm, plate diam = 19cm, soil freshly prepared %DATA NOT USED DUE TO SLIGHT VARIATION IN SOIL PREPARATION %Load_4a = [0 2 4 6 8 10 15 20 25 30 35 40 45 50]; %applied weights %(kg) %z_4a = -10^-3*[.20027 3.4903 5.3002 6.4902 7.2002 8.5001 10.9 13 15.3 %17.99 19.69 22.1 24.6 27.7]; %LVDT output (V/V) %f_4a = 1*[0 .0125 .0289 .0454 .0605 .0771 .1167 .158 .1992 .2388 .2825 %.3198 .3599 .3997]; %Load cell compression (mV/V)

%Test #5: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_5a = [0 2 4 6 8 10 15 20 25 30 35 40 45 50]; %applied weights (kg) z_5a = -10^-3*[.31042 5.9003 11.4 13.39 16.7 19.3 26 30.3 33.3 36.2 38.5 40.8 43.2 46.1]'; %LVDT output (V/V) f_5a = 1*[-.0026 .0113 .0262 .0419 .0579 .0741 .1151 .1562 .1969 .2361 .2771 .3169 .3573 .399]'; %Load cell compression (mV/V)

%Offset correction to 0-intercept z_5a = [(z_5a+(-10^-3*-.31042))]; f_5a = [(f_5a+.0026)];

%curve-fit the data with the exponential equation: M_5a = [(exp(-f_5a)-1) f_5a.*exp(-f_5a) f_5a.^2.*exp(-(f_5a))]; C_5a = M_5a\z_5a; N = 14; F_5a = (linspace(0,max(f_5a),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_5a = ([(exp(-F_5a)-1) F_5a.*exp(-F_5a) F_5a.^2.*exp(-(F_5a))]*C_5a); %Curve-fit LVDT Ouput (V/V)

F_5a = F_5a*1170.2; %Converting (mV/V) to N Z_5a = Z_5a*1091.1; %Converting (V/V) to mm f_5a = f_5a*1170.2; z_5a = z_5a*1091.1;

%Test #6: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_6a = [0 2 4 6 8 10 15 20 25 30 35 40 45 50]; %applied weights (kg) z_6a = -10^-3*[.90015 5.3903 9.1002 11.6 14.7 16.4 21.7 26.6 30.09 32.8 35.8 38.5 40.9 43.2]'; %LVDT output (V/V) f_6a = 1*[0 .0141 .0295 .044 .0597 .0758 .1149 .1549 .1959 .235 .2765 .3163 .3571 .3966]'; %Load cell compression (mV/V)

%Offset correction to 0-intercept z_6a = [z_6a+(-10^-3*-.90015)]; f_6a = [f_6a+0];

%curve-fit the data with the exponential equation: M_6a = [(exp(-f_6a)-1) f_6a.*exp(-f_6a) f_6a.^2.*exp(-(f_6a))]; C_6a = M_6a\z_6a; N = 14; F_6a = (linspace(0,max(f_6a),N))'; %Curve-fit Load Cell Ouput (mV/V)

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Z_6a = ([(exp(-F_6a)-1) F_6a.*exp(-F_6a) F_6a.^2.*exp(-(F_6a))]*C_6a); %Curve-fit LVDT Ouput (V/V)

F_6a = F_6a*1170.2; %Converting (mV/V) to N Z_6a = Z_6a*1091.1; %Converting (V/V) to mm f_6a = f_6a*1170.2; z_6a = z_6a*1091.1;

%Test #7: depth = 12cm, plate diam = 19cm, soil freshly prepared Load_7a = [0 2 4 6 8 10 15 20 25 30 35 40 45 50]; %applied weights (kg) z_7a = -10^-3*[.80013 8.6901 13.49 17.6 21 22.7 29 33.89 38 41.3 46.5 50.3 51.79 54.39]'; %LVDT output (V/V) f_7a=1*[-.0001 .0154 .0307 .0468 .0629 .0791 .1207 .1617 .2027 .2427 .283 .3251 .3644 .4049]'; %Load cell compression (mV/V)

%Offset correction to 0-intercept z_7a = [z_7a+(-10^-3*-.80013)]; f_7a = [f_7a+.0001];

%curve-fit the data with the exponential equation: M_7a = [(exp(-f_7a)-1) f_7a.*exp(-f_7a) f_7a.^2.*exp(-(f_7a))]; C_7a = M_7a\z_7a; N = 14; F_7a = (linspace(0,max(f_7a),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_7a = ([(exp(-F_7a)-1) F_7a.*exp(-F_7a) F_7a.^2.*exp(-(F_7a))]*C_7a); %Curve-fit LVDT Ouput (V/V)

F_7a = F_7a*1170.2; %Converting (mV/V) to N Z_7a = Z_7a*1091.1; %Converting (V/V) to mm f_7a = f_7a*1170.2; z_7a = z_7a*1091.1;

%Determining the mean value of the new data set Matrix_new_F = (cat(2,F_1a,F_2a,F_5a,F_6a,F_7a))'; Mean_new_F = mean(Matrix_new_F); Matrix_new_Z = (cat(2,Z_1a,Z_2a,Z_5a,Z_6a,Z_7a))'; Mean_new_Z = mean(Matrix_new_Z);

%Figure without curve-fit figure %New Data - Hopper plot(f_1a,z_1a,'ko');hold on; plot(f_2a,z_2a,'ko');hold on; plot(f_5a,z_5a,'ko');hold on; plot(f_6a,z_6a,'ko');hold on; plot(f_7a,z_7a,'ko');hold on; text(450,-3,'\o Hopper Data') %Old Data - Random plot(f_1,z_1,'k+');hold on; plot(f_3,z_3,'k+');hold on; plot(f_4,z_4,'k+');hold on; plot(f_5,z_5,'k+');hold on; plot(f_6,z_6,'k+');hold on; plot(f_7,z_7,'k+');hold on; text(450,-6,'+ Random Data') axis([0 600 -70 0]); grid on xlabel('Load (N)') ylabel('Depth (mm)')

%Figure with both sets of data figure plot(f_1a,z_1a,'ko');hold on; plot(f_2a,z_2a,'ko');hold on; plot(f_5a,z_5a,'ko');hold on; plot(f_6a,z_6a,'ko');hold on; plot(f_7a,f_7a,'ko');hold on; text(400,-3,'\o Hopper Data') plot(Mean_new_F,Mean_new_Z,'k-');hold on text(400,-6,'- Mean of Hopper Data') plot(f_1,z_1,'k+');hold on;

498 plot(f_3,z_3,'k+');hold on; plot(f_4,z_4,'k+');hold on; plot(f_5,z_5,'k+');hold on; plot(f_6,z_6,'k+');hold on; plot(f_7,z_7,'k+');hold on; text(400,-9,'+ Random Data') plot(Mean_old_F,Mean_old_Z,'k--');hold on; text(400,-12,'-- Mean of Random Data') xlabel('Load (N)') ylabel('Depth (mm)') grid on axis([0 600 -70 0])

%Plot to check curve-fit for random soil pour: figure plot(f_1,z_1,'k+');hold on; plot(F_1,Z_1,'k-');hold on; plot(f_3,z_3,'k+');hold on; plot(F_3,Z_3,'k-');hold on; plot(f_4,z_4,'k+');hold on; plot(F_4,Z_4,'k-');hold on; plot(f_5,z_5,'k+');hold on; plot(F_5,Z_5,'k-');hold on; plot(f_6,z_6,'k+');hold on; plot(F_6,Z_6,'k-');hold on; plot(f_7,z_7,'k+');hold on; plot(F_7,Z_7,'k-');hold on; xlabel('Load (N)') ylabel('Depth (mm)') grid on axis([0 600 -70 0]) text(450,-3,'+ Raw Data') text(450,-6,'- Curve Fit')

%Plot to check curve-fit for hopper soil pour: figure plot(f_1a,z_1a,'ko');hold on; plot(F_1a,Z_1a,'k-');hold on; plot(f_2a,z_2a,'ko');hold on; plot(F_2a,Z_2a,'k-');hold on; plot(f_5a,z_5a,'ko');hold on; plot(F_5a,Z_5a,'k-');hold on; plot(f_6a,z_6a,'ko');hold on; plot(F_6a,Z_6a,'k-');hold on; plot(f_7a,z_7a,'ko');hold on; plot(F_7a,Z_7a,'k-');hold on; xlabel('Load (N)') ylabel('Depth (mm)') grid on axis([0 600 -70 0]) text(450,-3,'+ Raw Data') text(450,-6,'- Curve Fit')

%Standard Deviation Calculation for random data %For all Loads Matrix_old_SD = (cat(2,Z_1,Z_3,Z_4,Z_5,Z_6,Z_7))'; Standard_Deviation_old = std(Matrix_old_SD);

%Standard Deviation Calculation for hopper data %For all Loads Matrix_new_SD = (cat(2,Z_1a,Z_2a,Z_5a,Z_6a,Z_7a))'; Standard_Deviation_new = std(Matrix_new_SD);

%Plot for Standard Deviation figure plot(F_1,Standard_Deviation_old,'k+');hold on; plot(F_1a,Standard_Deviation_new,'ko');hold on; text(45,7.5,'+ Random') text(45,7.1,'\o Hopper') xlabel('Load (N)')

499 ylabel('Standard Deviation of Depth (mm)') grid on

Code D2: Determination of Minimum Soil Depth for 7.6 cm Plate

500

%Soil Depth Experiment - Run test preparing the soil to the same exact %density every time. To do this back calculate the weight of the soil %needed to create 1.75g/cc sample at predetermined soil depth. The %Measure that amount of soil using the scale then pour it into soil %bin. Shake the soil down to the desired depth. Run pressure-sinkage %test. December 5, 2007: 7.6cm diameter plate close all; clear all; clc;

A1 = pi*(7.6/2)^2*100; %small plate area mm^2

%Test #1: 3cm depth Vin1 = 10.0058; Z_11 = -10^-3*[-.19991 9.3001 10.9 12.3 13.6 15.89 18.4 19.7 20.9 22.2 23.1 24.7 26 27.8 28.29]';%(V/V) F_11 = [-.0001 .0089 .0244 .0402 .0559 .0735 .1128 .1531 .1935 .234 .274 .3138 .3545 .395 .4349]';%(mV/V)

Z_11 = Z_11-(-.19991*-10^-3);%zeroing the sinkage F_11 = F_11+.0001;%zeroing the load

%curve-fit the data with the exponential equation M_11 = [(exp(-(F_11))-1) F_11.*exp(-(F_11)) F_11.^2.*exp(-(F_11))]; C_11 = M_11\Z_11; N = 15; F_11 = (linspace(0,max(F_11),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_11 = ([(exp(-F_11)-1) F_11.*exp(-F_11) F_11.^2.*exp(-(F_11))]*C_11); %Curve-fit LVDT Ouput (V/V)

Z_11 = 1126.3*Z_11/Vin1;%mm F_11 = 1170.2*F_11;%N F_11 = F_11/A1*1000; %kPa

%Test #2: 3cm depth Vin2 = 10.0059; Z_21 = -10^-3*[-.29993 4.4901 6.5901 7.7002 8.4001 10.4 12 13.1 14.29 15.59 16.5 17.8 18.7 19.79 20.9]';%(V/V) F_21 = [-.0006 .0112 .027 .0432 .0598 .0768 .1161 .1554 .1954 .236 .2751 .3168 .355 .3956 .4356]';%(mV/V)

Z_21 = Z_21-(-.29993*-10^-3);%zeroing the sinkage F_21 = F_21+.0006;%zeroing the load

%curve-fit the data with the exponential equation M_21 = [(exp(-(F_21))-1) F_21.*exp(-(F_21)) F_21.^2.*exp(-(F_21))]; C_21 = M_21\Z_21; N = 15; F_21 = (linspace(0,max(F_21),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_21 = ([(exp(-F_21)-1) F_21.*exp(-F_21) F_21.^2.*exp(-(F_21))]*C_21); %Curve-fit LVDT Ouput (V/V)

Z_21 = 1126.3*Z_21/Vin2;%mm F_21 = 1170.2*F_21;%N F_21 = F_21/A1*1000; %kPa

%Test #3: 3cm depth Vin3 = 10.006; Z_31 = -10^-3*[.23842*10^-3 3.8002 7.1002 9.4901 11.5 14.3 17 19.4 20.6 22.1 23.6 25.1 26.4 28.4 30]';%(V/V) F_31 = [.0001 .0139 .0305 .0469 .0633 .0802 .1206 .1616 .2015 .242 .2824 .3231 .3639 .4044 .4449]';%(mV/V)

Z_31 = Z_31-(.23842*10^-3*-10^-3);%zeroing the sinkage F_31 = F_31-.0001;%zeroing the load

%curve-fit the data with the exponential equation M_31 = [(exp(-(F_31))-1) F_31.*exp(-(F_31)) F_31.^2.*exp(-(F_31))];

501

C_31 = M_31\Z_31; N = 15; F_31 = (linspace(0,max(F_31),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_31 = ([(exp(-F_31)-1) F_31.*exp(-F_31) F_31.^2.*exp(-(F_31))]*C_31); %Curve-fit LVDT Ouput (V/V)

Z_31 = 1126.3*Z_31/Vin3;%mm F_31 = 1170.2*F_31;%N F_31 = F_31/A1*1000; %kPa

%Test #4: 3cm depth Vin4 = 10.006; Z_41 = -10^-3*[.11921*10^-3 2.8001 5.3 6.8001 8.3002 11.5 13.49 16 17.2 18.4 20.3 21.3 22.3 23.6 25.09]';%(V/V) F_41 = [0 .0125 .0282 .0441 .0603 .0801 .118 .1591 .1979 .2384 .2795 .3185 .3579 .3975 .4384]';%(mV/V)

Z_41 = Z_41-(.11921*10^-3*-10^-3);%zeroing the sinkage F_41 = F_41-0;%zeroing the load

%curve-fit the data with the exponential equation M_41 = [(exp(-(F_41))-1) F_41.*exp(-(F_41)) F_41.^2.*exp(-(F_41))]; C_41 = M_41\Z_41; N = 15; F_41 = (linspace(0,max(F_41),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_41 = ([(exp(-F_41)-1) F_41.*exp(-F_41) F_41.^2.*exp(-(F_41))]*C_41); %Curve-fit LVDT Ouput (V/V)

Z_41 = 1126.3*Z_41/Vin4;%mm F_41 = 1170.2*F_41;%N F_41 = F_41/A1*1000; %kPa

%Test #5: 3cm depth Vin5 = 10.006; Z_51 = -10^-3*[.11009 2.6001 5.7101 7.8101 9.910 13.41 16.51 18.11 20.1 21.31 22.6 24.21 25.31 26.5 27.91]';%(V/V) F_51 = [-.0001 .0094 .0265 .0425 .0585 .0754 .1152 .1542 .1951 .2341 .2739 .3153 .3533 .3921 .4345]';%(mV/V)

Z_51 = Z_51-(.11009*-10^-3);%zeroing the sinkage F_51 = F_51+.0001;%zeroing the load

%curve-fit the data with the exponential equation M_51 = [(exp(-(F_51))-1) F_51.*exp(-(F_51)) F_51.^2.*exp(-(F_51))]; C_51 = M_51\Z_51; N = 15; F_51 = (linspace(0,max(F_51),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_51 = ([(exp(-F_51)-1) F_51.*exp(-F_51) F_51.^2.*exp(-(F_51))]*C_51); %Curve-fit LVDT Ouput (V/V)

Z_51 = 1126.3*Z_51/Vin5;%mm F_51 = 1170.2*F_51;%N F_51 = F_51/A1*1000; %kPa %------%Determining the mean value of the scattered curves. Matrix_Z1 = [Z_11 Z_21 Z_31 Z_41 Z_51]'; Matrix_F1 = [F_11 F_21 F_31 F_41 F_51]';

Std_Z1 = std(Matrix_Z1);

Mean_Z1 = Mean(Matrix_Z1,1); Mean_F1 = Mean(Matrix_F1,1);

W1 = mean(Std_Z1); %------figure plot(F_11,Z_11,'ko'); hold on; plot(F_21,Z_21,'ko'); hold on; plot(F_31,Z_31,'ko'); hold on; plot(F_41,Z_41,'ko'); hold on; plot(F_51,Z_51,'ko'); hold on;

502 plot(Mean_F1,Mean_Z1,'k-','linewidth',2); hold on; text(90, -0.5,'\o Raw Data') text(90, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 120 -10 0])

%------%Test #1: 6cm depth Vin7 = 10.0052; Z_13 = -10^-3*[.0098944 1.9001 6.6001 10.59 14.49 20.3 27.5 33.1 37.2 40.49 43.3 46.7 49.2 52.6 55.5]';%(V/V) F_13 = [.0003 .0127 .0295 .0465 .063 .0814 .1212 .1619 .2032 .2432 .283 .3235 .3633 .404 .4442]';%(mV/V)

Z_13 = Z_13-(.0098944*-10^-3);%zeroing the sinkage F_13 = F_13-.0003;%zeroing the load

%curve-fit the data with the exponential equation M_13 = [(exp(-(F_13))-1) F_13.*exp(-(F_13)) F_13.^2.*exp(-(F_13))]; C_13 = M_13\Z_13; N = 15; F_13 = (linspace(0,max(F_13),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_13 = ([(exp(-F_13)-1) F_13.*exp(-F_13) F_13.^2.*exp(-(F_13))]*C_13); %Curve-fit LVDT Ouput (V/V)

Z_13 = 1126.3*Z_13/Vin7;%mm F_13 = 1170.2*F_13;%N F_13 = F_13/A1*1000; %kPa

%Test #2: 6cm depth Vin8 = 10.0062; Z_23 = -10^-3*[-.10002 1.0002 2.8001 5.3001 7.2001 12.2 16.69 21.3 26.09 29.7 33.1 37 39.7 43 46.4]';%(V/V) F_23 = [.0001 .0114 .0278 .0438 .0606 .0787 .1187 .1593 .2006 .2403 .2809 .3219 .3616 .4003 .441]';%(mV/V)

Z_23 = Z_23-(-.10002*-10^-3);%zeroing the sinkage F_23 = F_23-.0001;%zeroing the load

%curve-fit the data with the exponential equation M_23 = [(exp(-(F_23))-1) F_23.*exp(-(F_23)) F_23.^2.*exp(-(F_23))]; C_23 = M_23\Z_23; N = 15; F_23 = (linspace(0,max(F_23),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_23 = ([(exp(-F_23)-1) F_23.*exp(-F_23) F_23.^2.*exp(-(F_23))]*C_23); %Curve-fit LVDT Ouput (V/V)

Z_23 = 1126.3*Z_23/Vin8;%mm F_23 = 1170.2*F_23;%N F_23 = F_23/A1*1000; %kPa

%Test #3: 6cm depth Vin9 = 10.0056; Z_33 = -10^-3*[-.10991 1.1902 3.9002 5.7 7.7001 12.2 16.6 19.7 22.6 25 27.59 29.79 32.69 34.6 37.5]';%(V/V) F_33 = [-.0006 .0091 .0241 .0394 .0557 .0725 .1115 .1519 .192 .2318 .2726 .3122 .3523 .3913 .4307]';%(mV/V)

Z_33 = Z_33-(-.10991*-10^-3);%zeroing the sinkage F_33 = F_33+.0006;%zeroing the load

%curve-fit the data with the exponential equation M_33 = [(exp(-(F_33))-1) F_33.*exp(-(F_33)) F_33.^2.*exp(-(F_33))]; C_33 = M_33\Z_33; N = 15; F_33 = (linspace(0,max(F_33),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_33 = ([(exp(-F_33)-1) F_33.*exp(-F_33) F_33.^2.*exp(-(F_33))]*C_33); %Curve-fit LVDT Ouput (V/V)

503

Z_33 = 1126.3*Z_33/Vin9;%mm F_33 = 1170.2*F_33;%N F_33 = F_33/A1*1000; %kPa

%Test #4: 6cm depth Vin10 = 10.0056; Z_43 = -10^-3*[.090182 1.5001 5.1901 6.6001 7.7901 11.19 14.4 16.4 18.3 21.39 23 24.79 26.49 28.9 31.6]';%(V/V) F_43 = [0 .0098 .0254 .0425 .0579 .0753 .1164 .1571 .1968 .2383 .278 .3183 .3581 .3986 .4404]';%(mV/V)

Z_43 = Z_43-(.09018*-10^-3);%zeroing the sinkage F_43 = F_43;%zeroing the load

%curve-fit the data with the exponential equation M_43 = [(exp(-(F_43))-1) F_43.*exp(-(F_43)) F_43.^2.*exp(-(F_43))]; C_43 = M_43\Z_43; N = 15; F_43 = (linspace(0,max(F_43),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_43 = ([(exp(-F_43)-1) F_43.*exp(-F_43) F_43.^2.*exp(-(F_43))]*C_43); %Curve-fit LVDT Ouput (V/V)

Z_43 = 1126.3*Z_43/Vin10;%mm F_43 = 1170.2*F_43;%N F_43 = F_43/A1*1000; %kPa

%Test #5: 6cm depth Vin11 = 10.0056; Z_53 = -10^-3*[.10014 1.3001 4.8001 6.5001 8.3001 12.6 17.5 21.5 25.6 29.1 34.7 38.4 43.1 47.9 53.19]';%(V/V) F_53 = [0 .0106 .0282 .0442 .0601 .0784 .1193 .1602 .2012 .2421 .2824 .3223 .3609 .4009 .11406]';%(mV/V)

Z_53 = Z_53-(.10014*-10^-3);%zeroing the sinkage F_53 = F_53;%zeroing the load

%curve-fit the data with the exponential equation M_53 = [(exp(-(F_53))-1) F_53.*exp(-(F_53)) F_53.^2.*exp(-(F_53))]; C_53 = M_53\Z_53; N = 15; F_53 = (linspace(0,max(F_53),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_53 = ([(exp(-F_53)-1) F_53.*exp(-F_53) F_53.^2.*exp(-(F_53))]*C_53); %Curve-fit LVDT Ouput (V/V)

Z_53 = 1126.3*Z_53/Vin11;%mm F_53 = 1170.2*F_53;%N F_53 = F_53/A1*1000; %kPa %------%Determining the mean value of the scattered curves. Matrix_Z3 = [Z_13 Z_23 Z_33 Z_43 Z_53]'; Matrix_F3 = [F_13 F_23 F_33 F_43 F_53]';

Std_Z3 = std(Matrix_Z3);

Mean_Z3 = Mean(Matrix_Z3,1); Mean_F3 = Mean(Matrix_F3,1);

W3 = mean(Std_Z3); %------figure plot(F_13,Z_13,'ko'); hold on; plot(F_23,Z_23,'ko'); hold on; plot(F_33,Z_33,'ko'); hold on; plot(F_43,Z_43,'ko'); hold on; plot(F_53,Z_53,'ko'); hold on; plot(Mean_F3,Mean_Z3,'k-','linewidth',2'); hold on; text(90, -0.5,'\o Raw Data') text(90, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on

504 axis([0 120 -10 0]) %------%Test #1: 12cm depth Vin12 = 10.0058; Z_14 = -10^-3*[-.49996 1.9001 6.9002 11.79 14.4 20.6 27.3 31.6 35.3 38.7 42.3 45.49 49.1 52.5 56.5]';%(V/V) F_14 = [0 .0106 .026 .042 .0579 .0764 .1157 .157 .1976 .2366 .2768 .3171 .3574 .3968 .4361]';%(mV/V)

Z_14 = Z_14-(-.49996*-10^-3);%zeroing the sinkage F_14 = F_14;%zeroing the load

%curve-fit the data with the exponential equationM_14 = [(exp(-(F_14))-1) F_14.*exp(- (F_14)) F_14.^2.*exp(-(F_14))]; C_14 = M_14\Z_14; N = 15; F_14 = (linspace(0,max(F_14),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_14 = ([(exp(-F_14)-1) F_14.*exp(-F_14) F_14.^2.*exp(-(F_14))]*C_14); %Curve-fit LVDT Ouput (V/V)

Z_14 = 1126.3*Z_14/Vin12;%mm F_14 = 1170.2*F_14;%N F_14 = F_14/A1*1000; %kPa

%Test #2: 12cm depth Vin13 = 10.0059; Z_24 = -10^-3*[.11921*10^-3 1.9002 5.4000 8.5001 11.3 15.8 20.99 25.29 29.2 32.49 36.4 40.1 43.99 48 52.99]';%(V/V) F_24 = [-.0015 .0097 .0258 .0414 .0579 .0748 .1145 .1551 .1949 .2351 .2754 .3148 .3549 .3945 .434]';%(mV/V)

Z_24 = Z_24-(.11921*10^-3*-10^-3);%zeroing the sinkage F_24 = F_24+.0015;%zeroing the load

%curve-fit the data with the exponential equation M_24 = [(exp(-(F_24))-1) F_24.*exp(-(F_24)) F_24.^2.*exp(-(F_24))]; C_24 = M_24\Z_24; N = 15; F_24 = (linspace(0,max(F_24),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_24 = ([(exp(-F_24)-1) F_24.*exp(-F_24) F_24.^2.*exp(-(F_24))]*C_24); %Curve-fit LVDT Ouput (V/V)

Z_24 = 1126.3*Z_24/Vin13;%mm F_24 = 1170.2*F_24;%N F_24 = F_24/A1*1000; %kPa

%Test #3: 12cm depth Vin14 = 10.006; Z_34 = -10^-3*[0 2.7001 7.1001 9.2001 11.2 16.09 20.1 24.1 27.5 31.7 34.6 38.29 42.5 46.2 49.79]';%(V/V) F_34 = [0 .0108 .0271 .0425 .0582 .0764 .1151 .1552 .1959 .2374 .2765 .3156 .3549 .3964 .435]';%(mV/V)

Z_34 = Z_34-(0*-10^-3);%zeroing the sinkage F_34 = F_34;%zeroing the load

%curve-fit the data with the exponential equation M_34 = [(exp(-(F_34))-1) F_34.*exp(-(F_34)) F_34.^2.*exp(-(F_34))]; C_34 = M_34\Z_34; N = 15; F_34 = (linspace(0,max(F_34),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_34 = ([(exp(-F_34)-1) F_34.*exp(-F_34) F_34.^2.*exp(-(F_34))]*C_34); %Curve-fit LVDT Ouput (V/V)

Z_34 = 1126.3*Z_34/Vin14;%mm F_34 = 1170.2*F_34;%N F_34 = F_34/A1*1000; %kPa

%Test #4: 12cm depth Vin15 = 10.0061;

505

Z_44 = -10^-3*[.10026 2.0902 4.5002 6.7002 8.8003 13.4 16.8 19.7 22.4 24.1 26.49 28.5 30.5 32.89 34.8]';%(V/V) F_44 = [-.0002 .0109 .0266 .0424 .0578 .0758 .115 .1547 .1954 .2339 .2738 .313 .3542 .3941 .4332]';%(mV/V)

Z_44 = Z_44-(.10026*-10^-3);%zeroing the sinkage F_44 = F_44+.0002;%zeroing the load

%curve-fit the data with the exponential equation M_44 = [(exp(-(F_44))-1) F_44.*exp(-(F_44)) F_44.^2.*exp(-(F_44))]; C_44 = M_44\Z_44; N = 15; F_44 = (linspace(0,max(F_44),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_44 = ([(exp(-F_44)-1) F_44.*exp(-F_44) F_44.^2.*exp(-(F_44))]*C_44); %Curve-fit LVDT Ouput (V/V)

Z_44 = 1126.3*Z_44/Vin15;%mm F_44 = 1170.2*F_44;%N F_44 = F_44/A1*1000; %kPa

%Test #5: 12cm depth Vin16 = 10.006; Z_54 = -10^-3*[.10002 1.1902 3.7901 6.4001 8.4901 12.9 16.3 20.89 22.99 24.69 27.5 30.19 32.2 35.2 37.7]';%(V/V) F_54 = [0 .0122 .0279 .0448 .0602 .0779 .118 .1599 .1994 .2383 .2778 .3192 .3576 .3975 .4376]';%(mV/V)

Z_54 = Z_54-(.10002*-10^-3);%zeroing the sinkage F_54 = F_54;%zeroing the load

%curve-fit the data with the exponential equation M_54 = [(exp(-(F_54))-1) F_54.*exp(-(F_54)) F_54.^2.*exp(-(F_54))]; C_54 = M_54\Z_54; N = 15; F_54 = (linspace(0,max(F_54),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_54 = ([(exp(-F_54)-1) F_54.*exp(-F_54) F_54.^2.*exp(-(F_54))]*C_54); %Curve-fit LVDT Ouput (V/V)

Z_54 = 1126.3*Z_54/Vin16;%mm F_54 = 1170.2*F_54;%N F_54 = F_54/A1*1000; %kPa %------%Determining the mean value of the scattered curves. Matrix_Z4 = [Z_14 Z_24 Z_34 Z_44 Z_54]'; Matrix_F4 = [F_14 F_24 F_34 F_44 F_54]';

Std_Z4 = std(Matrix_Z4);

Mean_Z4 = Mean(Matrix_Z4,1); Mean_F4 = Mean(Matrix_F4,1);

W4 = mean(Std_Z4); %------figure plot(F_14,Z_14,'ko'); hold on; plot(F_24,Z_24,'ko'); hold on; plot(F_34,Z_34,'ko'); hold on; plot(F_44,Z_44,'ko'); hold on; plot(F_54,Z_54,'ko'); hold on; plot(Mean_F4,Mean_Z4,'k-','linewidth',2'); hold on; text(90, -0.5,'\o Raw Data') text(90, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 120 -10 0]) %------%Test #1: 3cm depth REDO Vin17 = 10.0051; Z_11r = -10^-3*[-.19991 5.6902 13.3 18.8 21.89 27.2 31.8 35.09 37.8 39.5 41.59 43.8 44.99 46.4 47.99]';%(V/V)

506

F_11r = [-.0124 -.0143 -.0051 .0038 .0132 .0246 .0606 .094 .1311 .0654 .2017 .2378 .2741 .3111 .3484]';%(mV/V)

Z_11r = Z_11r-(-.19991*-10^-3);%zeroing the sinkage F_11r = F_11r+.0124;%zeroing the load

%curve-fit the data with the exponential equation: M_11r = [(exp(-(F_11r))-1) F_11r.*exp(-(F_11r)) F_11r.^2.*exp(-(F_11r))]; C_11r = M_11r\Z_11r; N = 15; F_11r = (linspace(0,max(F_11r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_11r = ([(exp(-F_11r)-1) F_11r.*exp(-F_11r) F_11r.^2.*exp(-(F_11r))]*C_11r); %Curve-fit LVDT Ouput (V/V)

Z_11r = 1126.3*Z_11r/Vin17;%mm F_11r = 1170.2*F_11r;%N F_11r = F_11r/A1*1000; %kPa

%Test #2: 3cm depth REDO Vin18 = 10.005; Z_21r = -10^-3*[.11921*10^-3 1.8902 6 12.3 15.6 21.49 26.59 30.6 34 36.5 38.8 40.5 42.2 44.6 46.3]';%(V/V) F_21r = [-.0042 .0042 .0182 .0324 .0456 .0608 .0989 .1366 .1754 .2134 .2518 .289 .3285 .3672 .4032]';%(mV/V)

Z_21r = Z_21r-(.11921*10^-3*-10^-3);%zeroing the sinkage F_21r = F_21r+.0042;%zeroing the load

%curve-fit the data with the exponential equation: M_21r = [(exp(-(F_21r))-1) F_21r.*exp(-(F_21r)) F_21r.^2.*exp( (F_21r))]; C_21r = M_21r\Z_21r; N = 15; F_21r = (linspace(0,max(F_21r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_21r = ([(exp(-F_21r)-1) F_21r.*exp(-F_21r) F_21r.^2.*exp(-(F_21r))]*C_21r); %Curve-fit LVDT Ouput (V/V)

Z_21r = 1126.3*Z_21r/Vin18;%mm F_21r = 1170.2*F_21r;%N F_21r = F_21r/A1*1000; %kPa

%Test #3: 3cm depth REDO Vin19 = 10.0052; Z_31r = -10^-3*[.099897 3.3 7.3 11 13.3 18.09 23.9 29.19 32.7 36.49 39.7 43.1 45.79 49.29 51.5]';%(V/V) F_31r = [-.0009 .0104 .0263 .0423 .0571 .0726 .1126 .1527 .1923 .2332 .2731 .3128 .3524 .3912 .4308]';%(mV/V)

Z_31r = Z_31r-(.099897*-10^-3);%zeroing the sinkage F_31r = F_31r+.0009;%zeroing the load

%curve-fit the data with the exponential equation: M_31r = [(exp(-(F_31r))-1) F_31r.*exp(-(F_31r)) F_31r.^2.*exp(-(F_31r))]; C_31r = M_31r\Z_31r; N = 15; F_31r = (linspace(0,max(F_31r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_31r = ([(exp(-F_31r)-1) F_31r.*exp(-F_31r) F_31r.^2.*exp(-(F_31r))]*C_31r); %Curve-fit LVDT Ouput (V/V)

Z_31r = 1126.3*Z_31r/Vin19;%mm F_31r = 1170.2*F_31r;%N F_31r = F_31r/A1*1000; %kPa

%Test #4: 3cm depth REDO Vin20 = 10.0054; Z_41r = -10^-3*[.20003 2.7 5.0901 6.8001 8.400 12.3 14.9 17.2 19.6 21.3 23.2 24.9 26.6 28.1 29.2]';%(V/V) F_41r = [-.0009 .0122 .0283 .0443 .0599 .0759 .1154 .1556 .1954 .2345 .2739 .3135 .3526 .3914 .4289]';%(mV/V)

Z_41r = Z_41r-(.20003*-10^-3);%zeroing the sinkage F_41r = F_41r+.0009;%zeroing the load

507

%curve-fit the data with the exponential equation: M_41r = [(exp(-(F_41r))-1) F_41r.*exp(-(F_41r)) F_41r.^2.*exp(-(F_41r))]; C_41r = M_41r\Z_41r; N = 15; F_41r = (linspace(0,max(F_41r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_41r = ([(exp(-F_41r)-1) F_41r.*exp(-F_41r) F_41r.^2.*exp(-(F_41r))]*C_41r); %Curve-fit LVDT Ouput (V/V)

Z_41r = 1126.3*Z_41r/Vin20;%mm F_41r = 1170.2*F_41r;%N F_41r = F_41r/A1*1000; %kPa

%Test #5: 3cm depth REDO Vin21 = 10.0056; Z_51r = -10^-3*[.059605*10^-3 2.5 6.8902 9.6001 13.2 17.8 22.19 24.3 28.19 29.89 31.7 33.2 34.9 36.4 38.7]';%(V/V) F_51r = [-.0002 .0113 .0269 .0426 .0579 .075 .1154 .1549 .1959 .2352 .2757 .3157 .3552 .3944 .4341]';%(mV/V)

Z_51r = Z_51r-(.059605*10^-3*-10^-3);%zeroing the sinkage F_51r = F_51r+.0002;%zeroing the load

%curve-fit the data with the exponential equation: M_51r = [(exp(-(F_51r))-1) F_51r.*exp(-(F_51r)) F_51r.^2.*exp(-(F_51r))]; C_51r = M_51r\Z_51r; N = 15; F_51r = (linspace(0,max(F_51r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_51r = ([(exp(-F_51r)-1) F_51r.*exp(-F_51r) F_51r.^2.*exp(-(F_51r))]*C_51r); %Curve-fit LVDT Ouput (V/V)

Z_51r = 1126.3*Z_51r/Vin21;%mm F_51r = 1170.2*F_51r;%N F_51r = F_51r/A1*1000; %kPa %------%Determining the mean value of the scattered curves. Matrix_Z1r = [Z_11r Z_21r Z_31r Z_41r Z_51r]'; Matrix_F1r = [F_11r F_21r F_31r F_41r F_51r]';

Std_Z1r = std(Matrix_Z1r);

Mean_Z1r = Mean(Matrix_Z1r,1); Mean_F1r = Mean(Matrix_F1r,1);

W1r = mean(Std_Z1r); %------figure plot(F_11r,Z_11r,'ko'); hold on; plot(F_21r,Z_21r,'ko'); hold on; plot(F_31r,Z_31r,'ko'); hold on; plot(F_41r,Z_41r,'ko'); hold on; plot(F_51r,Z_51r,'ko'); hold on; plot(Mean_F1r,Mean_Z1r,'k-','linewidth',2'); hold on; text(90, -0.5,'\o Raw Data') text(90, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 120 -10 0])

%------

%Test #1: 3cm depth REDO2 Vin22 = 10.0058; Z_11r2 = -10^-3*[-.099897 1.2002 2.8 3.7001 4.7902 7.7901 9.6002 11.19 12.6 13.6 14.9 15.89 17.1 18.3 19.29]';%(V/V) F_11r2 = [-.0007 .0114 .0275 .0436 .0591 .0765 .1156 .1556 .1953 .2343 .2737 .3142 .3539 .3942 .4338]';%(mV/V)

Z_11r2 = Z_11r2-(-.099897*-10^-3);%zeroing the sinkage F_11r2 = F_11r2+.0007;%zeroing the load

508

%curve-fit the data with the exponential equation: M_11r2 = [(exp(-(F_11r2))-1) F_11r2.*exp(-(F_11r2)) F_11r2.^2.*exp(-(F_11r2))]; C_11r2 = M_11r2\Z_11r2; N = 15; F_11r2 = (linspace(0,max(F_11r2),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_11r2 = ([(exp(-F_11r2)-1) F_11r2.*exp(-F_11r2) F_11r2.^2.*exp(-(F_11r2))]*C_11r2); %Curve-fit LVDT Ouput (V/V)

Z_11r2 = 1126.3*Z_11r2/Vin22;%mm F_11r2 = 1170.2*F_11r2;%N F_11r2 = F_11r2/A1*1000; %kPa

%Test #2: 3cm depth REDO2 Vin23 = 10.0059; Z_21r2 = -10^-3*[-.0097752 3.3002 6.3002 8.3002 9.5001 12.39 14.6 16.59 18 20 21.1 22.99 23.89 25.1 26.6]';%(V/V) F_21r2 = [-.0001 .0122 .0277 .0444 .0598 .0771 .1176 .1572 .1969 .2374 .2771 .3193 .3572 .3961 .4361]';%(mV/V)

Z_21r2 = Z_21r2-(-.0097752*-10^-3);%zeroing the sinkage F_21r2 = F_21r2+.0001;%zeroing the load

%curve-fit the data with the exponential equation: M_21r2 = [(exp(-(F_21r2))-1) F_21r2.*exp(-(F_21r2)) F_21r2.^2.*exp(-(F_21r2))]; C_21r2 = M_21r2\Z_21r2; N = 15; F_21r2 = (linspace(0,max(F_21r2),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_21r2 = ([(exp(-F_21r2)-1) F_21r2.*exp(-F_21r2) F_21r2.^2.*exp(-(F_21r2))]*C_21r2); %Curve-fit LVDT Ouput (V/V)

Z_21r2 = 1126.3*Z_21r2/Vin23;%mm F_21r2 = 1170.2*F_21r2;%N F_21r2 = F_21r2/A1*1000; %kPa

%Test #3: 3cm depth REDO2 Vin24 = 10.0059; Z_31r2 = -10^-3*[.11921*10^-3 2.4902 5.8901 8.4002 10.99 15.4 19.2 21.69 24 26.1 28.4 30.3 32.1 33.7 35.6 ]';%(V/V) F_31r2 = [-.0001 .012 .0286 .0448 .0612 .0784 .1183 .1592 .1991 .2403 .2815 .3251 .3621 .4015 .4431]';%(mV/V)

Z_31r2 = Z_31r2-(.11921*10^-3*-10^-3);%zeroing the sinkage F_31r2 = F_31r2+.0001;%zeroing the load

%curve-fit the data with the exponential equation: M_31r2 = [(exp(-(F_31r2))-1) F_31r2.*exp(-(F_31r2)) F_31r2.^2.*exp(-(F_31r2))]; C_31r2 = M_31r2\Z_31r2; N = 15; F_31r2 = (linspace(0,max(F_31r2),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_31r2 = ([(exp(-F_31r2)-1) F_31r2.*exp(-F_31r2) F_31r2.^2.*exp(-(F_31r2))]*C_31r2); %Curve-fit LVDT Ouput (V/V)

Z_31r2 = 1126.3*Z_31r2/Vin24;%mm F_31r2 = 1170.2*F_31r2;%N F_31r2 = F_31r2/A1*1000; %kPa

%Test #4: 3cm depth REDO2 Vin25 = 10.006; Z_41r2 = -10^-3*[.10014 2.6902 5.5001 7.3901 9.0001 12.3 15.8 18.3 21 22.1 23.8 26 27.6 29.19 30.8]';%(V/V) F_41r2 = [.0001 .0117 .0285 .0447 .0613 .0782 .1191 .1595 .2003 .2409 .2801 .321 .3607 .4007 .4399]';%(mV/V)

Z_41r2 = Z_41r2-(.10014*-10^-3);%zeroing the sinkage F_41r2 = F_41r2-.0001;%zeroing the load

%curve-fit the data with the exponential equation: M_41r2 = [(exp(-(F_41r2))-1) F_41r2.*exp(-(F_41r2)) F_41r2.^2.*exp(-(F_41r2))]; C_41r2 = M_41r2\Z_41r2; N = 15;

509

F_41r2 = (linspace(0,max(F_41r2),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_41r2= ([(exp(-F_41r2)-1) F_41r2.*exp(-F_41r2) F_41r2.^2.*exp(-(F_41r2))]*C_41r2); %Curve-fit LVDT Ouput (V/V)

Z_41r2 = 1126.3*Z_41r2/Vin25;%mm F_41r2 = 1170.2*F_41r2;%N F_41r2 = F_41r2/A1*1000; %kPa

%Test #5: 3cm depth REDO2 Vin40 = 10.006; Z_51r2 = -10^-3*[.10014 1.1002 2.8001 5.2001 7.6001 11.4 15.2 17.49 19.4 20.8 22.3 23.4 24.6 25.9 27]';%(V/V) F_51r2 = [.0007 .013 .0293 .046 .0622 .0798 .1213 .1625 .2031 .2435 .284 .3247 .3658 .4059 .4463]';%(mV/V)

Z_51r2 = Z_51r2-(.10014*-10^-3);%zeroing the sinkage F_51r2 = F_51r2-.0007;%zeroing the load

M_51r2 = [(exp(-(F_51r2))-1) F_51r2.*exp(-(F_51r2)) F_51r2.^2.*exp(-(F_51r2))]; C_51r2 = M_51r2\Z_51r2; N = 15; F_51r2 = (linspace(0,max(F_51r2),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_51r2 = ([(exp(-F_51r2)-1) F_51r2.*exp(-F_51r2) F_51r2.^2.*exp(-(F_51r2))]*C_51r2); %Curve-fit LVDT Ouput (V/V)

Z_51r2 = 1126.3*Z_51r2/Vin40;%mm F_51r2 = 1170.2*F_51r2;%N F_51r2 = F_51r2/A1*1000; %kPa %------%Determining the mean value of the scattered curves. Matrix_Z1r2 = [Z_11r2 Z_21r2 Z_31r2 Z_41r2 Z_51r2]'; Matrix_F1r2 = [F_11r2 F_21r2 F_31r2 F_41r2 F_51r2]';

Std_Z1r2 = std(Matrix_Z1r2);

Mean_Z1r2 = Mean(Matrix_Z1r2,1); Mean_F1r2 = Mean(Matrix_F1r2,1);

W1r2 = mean(Std_Z1r2); %------figure plot(F_11r2,Z_11r2,'ko'); hold on; plot(F_21r2,Z_21r2,'ko'); hold on; plot(F_31r2,Z_31r2,'ko'); hold on; plot(F_41r2,Z_41r2,'ko'); hold on; plot(F_51r2,Z_51r2,'ko'); hold on; plot(Mean_F1r2,Mean_Z1r2,'k-','linewidth',2'); hold on; text(90, -0.5,'\o Raw Data') text(90, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 120 -10 0])

%------%Test #1: 18cm depth Vin26 = 10.0065; Z_12 = -10^-3*[.090241 3 8.1002 11.1 13.7 18.3 23.3 26.99 31.4 34.5 38 40.6 44.4 46.59 50.4]';%(V/V) F_12 = [-.0002 .0102 .027 .0432 .0587 .0781 .1181 .1584 .1995 .2394 .2797 .3191 .3599 .401 .4411]';%(mV/V)

Z_12 = Z_12-(.090241*-10^-3);%zeroing the sinkage F_12 = F_12+.0002;%zeroing the load

M_12 = [(exp(-(F_12))-1) F_12.*exp(-(F_12)) F_12.^2.*exp(-(F_12))]; C_12 = M_12\Z_12; N = 15; F_12 = (linspace(0,max(F_12),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_12 = ([(exp(-F_12)-1) F_12.*exp(-F_12) F_12.^2.*exp(-(F_12))]*C_12); %Curve-fit LVDT Ouput (V/V)

510

Z_12 = 1126.3*Z_12/Vin26;%mm F_12 = 1170.2*F_12;%N F_12 = F_12/A1*1000; %kPa

%Test #2: 18cm depth Vin27 = 10.0065; Z_22 = -10^-3*[-.099778 5.1003 7.6002 9.4001 11.9 14.8 18.09 20.5 22.7 25.2 26.8 28.9 31.3 33.09 36]';%(V/V) F_22 = [.0002 .0146 .029 .0458 .0622 .0797 .1203 .1613 .2015 .2408 .2823 .3212 .3614 .4017 .4404]';%(mV/V)

Z_22 = Z_22-(-.099778*-10^-3);%zeroing the sinkage F_22 = F_22-.0002;%zeroing the load

M_22 = [(exp(-(F_22))-1) F_22.*exp(-(F_22)) F_22.^2.*exp(-(F_22))]; C_22 = M_22\Z_22; N = 15; F_22 = (linspace(0,max(F_22),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_22 = ([(exp(-F_22)-1) F_22.*exp(-F_22) F_22.^2.*exp(-(F_22))]*C_22); %Curve-fit LVDT Ouput (V/V)

Z_22 = 1126.3*Z_22/Vin27;%mm F_22 = 1170.2*F_22;%N F_22 = F_22/A1*1000; %kPa

%Test #3: 18cm depth Vin41 = 10.0059; Z_32 = -10^-3*[.11921*10^-3 4.9002 8.5002 11.2 13.09 17.6 22.2 26.1 28.89 33 35.29 38.6 41.8 44.7 48]';%(V/V) F_32 = [.0005 .0133 .0293 .0459 .0623 .0814 .121 .1621 .2029 .2446 .2834 .3238 .3642 .4048 .4443]';%(mV/V)

Z_32 = Z_32-(.11921*10^-3*-10^-3);%zeroing the sinkage F_32 = F_32-.0005;%zeroing the load

M_32 = [(exp(-(F_32))-1) F_32.*exp(-(F_32)) F_32.^2.*exp(-(F_32))]; C_32 = M_32\Z_32; N = 15; F_32 = (linspace(0,max(F_32),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_32 = ([(exp(-F_32)-1) F_32.*exp(-F_32) F_32.^2.*exp(-(F_32))]*C_32); %Curve-fit LVDT Ouput (V/V)

Z_32 = 1126.3*Z_32/Vin41;%mm F_32 = 1170.2*F_32;%N F_32 = F_32/A1*1000; %kPa

%Test #4: 18cm depth Vin28 = 10.006; Z_42 = -10^-3*[.11921*10^-3 2.8902 5.2001 7.3003 8.7003 14.5 16.4 19.9 22.99 25.7 27.9 31.8 35.29 37.6 40.3]';%(V/V) F_42 = [-.0002 .013 .0289 .045 .0615 .0793 .1198 .1608 .2019 .2418 .2811 .3225 .362 .4013 .4416]';%(mV/V)

Z_42 = Z_42-(.11921*10^-3*-10^-3);%zeroing the sinkage F_42 = F_42+.0002;%zeroing the load

M_42 = [(exp(-(F_42))-1) F_42.*exp(-(F_42)) F_42.^2.*exp(-(F_42))]; C_42 = M_42\Z_42; N = 15; F_42 = (linspace(0,max(F_42),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_42 = ([(exp(-F_42)-1) F_42.*exp(-F_42) F_42.^2.*exp(-(F_42))]*C_42); %Curve-fit LVDT Ouput (V/V)

Z_42 = 1126.3*Z_42/Vin28;%mm F_42 = 1170.2*F_42;%N F_42 = F_42/A1*1000; %kPa

%Test #5: 18cm depth Vin29 = 10.006;

511

Z_52 = -10^-3*[.30017 2.5002 5.7002 8.4903 11.09 14.89 18.79 22.5 25.4 29.2 32.3 35.2 38.2 41.1 45.5]';%(V/V) F_52 = [.0001 .0118 .0285 .0452 .0622 .0797 .1204 .1612 .2009 .2411 .2814 .3215 .3607 .3995 .4381]';%(mV/V)

Z_52 = Z_52-(.30017*-10^-3);%zeroing the sinkage F_52 = F_52-.0001;%zeroing the load

M_52 = [(exp(-(F_52))-1) F_52.*exp(-(F_52)) F_52.^2.*exp(-(F_52))]; C_52 = M_52\Z_52; N = 15; F_52 = (linspace(0,max(F_52),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_52 = ([(exp(-F_52)-1) F_52.*exp(-F_52) F_52.^2.*exp(-(F_52))]*C_52); %Curve-fit LVDT Ouput (V/V)

Z_52 = 1126.3*Z_52/Vin29;%mm F_52 = 1170.2*F_52;%N F_52 = F_52/A1*1000; %kPa %------%Determining the mean value of the scattered curves. Matrix_Z2 = [Z_12 Z_22 Z_32 Z_42 Z_52]'; Matrix_F2 = [F_12 F_22 F_32 F_42 F_52]';

Std_Z2 = std(Matrix_Z2);

Mean_Z2 = Mean(Matrix_Z2,1); Mean_F2 = Mean(Matrix_F2,1);

W2 = mean(Std_Z2); %------figure plot(F_12,Z_12,'ko'); hold on; plot(F_22,Z_22,'ko'); hold on; plot(F_32,Z_32,'ko'); hold on; plot(F_42,Z_42,'ko'); hold on; plot(F_52,Z_52,'ko'); hold on; plot(Mean_F2,Mean_Z2,'k-','linewidth',2'); hold on; text(90, -0.5,'\o Raw Data') text(90, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 120 -10 0])

%------

%Test #1: 18cm depth REDO Vin30 = 10.0061; Z_12r = -10^-3*[.20015 2.5901 6.9002 9.3001 11.7 16.19 22 27.29 33.6 39 45 59.6 91.1 210.7 211.3]';%(V/V) F_12r = [.0003 .0142 .031 .0474 .0636 .0806 .1214 .1616 .2023 .2427 .2826 .3219 .3625 .4036 .4436]';%(mV/V)

Z_12r = Z_12r-(.20015*-10^-3);%zeroing the sinkage F_12r = F_12r-.0003;%zeroing the load

M_12r = [(exp(-(F_12r))-1) F_12r.*exp(-(F_12r)) F_12r.^2.*exp(-(F_12r))]; C_12r = M_12r\Z_12r; N = 15; F_12r = (linspace(0,max(F_12r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_12r = ([(exp(-F_12r)-1) F_12r.*exp(-F_12r) F_12r.^2.*exp(-(F_12r))]*C_12r); %Curve-fit LVDT Ouput (V/V)

Z_12r = 1126.3*Z_12r/Vin30;%mm F_12r = 1170.2*F_12r;%N F_12r = F_12r/A1*1000; %kPa

%Test #2: 18cm depth REDO Vin31 = 10.0061; Z_22r = -10^-3*[.20015 3.8 11.2 14.79 18.59 24.7 32 38.8 48.09 56.8 73.8 105.8 203.2 203.7 204.5]';%(V/V)

512

F_22r = [0 .0147 .0306 .0468 .0631 .0804 .1203 .1307 .2012 .2415 .2814 .3214 .3632 .4015 .441]';%(mV/V)

Z_22r = Z_22r-(.20015*-10^-3);%zeroing the sinkage F_22r = F_22r;%zeroing the load

M_22r = [(exp(-(F_22r))-1) F_22r.*exp(-(F_22r)) F_22r.^2.*exp(-(F_22r))]; C_22r = M_22r\Z_22r; N = 15; F_22r = (linspace(0,max(F_22r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_22r = ([(exp(-F_22r)-1) F_22r.*exp(-F_22r) F_22r.^2.*exp(-(F_22r))]*C_22r); %Curve-fit LVDT Ouput (V/V)

Z_22r = 1126.3*Z_22r/Vin31;%mm F_22r = 1170.2*F_22r;%N F_22r = F_22r/A1*1000; %kPa

%Test #3: 18cm depth REDO Vin32 = 10.0062; Z_32r = -10^-3*[.10002 3.1 6.8902 9.7901 13.8 17.7 22.59 26.3 31 33.29 36.1 38.5 41 43.7 46.6]';%(V/V) F_32r = [0 .0137 .0303 .0466 .063 .0789 .1233 .161 .2022 .2426 .2835 .3223 .3639 .4018 .4429]';%(mV/V)

Z_32r = Z_32r-(.10002*-10^-3);%zeroing the sinkage F_32r = F_32r;%zeroing the load

M_32r = [(exp(-(F_32r))-1) F_32r.*exp(-(F_32r)) F_32r.^2.*exp(-(F_32r))]; C_32r = M_32r\Z_32r; N = 15; F_32r = (linspace(0,max(F_32r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_32r = ([(exp(-F_32r)-1) F_32r.*exp(-F_32r) F_32r.^2.*exp(-(F_32r))]*C_32r); %Curve-fit LVDT Ouput (V/V)

Z_32r = 1126.3*Z_32r/Vin32;%mm F_32r = 1170.2*F_32r;%N F_32r = F_32r/A1*1000; %kPa

%Test #4: 18cm depth REDO Vin33 = 10.0062; Z_42r = -10^-3*[.20027 2.8002 4.4003 5.5903 6.7002 9.8902 12.6 15.5 17.7 20.4 22.4 25 27.39 30 33.2]';%(V/V) F_42r = [-.0002 .0117 .0278 .0444 .0599 .0775 .117 .1569 .198 .2377 .2779 .3169 .3563 .3978 .4369]';%(mV/V)

Z_42r = Z_42r-(.20027*-10^-3);%zeroing the sinkage F_42r = F_42r+.0002;%zeroing the load

M_42r = [(exp(-(F_42r))-1) F_42r.*exp(-(F_42r)) F_42r.^2.*exp(-(F_42r))]; C_42r = M_42r\Z_42r; N = 15; F_42r = (linspace(0,max(F_42r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_42r = ([(exp(-F_42r)-1) F_42r.*exp(-F_42r) F_42r.^2.*exp(-(F_42r))]*C_42r); %Curve-fit LVDT Ouput (V/V)

Z_42r = 1126.3*Z_42r/Vin33;%mm F_42r = 1170.2*F_42r;%N F_42r = F_42r/A1*1000; %kPa

%Test #5: 18cm depth REDO Vin42 = 10.0062; Z_52r = -10^-3*[.10014 1.4001 3.3001 5.0002 6.3901 10.6 13.8 16.59 19.59 22.1 25.4 28.19 31.09 34.09 37.3]';%(V/V) F_52r = [.0003 .0216 .0303 .0452 .0611 .0788 .1191 .16 .2015 .2403 .2806 .3206 .3601 .4 .4403]';%(mV/V)

Z_52r = Z_52r-(.10014*-10^-3);%zeroing the sinkage F_52r = F_52r-.0003;%zeroing the load

M_52r = [(exp(-(F_52r))-1) F_52r.*exp(-(F_52r)) F_52r.^2.*exp(-(F_52r))]; C_52r = M_52r\Z_52r;

513

N = 15; F_52r = (linspace(0,max(F_52r),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_52r = ([(exp(-F_52r)-1) F_52r.*exp(-F_52r) F_52r.^2.*exp(-(F_52r))]*C_52r); %Curve-fit LVDT Ouput (V/V)

Z_52r = 1126.3*Z_52r/Vin42;%mm F_52r = 1170.2*F_52r;%N F_52r = F_52r/A1*1000; %kPa %------%Determining the mean value of the scattered curves. Matrix_Z2r = [Z_12r Z_22r Z_32r Z_42r Z_52r]'; Matrix_F2r = [F_12r F_22r F_32r F_42r F_52r]';

Std_Z2r = std(Matrix_Z2r);

Mean_Z2r = Mean(Matrix_Z2r,1); Mean_F2r = Mean(Matrix_F2r,1);

W2r = mean(Std_Z2r); %------figure plot(F_12r,Z_12r,'ko'); hold on; plot(F_22r,Z_22r,'ko'); hold on; plot(F_32r,Z_32r,'ko'); hold on; plot(F_42r,Z_42r,'ko'); hold on; plot(F_52r,Z_52r,'ko'); hold on; plot(Mean_F2r,Mean_Z2r,'k-','linewidth',2'); hold on; text(90, -0.5,'\o Raw Data') text(90, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 120 -10 0]) %------%Test #1: 9cm depth Vin9 =10.0058 ; Z_9 = -10^-3*[-.99981 1.3902 2.8001 8.1002 8.5002 10.3 12.4 16.29 19.2 20.8 22.1 26.3 38.6 43.0 49.4 57.29 95.69 181.8 182.69]';%(V/V) F_9 = [ -.05 -.0528 -.0491 -.0488 -.0422 -.0386 -.0277 -.0151 -.0034 .0096 .0209 .0572 .1023 .1384 .1774 .2156 .2535 .2871 .3250]';%(mV/V)

Z_9 = Z_9-(-.99981*-10^-3);%zeroing the sinkage F_9 = F_9+.05;%zeroing the load

%curve-fit the data with the exponential equation M_9 = [(exp(-(F_9))-1) F_9.*exp(-(F_9)) F_9.^2.*exp(-(F_9))]; C_9 = M_9\Z_9; N = 15; F_9 = (linspace(0,max(F_9),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_9 = ([(exp(-F_9)-1) F_9.*exp(-F_9) F_9.^2.*exp(-(F_9))]*C_9); %Curve-fit LVDT Ouput (V/V)

Z_9 = 1126.3*Z_9/Vin9;%mm F_9 = 1170.2*F_9;%N F_9 = F_9/A1*1000; %kPa

%Test #2: 9cm depth Vin91 = 10.0056; Z_91 = -10^-3*[.23842*10^-3 2.3001 2.9001 4.0902 4.6002 5.5002 7.8901 8.9003 12.4 13.8 15.19 27.4 32.3 38.19 48.6 76.4 152.3 153.6 288.1]';%(V/V) F_91 = [-.0078 -.0338 -.0315 -.0275 -.0249 -.0205 -.011 -.0058 .0072 .0208 .0344 .078 .117 .1559 .1949 .2344 .2719 .3101 .3493]';%(mV/V)

Z_91 = Z_91-(.23842*10^-3*-10^-3);%zeroing the sinkage F_91 = F_91+.0078;%zeroing the load

%curve-fit the data with the exponential equation M_91 = [(exp(-(F_91))-1) F_91.*exp(-(F_91)) F_91.^2.*exp(-(F_91))]; C_91 = M_91\Z_91; N = 15; F_91 = (linspace(0,max(F_91),N))'; %Curve-fit Load Cell Ouput (mV/V)

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Z_91 = ([(exp(-F_91)-1) F_91.*exp(-F_91) F_91.^2.*exp(-(F_91))]*C_91); %Curve-fit LVDT Ouput (V/V)

Z_91 = 1126.3*Z_91/Vin91;%mm F_91 = 1170.2*F_91;%N F_91 = F_91/A1*1000; %kPa

%Test #3: 9m depth Vin92 = 10.0054; Z_92 = -10^-3*[1.1002 1.9002 2.7002 3.1002 4.1002 5.4002 8.8 10.8 14.8 17.09 19.4 32.89 38.39 46.9 57.19 96.6 176 177.6 180.7]';%(V/V) F_92 = [-.0348 -.0415 -.0429 -.0408 -.0398 -.0388 -.0295 -.0189 -.0076 .0038 .0184 .0601 .0941 .1268 .1635 .2017 .2371 .2726 .3106]';%(mV/V)

Z_92 = Z_92-(1.1002*-10^-3);%zeroing the sinkage F_92 = F_92+.0348;%zeroing the load

%curve-fit the data with the exponential equation M_92 = [(exp(-(F_92))-1) F_92.*exp(-(F_92)) F_92.^2.*exp(-(F_92))]; C_92 = M_92\Z_92; N = 15; F_92 = (linspace(0,max(F_92),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_92 = ([(exp(-F_92)-1) F_92.*exp(-F_92) F_92.^2.*exp(-(F_92))]*C_92); %Curve-fit LVDT Ouput (V/V)

Z_92 = 1126.3*Z_92/Vin92;%mm F_92 = 1170.2*F_92;%N F_92 = F_92/A1*1000; %kPa

%Test #4: 9cm depth Vin93 =10.0057 ; Z_93 = -10^-3*[-.99981 7.2 8.0001 8.9002 9.7001 10.3 13.29 17.4 18.8 20.3 21.3 24.6 27.7 31.29 34.9 39.7 43.9 63.29 166.6]';%(V/V) F_93 = [-.0102 -.0105 -.006 -.0008 .0034 .0079 .0216 .0353 .0496 .0638 .0784 .1159 .1546 .1921 .2309 .2692 .3081 .3587 .3980]';%(mV/V)

Z_93 = Z_93-(-.99981*-10^-3);%zeroing the sinkage F_93 = F_93+.0102;%zeroing the load

%curve-fit the data with the exponential equation M_93 = [(exp(-(F_93))-1) F_93.*exp(-(F_93)) F_93.^2.*exp(-(F_93))]; C_93 = M_93\Z_93; N = 15; F_93 = (linspace(0,max(F_93),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_93 = ([(exp(-F_93)-1) F_93.*exp(-F_93) F_93.^2.*exp(-(F_93))]*C_93); %Curve-fit LVDT Ouput (V/V)

Z_93 = 1126.3*Z_93/Vin93;%mm F_93 = 1170.2*F_93;%N F_93 = F_93/A1*1000; %kPa

%Test #5: 9cm depth Vin94 =10.0057 ; Z_94 = -10^-3*[-3.3098 6.2002 7.9002 9.3002 10.2 11.3 12.6 15 19.2 19.8 20.99 31.29 34.5 37.69 40.5 43.8 46.59 49.9 53.6]';%(V/V) F_94 = [-.0048 -.004 .0015 .0072 .0128 .0195 .0335 .0478 .0634 .0772 .0917 .1385 .1777 .2169 .2565 .296 .336 .3757 .4154]';%(mV/V)

Z_94 = Z_94-(-3.3098*-10^-3);%zeroing the sinkage F_94 = F_94+.0048;%zeroing the load

%curve-fit the data with the exponential equation M_94 = [(exp(-(F_94))-1) F_94.*exp(-(F_94)) F_94.^2.*exp(-(F_94))]; C_94 = M_94\Z_94; N = 15; F_94 = (linspace(0,max(F_94),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_94 = ([(exp(-F_94)-1) F_94.*exp(-F_94) F_94.^2.*exp(-(F_94))]*C_94); %Curve-fit LVDT Ouput (V/V)

Z_94 = 1126.3*Z_94/Vin94;%mm F_94 = 1170.2*F_94;%N

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F_94 = F_94/A1*1000; %kPa

%Test #6: 9cm depth Vin95 = 10.0057; Z_95 = -10^-3*[-.58985 3.9999 5.8103 7.4 8.7001 10.2 13.6 17.31 19.1 21.4 22.8 34.6 38.5 50.4 52.31 60.3 105.1 189.8 193.7]';%(V/V) F_95 = [-.0401 -.0465 -.0421 -.0396 -.0362 -.0315 -.0186 -.0062 .0076 .0212 .0353 .0745 .01127 .152 .1913 .2306 .2699 .309 .3493]';%(mV/V)

Z_95 = Z_95-(-.58985*-10^-3);%zeroing the sinkage F_95 = F_95+.0401;%zeroing the load

%curve-fit the data with the exponential equation M_95 = [(exp(-(F_95))-1) F_95.*exp(-(F_95)) F_95.^2.*exp(-(F_95))]; C_95 = M_95\Z_95; N = 15; F_95 = (linspace(0,max(F_95),N))'; %Curve-fit Load Cell Ouput (mV/V) Z_95 = ([(exp(-F_95)-1) F_95.*exp(-F_95) F_95.^2.*exp(-(F_95))]*C_95); %Curve-fit LVDT Ouput (V/V)

Z_95 = 1126.3*Z_95/Vin95;%mm F_95 = 1170.2*F_95;%N F_95 = F_95/A1*1000; %kPa %------%Determining the mean value of the scattered curves. Matrix_Z9 = [Z_9 Z_91 Z_92 Z_93 Z_94 Z_95]'; Matrix_F9 = [F_9 F_91 F_92 F_93 F_94 F_95]';

Std_Z9 = std(Matrix_Z9);

Mean_Z9 = Mean(Matrix_Z9,1); Mean_F9 = Mean(Matrix_F9,1);

W9 = mean(Std_Z9); %------figure plot(F_9,Z_9,'ko'); hold on; plot(F_91,Z_91,'ko'); hold on; plot(F_92,Z_92,'ko'); hold on; plot(F_93,Z_93,'ko'); hold on; plot(F_94,Z_94,'ko'); hold on; plot(F_95,Z_95,'ko'); hold on; plot(Mean_F9,Mean_Z9,'k-','linewidth',2'); hold on; text(90, -0.5,'\o Raw Data') text(90, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 120 -10 0]) %------figure %plot of all the mean value curves at different soil height preparations plot(Mean_F1,Mean_Z1,'-kx','markersize',7); hold on; %3cm plot(Mean_F1r,Mean_Z1r,'--kx','markersize',7); hold on; %3cm REDO plot(Mean_F1r2,Mean_Z1r2,':kx','markersize',7); hold on; %3cm REDO2 plot(Mean_F3,Mean_Z3,'-ko'); hold on; %6cm plot(Mean_F9,Mean_Z9,'-ks'); hold on; %9cm plot(Mean_F4,Mean_Z4,'-kd'); hold on; %12cm plot(Mean_F2,Mean_Z2,'-k*','markersize',7); hold on; %18cm plot(Mean_F2r,Mean_Z2r,'-k+','markersize',7); hold on; %18cm REDO Title('Minimum Soil Depth Preparation Determination') Legend('3cm Test 1','3cm Test 2','3 Test 3','6cm Test 1','9cm Test 1','12cm Test 1','18cm Test 1','18cm Test 2','Location','SouthWest') xlabel('Pressure(kPa)') ylabel('Depth(mm)') axis([0 120 -10 0]) grid on figure %plot of all the mean value curves at different soil height preparations plot(Mean_F1,Mean_Z1,'-kx','markersize',7); hold on; %3cm

516 plot(Mean_F1r,Mean_Z1r,'--kx','markersize',7); hold on; %3cm REDO plot(Mean_F1r2,Mean_Z1r2,':kx','markersize',7); hold on; %3cm REDO2 plot(Mean_F3,Mean_Z3,'-ko'); hold on; %6cm plot(Mean_F9,Mean_Z9,'-ks'); hold on; %9cm plot(Mean_F4,Mean_Z4,'-kd'); hold on; %12cm plot(Mean_F2,Mean_Z2,'-k*','markersize',7); hold on; %18cm plot(Mean_F2r,Mean_Z2r,'-k+','markersize',7); hold on; %18cm REDO Title('Minimum Soil Depth Preparation Determination') Legend('3cm Test 1','3cm Test 2','3 Test 3','6cm Test 1','9cm Test 1','12cm Test 1','18cm Test 1','18cm Test 2','Location','SouthWest') xlabel('Pressure(kPa)') ylabel('Depth(mm)') axis([0 40 -5 0]) grid on figure %plot of all the mean value curves at different soil height preparations plot(Mean_F1,Mean_Z1,'-kx','markersize',7); hold on; %3cm plot(Mean_F1r2,Mean_Z1r2,':kx','markersize',7); hold on; %3cm REDO2 plot(Mean_F3,Mean_Z3,'-ko'); hold on; %6cm plot(Mean_F4,Mean_Z4,'-kd'); hold on; %12cm plot(Mean_F2,Mean_Z2,'-k*','markersize',7); hold on; %18cm Title('Minimum Soil Depth Preparation Determination') Legend('3cm Test 1','3 Test 3','6cm Test 1','12cm Test 1','18cm Test 1','Location','SouthWest') xlabel('Pressure(kPa)') ylabel('Depth(mm)') axis([0 120 -10 0]) grid on figure %plot of all the mean value curves at different soil height preparations plot(Mean_F1,Mean_Z1,'-kx','markersize',7); hold on; %3cm plot(Mean_F1r2,Mean_Z1r2,':kx','markersize',7); hold on; %3cm REDO2 plot(Mean_F3,Mean_Z3,'-ko'); hold on; %6cm plot(Mean_F4,Mean_Z4,'-kd'); hold on; %12cm plot(Mean_F2,Mean_Z2,'-k*','markersize',7); hold on; %18cm Title('Minimum Soil Depth Preparation Determination') Legend('3cm Test 1','3 Test 3','6cm Test 1','12cm Test 1','18cm Test 1','Location','SouthWest') xlabel('Pressure(kPa)') ylabel('Depth(mm)') axis([0 40 -5 0]) grid on

Code D3: Determination of Minimum Soil Depth for 19 cm Plate

close all; clear all; clc;

A2 = pi*(19/2)^2*100; %large plate area in mm^2 %------%Test #1: 3cm depth

517

V_in1 = 10.0066; %input voltage

Z_11 = -10^-3*[.20015 .89025 2.5902 4.7903 7.5002 11 12.7 14.3 16.4 17.99 19.4 22.4 24.7 27.9 29.3 31.3 33.1 35.2 36.7]';%sinkage in(V/V) F_11 = [-.0011 .0054 .0131 .0218 .0315 .0417 .056 .0707 .0876 .1044 .1204 .1608 .2018 .2438 .2837 .3241 .3642 .4069 .4465]';%load in (mV/V)

Z_11 = Z_11-(.20015*-10^-3);%zeroing the sinkage so we start with zero sinkage at time zero F_11 = F_11+.0011;%zeroing the load so we start with zero load at time zero

%curve-fit the data with the exponential equation: M_11 = [(exp(-(F_11))-1) F_11.*exp(-(F_11)) F_11.^2.*exp(-(F_11))]; C_11 = M_11\Z_11; %Determining the coefficients a, b, c N = 15; %Used below F_11 = (linspace(0,max(F_11),N))'; %Determining 15 regularly spaced load points to evaluate the model Z_11 = ([(exp(-F_11)-1) F_11.*exp(-F_11) F_11.^2.*exp(-(F_11))]*C_11); %Curve-fit LVDT Ouput (V/V) i.e. evaluating the model using evenly spaced load intervals

%convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_11 = 1126.3*Z_11/V_in1;%mm F_11 = 1170.2*F_11;%N F_11 = F_11/A2*1000;%kPa

%Test #2: 3cm depth V_in2 = 10.006; %input voltage

Z_12 = -10^-3*[.30017 1.7904 2.6002 3.0903 3.6001 5.1003 5.6901 6.7002 7.3001 10.4 14.3 15.49 16.8 18.49 19.8 20.3 21.7 23 27.5 ]';%sinkage in(V/V) F_12 = [.0006 .0041 .0123 .0204 .0277 .0359 .0499 .0667 .082 .0985 .1234 .1614 .2016 .2422 .2819 .3224 .3616 .4024 .4424]';%load in (mV/V)

Z_12 = Z_12-(.30017*-10^-3); F_12 = F_12-.0006;

%curve-fit the data with the exponential equation: M_12 = [(exp(-(F_12))-1) F_12.*exp(-(F_12)) F_12.^2.*exp(-(F_12))]; C_12 = M_12\Z_12; %Determining the coefficients a, b, c N = 15; %Used below F_12 = (linspace(0,max(F_12),N))'; Z_12 = ([(exp(-F_12)-1) F_12.*exp(-F_12) F_12.^2.*exp(-(F_12))]*C_12); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_12 = 1126.3*Z_12/V_in2;%mm F_12 = 1170.2*F_12;%N F_12 = F_12/A2*1000;%kPa

%Test #3: 3cm depth V_in3 = 10.0064; %input voltage

Z_13 = -10^-3*[.70012 1.8001 3.9002 6.7 8 9.9002 13.5 18.29 21.69 23.2 23.89 26.1 28.7 29.9 31.4 33.3 34.99 37.2 39.1 ]';%sinkage in(V/V) F_13 = [.0007 .007 .0152 .0242 .034 .0424 .0578 .0871 .097 .1148 .1302 .1706 .2157 .2551 .2935 .3339 .3727 .4141 .4558]';%load in (mV/V)

Z_13 = Z_13-(.70012*-10^-3); F_13 = F_13-.0007;

%curve-fit the data with the exponential equation: M_13 = [(exp(-(F_13))-1) F_13.*exp(-(F_13)) F_13.^2.*exp(-(F_13))]; C_13 = M_13\Z_13; %Determining the coefficients a, b, c N = 15; %Used below F_13 = (linspace(0,max(F_13),N))'; Z_13 = ([(exp(-F_13)-1) F_13.*exp(-F_13) F_13.^2.*exp(-(F_13))]*C_13); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell

518

Z_13 = 1126.3*Z_13/V_in3;%mm F_13 = 1170.2*F_13;%N F_13 = F_13/A2*1000;%kPa

%Test #4: 3cm depth V_in4 = 10.0066; %input voltage

Z_14 = -10^-3*[.11921*10^-3 2.5001 3.9001 4.7901 7.7901 9.8902 11.59 13.29 15.3 19.4 23.3 25.8 28.8 32.49 35 37.5 40.4 42.9 47.2]';%sinkage in(V/V) F_14 = [0 .0037 .0112 .0198 .0303 .0394 .0551 .0709 .0868 .1044 .1217 .1608 .2012 .2426 .2838 .3244 .3649 .407 .4596]';%load in (mV/V)

Z_14 = Z_14-(.11921*10^-3*-10^-3); F_14 = F_14-0;

%curve-fit the data with the exponential equation: M_14 = [(exp(-(F_14))-1) F_14.*exp(-(F_14)) F_14.^2.*exp(-(F_14))]; C_14 = M_14\Z_14; %Determining the coefficients a, b, c N = 15; %Used below F_14 = (linspace(0,max(F_14),N))'; Z_14 = ([(exp(-F_14)-1) F_14.*exp(-F_14) F_14.^2.*exp(-(F_14))]*C_14); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_14 = 1126.3*Z_14/V_in4;%mm F_14 = 1170.2*F_14;%N F_14 = F_14/A2*1000;%kPa

%Test #5: 3cm depth % NOT USED!!! DATA ERROR DURING TESTING. % V_in5 = 10.0066; %input voltage % % Z_15 = -10^-3*[.10014 5.1903 9.3001 12.5 14.49 15.39 18.2 20.49 24.3 28.59 30.7 33 34.9 36.9 38.39 39.9 41.39 43 49.6]';%sinkage in(V/V) % F_15 = [0 .0031 .0111 .0191 .028 .0352 .0498 .0645 .08 .0956 .1094 .1458 % .1832 .2208 .2587 .2972 .3359 .3752 .4521]';%load in (mV/V)

%Test #6: 3cm depth V_in11 = 10.0066; %input voltage

Z_16 = -10^-3*[-.99981 4.4001 6.1002 7.6 10.2 11 11.9 12.29 13.5 17 19.9 22 24.3 26.49 28.5 30.2 31.59 34 38.1]';%sinkage in(V/V) F_16 = [-.0418 -.0522 -.0561 -.057 -.0545 -.0571 -.0462 -.0338 -.0211 -.0146 -.0052 .0307 .067 .1049 .1426 .1801 .2165 .2542 .3011]';%load in (mV/V)

Z_16 = Z_16-(-.99981*-10^-3); F_16 = F_16+.0418;

%curve-fit the data with the exponential equation: M_16 = [(exp(-(F_16))-1) F_16.*exp(-(F_16)) F_16.^2.*exp(-(F_16))]; C_16 = M_16\Z_16; %Determining the coefficients a, b, c N = 15; %Used below F_16 = (linspace(0,max(F_16),N))'; Z_16 = ([(exp(-F_16)-1) F_16.*exp(-F_16) F_16.^2.*exp(-(F_16))]*C_16); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_16 = 1126.3*Z_16/V_in11;%mm F_16 = 1170.2*F_16;%N F_16 = F_16/A2*1000;%kPa %------%Determining the mean value of the scattered curves. Matrix_Z1 = [Z_11 Z_12 Z_13 Z_14 Z_16]'; Matrix_F1 = [F_11 F_12 F_13 F_14 F_16]';

Std_Z1 = std(Matrix_Z1);

Mean_Z1 = Mean(Matrix_Z1,1); Mean_F1 = Mean(Matrix_F1,1);

W1 = mean(Std_Z1);

519

%------figure plot(F_11,Z_11,'ko'); hold on; plot(F_12,Z_12,'ko'); hold on; plot(F_13,Z_13,'ko'); hold on; plot(F_14,Z_14,'ko'); hold on; plot(F_16,Z_16,'ko'); hold on; plot(Mean_F1,Mean_Z1,'k-','linewidth',2); hold on; text(15, -0.7,'\o Raw Data') text(15, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 20 -5 0]) %------%Test #1: 6cm depth V_in6 = 10.0061; %input voltage Z_21 = -10^-3*[-.10002 .19014 2.2902 4.6 5.5002 6.1901 7.1001 8.1 8.9 11.6 12.7 14.69 17 17.69 19.7 21.4 21.09 22.79 26.5]';%sinkage in(V/V) F_21 = [-.001 .004 .0127 .0206 .0285 .0368 .05121 .0676 .0829 .0981 .1134 .152 .1921 .2258 .2686 .3088 .3395 .3797 .4239 ]';%load in (mV/V)

Z_21 = Z_21-(-.10002*-10^-3); F_21 = F_21+.001;

%curve-fit the data with the exponential equation: M_21 = [(exp(-(F_21))-1) F_21.*exp(-(F_21)) F_21.^2.*exp(-(F_21))]; C_21 = M_21\Z_21; %Determining the coefficients a, b, c N = 15; %Used below F_21 = (linspace(0,max(F_21),N))'; Z_21 = ([(exp(-F_21)-1) F_21.*exp(-F_21) F_21.^2.*exp(-(F_21))]*C_21); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_21 = 1126.3*Z_21/V_in6;%mm F_21 = 1170.2*F_21;%N F_21 = F_21/A2*1000;%kPa

%Test #2: 6cm depth V_in7 = 10.0063; %input voltage

Z_22 = -10^-3*[-1.6998 3.9002 5.5001 7.6001 8.5002 10.5 11.6 12.7 13.9 16.2 17.7 20.19 22.5 23.59 15.4 26.9 29 30.5 36.7 ]';%sinkage in(V/V) F_22 = [0 .0056 .0133 .0215 .0284 .0374 .0523 .068 .0835 .0992 .114 .153 .1916 .2311 .1692 .3073 .3456 .3846 .4317]';%load in (mV/V)

Z_22 = Z_22-(-1.6998*-10^-3); F_22 = F_22-0;

%curve-fit the data with the exponential equation: M_22 = [(exp(-(F_22))-1) F_22.*exp(-(F_22)) F_22.^2.*exp(-(F_22))]; C_22 = M_22\Z_22; %Determining the coefficients a, b, c N = 15; %Used below F_22 = (linspace(0,max(F_22),N))'; Z_22 = ([(exp(-F_22)-1) F_22.*exp(-F_22) F_22.^2.*exp(-(F_22))]*C_22); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_22 = 1126.3*Z_22/V_in7;%mm F_22 = 1170.2*F_22;%N F_22 = F_22/A2*1000;%kPa

%Test #3: 6cm depth V_in8 = 10.0063; %input voltage

Z_23 = -10^-3*[-.49984 1.7 4.2 6.4 9.8 12 14.5 17.2 18.09 20.1 24.2 27.6 32.3 33.89 35.3 36.6 38.4 40.2 44 ]';%sinkage in(V/V) F_23 = [.0003 .0059 .0149 .0229 .0321 .0397 .0563 .0738 .0891 .1051 .1302 .1759 .2137 .2553 .2943 .3346 .3745 .4147 .4558]';%load in (mV/V)

Z_23 = Z_23-(-.49984*-10^-3);

520

F_23 = F_23-.0003;

%curve-fit the data with the exponential equation: M_23 = [(exp(-(F_23))-1) F_23.*exp(-(F_23)) F_23.^2.*exp(-(F_23))]; C_23 = M_23\Z_23; %Determining the coefficients a, b, c N = 15; %Used below F_23 = (linspace(0,max(F_23),N))'; Z_23 = ([(exp(-F_23)-1) F_23.*exp(-F_23) F_23.^2.*exp(-(F_23))]*C_23); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_23 = 1126.3*Z_23/V_in8;%mm F_23 = 1170.2*F_23;%N F_23 = F_23/A2*1000;%kPa

%Test #4: 6cm depth V_in9 = 10.0055; %input voltage

Z_24 = -10^-3*[-.49996 1.7002 4.1002 8.1002 9.9902 11.4 14.6 15.99 16.79 18.7 22.29 24.3 26 27.7 30.5 32.4 34.9 36.6 41.8]';%sinkage in(V/V) F_24 = [-.0128 -.0313 -.0285 -.0269 -.0247 -.0212 -.0082 .0026 .0151 .0288 .0484 .0697 .1082 .1464 .1856 .2251 .2648 .3031 .3411]';%load in (mV/V)

Z_24 = Z_24-(-.49996*-10^-3); F_24 = F_24+.0128;

%curve-fit the data with the exponential equation: z(f) M_24 = [(exp(-(F_24))-1) F_24.*exp(-(F_24)) F_24.^2.*exp(-(F_24))]; C_24 = M_24\Z_24; %Determining the coefficients a, b, c N = 15; %Used below F_24 = (linspace(0,max(F_24),N))'; Z_24 = ([(exp(-F_24)-1) F_24.*exp(-F_24) F_24.^2.*exp(-(F_24))]*C_24); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_24 = 1126.3*Z_24/V_in9;%mm F_24 = 1170.2*F_24;%N F_24 = F_24/A2*1000;%kPa

%Test #5: 6cm depth V_in10 = 10.0065; %input voltage

Z_25 = -10^-3*[-.099778 1.5001 2.6002 4.3 5.8001 6.4002 7.6002 9.0002 13.39 14.19 16 18.4 20.99 22.69 25.6 26.4 28.2 29.59 33.6]';%sinkage in(V/V) F_25 = [-.0016 .0037 .0106 .0184 .0259 .0332 .0485 .0642 .0851 .0963 .1115 .1516 .1926 .2335 .2733 .3140 .3544 .3939 .446 ]';%load in (mV/V)

Z_25 = Z_25-(-.099778*-10^-3); F_25 = F_25+.0016;

%curve-fit the data with the exponential equation: M_25 = [(exp(-(F_25))-1) F_25.*exp(-(F_25)) F_25.^2.*exp(-(F_25))]; C_25 = M_25\Z_25; %Determining the coefficients a, b, c N = 15; %Used below F_25 = (linspace(0,max(F_25),N))'; Z_25 = ([(exp(-F_25)-1) F_25.*exp(-F_25) F_25.^2.*exp(-(F_25))]*C_25); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_25 = 1126.3*Z_25/V_in10;%mm F_25 = 1170.2*F_25;%N F_25 = F_25/A2*1000;%kPa %------%Determining the mean value of the scattered curves. Matrix_Z2 = [Z_21 Z_22 Z_23 Z_24 Z_25]'; Matrix_F2 = [F_21 F_22 F_23 F_24 F_25]';

Std_Z2 = std(Matrix_Z2);

Mean_Z2 = Mean(Matrix_Z2,1); Mean_F2 = Mean(Matrix_F2,1);

521

W2 = mean(Std_Z2); %------figure plot(F_21,Z_21,'ko'); hold on; plot(F_22,Z_22,'ko'); hold on; plot(F_23,Z_23,'ko'); hold on; plot(F_24,Z_24,'ko'); hold on; plot(F_25,Z_25,'ko'); hold on; plot(Mean_F2,Mean_Z2,'k-','linewidth',2); hold on; text(15, -0.7,'\o Raw Data') text(15, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 20 -5 0]) %------%Test #1: 9cm depth V_in12 = 10.0067; %input voltage

Z_31 = -10^-3*[0 3 5.8901 7.7001 9.9001 10.6 14.2 15.9 19.7 22 22.7 24.59 31.1 33.3 35.29 39.6 39.49 41.1 42.6 ]';%sinkage in(V/V) F_31 = [.0004 .0061 .0148 .0218 .0301 .0363 .0594 .0759 .0907 .1072 .1229 .1625 .2093 .2510 .2918 .3321 .3676 .4074 .4482]';%load in (mV/V)

Z_31 = Z_31-(0*-10^-3); F_31 = F_31-.0004;

%curve-fit the data with the exponential equation: M_31 = [(exp(-(F_31))-1) F_31.*exp(-(F_31)) F_31.^2.*exp(-(F_31))]; C_31 = M_31\Z_31; %Determining the coefficients a, b, c N = 15; %Used below F_31 = (linspace(0,max(F_31),N))'; Z_31 = ([(exp(-F_31)-1) F_31.*exp(-F_31) F_31.^2.*exp(-(F_31))]*C_31); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_31 = 1126.3*Z_31/V_in12;%mm F_31 = 1170.2*F_31;%N F_31 = F_31/A2*1000;%kPa

%Test #2: 9cm depth V_in13 = 10.0059; %input voltage

Z_32 = -10^-3*[-.40972 .50020 2.2001 2.6001 4.0001 4.3002 4.6 5.4902 5.9901 7.7001 9.3002 10.8 11.49 12.39 13.5 14.3 22.7 25 25.5]';%sinkage in(V/V) F_32 = [-.0258 -.0408 -.0397 -.0389 -.0363 -.0374 -.0281 -.0232 -.0105 .0032 .0102 .0454 .0814 .1193 .1584 .1954 .2393 .278 .3117]';%load in (mV/V)

Z_32 = Z_32-(-.40972*-10^-3); F_32 = F_32+.0258;

%curve-fit the data with the exponential equation: M_32 = [(exp(-(F_32))-1) F_32.*exp(-(F_32)) F_32.^2.*exp(-(F_32))]; C_32 = M_32\Z_32; %Determining the coefficients a, b, c N = 15; %Used below F_32 = (linspace(0,max(F_32),N))'; Z_32 = ([(exp(-F_32)-1) F_32.*exp(-F_32) F_32.^2.*exp(-(F_32))]*C_32); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_32 = 1126.3*Z_32/V_in13;%mm F_32 = 1170.2*F_32;%N F_32 = F_32/A2*1000;%kPa

%Test #3: 9cm depth V_in14 = 10.0064; %input voltage

Z_33 = -10^-3*[-.29981 2.8001 5.8002 6.2002 7.0001 7.1901 10.19 11.39 12.69 14.2 16.3 18.29 20.6 23.39 25.8 27.59 29 30.4 35.1]';%sinkage in(V/V)

522

F_33 = [-.0002 .0059 .0148 .0226 .0311 .0384 .0531 .07 .0861 .102 .1175 .1578 .198 .2385 .2783 .3195 .3646 .4032 .4521]';%load in (mV/V)

Z_33 = Z_33-(-.29981*-10^-3); F_33 = F_33+.0002;

%curve-fit the data with the exponential equation: M_33 = [(exp(-(F_33))-1) F_33.*exp(-(F_33)) F_33.^2.*exp(-(F_33))]; C_33 = M_33\Z_33; %Determining the coefficients a, b, c N = 15; %Used below F_33 = (linspace(0,max(F_33),N))'; Z_33 = ([(exp(-F_33)-1) F_33.*exp(-F_33) F_33.^2.*exp(-(F_33))]*C_33); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_33 = 1126.3*Z_33/V_in14;%mm F_33 = 1170.2*F_33;%N F_33 = F_33/A2*1000;%kPa

%Test #4: 9cm depth V_in15 = 10.0062; %input voltage

Z_34 = -10^-3*[-.59974 1.3002 3.9003 5.4002 6.7003 8.9003 11.5 12.09 12.8 14.5 14.9 16.4 17.4 18.49 19.79 21.09 22.1 23.4 26.99]';%sinkage in(V/V) F_34 = [-.0286 -.0461 -.046 -.0444 -.0418 -.0413 -.0338 -.0225 -.0115 -.0055 .0034 .0389 .0736 .1088 .1454 .1812 .2166 .2538 .3017]';%load in (mV/V)

Z_34 = Z_34-(-.59974*-10^-3); F_34 = F_34+.0286;

%curve-fit the data with the exponential equation: M_34 = [(exp(-(F_34))-1) F_34.*exp(-(F_34)) F_34.^2.*exp(-(F_34))]; C_34 = M_34\Z_34; %Determining the coefficients a, b, c N = 15; %Used below F_34 = (linspace(0,max(F_34),N))'; Z_34 = ([(exp(-F_34)-1) F_34.*exp(-F_34) F_34.^2.*exp(-(F_34))]*C_34); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_34 = 1126.3*Z_34/V_in15;%mm F_34 = 1170.2*F_34;%N F_34 = F_34/A2*1000;%kPa

%Test #5: 9cm depth V_in16 = 10.0059; %input voltage

Z_35 = -10^-3*[-.49973 .30017 1.5001 3.8903 4.7003 4.9002 7.2002 10.6 12.4 13.4 15.3 23.5 25.2 26.99 28.9 30.39 32.09 33.39 35.3]';%sinkage in(V/V) F_35 = [-.0076 -.0244 -.0325 -.0282 -.0218 -.0192 -.0057 .0036 .0225 .0318 .0464 .0948 .1308 .1695 .2088 .2485 .2889 .3279 .3685 ]';%load in (mV/V)

Z_35 = Z_35-(-.49973*-10^-3); F_35 = F_35+.0076;

%curve-fit the data with the exponential equation: M_35 = [(exp(-(F_35))-1) F_35.*exp(-(F_35)) F_35.^2.*exp(-(F_35))]; C_35 = M_35\Z_35; %Determining the coefficients a, b, c N = 15; %Used below F_35 = (linspace(0,max(F_35),N))'; Z_35 = ([(exp(-F_35)-1) F_35.*exp(-F_35) F_35.^2.*exp(-(F_35))]*C_35); %convert units from voltage to engineering units (sinkage (mm) vs. pressure(kPa)) %1126.3 mm/(V/V)calibration factor for LVDT %1170.2 N/(mV/V)calibration factor for Load Cell Z_35 = 1126.3*Z_35/V_in16;%mm F_35 = 1170.2*F_35;%N F_35 = F_35/A2*1000;%kPa %------%Determining the mean value of the scattered curves. Matrix_Z3 = [Z_31 Z_32 Z_33 Z_34 Z_35]'; Matrix_F3 = [F_31 F_32 F_33 F_34 F_35]';

523

Std_Z3 = std(Matrix_Z3);

Mean_Z3 = Mean(Matrix_Z3,1); Mean_F3 = Mean(Matrix_F3,1);

W3 = mean(Std_Z3); %------figure plot(F_31,Z_31,'ko'); hold on; plot(F_32,Z_32,'ko'); hold on; plot(F_33,Z_33,'ko'); hold on; plot(F_34,Z_34,'ko'); hold on; plot(F_35,Z_35,'ko'); hold on; plot(Mean_F3,Mean_Z3,'k-','linewidth',2); hold on; text(15, -0.7,'\o Raw Data') text(15, -1, '- Mean') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 20 -5 0]) %------figure %plot of all the mean value curves at different soil height preparations plot(Mean_F1,Mean_Z1,'-kx','markersize',7); hold on; %3cm plot(Mean_F2,Mean_Z2,'-ko'); hold on; %6cm plot(Mean_F3,Mean_Z3,'-kd'); hold on; %9cm legend('3cm Test 1','6cm Test 1', '9cm Test 1') xlabel('Pressure (kPa)') ylabel('Depth (mm)') grid on axis([0 20 -5 0])

Code D4: Determination of Minimum Soil Depth for 10.2 cm Plate

%7/10/08 %Plate-Sinkage Testing to Determine Soil Depth at Which Boundary Conditions %Can be Ignored (Extension of Previous Testing Using New Plate Sizes: 10.2 cm)

%GRC-1 prepared in polypropylene bin, 74.2cm x 74.2cm, to a density of %1.75g/cc.

%Notation: i = soil depth suite (1 = 3cm, 2 = 6cm, etc.), j = test index (1-5) close all; clear all; clc;

%Sensitivity for LVDT and Load Cell: z = 1139.8; %mm/V f = 1155.1; %N/(mV/V)

%Plate Size: d1 = 10.2; %cm diameter a1 = pi*(d1/2)^2; %cm^2 area

524

%3cm Soil Depth------

%Test #1:

%Raw Data: v11 = 10.0522; %input voltage z11 = 10^-3.*[-.20003 -.20015 1 1.5001 2.1901 2.9901 3.4901 4.4 4.6901 5.2 5.3999 6.2001 6.7 7.1001 7.69 8.3001 10 11.49 13.1 14.2 15.7 17 18.5 19.9 21.39 28.4 31.59 34.59]'; %LVDT f11 = [.0005 .0067 .0159 .0238 .0322 .0408 .0495 .0581 .0664 .0741 .0828 .0994 .1158 .1319 .1486 .1653 .2069 .2486 .2905 .3327 .3747 .4161 .4583 .5006 .5423 .6114 .6855 .7599]'; %Load Cell (mV/V) %Zeroing the Data: z11 = z11-(10^-3*-.20003); f11 = f11-.0005; %Converting to Engineering Units Using Sensitivity: z11 = z11./v11.*z; %mm sinkage f11 = f11.*f; %N load %Convert to Pressure: p11 = f11./a1; %N/cm^2 pressure %Convert to cm and kPa: z11 = z11.*0.1; %cm sinkage p11 = p11.*10; %kPa pressure

%Test #2:

%Raw Data: v12 = 10.0523; %input voltage z12 = 10^-3.*[.00011921 .40019 1.8002 2.7001 3.6901 4.7001 6.1001 6.8002 7.1901 7.5902 7.9901 8.8902 9.9001 10.59 11.2 12 13.59 15 16.49 18 19.49 20.79 22.3 23.6 24.9 30.7 33.7 36.59]'; %LVDT f12 = [-.0003 .0063 .0149 .0234 .032 .0411 .0494 .0588 .0669 .0754 .084 .1002 .1167 .1337 .1505 .1676 .2094 .2511 .2933 .335 .3771 .4194 .4608 .5026 .5443 .6133 .6873 .7595]'; %Load Cell (mV/V) %Zeroing the Data: z12 = z12-(10^-3*.00011921); f12 = f12+.0003; %Converting to Engineering Units Using Sensitivity: z12 = z12./v12.*z; %mm sinkage f12 = f12.*f; %N load %Convert to Pressure: p12 = f12./a1; %N/cm^2 pressure %Convert to cm and kPa: z12 = z12.*0.1; %cm sinkage p12 = p12.*10; %kPa pressure

%Test #3:

%Raw Data: v13 = 10.0522; %input voltage z13 = 10^-3.*[.10014 .40007 1.2 2.2 3.0901 3.9901 5.0001 5.9001 6.3001 6.9001 7.3901 8.2901 8.6901 9.59 10.5 11.1 13.2 14.69 16.39 17.9 19.3 20.9 22.29 23.59 24.8 30.3 33.1 35.7]'; %LVDT f13 = [-.0009 .0059 .0149 .0236 .032 .0405 .0492 .0572 .0654 .0738 .0821 .099 .1153 .1316 .1486 .1654 .2069 .2484 .2911 .3334 .3744 .4166 .4589 .4998 .5424 .611 .6852 .7593]'; %Load Cell (mV/V) %Zeroing the Data: z13 = z13-(10^-3*.10014); f13 = f13+.0009; %Converting to Engineering Units Using Sensitivity: z13 = z13./v13.*z; %mm sinkage f13 = f13.*f; %N load %Convert to Pressure: p13 = f13./a1; %N/cm^2 pressure %Convert to cm and kPa: z13 = z13.*0.1; %cm sinkage p13 = p13.*10; %kPa pressure

%Test #4:

%Raw Data:

525 v14 = 10.0521; %input voltage z14 = 10^-3.*[.00011921 1.3002 2.9001 4.5002 5.9001 7.3901 8.4001 9.9901 10.6 11.4 11.9 13.6 14.4 15.2 16.1 17 18.89 20.19 21.6 23 24.49 25.79 26.99 28.4 29.8 35.19 37.8 40.2]'; %LVDT f14 = [.0003 .0084 .0164 .0248 .0333 .0425 .0497 .0538 .0657 .074 .082 .0982 .1148 .1309 .1475 .1640 .2049 .246 .2875 .3291 .3706 .4117 .4529 .4945 .536 .6032 .6768 .7500]'; %Load Cell (mV/V) %Zeroing the Data: z14 = z14-(10^-3*.00011921); f14 = f14-.0003; %Converting to Engineering Units Using Sensitivity: z14 = z14./v14.*z; %mm sinkage f14 = f14.*f; %N load %Convert to Pressure: p14 = f14./a1; %N/cm^2 pressure %Convert to cm and kPa: z14 = z14.*0.1; %cm sinkage p14 = p14.*10; %kPa pressure

%Test #5:

%Raw Data: v15 = 10.0521; %input voltage z15 = 10^-3.*[.00011921 .5002 1.6 2.8001 3.9001 4.7902 5.6001 6.8001 7.1001 7.6001 7.7902 9.0001 9.8001 10.5 11.3 12 14.1 15.8 17.5 19.29 20.59 22.1 23.4 24.89 27.2 32.3 35.09 38]'; %LVDT f15 = [.0005 .0059 .0146 .0235 .0315 .0398 .048 .0566 .0639 .0719 .0798 .096 .112 .1282 .1444 .1604 .2011 .2416 .2832 .3237 .3647 .4051 .4458 .4868 .5312 .5949 .6685 .7414]'; %Load Cell (mV/V) %Zeroing the Data: z15 = z15-(10^-3*.00011921); f15 = f15-.0005; %Converting to Engineering Units Using Sensitivity: z15 = z15./v15.*z; %mm sinkage f15 = f15.*f; %N load %Convert to Pressure: p15 = f15./a1; %N/cm^2 pressure %Convert to cm and kPa: z15 = z15.*0.1; %cm sinkage p15 = p15.*10; %kPa pressure m11z = mean([z11 z12 z13 z14 z15]')'; m11p = mean([p11 p12 p13 p14 p15]')';

%6cm Soil Depth------

%Test #1:

%Raw Data: v21 = 10.0518; %input voltage z21 = 10^-3.*[-.20969 .40007 1.4901 2.9 3.9001 4.7001 5.6901 6.5901 7.1002 7.6001 8 8.9 9.8001 10.6 11.4 12.09 13.79 15.49 17.2 18.9 20.4 21.8 23.4 25 27.09 32.59 35.8 39.3]'; %LVDT f21 = [-.0002 .0069 .016 .0249 .0332 .0418 .0502 .0587 .0673 .076 .0843 .1008 .1179 .1351 .1515 .1683 .2105 .2527 .295 .3366 .3789 .4207 .463 .5058 .5493 .6169 .6919 .7666]'; %Load Cell (mV/V) %Zeroing the Data: z21 = z21-(10^-3*-.20969); f21 = f21+.0002; %Converting to Engineering Units Using Sensitivity: z21 = z21./v21.*z; %mm sinkage f21 = f21.*f; %N load %Convert to Pressure: p21 = f21./a1; %N/cm^2 pressure %Convert to cm and kPa: z21 = z21.*0.1; %cm sinkage p21 = p21.*10; %kPa pressure

%Test #2:

%Raw Data:

526 v22 = 10.0518; %input voltage z22 = 10^-3.*[-.0098944 .30005 1.4002 2.3001 3.3001 4.0002 4.9002 5.7001 5.99 6.5001 6.9002 8.09 8.8 9.7001 10.1 10.8 13 14.49 15.9 17.4 19.1 20.6 22.1 23.7 25.1 30.9 33.69 36.9]'; %LVDT f22 = [0 .0057 .0146 .0241 .033 .041 .0496 .0584 .0659 .0745 .0828 .0999 .1169 .1338 .1508 .1677 .2096 .2518 .2933 .3355 .3779 .4191 .4608 .5026 .5446 .6131 .6852 .7584]'; %Load Cell (mV/V) %Zeroing the Data: z22 = z22-(10^-3*-.0098944); f22 = f22-0; %Converting to Engineering Units Using Sensitivity: z22 = z22./v22.*z; %mm sinkage f22 = f22.*f; %N load %Convert to Pressure: p22 = f22./a1; %N/cm^2 pressure %Convert to cm and kPa: z22 = z22.*0.1; %cm sinkage p22 = p22.*10; %kPa pressure

%Test #3:

%Raw Data: v23 = 10.0517; %input voltage z23 = 10^-3.*[.00011921 .70012 1.3901 2.3001 3.2002 4.1 5.1901 6 6.4002 7.0001 7.7002 8.5902 9.4 10.29 10.9 11.8 13.5 15.2 16.69 18.2 19.6 20.99 22.29 23.9 25.29 30.79 33.7 37.3]'; %LVDT f23 = [.0007 .0089 .0161 .0253 .034 .043 .0509 .0607 .0684 .0767 .0854 .1023 .1188 .1357 .1524 .1694 .2111 .2532 .2957 .3379 .3793 .4212 .4634 .506 .5479 .6155 .6899 .764]'; %Load Cell (mV/V) %Zeroing the Data: z23 = z23-(10^-3*.00011921); f23 = f23-.0007; %Converting to Engineering Units Using Sensitivity: z23 = z23./v23.*z; %mm sinkage f23 = f23.*f; %N load %Convert to Pressure: p23 = f23./a1; %N/cm^2 pressure %Convert to cm and kPa: z23 = z23.*0.1; %cm sinkage p23 = p23.*10; %kPa pressure

%Test #4:

%Raw Data: v24 = 10.0516; %input voltage z24 = 10^-3.*[.00011921 2.8 3.7001 4.3001 5.1001 6 6.6001 7.5002 7.9002 9.0901 9.4001 11.1 11.6 12.3 13.2 13.9 15.89 17.69 19.29 20.59 22.1 23.5 25.2 26.5 27.8 33.7 36.5 39.3]'; %LVDT f24 = [.0001 .01 .0194 .0271 .0339 .0425 .0504 .0591 .0667 .0751 .0831 .1005 .1162 .1327 .1487 .1655 .2073 .2486 .2901 .3322 .3751 .4152 .4577 .4992 .5412 .6092 .6834 .7573]'; %Load Cell (mV/V) %Zeroing the Data: z24 = z24-(10^-3*.00011921); f24 = f24-.0001; %Converting to Engineering Units Using Sensitivity: z24 = z24./v24.*z; %mm sinkage f24 = f24.*f; %N load %Convert to Pressure: p24 = f24./a1; %N/cm^2 pressure %Convert to cm and kPa: z24 = z24.*0.1; %cm sinkage p24 = p24.*10; %kPa pressure

%Test #5:

%Raw Data: v25 = 10.0516; %input voltage z25 = 10^-3.*[-.0097752 .5002 1.5002 2.7001 3.7001 4.6 5.7001 6.6001 6.7902 7.5002 7.6901 8.8 9.3902 10.3 10.8 11.6 13.59 15.29 17.1 18.7 20.1 21.5 23.5 25.19 26.7 33.29 36.5 39.6]'; %LVDT

527 f25 = [.0003 .0059 .0139 .023 .0318 .0402 .0486 .0568 .0646 .0734 .0812 .0975 .1139 .1303 .1469 .1635 .2056 .2468 .2887 .3303 .3718 .4137 .456 .4984 .5393 .6071 .6822 .7561]'; %Load Cell (mV/V) %Zeroing the Data: z25 = z25-(10^-3*-.0097752); f25 = f25-.0003; %Converting to Engineering Units Using Sensitivity: z25 = z25./v25.*z; %mm sinkage f25 = f25.*f; %N load %Convert to Pressure: p25 = f25./a1; %N/cm^2 pressure %Convert to cm and kPa: z25 = z25.*0.1; %cm sinkage p25 = p25.*10; %kPa pressure m21z = mean([z21 z22 z23 z24 z25]')'; m21p = mean([p21 p22 p23 p24 p25]')';

%9cm Soil Depth------

%Test #1:

%Raw Data: v31 = 10.0515; %input voltage z31 = 10^-3.*[0 .30017 .80013 1.6001 2.4 2.9001 3.89 4.6 5.0001 5.3002 5.5903 6.4901 7.4 8.19 8.8 9.49 11.7 13.69 15.5 17.09 18.79 20.6 22.4 26 26.8 32.4 36 39.29]'; %LVDT f31 = [-.0005 .0069 .0146 .023 .0307 .0387 .0473 .0557 .0636 .0714 .0797 .096 .1128 .1291 .1458 .1623 .2044 .2457 .2876 .328 .3697 .4111 .4533 .4972 .5365 .6035 .6781 .7501]'; %Load Cell (mV/V) %Zeroing the Data: z31 = z31-(10^-3*0); f31 = f31+.0005; %Converting to Engineering Units Using Sensitivity: z31 = z31./v31.*z; %mm sinkage f31 = f31.*f; %N load %Convert to Pressure: p31 = f31./a1; %N/cm^2 pressure %Convert to cm and kPa: z31 = z31.*0.1; %cm sinkage p31 = p31.*10; %kPa pressure

%Test #2:

%Raw Data: v32 = 10.0517; %input voltage z32 = 10^-3.*[0 1.09 2.7002 4.8002 6.1002 6.9903 8.2902 9.0002 9.5001 10.6 10.89 12.3 13.3 14.29 15 15.9 18.2 19.7 21.3 22.79 24.3 25.79 27.4 29.1 30.8 37.5 40.5 43.8]'; %LVDT f32 = [-.0003 .0061 .0142 .0239 .0319 .0405 .0488 .057 .0645 .0731 .0811 .0972 .1136 .1298 .1463 .1633 .2048 .246 .2869 .3283 .3692 .4106 .4524 .4941 .5358 .6052 .6773 .7513]'; %Load Cell (mV/V) %Zeroing the Data: z32 = z32-(10^-3*0); f32 = f32+.0003; %Converting to Engineering Units Using Sensitivity: z32 = z32./v32.*z; %mm sinkage f32 = f32.*f; %N load %Convert to Pressure: p32 = f32./a1; %N/cm^2 pressure %Convert to cm and kPa: z32 = z32.*0.1; %cm sinkage p32 = p32.*10; %kPa pressure

%Test #3:

%Raw Data: v33 = 10.0518; %input voltage z33 = 10^-3.*[.10014 .90015 2.4001 3.5902 4.7902 5.8002 6.5001 7.9001 8.4001 9.0903 9.5901 11.19 12.09 13.1 14 15 17.7 19.5 21.4 23 24.7 26.19 27.8 29.59 31.29 38 41.3 44.7]'; %LVDT

528 f33 = [.0005 .0079 .0168 .0254 .0334 .0415 .0503 .0596 .0671 .0753 .0833 .1001 .1167 .1335 .15 .167 .2097 .2519 .2938 .3356 .378 .4196 .4617 .5032 .545 .6093 .6817 .754]'; %Load Cell (mV/V) %Zeroing the Data: z33 = z33-(10^-3*.10014); f33 = f33-.0005; %Converting to Engineering Units Using Sensitivity: z33 = z33./v33.*z; %mm sinkage f33 = f33.*f; %N load %Convert to Pressure: p33 = f33./a1; %N/cm^2 pressure %Convert to cm and kPa: z33 = z33.*0.1; %cm sinkage p33 = p33.*10; %kPa pressure

%Test #4:

%Raw Data: v34 = 10.0518; %input voltage z34 = 10^-3.*[.10014 1 2.4 3.7001 5.0001 5.9901 6.8902 8 8.5001 9.1001 9.5 10.8 11.5 12.5 13.4 14.3 16.29 17.99 19.8 21.6 22.9 24.3 25.8 27.39 29 34.99 37.8 40.59]'; %LVDT f34 = [.0002 .0082 .0172 .0262 .035 .0435 .0523 .0614 .0693 .0774 .0857 .103 .1194 .1364 .153 .1699 .2123 .2545 .2965 .3391 .3798 .4214 .4639 .5066 .5477 .6107 .6846 .7622]'; %Load Cell (mV/V) %Zeroing the Data: z34 = z34-(10^-3*.10014); f34 = f34-.0002; %Converting to Engineering Units Using Sensitivity: z34 = z34./v34.*z; %mm sinkage f34 = f34.*f; %N load %Convert to Pressure: p34 = f34./a1; %N/cm^2 pressure %Convert to cm and kPa: z34 = z34.*0.1; %cm sinkage p34 = p34.*10; %kPa pressure

%Test #5:

%Raw Data: v35 = 10.0518; %input voltage z35 = 10^-3.*[-.10979 .50008 1.5001 2.6002 3.7903 5.0002 6.0002 6.9002 7.8 8.8001 9.2902 10.3 11.3 11.89 12.9 13.9 15.8 17.7 19.4 21.2 22.8 24.4 25.9 27.5 29.1 35 38.2 41.29]'; %LVDT f35 = [-.0002 .0052 .0134 .0205 .029 .0373 .0458 .0537 .0619 .0702 .0779 .0947 .1113 .1275 .144 .1608 .2017 .2438 .2848 .3262 .3679 .4092 .4511 .4932 .5348 .6024 .6757 .7502]'; %Load Cell (mV/V) %Zeroing the Data: z35 = z35-(10^-3*-.10979); f35 = f35+.0002; %Converting to Engineering Units Using Sensitivity: z35 = z35./v35.*z; %mm sinkage f35 = f35.*f; %N load %Convert to Pressure: p35 = f35./a1; %N/cm^2 pressure %Convert to cm and kPa: z35 = z35.*0.1; %cm sinkage p35 = p35.*10; %kPa pressure m31z = mean([z31 z32 z33 z34 z35]')'; m31p = mean([p31 p32 p33 p34 p35]')';

%12cm Soil Depth------

%Test #1:

%Raw Data: v41 = 10.0516; %input voltage z41 = 10^-3.*[.20003 .70012 1.8002 3.2903 4.5903 5.8901 6.8003 7.9901 8.4902 9.6903 10 11.2 12.1 12.8 13.59 14.5 16.9 19 21.1 23.1 25 27 28.89 31.3 33.59 40.7 44.8 49.89]'; %LVDT

529 f41 = [.0008 .0088 .0176 .0272 .0345 .0431 .0517 .0596 .068 .0765 .0843 .102 .1185 .1349 .1518 .1684 .2102 .252 .2938 .3361 .3777 .4192 .461 .5053 .5455 .6133 .6854 .7593]'; %Load Cell (mV/V) %Zeroing the Data: z41 = z41-(10^-3*.20003); f41 = f41-.0008; %Converting to Engineering Units Using Sensitivity: z41 = z41./v41.*z; %mm sinkage f41 = f41.*f; %N load %Convert to Pressure: p41 = f41./a1; %N/cm^2 pressure %Convert to cm and kPa: z41 = z41.*0.1; %cm sinkage p41 = p41.*10; %kPa pressure

%Test #2:

%Raw Data: v42 = 10.0516; %input voltage z42 = 10^-3.*[.19038 .60016 2.1001 3.4001 4.8003 6.3002 7.3003 8.5002 8.9002 9.8003 10.2 11.4 12.4 13.49 14.29 15.1 17.6 19.6 21.99 23.69 26 27.99 30 32.3 34.5 43.1 47.1 51.3]'; %LVDT f42 = [.0002 .0052 .0136 .0217 .0299 .0388 .0474 .0556 .0635 .0716 .0795 .0958 .1128 .1292 .1459 .1625 .2048 .2462 .2882 .3297 .3719 .4134 .4553 .4972 .5393 .6085 .6807 .7545]'; %Load Cell (mV/V) %Zeroing the Data: z42 = z42-(10^-3*.19038); f42 = f42-.0002; %Converting to Engineering Units Using Sensitivity: z42 = z42./v42.*z; %mm sinkage f42 = f42.*f; %N load %Convert to Pressure: p42 = f42./a1; %N/cm^2 pressure %Convert to cm and kPa: z42 = z42.*0.1; %cm sinkage p42 = p42.*10; %kPa pressure

%Test #3:

%Raw Data: v43 = 10.0515; %input voltage z43 = 10^-3.*[.090122 .6001 1.3901 2.6002 3.7001 4.7902 6.0902 7.0001 7.7001 8.3001 8.7001 10.29 11.19 11.9 12.49 13.4 16 17.7 19.69 21.39 23.09 24.79 26.7 28.69 30.6 37.1 40.4 43.99]'; %LVDT f43 = [-.0004 .0045 .0127 .0215 .0298 .0388 .047 .0549 .063 .0706 .0792 .0956 .112 .1285 .1454 .1619 .2033 .2445 .286 .3275 .3688 .4103 .4518 .4945 .5364 .6036 .6774 .7509]'; %Load Cell (mV/V) %Zeroing the Data: z43 = z43-(10^-3*.090122); f43 = f43+.0004; %Converting to Engineering Units Using Sensitivity: z43 = z43./v43.*z; %mm sinkage f43 = f43.*f; %N load %Convert to Pressure: p43 = f43./a1; %N/cm^2 pressure %Convert to cm and kPa: z43 = z43.*0.1; %cm sinkage p43 = p43.*10; %kPa pressure

%Test #4:

%Raw Data: v44 = 10.0515; %input voltage z44 = 10^-3.*[.00011921 1 2.7002 4.8903 7.3001 9.1002 10.8 12.3 12.99 14 14.5 15.99 16.89 17.69 18.99 19.8 21.99 23.9 25.9 27.9 29.5 31.7 33.89 36.09 37.9 45.89 49.8 54.1]'; %LVDT f44 = [-.0001 .0072 .0156 .0235 .0324 .0409 .0491 .0584 .0665 .0748 .0832 .1002 .1163 .1334 .1506 .167 .2093 .2511 .2935 .3356 .3771 .4186 .4611 .5038 .5459 .609 .683 .7552]'; %Load Cell (mV/V) %Zeroing the Data: z44 = z44-(10^-3*.00011921); f44 = f44+.0001;

530

%Converting to Engineering Units Using Sensitivity: z44 = z44./v44.*z; %mm sinkage f44 = f44.*f; %N load %Convert to Pressure: p44 = f44./a1; %N/cm^2 pressure %Convert to cm and kPa: z44 = z44.*0.1; %cm sinkage p44 = p44.*10; %kPa pressure

%Test #5:

%Raw Data: v45 = 10.0515; %input voltage z45 = 10^-3.*[.00011921 .00030017 1.2002 2.2901 3.4903 4.5002 5.5002 6.4903 7.3003 7.9002 8.4001 9.4903 10.5 11.7 12.6 13.6 16.4 18.7 21.1 23.3 25.6 27.89 30.3 32.3 34.6 43.3 47.4 51.69]'; %LVDT f45 = [.0002 .0052 .0131 .0215 .0301 .0382 .0464 .0542 .0622 .0699 .078 .0946 .1113 .1277 .1446 .1608 .2015 .2428 .284 .3257 .3666 .4085 .4504 .4919 .5338 .6304 .6751 .749]'; %Load Cell (mV/V) %Zeroing the Data: z45 = z45-(10^-3*.00011921); f45 = f45-.0002; %Converting to Engineering Units Using Sensitivity: z45 = z45./v45.*z; %mm sinkage f45 = f45.*f; %N load %Convert to Pressure: p45 = f45./a1; %N/cm^2 pressure %Convert to cm and kPa: z45 = z45.*0.1; %cm sinkage p45 = p45.*10; %kPa pressure m41z = mean([z41 z42 z43 z44 z45]')'; m41p = mean([p41 p42 p43 p44 p45]')';

%15cm Soil Depth------

%Test #1:

%Raw Data: v51 = 10.0514; %input voltage z51 = 10^-3.*[-.20981 .19002 1.0902 2.3 3.1902 4.4001 5.2902 6.1902 6.7002 7.1999 7.8901 9.0001 9.8001 10.6 11.6 12.4 15 16.8 18.9 20.8 22.7 24.49 26.4 28.7 30.2 37.2 41.4 45.6]'; %LVDT f51 = [0 .0076 .0157 .0249 .0326 .0415 .0499 .0585 .0662 .0743 .0826 .0996 .1163 .1331 .15 .1666 .2082 .2495 .2922 .3339 .3752 .4171 .4584 .5021 .5428 .6105 .6851 .7597]'; %Load Cell (mV/V) %Zeroing the Data: z51 = z51-(10^-3*-.20981); f51 = f51-0; %Converting to Engineering Units Using Sensitivity: z51 = z51./v51.*z; %mm sinkage f51 = f51.*f; %N load %Convert to Pressure: p51 = f51./a1; %N/cm^2 pressure %Convert to cm and kPa: z51 = z51.*0.1; %cm sinkage p51 = p51.*10; %kPa pressure

%Test #2:

%Raw Data: v52 = 10.0515; %input voltage z52 = 10^-3.*[-.009656 -.19991 .89014 2.1901 3.6001 4.9001 5.9901 7.1002 7.6902 8.5902 9.5001 10.690 12.3 13.5 14.6 15.9 18.9 21.79 24.29 27 29.4 31.9 34.7 36.9 43.8 50.3 54.59 60.99]'; %LVDT f52 = [.0002 .0056 .0132 .0216 .0298 .0384 .0472 .0546 .0629 .0714 .0794 .096 .1126 .129 .1459 .1625 .2042 .2461 .2881 .3298 .3716 .4131 .4554 .4973 .5403 .6092 .6802 .7536]'; %Load Cell (mV/V) %Zeroing the Data: z52 = z52-(10^-3*-.009656); f52 = f52-.0002;

531

%Converting to Engineering Units Using Sensitivity: z52 = z52./v52.*z; %mm sinkage f52 = f52.*f; %N load %Convert to Pressure: p52 = f52./a1; %N/cm^2 pressure %Convert to cm and kPa: z52 = z52.*0.1; %cm sinkage p52 = p52.*10; %kPa pressure

%Test #3:

%Raw Data: v53 = 10.0515; %input voltage z53 = 10^-3.*[.20015 .89014 1.6001 6.3902 6.7002 9.3902 9.9002 10.5 10.69 11.09 11.4 11.89 12.7 13.5 14.2 14.7 17 19 20.89 22.7 24.69 26.49 28.4 30.29 32.39 39.19 43.2 46.8]'; %LVDT f53 = [.0011 .0089 .0169 .0284 .0343 .0424 .0507 .0601 .0677 .0768 .0842 .1004 .1176 .1344 .1509 .1676 .2094 .2512 .2928 .3347 .3763 .4182 .46 .5016 .5436 .6107 .6849 .7589]'; %Load Cell (mV/V) %Zeroing the Data: z53 = z53-(10^-3*.20015); f53 = f53-.0011; %Converting to Engineering Units Using Sensitivity: z53 = z53./v53.*z; %mm sinkage f53 = f53.*f; %N load %Convert to Pressure: p53 = f53./a1; %N/cm^2 pressure %Convert to cm and kPa: z53 = z53.*0.1; %cm sinkage p53 = p53.*10; %kPa pressure

%Test #4:

%Raw Data: v54 = 10.0515; %input voltage z54 = 10^-3.*[.00011921 .30005 1.4001 2.0001 3.1003 3.9001 4.7002 5.6901 6.3001 6.9902 7.3 9.6901 9.8001 10.39 11.2 12.09 14.8 16.6 18.8 21.2 23.4 25.2 27.3 29.1 31.29 38.9 42.89 46.8]'; %LVDT f54 = [-.0012 .005 .0141 .0212 .0305 .0389 .047 .0555 .0633 .072 .08 .0969 .1135 .1305 .1472 .1638 .206 .2472 .2891 .3307 .3724 .4141 .4553 .4971 .539 .6064 .6804 .7537]'; %Load Cell (mV/V) %Zeroing the Data: z54 = z54-(10^-3*.00011921); f54 = f54+.0012; %Converting to Engineering Units Using Sensitivity: z54 = z54./v54.*z; %mm sinkage f54 = f54.*f; %N load %Convert to Pressure: p54 = f54./a1; %N/cm^2 pressure %Convert to cm and kPa: z54 = z54.*0.1; %cm sinkage p54 = p54.*10; %kPa pressure

%Test #5:

%Raw Data: v55 = 10.0516; %input voltage z55 = 10^-3.*[.00011921 .10026 .5002 1.4902 2.1002 3.1902 3.7001 4.6002 5.2001 5.5002 6.0002 7.1002 8.1002 8.8001 9.8001 10.7 12.8 14.8 17.19 19.1 20.9 22.7 24.6 26.59 28.5 35.59 39.5 43.4]'; %LVDT f55 = [-.0002 .0055 .0122 .0218 .0294 .0385 .0464 .0553 .0635 .0714 .0796 .0961 .1126 .1291 .1465 .1628 .2046 .2464 .2886 .3303 .3714 .4132 .4548 .4964 .538 .6055 .6793 .7533]'; %Load Cell (mV/V) %Zeroing the Data: z55 = z55-(10^-3*.00011921); f55 = f55+.0002; %Converting to Engineering Units Using Sensitivity: z55 = z55./v55.*z; %mm sinkage f55 = f55.*f; %N load %Convert to Pressure: p55 = f55./a1; %N/cm^2 pressure

532

%Convert to cm and kPa: z55 = z55.*0.1; %cm sinkage p55 = p55.*10; %kPa pressure m51z = mean([z51 z52 z53 z54 z55]')'; m51p = mean([p51 p52 p53 p54 p55]')';

%15cm Soil Depth (Retest)------

%Test #1:

%Raw Data: v61 = 10.0515; %input voltage z61 = 10^-3.*[.00011921 .10002 .69022 1.4001 2.3 2.8001 3.6001 4.5002 4.7002 5.2001 5.7 6.5002 7.5002 7.9002 9.2001 9.6002 11.7 13.49 15.6 17.39 18.9 20.7 22.7 24.19 26.1 32.5 36.2 39.3]'; %LVDT f61 = [-.0001 .0069 .0157 .0248 .0339 .0413 .0503 .0589 .0674 .0758 .0847 .1013 .1187 .1353 .1522 .1691 .2108 .2535 .2963 .3381 .3807 .4426 .4646 .5072 .549 .6148 .6874 .7593]'; %Load Cell (mV/V) %Zeroing the Data: z61 = z61-(10^-3*.00011921); f61 = f61+.0001; %Converting to Engineering Units Using Sensitivity: z61 = z61./v61.*z; %mm sinkage f61 = f61.*f; %N load %Convert to Pressure: p61 = f61./a1; %N/cm^2 pressure %Convert to cm and kPa: z61 = z61.*0.1; %cm sinkage p61 = p61.*10; %kPa pressure

%Test #2:

%Raw Data: v62 = 10.0515; %input voltage z62 = 10^-3.*[.00023842 .60022 2.1002 3.5002 5.0002 6.1001 7.2001 8.7001 9.1903 10.09 10.6 11.9 13.2 14.29 15 15.9 18.7 21 23.29 25.9 28.2 30.09 32.5 34.9 37.4 46.69 50.99 55.9]'; %LVDT f62 = [-.0013 .0051 .0143 .0233 .0318 .04 .0483 .0566 .065 .0732 .0818 .0983 .115 .1322 .1488 .1656 .2073 .249 .2915 .3339 .3761 .4183 .4603 .5021 .544 .6107 .6847 .7579]'; %Load Cell (mV/V) %Zeroing the Data: z62 = z62-(10^-3*.00023842); f62 = f62+.0013; %Converting to Engineering Units Using Sensitivity: z62 = z62./v62.*z; %mm sinkage f62 = f62.*f; %N load %Convert to Pressure: p62 = f62./a1; %N/cm^2 pressure %Convert to cm and kPa: z62 = z62.*0.1; %cm sinkage p62 = p62.*10; %kPa pressure

%Test #3:

%Raw Data: v63 = 10.0515; %input voltage z63 = 10^-3.*[.00023842 .20027 1.0002 1.9002 2.8002 3.6001 4.3001 5.3002 5.7002 6.1001 6.4002 7.3001 8.3901 9.1001 9.6002 10 11.39 12.9 14.2 16.09 17.3 19 20.5 22.7 24.09 30.3 33.8 37.9]'; %LVDT f63 = [-.0004 .0057 .0122 .0216 .0298 .0385 .0474 .0558 .0641 .0727 .0808 .0975 .1153 .1319 .1487 .165 .2068 .2486 .2901 .3326 .3738 .416 .4573 .5001 .542 .6081 .6819 .7571]'; %Load Cell (mV/V) %Zeroing the Data: z63 = z63-(10^-3*.00023842); f63 = f63+.0004; %Converting to Engineering Units Using Sensitivity: z63 = z63./v63.*z; %mm sinkage f63 = f63.*f; %N load %Convert to Pressure: p63 = f63./a1; %N/cm^2 pressure

533

%Convert to cm and kPa: z63 = z63.*0.1; %cm sinkage p63 = p63.*10; %kPa pressure

%Test #4:

%Raw Data: v64 = 10.0514; %input voltage z64 = 10^-3.*[.00011921 .59021 1.8002 2.6902 3.5902 4.5 5.5001 6.3001 6.9901 7.3003 7.9002 9.0902 9.9902 11 11.8 12.6 14.69 17.1 19.1 20.8 23.19 25.1 27.2 29.7 31.8 40 44.2 49.5]'; %LVDT f64 = [.0002 .0084 .0171 .0258 .0348 .0427 .0511 .06 .068 .0763 .0848 .1013 .1177 .1344 .1513 .1685 .2101 .2519 .2937 .3351 .3767 .4187 .4605 .5026 .5445 .6105 .6851 .7609]'; %Load Cell (mV/V) %Zeroing the Data: z64 = z64-(10^-3*.00011921); f64 = f64-.0002; %Converting to Engineering Units Using Sensitivity: z64 = z64./v64.*z; %mm sinkage f64 = f64.*f; %N load %Convert to Pressure: p64 = f64./a1; %N/cm^2 pressure %Convert to cm and kPa: z64 = z64.*0.1; %cm sinkage p64 = p64.*10; %kPa pressure

%Test #5:

%Raw Data: v65 = 10.0513; %input voltage z65 = 10^-3.*[.00011921 1.4901 2.5001 3.6001 4.9002 5.7902 6.6901 7.7002 8.2002 8.6001 8.7 10.2 10.89 11.39 12 12.8 14.7 17.2 18.5 20.4 22.4 24.4 26.4 28.39 30.3 37.79 41.8 46.2]'; %LVDT f65 = [.0018 .0097 .0173 .0261 .0345 .043 .0516 .0598 .0681 .0764 .0848 .1016 .1183 .1354 .1524 .1689 .2113 .2542 .296 .3382 .3803 .422 .4646 .5066 .5482 .6151 .6891 .7633]'; %Load Cell (mV/V) %Zeroing the Data: z65 = z65-(10^-3*.00011921); f65 = f65-.0018; %Converting to Engineering Units Using Sensitivity: z65 = z65./v65.*z; %mm sinkage f65 = f65.*f; %N load %Convert to Pressure: p65 = f65./a1; %N/cm^2 pressure %Convert to cm and kPa: z65 = z65.*0.1; %cm sinkage p65 = p65.*10; %kPa pressure m61z = mean([z61 z62 z63 z64 z65]')'; m61p = mean([p61 p62 p63 p64 p65]')';

%18cm Soil Depth------

%Test #1:

%Raw Data: v71 = 10.0511; %input voltage z71 = 10^-3.*[.00023842 .80013 1.7903 2.6902 3.4001 4.2 4.9002 5.8001 6.3002 6.6003 7.1001 8.1002 8.7003 9.4002 10.1 11.19 13 14.5 16.29 17.7 19.6 21.2 23.7 25 26.8 33.5 36.79 40.4]'; %LVDT f71 = [.0002 .0088 .0179 .0265 .0345 .0426 .0514 .0606 .0688 .0774 .0858 .1025 .1194 .1358 .1526 .1703 .2115 .2533 .2949 .3366 .3783 .42 .4633 .5045 .5463 .6136 .6865 .7605]'; %Load Cell (mV/V) %Zeroing the Data: z71 = z71-(10^-3*.00023842); f71 = f71-.0002; %Converting to Engineering Units Using Sensitivity: z71 = z71./v71.*z; %mm sinkage f71 = f71.*f; %N load %Convert to Pressure: p71 = f71./a1; %N/cm^2 pressure

534

%Convert to cm and kPa: z71 = z71.*0.1; %cm sinkage p71 = p71.*10; %kPa pressure

%Test #2:

%Raw Data: v72 = 10.0510; %input voltage z72 = 10^-3.*[-.099659 .30029 1.6904 2.9002 4.0002 5.0002 5.8004 6.9003 7.6001 8.7003 8.8903 9.9003 10.8 11.49 13.1 13.5 16 18.1 20.3 22.5 24.6 26.5 28.8 31.2 33.29 41.5 46.3 50.1]'; %LVDT f72 = [-.0012 .0056 .0148 .0233 .0322 .041 .0501 .0585 .0664 .0753 .0834 .1003 .117 .1337 .1508 .1667 .2091 .2505 .2923 .3343 .3757 .4175 .4596 .5019 .5436 .6107 .6858 .7592]'; %Load Cell (mV/V) %Zeroing the Data: z72 = z72-(10^-3*-.099659); f72 = f72+.0012; %Converting to Engineering Units Using Sensitivity: z72 = z72./v72.*z; %mm sinkage f72 = f72.*f; %N load %Convert to Pressure: p72 = f72./a1; %N/cm^2 pressure %Convert to cm and kPa: z72 = z72.*0.1; %cm sinkage p72 = p72.*10; %kPa pressure

%Test #3:

%Raw Data: v73 = 10.0509; %input voltage z73 = 10^-3.*[.29027 1.2001 2.2 3.0003 4.0901 4.8901 5.7001 6.6 7.4002 7.8902 8.1002 9.1901 9.8001 10.3 11.1 11.7 13.89 15.8 17.8 19.7 21.4 23.69 25.89 27.99 30.2 38.9 43.2 48.09]'; %LVDT f73 = [-.0007 .0071 .0162 .0243 .0338 .0421 .0503 .0589 .0671 .0752 .0838 .1004 .117 .1338 .1505 .1674 .2091 .2511 .2927 .3347 .3763 .4181 .4601 .5019 .5441 .6111 .6856 .7601]'; %Load Cell (mV/V) %Zeroing the Data: z73 = z73-(10^-3*.29027); f73 = f73+.0007; %Converting to Engineering Units Using Sensitivity: z73 = z73./v73.*z; %mm sinkage f73 = f73.*f; %N load %Convert to Pressure: p73 = f73./a1; %N/cm^2 pressure %Convert to cm and kPa: z73 = z73.*0.1; %cm sinkage p73 = p73.*10; %kPa pressure

%Test #4:

%Raw Data: v74 = 10.0509; %input voltage z74 = 10^-3.*[.10026 .30017 1.1003 2.0001 3.1002 4.1003 4.9002 5.8001 6.1002 6.7903 7.1002 8.4002 9.1002 10.1 11.09 12.1 14.4 16.7 19.4 21.1 23.2 25.59 28.9 30.6 32.9 42 46.4 51.3]'; %LVDT f74 = [0 .0063 .0143 .0231 .0321 .0411 .0493 .0581 .0665 .0747 .083 .1008 .1174 .1345 .1519 .1685 .2097 .2518 .2939 .3353 .377 .4188 .4614 .503 .5445 .6084 .6818 .7554]'; %Load Cell (mV/V) %Zeroing the Data: z74 = z74-(10^-3*.10026); f74 = f74-0; %Converting to Engineering Units Using Sensitivity: z74 = z74./v74.*z; %mm sinkage f74 = f74.*f; %N load %Convert to Pressure: p74 = f74./a1; %N/cm^2 pressure %Convert to cm and kPa: z74 = z74.*0.1; %cm sinkage p74 = p74.*10; %kPa pressure

%Test #5:

535

%Raw Data: v75 = 10.0508; %input voltage z75 = 10^-3.*[.10026 .30017 1.2002 2.0002 2.9002 3.5001 4.4001 5.2001 5.6003 6.2002 6.3901 7.6002 8.7001 9.3902 10.19 11.2 13.8 15.79 17.8 20.4 23.09 24.8 26.6 28.99 31.9 39.69 45 50]'; %LVDT f75 = [.0011 .0072 .0153 .0235 .0319 .0406 .0491 .0571 .0649 .0737 .0814 .0988 .1153 .1321 .1486 .1658 .2109 .2512 .294 .3354 .3796 .419 .4601 .5019 .5475 .6115 .6815 .7527]'; %Load Cell (mV/V) %Zeroing the Data: z75 = z75-(10^-3*.10026); f75 = f75-.0011; %Converting to Engineering Units Using Sensitivity: z75 = z75./v75.*z; %mm sinkage f75 = f75.*f; %N load %Convert to Pressure: p75 = f75./a1; %N/cm^2 pressure %Convert to cm and kPa: z75 = z75.*0.1; %cm sinkage p75 = p75.*10; %kPa pressure m71z = mean([z71 z72 z73 z74 z75]')'; m71p = mean([p71 p72 p73 p74 p75]')';

%21cm Soil Depth------

%Test #1:

%Raw Data: v81 = 10.0507; %input voltage z81 = 10^-3.*[1.0003 1.9002 2.8001 4.6 5.2003 6.4104 7.2001 8.2002 8.9002 9.4101 10.2 10.9 11.9 12.81 13.5 14.4 17.111 19.5 21.8 24.5 27.4 29.6 34.49 37.6 39.4 52.3 60.09 72.4]'; %LVDT f81 = [.0031 .0103 .0182 .0283 .036 .0449 .0532 .0625 .0706 .0794 .0881 .1052 .1222 .1391 .1549 .1717 .2137 .2566 .2987 .3412 .3836 .4243 .4678 .5093 .5488 .6147 .687 .7568]'; %Load Cell (mV/V) %Zeroing the Data: z81 = z81-(10^-3*1.0003); f81 = f81-.0031; %Converting to Engineering Units Using Sensitivity: z81 = z81./v81.*z; %mm sinkage f81 = f81.*f; %N load %Convert to Pressure: p81 = f81./a1; %N/cm^2 pressure %Convert to cm and kPa: z81 = z81.*0.1; %cm sinkage p81 = p81.*10; %kPa pressure

%Test #2:

%Raw Data: v82 = 10.0507; %input voltage z82 = 10^-3.*[.20015 .51033 2.0001 3.8002 5.4002 6.9102 8.0001 9.4101 10.31 10.9 11.7 13.1 14.8 16.2 17.2 18.3 22.31 25.5 28.71 32.3 35.3 38.91 42.9 47.91 51.4 71.6 92.21 140.79]'; %LVDT f82 = [0 .006 .0142 .023 .0318 .0405 .0492 .058 .0662 .0747 .0835 .1009 .1177 .1344 .1511 .1684 .2104 .2528 .2938 .3371 .3775 .4186 .4612 .5034 .5433 .6091 .6836 .7588]'; %Load Cell (mV/V) %Zeroing the Data: z82 = z82-(10^-3*.20015); f82 = f82-0; %Converting to Engineering Units Using Sensitivity: z82 = z82./v82.*z; %mm sinkage f82 = f82.*f; %N load %Convert to Pressure: p82 = f82./a1; %N/cm^2 pressure %Convert to cm and kPa: z82 = z82.*0.1; %cm sinkage p82 = p82.*10; %kPa pressure

%Test #3:

536

%Raw Data: v83 = 10.0507; %input voltage z83 = 10^-3.*[.090241 .090241 .70024 2.1002 3.4002 5.0001 5.9004 7.4004 8.3002 8.9903 9.6003 11.5 12.4 13.69 14.59 15.6 18.8 21.2 23.6 25.69 28 30 32.8 34.59 36.79 48.6 52.2 56.79]'; %LVDT f83 = [.0001 .0057 .0129 .0212 .0298 .0382 .0464 .0558 .0641 .0724 .0804 .0974 .1137 .1304 .1471 .1643 .2058 .2482 .289 .3306 .3736 .4142 .4558 .4972 .5391 .6072 .6824 .7572]'; %Load Cell (mV/V) %Zeroing the Data: z83 = z83-(10^-3*.090241); f83 = f83-.0001; %Converting to Engineering Units Using Sensitivity: z83 = z83./v83.*z; %mm sinkage f83 = f83.*f; %N load %Convert to Pressure: p83 = f83./a1; %N/cm^2 pressure %Convert to cm and kPa: z83 = z83.*0.1; %cm sinkage p83 = p83.*10; %kPa pressure

%Test #4:

%Raw Data: v84 = 10.0506; %input voltage z84 = 10^-3.*[-.089765 .80013 1.3001 2.4102 3.5002 4.4001 5.4102 6.3103 6.8001 7.3003 7.9001 9.0002 10 11.1 12 12.9 16.51 19.3 22.51 25.51 29.5 33.21 37.1 43.3 46.81 70.59 94.09 138.6]'; %LVDT f84 = [-.0015 .0059 .0138 .022 .0316 .0392 .047 .0551 .0634 .072 .0804 .0974 .1135 .1304 .1473 .1633 .2066 .2483 .2905 .3323 .3742 .4159 .4573 .5013 .5412 .6126 .6826 .7585]'; %Load Cell (mV/V) %Zeroing the Data: z84 = z84-(10^-3*-.089765); f84 = f84+.0015; %Converting to Engineering Units Using Sensitivity: z84 = z84./v84.*z; %mm sinkage f84 = f84.*f; %N load %Convert to Pressure: p84 = f84./a1; %N/cm^2 pressure %Convert to cm and kPa: z84 = z84.*0.1; %cm sinkage p84 = p84.*10; %kPa pressure

%Test #5:

%Raw Data: v85 = 10.0506; %input voltage z85 = 10^-3.*[.10026 1.1001 2.09 3.2001 4.1902 5.0901 6.2 6.9002 7.5001 8.0001 8.4901 9.3902 10.59 11.4 12.29 13.1 16.19 18.69 21 23.49 25.99 28.8 31.6 34.4 37.6 50.8 60 74.8]'; %LVDT f85 = [-.0018 .0039 .0132 .0214 .0303 .039 .0473 .0549 .0636 .072 .0804 .0975 .1148 .1309 .1485 .1658 .208 .249 .2915 .3334 .3757 .4167 .4577 .5007 .5417 .6114 .6851 .7573]'; %Load Cell (mV/V) %Zeroing the Data: z85 = z85-(10^-3*.10026); f85 = f85+.0018; %Converting to Engineering Units Using Sensitivity: z85 = z85./v85.*z; %mm sinkage f85 = f85.*f; %N load %Convert to Pressure: p85 = f85./a1; %N/cm^2 pressure %Convert to cm and kPa: z85 = z85.*0.1; %cm sinkage p85 = p85.*10; %kPa pressure m81z = mean([z81 z82 z83 z84 z85]')'; m81p = mean([p81 p82 p83 p84 p85]')';

%24cm Soil Depth------

%Test #1:

537

%Raw Data: v91 = 10.0511; %input voltage z91 = 10^-3.*[.00023842 .50008 1.9903 3.6001 5.1001 6.1001 7.5903 9.0002 9.6902 10.59 11.3 12.6 13.9 15.2 15.69 16.9 19.7 21.5 23.39 25.3 27.59 29.3 31.3 33.4 35.7 43.1 48.4 53.1]'; %LVDT f91 = [.0031 .0106 .0187 .0273 .0361 .0439 .0521 .0604 .0684 .0766 .0847 .1005 .117 .1331 .1497 .1666 .208 .2491 .2908 .3321 .3752 .4164 .4571 .5001 .5441 .6075 .6833 .7553]'; %Load Cell (mV/V) %Zeroing the Data: z91 = z91-(10^-3*.00023842); f91 = f91-.0031; %Converting to Engineering Units Using Sensitivity: z91 = z91./v91.*z; %mm sinkage f91 = f91.*f; %N load %Convert to Pressure: p91 = f91./a1; %N/cm^2 pressure %Convert to cm and kPa: z91 = z91.*0.1; %cm sinkage p91 = p91.*10; %kPa pressure

%Test #2:

%Raw Data: v92 = 10.0512; %input voltage z92 = 10^-3.*[.00023842 .70012 1.3001 2.1001 3.0001 3.5901 4.3001 5.0002 5.6002 6.09 6.3001 7.3001 8.0001 8.8 9.5901 10.3 12.8 14.69 17.19 19.3 21.49 23.7 26.9 29 32.19 41.59 48.39 57.79]'; %LVDT f92 = [.0002 .007 .015 .0236 .0323 .0406 .0487 .0568 .0651 .0734 .0815 .0985 .1148 .1317 .1481 .1647 .2081 .2489 .2917 .3338 .3748 .4167 .4594 .5019 .5433 .6079 .6837 .7549]'; %Load Cell (mV/V) %Zeroing the Data: z92 = z92-(10^-3*.00023842); f92 = f92-.0002; %Converting to Engineering Units Using Sensitivity: z92 = z92./v92.*z; %mm sinkage f92 = f92.*f; %N load %Convert to Pressure: p92 = f92./a1; %N/cm^2 pressure %Convert to cm and kPa: z92 = z92.*0.1; %cm sinkage p92 = p92.*10; %kPa pressure

%Test #3:

%Raw Data: v93 = 10.0513; %input voltage z93 = 10^-3.*[-.099897 1.9001 4.2002 5.5903 7.4 8.4002 9.7003 10.6 11.3 12.7 13.5 14.49 15.39 16.5 17.49 18.5 21.6 23.8 25.9 28.3 29.89 31.99 34.09 36.69 39 46.2 50.39 54.7]'; %LVDT f93 = [-.0002 .0073 .0164 .0254 .0334 .0413 .0503 .0579 .0659 .0746 .0832 .0998 .1165 .1332 .1498 .1665 .21 .2515 .2931 .3349 .3767 .419 .4594 .5031 .5443 .6111 .6846 .7583]'; %Load Cell (mV/V) %Zeroing the Data: z93 = z93-(10^-3*-.099897); f93 = f93+.0002; %Converting to Engineering Units Using Sensitivity: z93 = z93./v93.*z; %mm sinkage f93 = f93.*f; %N load %Convert to Pressure: p93 = f93./a1; %N/cm^2 pressure %Convert to cm and kPa: z93 = z93.*0.1; %cm sinkage p93 = p93.*10; %kPa pressure

%Test #4:

%Raw Data: v94 = 10.0514; %input voltage

538 z94 = 10^-3.*[.20015 1.3001 2.6002 3.6001 4.9001 6.1002 7.2001 7.8903 8.5002 9.1001 9.9002 11.2 12.5 13.4 14.29 15.19 18 20.5 23.1 25.89 28.2 30.8 33.4 36.7 39.09 49.9 56 63.5]'; %LVDT f94 = [.0008 .0074 .0166 .0247 .0338 .0432 .052 .0604 .0691 .0778 .0862 .1033 .1198 .1369 .1536 .1707 .2125 .2563 .2972 .339 .3807 .4242 .4642 .5072 .548 .6145 .6875 .7598]'; %Load Cell (mV/V) %Zeroing the Data: z94 = z94-(10^-3*.20015); f94 = f94-.0008; %Converting to Engineering Units Using Sensitivity: z94 = z94./v94.*z; %mm sinkage f94 = f94.*f; %N load %Convert to Pressure: p94 = f94./a1; %N/cm^2 pressure %Convert to cm and kPa: z94 = z94.*0.1; %cm sinkage p94 = p94.*10; %kPa pressure

%Test #5:

%Raw Data: v95 = 10.0514; %input voltage z95 = 10^-3.*[.10014 .90003 1.8002 3.7901 4.5002 5.8903 6.6901 7.4002 7.9001 8.6002 9.6002 10.59 11.39 12.29 13.09 15.69 17.7 20.5 22.4 24.5 26.79 29.2 21.4 33.8 42.19 47.69 52.6]'; %LVDT f95 = [-.0012 .0068 .0142 .025 .0328 .049 .0574 .0665 .0745 .0835 .1005 .1176 .1343 .1508 .1677 .21 .2516 .2945 .3351 .3772 .4202 .461 .5033 .5457 .6122 .6871 .7587]'; %Load Cell (mV/V) %Zeroing the Data: z95 = z95-(10^-3*.10014); f95 = f95+.0012; %Converting to Engineering Units Using Sensitivity: z95 = z95./v95.*z; %mm sinkage f95 = f95.*f; %N load %Convert to Pressure: p95 = f95./a1; %N/cm^2 pressure %Convert to cm and kPa: z95 = z95.*0.1; %cm sinkage p95 = p95.*10; %kPa pressure m91z = mean([z91 z92 z93 z94]')'; m91p = mean([p91 p92 p93 p94]')';

%27cm Soil Depth------

%Test #1:

%Raw Data: v101 = 10.0512; %input voltage z101 = 10^-3.*[.10002 1.5903 3.0001 4.3002 6.0002 7.5002 8.4902 9.6002 10.2 11.1 11.8 13 14.1 15 16.09 17.2 19.9 22.3 24.19 26.39 28.8 31.6 33.9 37.49 40.89 52.7 65.5 97.9]'; %LVDT f101 = [-.0001 .0085 .0167 .0252 .0338 .0436 .0512 .0596 .0678 .0765 .0847 .1018 .1181 .1346 .1513 .1684 .2107 .254 .2945 .3356 .3777 .4222 .4619 .5056 .5488 .6154 .6875 .7614]'; %Load Cell (mV/V) %Zeroing the Data: z101 = z101-(10^-3*.10002); f101 = f101+.0001; %Converting to Engineering Units Using Sensitivity: z101 = z101./v101.*z; %mm sinkage f101 = f101.*f; %N load %Convert to Pressure: p101 = f101./a1; %N/cm^2 pressure %Convert to cm and kPa: z101 = z101.*0.1; %cm sinkage p101 = p101.*10; %kPa pressure

%Test #2:

%Raw Data: v102 = 10.0512; %input voltage

539 z102 = 10^-3.*[-.099897 2.2004 4.2002 6.1003 7.8903 9.1004 10.49 11.7 12.7 13.49 15.1 16.6 18.19 19.39 20.6 21.99 25.79 29 32 35.5 38.59 42.6 45.8 50.8 54.2 72.1 90.5 124.9]'; %LVDT f102 = [.0009 .009 .0172 .0262 .0352 .0431 .0516 .0603 .0687 .0768 .0852 .1018 .1183 .1346 .1515 .1683 .2113 .253 .294 .336 .3793 .4207 .4628 .5052 .5462 .6138 .6882 .763]'; %Load Cell (mV/V) %Zeroing the Data: z102 = z102-(10^-3*-.099897); f102 = f102-.0009; %Converting to Engineering Units Using Sensitivity: z102 = z102./v102.*z; %mm sinkage f102 = f102.*f; %N load %Convert to Pressure: p102 = f102./a1; %N/cm^2 pressure %Convert to cm and kPa: z102 = z102.*0.1; %cm sinkage p102 = p102.*10; %kPa pressure

%Test #3:

%Raw Data: v103 = 10.0512; %input voltage z103 = 10^-3.*[.19026 1.3902 4.7901 4.9002 5.9001 6.9902 8.2 9.0001 9.5903 10.39 10.9 12.4 13.3 14.4 15.3 16.5 19.79 21.8 23.8 25.6 27.7 29.59 32.3 34.2 36.2 43.4 48.6 52.8]'; %LVDT f103 = [.0004 .0079 .0192 .0256 .034 .0426 .0523 .06 .0688 .0775 .0863 .1031 .1203 .1368 .1536 .1727 .2138 .2568 .2979 .3392 .3812 .423 .4653 .5089 .5497 .615 .6918 .7633]'; %Load Cell (mV/V) %Zeroing the Data: z103 = z103-(10^-3*.19026); f103 = f103-.0004; %Converting to Engineering Units Using Sensitivity: z103 = z103./v103.*z; %mm sinkage f103 = f103.*f; %N load %Convert to Pressure: p103 = f103./a1; %N/cm^2 pressure %Convert to cm and kPa: z103 = z103.*0.1; %cm sinkage p103 = p103.*10; %kPa pressure

%Test #4:

%Raw Data: v104 = 10.0511; %input voltage z104 = 10^-3.*[.20015 1.9002 3.7001 5.1903 6.4002 7.7901 8.5901 10 10.69 11.1 11.59 12.5 13.6 14.5 15.3 16.2 19.4 21.6 23.7 25.9 28 29.89 32.3 34.5 36.79 45.1 49.9 56.39]'; %LVDT f104 = [-.0016 .0061 .0141 .0229 .0323 .0414 .0489 .0579 .0665 .0747 .0831 .1003 .1171 .1339 .1502 .1672 .2106 .2521 .2936 .3349 .3758 .4137 .4595 .5009 .5426 .6072 .6805 .7535]'; %Load Cell (mV/V) %Zeroing the Data: z104 = z104-(10^-3*.20015); f104 = f104+.0016; %Converting to Engineering Units Using Sensitivity: z104 = z104./v104.*z; %mm sinkage f104 = f104.*f; %N load %Convert to Pressure: p104 = f104./a1; %N/cm^2 pressure %Convert to cm and kPa: z104 = z104.*0.1; %cm sinkage p104 = p104.*10; %kPa pressure

%Test #5:

%Raw Data: v105 = 10.0511; %input voltage z105 = 10^-3.*[.090241 .99027 2.1002 3.0901 4.2002 5.1903 5.9001 6.8901 7.6002 8.0001 8.5001 9.6 10.4 11.4 12.2 12.89 15.5 17.7 19.8 21.79 23.9 26.4 28.4 31.19 33.6 42.79 48.69 55.9]'; %LVDT f105 = [-.0013 .0072 .0158 .0241 .033 .0412 .0496 .0582 .0667 .075 .0834 .1 .1166 .133 .1496 .166 .209 .2506 .2928 .3334 .3755 .4175 .4592 .504 .5433 .613 .6865 .7602]'; %Load Cell (mV/V)

540

%Zeroing the Data: z105 = z105-(10^-3*.090241); f105 = f105+.0013; %Converting to Engineering Units Using Sensitivity: z105 = z105./v105.*z; %mm sinkage f105 = f105.*f; %N load %Convert to Pressure: p105 = f105./a1; %N/cm^2 pressure %Convert to cm and kPa: z105 = z105.*0.1; %cm sinkage p105 = p105.*10; %kPa pressure m101z = mean([z101 z102 z103 z104 z105]')'; m101p = mean([p101 p102 p103 p104 p105]')'; figure plot(m11p,m11z,'k-x','markersize',7); hold on plot(m21p,m21z,'k-o'); hold on plot(m31p,m31z,'k-d'); hold on plot(m41p,m41z,'k-*','markersize',7); hold on plot(m51p,m51z,'k-+','markersize',7); hold on plot(m61p,m61z,'k-.','markersize',7); hold on plot(m71p,m71z,'k-p','markersize',7); hold on plot(m81p,m81z,'k-h','markersize',7); hold on plot(m91p,m91z,'k-^','markersize',7); hold on plot(m101p,m101z,'k-v','markersize',7); hold on legend('3cm','6cm','9cm','12cm','15cm','15 cm', '18cm','21cm','24cm','27cm','location','SouthWest') title('Boundary Effect on Soil Depth') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(m11p,m11z,'k-x','markersize',7); hold on plot(m21p,m21z,'k-o'); hold on plot(m31p,m31z,'k-d'); hold on plot(m41p,m41z,'k-*','markersize',7); hold on plot(m51p,m51z,'k-+','markersize',7); hold on plot(m61p,m61z,'k-.','markersize',7); hold on plot(m71p,m71z,'k-p','markersize',7); hold on plot(m81p,m81z,'k-h','markersize',7); hold on plot(m91p,m91z,'k-^','markersize',7); hold on plot(m101p,m101z,'k-v','markersize',7); hold on legend('3cm','6cm','9cm','12cm','15cm','15 cm', '18cm','21cm','24cm','27cm','location','SouthWest') title('Boundary Effect on Soil Depth') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 40 0 0.3]) grid on set(gca,'YDir','reverse') figure plot(p11,z11,'ko',p12,z12,'ko',p13,z13,'ko',p14,z14,'ko',p15,z15,'ko'); hold on plot(m11p,m11z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(p21,z21,'ko',p22,z22,'ko',p23,z23,'ko',p24,z24,'ko',p25,z25,'ko'); hold on plot(m21p,m21z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean')

541 xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(p31,z31,'ko',p32,z32,'ko',p33,z33,'ko',p34,z34,'ko',p35,z35,'ko'); hold on plot(m31p,m31z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(p41,z41,'ko',p42,z42,'ko',p43,z43,'ko',p44,z44,'ko',p45,z45,'ko'); hold on plot(m41p,m41z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(p51,z51,'ko',p52,z52,'ko',p53,z53,'ko',p54,z54,'ko',p55,z55,'ko'); hold on plot(m51p,m51z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(p61,z61,'ko',p62,z62,'ko',p63,z63,'ko',p64,z64,'ko',p65,z65,'ko'); hold on plot(m61p,m61z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(p71,z71,'ko',p72,z72,'ko',p73,z73,'ko',p74,z74,'ko',p75,z75,'ko'); hold on plot(m71p,m71z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(p81,z81,'ko',p82,z82,'ko',p83,z83,'ko',p84,z84,'ko',p85,z85,'ko'); hold on plot(m81p,m81z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse')

542

figure plot(p91,z91,'ko',p92,z92,'ko',p93,z93,'ko',p94,z94,'ko',p95,z95,'ko'); hold on plot(m91p,m91z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse') figure plot(p101,z101,'ko',p102,z102,'ko',p103,z103,'ko',p104,z104,'ko',p105,z105,'ko'); hold on plot(m101p,m101z,'k-'); hold on text(10,1.2,'\o Raw Data') text(10, 1.3,'- Mean') xlabel('Pressure, kPa') ylabel('Sinkage, cm') axis([0 120 0 1.5]) grid on set(gca,'YDir','reverse')

543

Code D5: Determination of Bekker Parameters for GRC-1

%Determining Bekker Parameters from good plate sinkage data: Plate sinkage %data was taken using 7.6, 10.2, and 19 cm plate diameters. The square %polypropylene bin was filled with GRC-1 to a depth of 24 cm. The density %is 1.67 g/cc or 24% relative density. Each test was repeated a total of %5 times. Wong’s data processing methodology is used to determine the kc, %kphi, and n parameters for GRC-1.

%Data processing using all THREE plates!!! close all; clear all; clc;

%Constants///////////////////////////////////////////////////////////////// %i indicates plate size: 1 = small, 2 = medium, 3 = large d1 = .076; %m diameter "small plate" d2 = .102; %m diameter "medium plate" d3 = .19; %m diameter "large plate" b1 = d1/2; %m radius "small plate" b2 = d2/2; %m radius "medium plate" b3 = d3/2; %m radius "large plate"

%Area of Plates: a1 = pi*b1^2; %m^2 a2 = pi*b2^2; %m^2 a3 = pi*b3^2; %m^2

%Sensitivity for load cell and LVDT: z = 1139.8; %mm*V f = 1155.1; %N/(mV/V)

%Test Data/////////////////////////////////////////////////////////////////

%Small plate (7.6 cm diameter):------

%Test 1: v11 = 10.0511; %input voltage z11 = 10^-3.*[-.99981 -.66976 .80025 2.0003 4.2002 5.5001 7.1002 8 8.9003 10 13 14.31 16.71 18.7 21 29.51 39.4 59.2 100.5 166.7 169.5 275.99 294.9 401.3 403.99 516.59 535.6]'; %LVDT f11 = [.0001 .0085 .0178 .025 .0342 .0428 .0518 .0602 .0686 .0772 .0945 .111 .1289 .1457 .1629 .2049 .2465 .2888 .3302 .3715 .413 .4557 .4957 .5503 .5997 .6907 .7482]'; %Load Cell (mV/V) z11 = z11 - (10^-3*-.99981); f11 = f11 - (.0001); z11 = (z11./v11).*z./1000; %m sinkage f11 = f11.*f./1000; %kN p11 = f11./a1; %kPa

544

%Test 2: v12 = 10.051; z12 = 10^-3.*[.00011921 .11039 .5002 1.6 2.8001 3.8003 5.2002 5.9001 6.7003 7.3001 8.1003 9.4002 10.5 11.8 13.1 14.5 18.2 22 25.4 29.9 34.1 40.9 64.5 168.9 271.39 278.1 393.6 534.8]'; f12 = [-.0008 .0041 .0104 .0187 .027 .0355 .0443 .0533 .062 .0699 .0783 .0953 .1121 .1294 .1462 .1639 .2054 .2475 .2896 .3314 .3732 .4161 .4591 .5001 .5462 .6036 .6842 .7705]'; z12 = z12 - (10^-3*.00011921); f12 = f12 - (-.0008); z12 = (z12./v12).*z./1000; %m sinkage f12 = f12.*f./1000; %kN p12 = f12./a1; %kPa

%Test 3: v13 = 10.0506; z13 = 10^-3.*[.10026 1.5104 2.9002 3.9001 5.1003 6.1002 7.0003 7.9105 8.3002 9.1001 9.6105 11.1 12.21 13.6 14.81 16.3 22.5 30.4 52.8 115.41 183.6 186 341.89 342.6 343.3 423.5 436.59 565.89]'; f13 = [.0007 .0105 .0196 .028 .0366 .0448 .0543 .0627 .0709 .0796 .0881 .1045 .1212 .1378 .1544 .1712 .2128 .2546 .2945 .3354 .3761 .4156 .4665 .5062 .5455 .5999 .6741 .7487]'; z13 = z13 - (10^-3*.10026); f13 = f13 - (.0007); z13 = (z13./v13).*z./1000; %m sinkage f13 = f13.*f./1000; %kN p13 = f13./a1; %kPa

%Test 4: v14 = 10.0506; z14 = 10^-3.*[.41032 2.2103 4.5003 6.3002 8 9.6002 11 12.41 13.5 15.01 16 17.4 18.41 20.11 21.41 23.4 27.7 32.6 39.6 48.4 70.81 152.4 156.8 335 335.2 340.39 438.59 443.6]'; f14 = [0 .0086 .0182 .0267 .0356 .0442 .0525 .0609 .0692 .0781 .087 .1035 .1198 .1364 .1529 .1696 .2131 .2547 .2965 .3383 .3802 .4146 .4567 .5057 .5447 .6048 .68 .7527]'; z14 = z14 - (10^-3*.41032); f14 = f14 - (0); z14 = (z14./v14).*z./1000; %m sinkage f14 = f14.*f./1000; %kN p14 = f14./a1; %kPa

%Test 5: v15 = 10.0507; z15 = 10^-3.*[.00023842 .90003 2.3 4.0001 5.1 6.5 7.8001 9.0001 10 10.7 11.41 13.4 14.3 16 17.5 18.31 22.2 25.3 28.3 31.3 33.9 37.01 41 44.6 47.31 60.51 70.9 407.1]'; f15 = [-.0002 .0075 .0159 .0252 .034 .0429 .0516 .0597 .0682 .0769 .0851 .1029 .1187 .1356 .1529 .1693 .2119 .2539 .2963 .3399 .3802 .4218 .4661 .5082 .5477 .6171 .6896 .7515]'; z15 = z15 - (10^-3*.00023842); f15 = f15 - (-.0002); z15 = (z15./v15).*z./1000; %m sinkage f15 = f15.*f./1000; %kN p15 = f15./a1; %kPa

%Medium Plate (10.2 cm diameter):------

%Test 1: v21 = 10.0511; %input voltage z21 = 10^-3.*[.00023842 .50008 1.9903 3.6001 5.1001 6.1001 7.5903 9.0002 9.6902 10.59 11.3 12.6 13.9 15.2 15.69 16.9 19.7 21.5 23.39 25.3 27.59 29.3 31.3 33.4 35.7 43.1 48.4 53.1]'; %LVDT f21 = [.0031 .0106 .0187 .0273 .0361 .0439 .0521 .0604 .0684 .0766 .0847 .1005 .117 .1331 .1497 .1666 .208 .2491 .2908 .3321 .3752 .4164 .4571 .5001 .5441 .6075 .6833 .7553]'; %Load Cell (mV/V) z21 = z21 - (10^-3*.00023842); f21 = f21 - (.0031); z21 = (z21./v21).*z./1000; %m sinkage f21 = f21.*f./1000; %kN p21 = f21./a2; %kPa

%Test 2: v22 = 10.0512; %input voltage

545 z22 = 10^-3.*[.00023842 .70012 1.3001 2.1001 3.0001 3.5901 4.3001 5.0002 5.6002 6.09 6.3001 7.3001 8.0001 8.8 9.5901 10.3 12.8 14.69 17.19 19.3 21.49 23.7 26.9 29 32.19 41.59 48.39 57.79]'; %LVDT f22 = [.0002 .007 .015 .0236 .0323 .0406 .0487 .0568 .0651 .0734 .0815 .0985 .1148 .1317 .1481 .1647 .2081 .2489 .2917 .3338 .3748 .4167 .4594 .5019 .5433 .6079 .6837 .7549]'; %Load Cell (mV/V) z22 = z22 - (10^-3*.00023842); f22 = f22 - (.0002); z22 = (z22./v22).*z./1000; %m sinkage f22 = f22.*f./1000; %kN p22 = f22./a2; %kPa

%Test 3: v23 = 10.0513; %input voltage z23 = 10^-3.*[-.099897 1.9001 4.2002 5.5903 7.4 8.4002 9.7003 10.6 11.3 12.7 13.5 14.49 15.39 16.5 17.49 18.5 21.6 23.8 25.9 28.3 29.89 31.99 34.09 36.69 39 46.2 50.39 54.7]'; %LVDT f23 = [-.0002 .0073 .0164 .0254 .0334 .0413 .0503 .0579 .0659 .0746 .0832 .0998 .1165 .1332 .1498 .1665 .21 .2515 .2931 .3349 .3767 .419 .4594 .5031 .5443 .6111 .6846 .7583]'; %Load Cell (mV/V) z23 = z23 - (10^-3*-.099897); f23 = f23 - (-.0002); z23 = (z23./v23).*z./1000; %m sinkage f23 = f23.*f./1000; %kN p23 = f23./a2; %kPa

%Test 4: v24 = 10.0514; %input voltage z24 = 10^-3.*[.20015 1.3001 2.6002 3.6001 4.9001 6.1002 7.2001 7.8903 8.5002 9.1001 9.9002 11.2 12.5 13.4 14.29 15.19 18 20.5 23.1 25.89 28.2 30.8 33.4 36.7 39.09 49.9 56 63.5]'; %LVDT f24 = [.0008 .0074 .0166 .0247 .0338 .0432 .052 .0604 .0691 .0778 .0862 .1033 .1198 .1369 .1536 .1707 .2125 .2563 .2972 .339 .3807 .4242 .4642 .5072 .548 .6145 .6875 .7598]'; %Load Cell (mV/V) z24 = z24 - (10^-3*.20015); f24 = f24 - (.0008); z24 = (z24./v24).*z./1000; %m sinkage f24 = f24.*f./1000; %kN p24 = f24./a2; %kPa

%Test 5: v25 = 10.0514; %input voltage z25 = 10^-3.*[.10014 .90003 1.8002 3.7901 4.5002 5.8903 6.6901 7.4002 7.9001 8.6002 9.6002 10.59 11.39 12.29 13.09 15.69 17.7 20.5 22.4 24.5 26.79 29.2 31.4 33.8 42.19 47.69 52.6]'; %LVDT f25 = [-.0012 .0068 .0142 .025 .0328 .049 .0574 .0665 .0745 .0835 .1005 .1176 .1343 .1508 .1677 .21 .2516 .2945 .3351 .3772 .4202 .461 .5033 .5457 .6122 .6871 .7587]'; %Load Cell (mV/V) z25 = z25 - (10^-3*.10014); f25 = f25 - (-.0012); z25 = (z25./v25).*z./1000; %m sinkage f25 = f25.*f./1000; %kN p25 = f25./a2; %kPa

%Large Plate (19 cm diameter):

%Test 1: v31 = 10.052; %input voltage z31 = 10^-3.*[.20027 1 2.1102 3.2002 5.3002 6.2002 7.3001 8.4001 9.0002 9.8102 10.4 13.1 13.7 15 16 17.01 19.9 22.51 24.4 26.5 28.3 30.1 39.5 42.8 46.6 49.7 60.8 65.99]'; %LVDT f31 = [0 .0082 .0162 .0243 .0326 .0406 .0492 .0574 .0653 .0736 .0817 .0979 .1137 .1303 .1463 .1622 .2029 .2434 .2839 .3247 .3656 .4073 .4663 .5121 .5553 .5976 .6995 .7746]'; %Load Cell (mV/V) z31 = z31 - (10^-3*.20027); f31 = f31 - (0); z31 = (z31./v31).*z./1000; %m sinkage f31 = f31.*f./1000; %kN p31 = f31./a3; %kPa

%Test 2: v32 = 10.0519;

546 z32 = 10^-3.*[ .10026 .31042 1 1.7003 2.6002 3.5002 4.3002 4.8003 5.3 5.7002 6.9001 7.5103 8.4106 9.4 9.8002 11.81 13.7 15.5 17.31 18.8 20.6 32.6 34.9 36.2 38.9 45.51 49.9]'; f32 = [ .0035 .0093 .0178 .0262 .0353 .0441 .0532 .0617 .0702 .0784 .0962 .1127 .1295 .1461 .1631 .2057 .2475 .2892 .331 .3734 .4148 .4702 .5129 .5565 .6119 .7002 .7768]'; z32 = z32 - (10^-3*.10026); f32 = f32 - (.0035); z32 = (z32./v32).*z./1000; %m sinkage f32 = f32.*f./1000; %kN p32 = f32./a3; %kPa

%Test 3: v33 = 10.0514; z33 = 10^-3.*[.10014 .90015 1.9001 2.8104 3.8 5.3002 6.5001 7.3003 8.2 9.5001 10.91 12.4 13.7 15.21 16.11 18.61 21.21 23.1 25.01 26.8 28.41 37.41 39.4 41.5 45.11 50.61 54.8]'; f33 = [.0017 .0158 .0248 .0334 .0423 .0513 .06 .0678 .0762 .0844 .101 .1175 .1338 .1509 .167 .2086 .2501 .2921 .3346 .377 .4191 .4826 .5242 .5685 .62 .7072 .7833]'; z33 = z33 - (10^-3*.10014); f33 = f33 - (.0017); z33 = (z33./v33).*z./1000; %m sinkage f33 = f33.*f./1000; %kN p33 = f33./a3; %kPa

%Test 4: v34 = 10.0514; z34 = 10^-3.*[.00011921 .60022 1.9001 3.5102 5.0002 6.3001 7.5002 8.9002 9.5104 10.6 11.3 12.2 13.71 14.3 14.9 15.7 17.8 19.5 21.3 22.8 24.6 29 39.6 42.4 44.8 46.7 54.9 58.91]'; f34 = [.0006 .0075 .016 .0247 .0338 .0414 .0494 .0578 .0662 .0744 .0821 .0976 .1143 .1304 .1468 .1632 .2047 .2455 .2872 .3293 .3714 .4219 .4831 .5228 .5673 .6101 .7102 .7863]'; z34 = z34 - (10^-3*.00011921); f34 = f34 - (.0006); z34 = (z34./v34).*z./1000; %m sinkage f34 = f34.*f./1000; %kN p34 = f34./a3; %kPa

%Test 5: v35 = 10.0512; z35 = 10^-3.*[.00011921 .51033 1.9002 2.8001 4.1 4.8102 5.9001 7.2001 7.5002 8.2103 8.6105 9.3001 9.9103 10.6 11.21 11.61 13.1 14.7 16 17.4 18.5 20 29.51 31.5 33.5 36.6 43.5 47.7]'; f35 = [-.0003 .0078 .0171 .0248 .0331 .0408 .0485 .0579 .0662 .0738 .0816 .0977 .1139 .1309 .1469 .1629 .2046 .2464 .2876 .3297 .3712 .4132 .4718 .5128 .5576 .6095 .6985 .7753]'; z35 = z35 - (10^-3*.00011921); f35 = f35 - (-.0003); z35 = (z35./v35).*z./1000; %m sinkage f35 = f35.*f./1000; %kN p35 = f35./a3; %kPa

%Create a common and uniformly distributed pressure vector in order to %determine the mean pressure-sinkage curve of all five data sets for each %plate size. //////////////////////////////////////////////////////////////

%Small Plate:------x1 = 0:.5:50; %new uniformly distributed pressure vector, kN/m^2 y11 = spline(p11,z11,x1); %new sinkage vector, m y12 = spline(p12,z12,x1); %new sinkage vector, m y13 = spline(p13,z13,x1); %new sinkage vector, m y14 = spline(p14,z14,x1); %new sinkage vector, m y15 = spline(p15,z15,x1); %new sinkage vector, m

%Medium Plate:------x2 = 0:.5:50; %new uniformly distributed pressure vector, kN/m^2 y21 = spline(p21,z21,x2); %new sinkage vector, m y22 = spline(p22,z22,x2); %new sinkage vector, m y23 = spline(p23,z23,x2); %new sinkage vector, m y24 = spline(p24,z24,x2); %new sinkage vector, m

547 y25 = spline(p25,z25,x2); %new sinkage vector, m

%Large Plate:------x3 = 0:.5:30; %new uniformly distributed pressure vector, kN/m^2 y31 = spline(p31,z31,x3); %new sinkage vector, m y32 = spline(p32,z32,x3); %new sinkage vector, m y33 = spline(p33,z33,x3); %new sinkage vector, m y34 = spline(p34,z34,x3); %new sinkage vector, m y35 = spline(p35,z35,x3); %new sinkage vector, m

%Determine the mean sinkage values of each plate size test series//////////

%Small Plate:------matrix1 = [y11; y12; y13; y14; y15]; %5X321 matrix containing all sinkage test results m1 = mean(matrix1); %mean of the sinkage vectors s1 = std(matrix1) %standard deviation of the sinkage vectors figure(1) %of all data plotted with the mean pressure-sinkage vector plot(p11,z11*1000,'ko',p12,z12*1000,'ko',p13,z13*1000,'ko',p14*1000,z14,'ko',p15,z15*1000 ,'ko'); hold on plot(x1,m1*1000,'k-'); hold on title('Mean Pressure-Sinkage Curves'); xlabel('Pressure, kN/m^2'); ylabel('Sinkage, mm'); text(41,1.2,'7.6 cm Plate') grid on axis([0 50 0 10]) set(gca,'YDir','reverse')

%Medium Plate:------matrix2 = [y21; y22; y23; y24; y25]; %5X211 matrix containing all sinkage test results m2 = mean(matrix2); %mean of the sinkage vectors s2 = std(matrix2) %standard deviation of the sinkage vectors figure(1) %of all data plotted with the mean pressure-sinkage vector plot(p21,z21*1000,'k^',p22,z22*1000,'k^',p23,z23*1000,'k^',p24,z24*1000,'k^',p25,z25*1000 ,'k^'); hold on plot(x2,m2*1000,'k--'); hold on title('Mean Pressure-Sinkage Curves'); xlabel('Pressure, kN/m^2'); ylabel('Sinkage, mm'); text(35.5,3.2,'10.2 cm Plate') grid on axis([0 50 0 10]) set(gca,'YDir','reverse')

%Large Plate:------matrix3 = [y31; y32; y33; y34; y35]; %5X61 matrix containing all sinkage test results m3 = mean(matrix3); %mean of the sinkage vectors s3 = std(matrix3) %standard deviation of the sinkage vectors figure(1) %of all data plotted with the mean pressure-sinkage vector plot(p31,z31*1000,'ks',p32,z32*1000,'ks',p33,z33*1000,'ks',p34,z34*1000,'ks',p35,z35*1000 ,'ks'); hold on plot(x3,m3*1000,'k.'); hold on title('Mean Pressure-Sinkage Curves'); xlabel('Pressure, kN/m^2'); ylabel('Sinkage, m'); text(31,4.5,'19 cm Plate') grid on axis([0 50 0 10]) set(gca,'YDir','reverse')

%Determining the Bekker parameters for the mean pressure-sinkage data. %Analysis cannot handle log zero:------

548

%Data for small plate: m1_edit = m1(4:end); x1_edit = x1(4:end);

%Data for medium plate: m2_edit = m2(2:end); x2_edit = x2(2:end);

%Data for small plate: m3_edit = m3(2:end); x3_edit = x3(2:end);

%n value:------

%Small Plate: num1 = sum(x1_edit.^2).*sum(x1_edit.^2.*log(x1_edit).*log(m1_edit))- sum(x1_edit.^2.*log(x1_edit)).*sum(x1_edit.^2.*log(m1_edit)); den1 = sum(x1_edit.^2).*sum(x1_edit.^2.*(log(m1_edit)).^2)- (sum(x1_edit.^2.*log(m1_edit))).^2; n1 = num1/den1;

%Medium Plate num2 = sum(x2_edit.^2).*sum(x2_edit.^2.*log(x2_edit).*log(m2_edit))- sum(x2_edit.^2.*log(x2_edit)).*sum(x2_edit.^2.*log(m2_edit)); den2 = sum(x2_edit.^2).*sum(x2_edit.^2.*(log(m2_edit)).^2)- (sum(x2_edit.^2.*log(m2_edit))).^2; n2 = num2/den2;

%Large Plate num3 = sum(x3_edit.^2).*sum(x3_edit.^2.*log(x3_edit).*log(m3_edit))- sum(x3_edit.^2.*log(x3_edit)).*sum(x3_edit.^2.*log(m3_edit)); den3 = sum(x3_edit.^2).*sum(x3_edit.^2.*(log(m3_edit)).^2)- (sum(x3_edit.^2.*log(m3_edit))).^2; n3 = num3/den3; navg = (n1+n2+n3)/3;

%keq:------ln_keq1 = (sum(x1_edit.^2.*log(x1_edit))- navg.*sum(x1_edit.^2.*log(m1_edit)))./(sum(x1_edit.^2)); ln_keq2 = (sum(x2_edit.^2.*log(x2_edit))- navg.*sum(x2_edit.^2.*log(m2_edit)))./(sum(x2_edit.^2)); ln_keq3 = (sum(x3_edit.^2.*log(x3_edit))- navg.*sum(x3_edit.^2.*log(m3_edit)))./(sum(x3_edit.^2)); keq1 = exp(ln_keq1); keq2 = exp(ln_keq2); keq3 = exp(ln_keq3);

%kc and kphi------

A = [1/b1 1; 1/b2 1; 1/b3 1]; %Matrix for least squares evaluation of kc and kphi b = [keq1; keq2; keq3]; %Matrix of observations x = A\b; %least squares evaluation kc = x(1); kphi = x(2);

%Determining Goodness of Fit (Zero is Perfect)------%APPLY TO ALL PLATES

%Apply Bekker Parameters/Equation to get the Curve-Fit: p1_calc = ((kc/b1)+kphi).*(m1).^navg; p2_calc = ((kc/b2)+kphi).*(m2).^navg; p3_calc = ((kc/b3)+kphi).*(m3).^navg;

%Goodness of Fit: e1 = sqrt(sum((x1-p1_calc).^2)./(length(m1)-2))./(sum(x1)/length(m1)) e2 = sqrt(sum((x2-p2_calc).^2)./(length(m2)-2))./(sum(x2)/length(m2)) e3 = sqrt(sum((x3-p3_calc).^2)./(length(m3)-2))./(sum(x3)/length(m3))

%Plots/////////////////////////////////////////////////////////////////////

549

figure %Original pressure-sinkage data vs curve-fit (entire range) plot(p11,z11*1000,'ko',p12,z12*1000,'ko',p13,z13*1000,'ko',p14,z14*1000,'ko',p15,z15*1000 ,'ko',p1_calc,m1*1000,'k-'); hold on plot(p21,z21*1000,'k^',p22,z22*1000,'k^',p23,z23*1000,'k^',p24,z24*1000,'k^',p25,z25*1000 ,'k^',p2_calc,m2*1000,'k--'); hold on plot(p31,z31*1000,'ks',p32,z32*1000,'ks',p33,z33*1000,'ks',p34,z34*1000,'ks',p35,z35*1000 ,'ks',p3_calc,m3*1000,'k.'); hold on title('Experimental Pressure-Sinkage Data Vs. Bekker Curve-Fit') xlabel('Pressure, kN/m^2'); ylabel('Sinkage, mm'); axis([0 50 0 10]); text(41,1.2,'7.6 cm Plate') text(35.5,3.2,'10.2 cm Plate') text(31,4.5,'19 cm Plate') grid on set(gca,'YDir','reverse') gtext(['n = ',num2str(navg),', kc = ',num2str(kc) ' kN/m^n^+^1',', kphi = ',num2str(kphi) ' kN/m^n^+^2'])

550

Table D1: Shear bevameter results for tests at low pressure and low density.

Low Pressure (approximately 5 kPa) 1.64 g/cc Density

Grousers: Sandpaper: Calculated Calculated Shear Shear Shear Shear Shear Shear Displacement Stress Stress Displacement Stress Stress -0.0006 -22.45 -139.39 0.0009 221.56 224.69 -0.0009 68.06 -210.95 0.0005 244.01 126.75 -0.0005 76.75 -115.82 0.0015 244.01 366.06 -0.0001 135.40 -22.89 0.0007 203.46 176.09 -0.0013 112.95 -308.34 -0.0001 244.01 -25.94 -0.0005 122.36 -115.82 0.0011 212.87 272.54 -0.0006 94.85 -139.39 0.0013 239.66 319.66 -0.0005 26.79 -115.82 0.0007 235.32 176.09 -0.0005 -26.79 -115.82 0.0005 217.22 126.75 -0.0008 -99.20 -186.96 0.0003 257.76 76.63 -0.0006 -99.20 -139.39 0.0017 217.22 411.75 -0.0006 -58.65 -139.39 0.0008 253.42 200.49 -0.0006 -26.79 -139.39 0.0013 253.42 319.66 -0.0014 31.86 -333.04 0.0011 239.66 272.54 0 -13.76 0.00 0.0004 293.97 101.79 -0.0001 -22.45 -22.89 0.0004 262.11 101.79 -0.0009 26.79 -210.95 0.0004 289.62 101.79 -0.0004 58.65 -92.38 0.0007 285.28 176.09 -0.0009 131.05 -210.95 0.0005 257.76 126.75 -0.0014 135.40 -333.04 0.0003 289.62 76.63 -0.0004 144.81 -92.38 0.0009 244.01 224.69 -0.0006 153.50 -139.39 0.0001 253.42 25.74 -0.0002 140.47 -45.92 0.0003 235.32 76.63 -0.0009 162.91 -210.95 0.0005 212.87 126.75 0 153.50 0.00 0.0007 262.11 176.09 -0.0004 167.26 -92.38 0.0007 235.32 176.09 -0.0006 162.91 -139.39 0 257.76 0.00 -0.0008 135.40 -186.96 0.0007 271.52 176.09 -0.001 158.57 -235.08 0.0005 253.42 126.75 -0.0002 117.30 -45.92 0.0009 303.38 224.69

551

-0.0012 144.81 -283.78 0.0007 280.21 176.09 -0.0001 135.40 -22.89 0.0012 312.07 296.19 -0.0004 62.99 -92.38 0.0008 303.38 200.49 -0.0004 49.96 -92.38 0.0008 293.97 200.49 0.0003 0.00 67.88 0.0005 330.17 126.75 -0.0005 -4.34 -115.82 0.0004 307.72 101.79 -0.0012 -13.76 -283.78 -0.0009 339.58 -240.82 -0.0001 -44.89 -22.89 0.0003 334.51 76.63 -0.0005 -26.79 -115.82 0.0009 321.48 224.69 -0.0012 -62.99 -283.78 0.0009 362.03 224.69 -0.0014 -54.30 -333.04 0.0008 334.51 200.49 -0.0005 -31.86 -115.82 0.0008 380.13 200.49 -0.001 -54.30 -235.08 0.0012 366.37 296.19 -0.0012 -31.86 -283.78 0.002 352.61 478.97 -0.0006 -36.20 -139.39 0.0007 416.33 176.09 -0.0005 4.34 -115.82 0.0003 402.57 76.63 -0.0002 31.86 -45.92 0.0003 416.33 76.63 -0.0012 36.20 -283.78 0.0008 406.92 200.49 -0.0001 72.41 -22.89 0.0004 398.23 101.79 -0.0004 49.96 -92.38 0 430.09 0.00 -0.0004 58.65 -92.38 0.0007 402.57 176.09 -0.0004 62.99 -92.38 0.0005 416.33 126.75 -0.0006 36.20 -139.39 0.0011 406.92 272.54 -0.0016 58.65 -382.89 0.0004 402.57 101.79 -0.0013 -26.79 -308.34 0.0008 448.19 200.49 -0.001 -90.51 -235.08 0.0009 443.12 224.69 0.0002 -144.81 45.39 0.0009 461.22 224.69 -0.0005 -221.56 -115.82 0.0017 488.73 411.75 -0.0004 -207.80 -92.38 0.0005 466.29 126.75 0.0002 -207.80 45.39 0.0009 533.63 224.69 0.0002 -140.47 45.39 0.0012 511.18 296.19 -0.0006 -8.69 -139.39 0.0007 561.14 176.09 -0.001 90.51 -235.08 0.0009 574.90 224.69 -0.0006 176.67 -139.39 0.0011 561.14 272.54 -0.0009 86.16 -210.95 -0.0007 601.69 -185.85 -0.001 26.79 -235.08 0.0011 587.93 272.54 -0.001 -36.20 -235.08 0.0008 615.44 200.49 -0.0014 -104.26 -333.04 0.0011 619.79 272.54 -0.0008 -54.30 -186.96 0.0012 647.30 296.19 -0.0005 -26.79 -115.82 0.0003 742.15 76.63 -0.0008 8.69 -186.96 0.0009 724.05 224.69 -0.0017 36.20 -408.04 -0.0001 778.36 -25.94 -0.0009 49.96 -210.95 0.0003 796.46 76.63 -0.0008 104.26 -186.96 0.0008 800.80 200.49 -0.0002 117.30 -45.92 0.0008 859.45 200.49 -0.0002 122.36 -45.92 0.0016 873.21 388.99 -0.0006 122.36 -139.39 0.0015 981.81 366.06 0 36.20 0.00 0.0011 1076.66 272.54 -0.0006 0.00 -139.39 0.0019 1212.79 456.74 -0.0005 -62.99 -115.82 0.0016 1430.00 388.99

552

0.0002 -86.16 45.39 0.0026 1583.50 608.86 -0.0005 -104.26 -115.82 0.003 1782.62 692.17 -0.0004 -140.47 -92.38 0.0026 1950.60 608.86 -0.001 -126.71 -235.08 0.0029 2063.55 671.59 0.0003 -140.47 67.88 0.0034 2226.46 772.96 -0.0009 -135.40 -210.95 0.0042 2303.21 927.26 -0.0012 -104.26 -283.78 0.0053 2411.82 1124.47 -0.0004 -104.26 -92.38 0.0052 2479.88 1107.22 0 -26.79 0.00 0.0062 2484.22 1273.85 -0.0009 -8.69 -210.95 0.007 2570.38 1398.22 -0.0008 44.89 -186.96 0.0081 2574.73 1557.17 -0.0006 104.26 -139.39 0.0087 2629.03 1638.36 0.0002 86.16 45.39 0.0091 2660.89 1690.44 -0.0006 122.36 -139.39 0.0103 2647.13 1837.40 -0.0008 99.20 -186.96 0.0114 2697.09 1960.68 -0.0008 126.71 -186.96 0.0123 2660.89 2054.06 -0.0008 158.57 -186.96 0.0143 2669.58 2239.78 -0.0004 117.30 -92.38 0.0146 2678.99 2265.26 -0.0008 112.95 -186.96 0.0154 2651.48 2330.38 -0.0002 49.96 -45.92 0.0171 2710.85 2456.13 -0.0005 31.86 -115.82 0.0196 2692.75 2613.56 -0.0009 18.10 -210.95 0.02 2733.29 2636.06 -0.0008 -31.86 -186.96 0.0219 2751.40 2733.93 -0.0001 -8.69 -22.89 0.0232 2747.05 2793.11 -0.0002 -40.55 -45.92 0.0254 2823.80 2880.69 -0.0008 -31.86 -186.96 0.0266 2810.04 2922.56 -0.0009 -18.10 -210.95 0.0282 2832.49 2972.70 -0.0009 -54.30 -210.95 0.0302 2846.25 3027.28 -0.0012 -8.69 -283.78 0.0322 2841.90 3074.07 -0.0002 -36.20 -45.92 0.035 2896.21 3128.56 -0.0002 -22.45 -45.92 0.0362 2882.45 3148.55 0 13.76 0.00 0.0384 2914.31 3180.73 -0.0002 49.96 -45.92 0.0396 2909.96 3196.12 -0.0012 167.26 -283.78 0.0421 2900.55 3223.95 -0.0004 207.80 -92.38 0.0434 2964.27 3236.43 0.0007 285.28 156.55 0.0456 2950.51 3254.91 -0.0001 352.61 -22.89 0.0468 2959.20 3263.75 -0.0001 388.82 -22.89 0.0487 2986.71 3276.17 -0.0005 488.73 -115.82 0.0503 2972.96 3285.31 -0.0006 533.63 -139.39 0.0521 3022.92 3294.33 -0.0006 619.79 -139.39 0.0536 2995.40 3300.95 -0.001 696.54 -235.08 0.0551 3031.60 3306.85 -0.0013 728.40 -308.34 0.0567 3059.12 3312.43 -0.0008 814.56 -186.96 0.0585 3049.71 3317.94 -0.0004 832.66 -92.38 0.0605 3131.52 3323.23 0.0004 877.55 90.24 0.0621 3117.77 3326.92 -0.0014 931.85 -333.04 0.0633 3158.31 3329.40 -0.0008 941.27 -186.96 0.0657 3185.83 3333.72 -0.0004 1013.67 -92.38 0.0673 3172.07 3336.18 0 1022.36 0.00 0.0683 3230.72 3337.58

553

0 1090.42 0.00 0.0697 3217.69 3339.36 0.0008 1180.93 178.39 0.0718 3248.82 3341.70 0.0008 1248.99 178.39 0.0734 3248.82 3343.24 -0.0001 1384.39 -22.89 0.0748 3222.03 3344.44 0.0008 1498.06 178.39 0.0756 3266.92 3345.07 0 1655.91 0.00 0.0784 3244.48 3347.00 0.0015 1810.13 327.76 0.0792 3262.58 3347.48 -0.0001 1936.84 -22.89 0.0801 3280.68 3347.98 0.001 2099.75 221.70 0.0823 3266.92 3349.07 0.002 2172.15 430.77 0.0833 3294.43 3349.51 0.0021 2253.25 451.01 0.0856 3262.58 3350.40 0.0016 2298.86 348.61 0.0865 3262.58 3350.71 0.002 2285.11 430.77 0.0881 3258.23 3351.21 0.0028 2357.51 589.42 0.0898 3248.82 3351.67 0.0025 2393.71 530.79 0.092 3280.68 3352.19 0.0036 2403.13 740.80 0.0927 3244.48 3352.34 0.0039 2421.23 795.76 0.0956 3248.82 3352.87 0.0055 2407.47 1073.11 0.0956 3266.92 3352.87 0.006 2466.12 1154.58 0.0981 3262.58 3353.25 0.0052 2497.98 1023.07 0.0995 3330.64 3353.42 0.0062 2674.65 1186.50 0.102 3308.19 3353.70 0.0074 2868.69 1370.39 0.1022 3321.22 3353.72 0.0074 2986.71 1370.39 0.1045 3316.88 3353.93 0.0078 3145.28 1428.86 0.1069 3294.43 3354.11 0.0086 3208.27 1541.78 0.1082 3348.74 3354.19 0.0105 3276.33 1789.65 0.1106 3326.29 3354.33 0.0115 3330.64 1909.43 0.1105 3362.50 3354.32 0.0122 3357.43 1989.19 0.1134 3384.94 3354.46 0.0122 3443.59 1989.19 0.1148 3384.94 3354.52 0.0133 3439.25 2108.11 0.1175 3439.25 3354.61 0.0139 3493.55 2169.81 0.1187 3425.49 3354.64 0.0143 3584.06 2209.75 0.1207 3443.59 3354.69 0.0153 3615.91 2305.61 0.1238 3466.04 3354.76 0.0167 3697.01 2430.71 0.1253 3421.14 3354.78 0.0161 3674.56 2378.35 0.1271 3471.10 3354.81 0.0172 3624.60 2472.95 0.1294 3447.93 3354.84 0.0187 3534.10 2592.51 0.131 3461.69 3354.86 0.0188 3429.83 2600.11 0.1322 3457.35 3354.87 0.0196 3471.10 2659.36 0.1346 3425.49 3354.89 0.0209 3493.55 2749.90 0.1365 3475.45 3354.91 0.0211 3475.45 2763.22 0.1392 3461.69 3354.93 0.0224 3421.14 2846.14 0.1412 3484.14 3354.94 0.0227 3330.64 2864.39 0.1421 3529.75 3354.94 0.0233 3285.02 2899.95 0.144 3520.34 3354.95 0.0245 3145.28 2967.42 0.1458 3588.40 3354.96 0.026 3099.67 3045.34 0.1491 3584.06 3354.97 0.0257 3131.52 3030.30 0.1498 3615.91 3354.97 0.0257 3131.52 3030.30 0.1527 3606.50 3354.97 0.0274 3199.58 3112.15 0.1539 3584.06 3354.98 0.0285 3176.41 3160.92 0.1559 3624.60 3354.98

554

0.0289 3167.73 3177.89 0.1585 3574.64 3354.98 0.0302 3172.07 3230.37 0.1607 3574.64 3354.99 0.031 3104.01 3260.74 0.1622 3547.85 3354.99 0.0323 3127.18 3307.14 0.1634 3511.65 3354.99 0.0325 3131.52 3313.97 0.1654 3538.44 3354.99 0.0345 3217.69 3378.04 0.1678 3497.89 3354.99 0.0351 3316.88 3395.84 0.1691 3497.89 3354.99 0.0357 3290.09 3413.03 0.172 3511.65 3354.99 0.0376 3312.54 3463.63 0.173 3511.65 3354.99 0.0374 3280.68 3458.56 0.175 3552.20 3355.00 0.0398 3298.78 3515.59 0.1767 3547.85 3355.00 0.0404 3312.54 3528.63 0.1785 3565.95 3355.00 0.0406 3303.12 3532.88 0.1807 3552.20 3355.00 0.0419 3366.84 3559.31 0.1833 3511.65 3355.00 0.0432 3394.35 3583.80 0.1845 3552.20 3355.00 0.0447 3429.83 3609.83 0.1858 3515.99 3355.00 0.0455 3489.20 3622.81 0.1877 3552.20 3355.00 0.0465 3479.79 3638.20 0.1894 3561.61 3355.00 0.0468 3511.65 3642.64 0.1914 3529.75 3355.00 0.0478 3457.35 3656.90 0.1931 3579.71 3355.00 0.0504 3407.39 3690.28 0.1943 3552.20 3355.00 0.0506 3403.04 3692.64 0.196 3597.81 3355.00 0.0521 3334.98 3709.51 0.1981 3602.16 3355.00 0.0518 3357.43 3706.26 0.1999 3579.71 3355.00 0.0529 3339.33 3717.92 0.2014 3638.36 3355.00 0.0541 3366.84 3729.82 0.2024 3602.16 3355.00 0.0554 3394.35 3741.79 0.2046 3634.02 3355.00 0.0561 3380.60 3747.87 0.2065 3634.02 3355.00 0.0567 3457.35 3752.89 0.209 3592.74 3355.00 0.058 3475.45 3763.17 0.2106 3656.46 3355.00 0.0592 3547.85 3771.99 0.2115 3634.02 3355.00 0.0598 3620.26 3776.18 0.2142 3670.22 3355.00 0.0613 3602.16 3786.01 0.2148 3665.15 3355.00 0.0627 3642.70 3794.44 0.2169 3660.81 3355.00 0.0636 3610.85 3799.51 0.2172 3710.76 3355.00 0.0637 3606.50 3800.06 0.2203 3683.25 3355.00 0.0648 3610.85 3805.86 0.222 3715.11 3355.00 0.0657 3556.54 3810.34 0.2237 3728.87 3355.00 0.067 3534.10 3816.41 0.2252 3701.35 3355.00 0.0672 3484.14 3817.30 0.2265 3733.21 3355.00 0.069 3466.04 3824.88 0.2289 3710.76 3355.00 0.0705 3479.79 3830.62 0.2312 3733.21 3355.00 0.0711 3461.69 3832.77 0.2331 3728.87 3355.00 0.0718 3502.24 3835.19 0.2343 3678.91 3355.00 0.0738 3479.79 3841.59 0.2363 3706.42 3355.00 0.0737 3507.31 3841.29 0.2383 3660.81 3355.00 0.076 3552.20 3847.81 0.2395 3688.32 3355.00 0.0767 3507.31 3849.63 0.2412 3688.32 3355.00 0.0783 3520.34 3853.51 0.2436 3652.12 3355.00 0.0795 3502.24 3856.20 0.2453 3697.01 3355.00

555

0.0802 3511.65 3857.68 0.2474 3678.91 3355.00 0.0817 3534.10 3860.65 0.2482 3719.45 3355.00 0.0837 3525.41 3864.23 0.2498 3733.21 3355.00 0.0847 3584.06 3865.87 0.2518 3715.11 3355.00 0.0861 3584.06 3868.01 0.253 3751.31 3355.00 0.0885 3615.91 3871.29 0.2539 3719.45 3355.00 0.0894 3620.26 3872.40 0.2567 3728.87 3355.00 0.0901 3552.20 3873.23 0.258 3715.11 3355.00 0.0917 3529.75 3875.00 0.2587 3678.91 3355.00 0.0933 3421.14 3876.61 0.2603 3715.11 3355.00 0.0949 3384.94 3878.08 0.2622 3674.56 3355.00 0.097 3389.29 3879.81 0.262 3683.25 3355.00 0.0984 3384.94 3880.85 0.2651 3683.25 3355.00 0.1007 3475.45 3882.38 0.2657 3674.56 3355.00 0.1007 3574.64 3882.38 0.2674 3728.87 3355.00 0.1023 3697.01 3883.33 0.2687 3697.01 3355.00 0.1047 3755.66 3884.60 0.2698 3733.21 3355.00 0.1062 3710.76 3885.31 0.2701 3719.45 3355.00 0.108 3697.01 3886.08 0.2722 3683.25 3355.00 0.1105 3624.60 3887.02 0.2734 3719.45 3355.00 0.1114 3597.81 3887.33 0.275 3683.25 3355.00 0.1141 3579.71 3888.16 0.275 3692.66 3355.00 0.1154 3507.31 3888.52 0.2752 3697.01 3355.00 0.117 3493.55 3888.92 0.1196 3461.69 3889.49 0.1219 3425.49 3889.94 0.1224 3461.69 3890.03 0.1248 3479.79 3890.42 0.1265 3529.75 3890.66 0.1286 3534.10 3890.93 0.1305 3570.30 3891.15 0.131 3620.26 3891.20 0.1341 3656.46 3891.50 0.1354 3728.87 3891.61 0.1372 3701.35 3891.75 0.1395 3692.66 3891.91 0.1409 3683.25 3891.99 0.1424 3624.60 3892.08 0.1449 3602.16 3892.20 0.146 3529.75 3892.25 0.1474 3497.89 3892.31 0.1497 3493.55 3892.40 0.1513 3479.79 3892.45 0.1527 3502.24 3892.50 0.1541 3529.75 3892.54 0.1557 3588.40 3892.58 0.1574 3624.60 3892.62 0.159 3656.46 3892.65 0.1594 3710.76 3892.66 0.1621 3715.11 3892.71

556

0.1625 3733.21 3892.72 0.1647 3728.87 3892.75 0.1662 3660.81 3892.77 0.1681 3628.95 3892.80 0.1697 3565.95 3892.81 0.1715 3565.95 3892.83 0.1726 3597.81 3892.84 0.1746 3588.40 3892.86 0.1762 3656.46 3892.87 0.1778 3638.36 3892.88 0.1794 3665.15 3892.89 0.1807 3660.81 3892.90 0.1832 3579.71 3892.92 0.185 3565.95 3892.92 0.1864 3493.55 3892.93 0.1873 3475.45 3892.93 0.1897 3525.41 3892.94 0.1909 3565.95 3892.95 0.1937 3634.02 3892.95 0.1946 3620.26 3892.96 0.1956 3715.11 3892.96 0.1972 3833.13 3892.96 0.1998 3882.36 3892.97 0.2015 3986.63 3892.97 0.2035 3946.08 3892.97 0.2057 3964.18 3892.98 0.2074 3982.28 3892.98 0.2081 3972.87 3892.98 0.2109 4009.07 3892.98 0.2109 3964.18 3892.98 0.2134 3927.98 3892.99 0.2148 3905.53 3892.99 0.2174 3841.82 3892.99 0.2192 3805.62 3892.99 0.2203 3746.97 3892.99 0.2211 3728.87 3892.99 0.2225 3728.87 3892.99 0.2241 3701.35 3892.99 0.2257 3751.31 3892.99 0.2268 3746.97 3892.99 0.2277 3787.51 3892.99 0.2296 3833.13 3892.99 0.2302 3819.37 3892.99 0.2311 3873.68 3892.99 0.2331 3873.68 3893.00 0.2339 3918.57 3893.00 0.2354 3982.28 3893.00 0.2359 3986.63 3893.00 0.2367 4063.38 3893.00 0.2376 4068.45 3893.00

557

0.2376 4127.09 3893.00 0.2386 4213.26 3893.00 0.2392 4208.19 3893.00 0.239 4235.70 3893.00 0.2407 4203.84 3893.00 0.2415 4221.95 3893.00 0.2413 4258.15 3893.00 0.2427 4240.05 3893.00 0.2421 4249.46 3893.00 0.2421 4231.36 3893.00 0.2435 4213.26 3893.00 0.2444 4217.60 3893.00 0.2444 4171.99 3893.00 0.2443 4231.36 3893.00 0.2435 4240.05 3893.00 0.2448 4262.49 3893.00 0.2452 4285.66 3893.00 0.2454 4267.56 3893.00 0.2465 4312.45 3893.00 0.2461 4298.69 3893.00 0.2466 4316.80 3893.00 0.2478 4298.69 3893.00 0.2476 4208.19 3893.00 0.2482 4181.40 3893.00 0.248 4122.75 3893.00 0.2493 4090.89 3893.00 0.2488 4072.79 3893.00 0.2494 4018.49 3893.00 0.2505 4045.28 3893.00 0.2505 4059.03 3893.00 0.2506 4086.55 3893.00 0.2526 4095.24 3893.00 0.2527 4095.24 3893.00 0.2529 4131.44 3893.00 0.2535 4131.44 3893.00 0.2533 4149.54 3893.00 0.2548 4181.40 3893.00 0.2556 4185.74 3893.00 0.2559 4240.05 3893.00 0.2566 4258.15 3893.00 0.2566 4298.69 3893.00 0.258 4326.21 3893.00 0.2582 4298.69 3893.00 0.2592 4362.41 3893.00 0.2594 4376.17 3893.00 0.2592 4380.51 3893.00 0.2598 4380.51 3893.00 0.2596 4344.31 3893.00 0.2603 4366.76 3893.00 0.2611 4330.55 3893.00

558

0.2609 4358.07 3893.00 0.2617 4366.76 3893.00 0.262 4353.00 3893.00 0.2617 4366.76 3893.00 0.2629 4344.31 3893.00 0.2631 4348.65 3893.00 0.2629 4348.65 3893.00 0.2633 4316.80 3893.00 0.2637 4344.31 3893.00 0.2646 4362.41 3893.00 0.2646 4507.22 3893.00 0.2645 4652.03 3893.00 0.2649 4724.44 3893.00 0.2648 4760.64 3893.00 0.2657 4715.02 3893.00 0.2664 4638.27 3893.00 0.2665 4597.73 3893.00 0.2674 4484.78 3893.00 0.2678 4461.61 3893.00 0.2684 4412.37 3893.00 0.2684 4407.30 3893.00 0.2692 4466.67 3893.00 0.2693 4489.12 3893.00 0.2697 4529.67 3893.00 0.2703 4529.67 3893.00 0.2702 4633.93 3893.00 0.2711 4706.34 3893.00 0.2722 4715.02 3893.00 0.2719 4738.19 3893.00 0.2734 4701.99 3893.00 0.2734 4683.89 3893.00 0.2739 4674.48 3893.00 0.2745 4633.93 3893.00 0.2745 4660.72 3893.00 0.2742 4656.38 3893.00 0.275 4701.99 3893.00

559

Table D2: Shear bevameter results for tests at low pressure and high density.

Low Pressure (approximately 5 kPa) 1.75 g/cc Density

Grousers: Sandpaper: Calculated Calculated Shear Shear Shear Shear Shear Shear Displacement Stress Stress Displacement Stress Stress 0.0003 19.55 48.84 -0.0001 58.65 -23.44 -0.0001 33.31 -16.46 -0.0001 31.86 -23.44 -0.0005 46.34 -83.18 -0.0002 76.75 -47.04 0 19.55 0.00 0 44.89 0.00 -0.0001 51.41 -16.46 0.0006 68.06 137.15 -0.0004 42.00 -66.36 0.0002 76.75 46.37 -0.0004 37.65 -66.36 0.0007 31.86 159.44 0.0004 73.85 64.95 0.0015 68.06 332.14 -0.0002 33.31 -33.00 0.0003 36.20 69.31 0.0003 55.75 48.84 0.0008 62.99 181.58 0.0006 28.24 96.90 0.0012 62.99 268.54 0.0006 23.89 96.90 0.0008 36.20 181.58 0 46.34 0.00 0.0002 90.51 46.37 0.0008 19.55 128.51 -0.0002 40.55 -47.04 0 51.41 0.00 0 76.75 0.00 -0.0001 23.89 -16.46 0.0002 72.41 46.37 0.0008 37.65 128.51 0.0002 40.55 46.37 0.0006 60.10 96.90 -0.0001 81.09 -23.44 -0.0006 19.55 -100.09 0.0004 58.65 92.09 0 51.41 0.00 0.0002 62.99 46.37 0.0006 23.89 96.90 0.0008 58.65 181.58 0.0002 23.89 32.65 0.0003 40.55 69.31 0.0004 55.75 64.95 0.0002 68.06 46.37 0.0006 5.79 96.90 0.001 36.20 225.37 0.0002 37.65 32.65 0.0007 44.89 159.44 0.0002 23.89 32.65 0 54.30 0.00 0.0002 15.21 32.65 0 31.86 0.00 0.0007 46.34 112.75 0 72.41 0.00 0 23.89 0.00 0.0003 40.55 69.31

560

0 42.00 0.00 0.0007 54.30 159.44 0.0003 33.31 48.84 0 58.65 0.00 -0.0009 23.89 -151.36 0.0002 40.55 46.37 0.0004 33.31 64.95 0.0006 68.06 137.15 -0.0001 5.79 -16.46 0.0002 36.20 46.37 -0.0002 55.75 -33.00 0.0006 58.65 137.15 -0.0002 23.89 -33.00 0.0002 58.65 46.37 -0.0008 37.65 -134.17 0.0006 36.20 137.15 0.0011 51.41 175.29 -0.0005 72.41 -118.88 -0.001 10.14 -168.63 0.001 31.86 225.37 0.0003 42.00 48.84 -0.0006 49.96 -143.17 -0.0002 15.21 -33.00 0.0007 44.89 159.44 0 23.89 0.00 -0.0002 31.86 -47.04 -0.0001 55.75 -16.46 0.0003 62.99 69.31 0.001 19.55 159.78 -0.0005 31.86 -118.88 0.0002 64.44 32.65 0.0003 44.89 69.31 0.0002 23.89 32.65 0.0004 49.96 92.09 -0.0005 33.31 -83.18 0 26.79 0.00 -0.0001 42.00 -16.46 -0.0005 68.06 -118.88 -0.0008 10.14 -134.17 0.0006 22.45 137.15 0.0002 46.34 32.65 -0.0002 49.96 -47.04 0.0003 37.65 48.84 0.0003 26.79 69.31 0.0007 23.89 112.75 0.0008 13.76 181.58 -0.0002 46.34 -33.00 0.0006 54.30 137.15 -0.0002 10.14 -33.00 0.0003 18.10 69.31 0.0006 28.24 96.90 -0.0004 44.89 -94.76 0 15.21 0.00 0 58.65 0.00 0.0012 37.65 190.71 0.0006 8.69 137.15 0.0003 51.41 48.84 0.0003 62.99 69.31 0.0004 19.55 64.95 0.0012 36.20 268.54 -0.0001 60.10 -16.46 -0.0009 62.99 -217.10 0 46.34 0.00 0.0004 62.99 92.09 0.0002 46.34 32.65 -0.0006 13.76 -143.17 0.0004 69.51 64.95 0.001 68.06 225.37 -0.0002 37.65 -33.00 0.0002 31.86 46.37 -0.0006 69.51 -100.09 -0.0002 44.89 -47.04 0 33.31 0.00 0.0006 58.65 137.15 -0.0002 37.65 -33.00 0.0006 22.45 137.15 0 46.34 0.00 0.0008 76.75 181.58 0.001 23.89 159.78 0.0007 40.55 159.44 0.0004 46.34 64.95 -0.0001 49.96 -23.44 0.0003 33.31 48.84 -0.0001 76.75 -23.44 0.0002 23.89 32.65 0.0004 36.20 92.09 0 55.75 0.00 -0.0001 86.16 -23.44 0 15.21 0.00 0 49.96 0.00 0.0012 51.41 190.71 0.0004 58.65 92.09 -0.0001 42.00 -16.46 0.0007 76.75 159.44 0 51.41 0.00 0.0006 36.20 137.15 0 82.54 0.00 0.0003 72.41 69.31 0 60.10 0.00 0.0007 40.55 159.44

561

-0.0002 96.30 -33.00 0.0011 58.65 247.03 0.0003 60.10 48.84 0.0008 68.06 181.58 0.0003 69.51 48.84 -0.0001 31.86 -23.44 0.0002 100.64 32.65 0.0007 81.09 159.44 -0.0005 37.65 -83.18 0.001 58.65 225.37 0.0002 78.20 32.65 0.0003 54.30 69.31 0.0007 55.75 112.75 0.0004 68.06 92.09 0.0003 46.34 48.84 0.0006 26.79 137.15 -0.0004 73.85 -66.36 0.0011 68.06 247.03 0.0006 37.65 96.90 0 31.86 0.00 0.0002 73.85 32.65 0.0008 40.55 181.58 -0.0001 51.41 -16.46 -0.0002 62.99 -47.04 -0.0005 55.75 -83.18 0.0002 22.45 46.37 0.0003 78.20 48.84 0.0015 62.99 332.14 -0.0004 55.75 -66.36 0.0004 36.20 92.09 0.0003 69.51 48.84 0.0014 54.30 311.09 0.0006 46.34 96.90 0.0003 76.75 69.31 -0.0001 55.75 -16.46 0.0004 58.65 92.09 -0.0001 82.54 -16.46 0.0011 94.85 247.03 0.0003 46.34 48.84 0.0015 76.75 332.14 0.0006 82.54 96.90 -0.0005 144.81 -118.88 0.0006 55.75 96.90 0.0007 185.36 159.44 0 69.51 0.00 -0.0002 212.87 -47.04 0 96.30 0.00 0.0002 321.48 46.37 0.0004 60.10 64.95 0.0003 362.03 69.31 0.001 96.30 159.78 0.0004 448.19 92.09 -0.0004 78.20 -66.36 0.0006 538.69 137.15 0.0002 69.51 32.65 0.0012 606.03 268.54 0.0004 114.40 64.95 -0.0001 728.40 -23.44 0.001 60.10 159.78 0.0007 810.21 159.44 0.0003 96.30 48.84 0.0002 927.51 46.37 0.0004 60.10 64.95 0.0004 1031.77 92.09 0.0011 60.10 175.29 -0.0002 1112.87 -47.04 -0.0001 69.51 -16.46 -0.0002 1267.09 -47.04 -0.0004 28.24 -66.36 -0.0002 1343.84 -47.04 0.0004 69.51 64.95 0.0006 1488.65 137.15 0.0011 60.10 175.29 0.0008 1651.56 181.58 0.0004 73.85 64.95 0.0011 1773.93 247.03 -0.0002 91.95 -33.00 0.0016 1954.94 353.04 -0.0009 42.00 -151.36 0.0014 2072.24 311.09 0 64.44 0.00 0.002 2217.05 435.16 0.0006 37.65 96.90 0.0024 2343.76 514.96 -0.0001 46.34 -16.46 0.0014 2403.13 311.09 -0.0001 73.85 -16.46 0.0026 2516.08 554.01 0.0008 23.89 128.51 0.0028 2520.42 592.51 0.0003 60.10 48.84 0.0028 2520.42 592.51 -0.0002 37.65 -33.00 0.0036 2502.32 741.09 0.0006 42.00 96.90 0.0028 2484.22 592.51 0.0003 64.44 48.84 0.0048 2511.74 948.60 0.0003 23.89 48.84 0.0044 2560.97 881.40

562

0.0003 64.44 48.84 0.0056 2647.13 1077.36 -0.0001 46.34 -16.46 0.006 2741.98 1139.02 0.0006 33.31 96.90 0.0071 2783.25 1299.77 0.0007 46.34 112.75 0.0071 2868.69 1299.77 0.001 37.65 159.78 0.0093 2850.59 1585.65 0.0006 73.85 96.90 0.0093 2878.11 1585.65 0.0004 46.34 64.95 0.01 2886.79 1667.57 0.0003 60.10 48.84 0.0106 2837.56 1734.59 0.0007 69.51 112.75 0.012 2896.21 1880.20 -0.0002 42.00 -33.00 0.0118 2864.35 1860.28 0.0003 73.85 48.84 0.013 2868.69 1975.63 0 51.41 0.00 0.0143 2882.45 2089.89 0.0003 37.65 48.84 0.0158 2828.15 2209.18 0.0002 60.10 32.65 0.0177 2860.00 2342.98 -0.0002 37.65 -33.00 0.0177 2873.76 2342.98 0.0012 60.10 190.71 0.0192 2904.90 2436.49 0.0003 33.31 48.84 0.0195 2936.75 2454.01 0.0007 37.65 112.75 0.0212 2878.11 2546.51 -0.0001 69.51 -16.46 0.0222 2860.00 2595.89 0.0003 37.65 48.84 0.0238 2778.19 2667.90 0.0006 60.10 96.90 0.0259 2760.08 2750.71 0 37.65 0.00 0.0269 2783.25 2785.98 0.0008 37.65 128.51 0.0287 2796.29 2843.43 0.0011 55.75 175.29 0.0298 2846.25 2875.06 0 33.31 0.00 0.0328 2814.39 2949.68 0.0007 60.10 112.75 0.0338 2860.00 2971.19 0.0003 55.75 48.84 0.0346 2900.55 2987.33 -0.0006 60.10 -100.09 0.0367 2900.55 3025.54 0.0003 96.30 48.84 0.0392 2972.96 3064.14 0 60.10 0.00 0.0408 2964.27 3085.45 -0.0001 96.30 -16.46 0.0415 2936.75 3094.03 0.0002 69.51 32.65 0.0434 2882.45 3115.27 0.0004 69.51 64.95 0.0456 2855.66 3136.52 0.0003 87.61 48.84 0.0475 2886.79 3152.35 0 42.00 0.00 0.0492 2882.45 3164.81 -0.0001 78.20 -16.46 0.0505 2932.41 3173.36 -0.0002 60.10 -33.00 0.0529 2972.96 3187.20 0.0006 69.51 96.90 0.0543 2959.20 3194.24 0 82.54 0.00 0.0577 3000.47 3208.67 0.0013 55.75 206.05 0.0591 3000.47 3213.66 0.0007 69.51 112.75 0.0603 3013.50 3217.56 -0.0004 73.85 -66.36 0.0622 3013.50 3223.08 0.0004 73.85 64.95 0.0648 2972.96 3229.53 0.0004 78.20 64.95 0.0661 3041.02 3232.32 0.0002 42.00 32.65 0.0688 3022.92 3237.37 -0.0002 73.85 -33.00 0.07 3031.60 3239.31 0.0008 46.34 128.51 0.0725 3063.46 3242.87 0 46.34 0.00 0.0745 3049.71 3245.29 0.0003 55.75 48.84 0.0763 3109.08 3247.19 0.0003 33.31 48.84 0.0787 3117.77 3249.37

563

-0.0006 55.75 -100.09 0.0807 3153.97 3250.92 0.0002 42.00 32.65 0.0823 3181.48 3252.01 0 60.10 0.00 0.0853 3140.21 3253.75 0.0002 82.54 32.65 0.0861 3172.07 3254.15 0.0006 51.41 96.90 0.0874 3117.77 3254.76 -0.0001 82.54 -16.46 0.0894 3135.87 3255.59 0 64.44 0.00 0.0916 3172.07 3256.38 -0.0006 60.10 -100.09 0.093 3172.07 3256.82 0 87.61 0.00 0.0951 3244.48 3257.41 0 51.41 0.00 0.0967 3244.48 3257.80 0.0008 73.85 128.51 0.0988 3258.23 3258.24 0.0003 55.75 48.84 0.1004 3316.88 3258.54 0.001 69.51 159.78 0.1021 3316.88 3258.82 0.001 96.30 159.78 0.104 3366.84 3259.10 0.0004 55.75 64.95 0.1052 3357.43 3259.26 0.0002 91.95 32.65 0.1077 3371.18 3259.54 0 51.41 0.00 0.109 3362.50 3259.67 0.0007 82.54 112.75 0.1108 3334.98 3259.83 0.001 82.54 159.78 0.1116 3394.35 3259.90 -0.0002 64.44 -33.00 0.1143 3362.50 3260.09 0 87.61 0.00 0.1155 3407.39 3260.17 -0.0001 55.75 -16.46 0.1178 3407.39 3260.29 0.0006 69.51 96.90 0.1184 3371.18 3260.32 -0.0001 91.95 -16.46 0.1202 3457.35 3260.40 0.0003 69.51 48.84 0.1229 3425.49 3260.51 0.0003 91.95 48.84 0.1245 3443.59 3260.56 -0.0006 73.85 -100.09 0.1255 3425.49 3260.59 -0.0006 87.61 -100.09 0.1285 3366.84 3260.67 0.0006 110.06 96.90 0.1301 3407.39 3260.71 0.0002 82.54 32.65 0.1331 3371.18 3260.76 0.001 128.16 159.78 0.1341 3425.49 3260.78 0.0003 91.95 48.84 0.1366 3489.20 3260.82 0 91.95 0.00 0.1388 3466.04 3260.84 0 100.64 0.00 0.14 3543.51 3260.86 0.0004 64.44 64.95 0.1428 3497.89 3260.88 0 82.54 0.00 0.1448 3484.14 3260.90 0.0003 69.51 48.84 0.1464 3520.34 3260.91 0.0008 69.51 128.51 0.1496 3502.24 3260.93 0.0002 87.61 32.65 0.1521 3588.40 3260.94 -0.0002 78.20 -33.00 0.1542 3565.95 3260.95 0.0006 123.81 96.90 0.156 3552.20 3260.95 0.0004 132.50 64.95 0.1579 3570.30 3260.96 0.0008 154.95 128.51 0.1616 3507.31 3260.97 -0.0005 164.36 -83.18 0.1643 3565.95 3260.97 0.0006 128.16 96.90 0.1658 3552.20 3260.98 0 164.36 0.00 0.1686 3579.71 3260.98 0.0002 146.26 32.65 0.171 3579.71 3260.98 0.0003 146.26 48.84 0.1735 3525.41 3260.99 -0.0002 150.60 -33.00 0.1758 3515.99 3260.99 0.0002 96.30 32.65 0.1768 3457.35 3260.99

564

0.0003 123.81 48.84 0.1803 3453.00 3260.99 -0.0001 91.95 -16.46 0.1827 3502.24 3260.99 0 91.95 0.00 0.1857 3497.89 3260.99 -0.0008 128.16 -134.17 0.1876 3547.85 3261.00 0.0004 118.74 64.95 0.1901 3507.31 3261.00 0.0008 160.02 128.51 0.1926 3497.89 3261.00 0 132.50 0.00 0.1937 3466.04 3261.00 0.0002 141.91 32.65 0.1958 3429.83 3261.00 0.0002 146.26 32.65 0.1995 3461.69 3261.00 0.0008 110.06 128.51 0.2009 3443.59 3261.00 0.0003 164.36 48.84 0.2035 3434.90 3261.00 -0.0001 154.95 -16.46 0.2057 3434.90 3261.00 -0.0002 186.81 -33.00 0.2074 3394.35 3261.00 -0.0006 232.42 -100.09 0.2095 3389.29 3261.00 -0.0006 218.66 -100.09 0.2119 3339.33 3261.00 0.0002 250.52 32.65 0.2141 3334.98 3261.00 -0.0005 245.45 -83.18 0.2154 3407.39 3261.00 0.0003 268.62 48.84 0.2172 3403.04 3261.00 0.0004 304.83 64.95 0.2195 3439.25 3261.00 0.0002 286.72 32.65 0.2205 3407.39 3261.00 0.0006 309.17 96.90 0.2227 3371.18 3261.00 0.0003 313.51 48.84 0.2235 3362.50 3261.00 0.0004 345.37 64.95 0.2252 3334.98 3261.00 0.0003 399.68 48.84 0.2268 3407.39 3261.00 0 385.92 0.00 0.2276 3398.70 3261.00 0.0003 472.08 48.84 0.2298 3416.80 3261.00 0.0007 480.77 112.75 0.231 3403.04 3261.00 0.0004 558.24 64.95 0.2318 3366.84 3261.00 0.0007 639.34 112.75 0.2329 3375.53 3261.00 -0.0005 679.88 -83.18 0.234 3375.53 3261.00 0.0004 779.80 64.95 0.2358 3407.39 3261.00 -0.0006 829.76 -100.09 0.2372 3447.93 3261.00 0.0004 924.61 64.95 0.2384 3447.93 3261.00 0.0008 1046.98 128.51 0.2401 3461.69 3261.00 0.0003 1119.38 48.84 0.24 3398.70 3261.00 -0.0001 1290.98 -16.46 0.2412 3389.29 3261.00 0.0004 1422.04 64.95 0.2423 3421.14 3261.00 -0.0002 1580.60 -33.00 0.2441 3434.90 3261.00 -0.0004 1739.17 -66.36 0.2442 3534.10 3261.00 0.0002 1797.82 32.65 0.2457 3511.65 3261.00 0.0008 1946.97 128.51 0.2461 3534.10 3261.00 0.0008 2065.00 128.51 0.2477 3484.14 3261.00 0.0002 2246.01 32.65 0.2487 3461.69 3261.00 0.0031 2481.32 468.53 0.2498 3479.79 3261.00 0.0027 2671.03 412.38 0.2511 3479.79 3261.00 0.0033 2861.45 496.15 0.2514 3520.34 3261.00 0.004 2960.65 590.51 0.2518 3534.10 3261.00 0.0047 3056.22 681.38 0.2538 3489.20 3261.00 0.0055 3087.36 781.11 0.2546 3511.65 3261.00 0.0063 2988.16 876.63 0.255 3475.45 3261.00

565

0.0074 2911.41 1001.42 0.2568 3489.20 3261.00 0.0089 2770.95 1160.08 0.257 3489.20 3261.00 0.0101 2707.23 1278.09 0.2583 3461.69 3261.00 0.0112 2684.78 1379.76 0.2597 3479.79 3261.00 0.013 2630.48 1533.64 0.26 3447.93 3261.00 0.0149 2630.48 1680.65 0.2616 3447.93 3261.00 0.0159 2603.69 1752.18 0.2616 3457.35 3261.00 0.018 2608.03 1890.41 0.2628 3447.93 3261.00 0.0196 2634.82 1985.70 0.2633 3484.14 3261.00 0.022 2576.18 2114.08 0.2645 3497.89 3261.00 0.0241 2621.79 2213.55 0.2646 3525.41 3261.00 0.0263 2652.93 2306.36 0.2658 3543.51 3261.00 0.0293 2657.99 2416.41 0.2668 3520.34 3261.00 0.0318 2621.79 2495.45 0.2682 3538.44 3261.00 0.0358 2521.87 2601.70 0.2676 3502.24 3261.00 0.0374 2521.87 2638.19 0.2695 3529.75 3261.00 0.0406 2508.11 2702.36 0.2709 3538.44 3261.00 0.0428 2567.49 2740.47 0.2711 3525.41 3261.00 0.0455 2662.34 2781.47 0.2713 3570.30 3261.00 0.0488 2652.93 2824.11 0.2728 3534.10 3261.00 0.0512 2698.54 2850.69 0.2738 3543.51 3261.00 0.0546 2652.93 2882.91 0.2752 3556.54 3261.00 0.0579 2644.24 2909.01 0.2746 3534.10 3261.00 0.0613 2630.48 2931.46 0.2764 3588.40 3261.00 0.0633 2567.49 2942.87 0.2759 3574.64 3261.00 0.0674 2553.73 2962.73 0.2763 3602.16 3261.00 0.0708 2481.32 2976.18 0.2768 3624.60 3261.00 0.0735 2499.43 2985.24 0.0761 2521.87 2992.79 0.0795 2521.87 3001.21 0.0825 2612.38 3007.45 0.0851 2626.14 3012.10 0.0893 2630.48 3018.36 0.0915 2680.44 3021.12 0.0951 2644.24 3024.98 0.0978 2676.09 3027.42 0.1009 2644.24 3029.82 0.1047 2666.68 3032.26 0.108 2730.40 3034.01 0.1098 2734.74 3034.85 0.1143 2807.15 3036.60 0.1175 2829.59 3037.62 0.1199 2893.31 3038.27 0.124 2983.82 3039.21 0.1266 3010.61 3039.70 0.1302 3056.22 3040.29 0.1327 3020.02 3040.63 0.136 3006.26 3041.02 0.1398 3014.95 3041.38 0.1417 2978.75 3041.54

566

0.1457 3014.95 3041.82 0.1481 3010.61 3041.97 0.1511 3046.81 3042.12 0.1542 3119.21 3042.26 0.1575 3123.56 3042.38 0.1608 3159.76 3042.48 0.1636 3123.56 3042.55 0.1669 3101.11 3042.63 0.17 3110.53 3042.68 0.1726 3083.01 3042.72 0.1756 3119.21 3042.77 0.1795 3128.63 3042.81 0.1825 3159.76 3042.84 0.1856 3182.93 3042.86 0.1884 3169.17 3042.88 0.1923 3241.58 3042.90 0.1955 3195.96 3042.92 0.1978 3191.62 3042.93 0.2011 3191.62 3042.94 0.2036 3123.56 3042.95 0.207 3155.42 3042.96 0.2101 3119.21 3042.96 0.2129 3114.87 3042.97 0.215 3141.66 3042.97 0.2184 3114.87 3042.98 0.2203 3155.42 3042.98 0.2241 3151.07 3042.98 0.2265 3173.52 3042.98 0.2288 3191.62 3042.99 0.2321 3169.17 3042.99 0.2339 3209.72 3042.99 0.2362 3209.72 3042.99 0.2374 3237.23 3042.99 0.2404 3268.37 3042.99 0.2428 3264.02 3042.99 0.2461 3309.64 3042.99 0.247 3309.64 3043.00 0.2488 3354.53 3043.00 0.2501 3404.49 3043.00 0.2518 3376.98 3043.00 0.2539 3445.04 3043.00 0.256 3445.04 3043.00 0.2572 3499.34 3043.00 0.2591 3549.30 3043.00 0.2607 3513.10 3043.00 0.2627 3563.06 3043.00 0.2631 3531.20 3043.00 0.2645 3539.89 3043.00 0.2665 3603.61 3043.00 0.2678 3589.85 3043.00

567

0.2686 3644.15 3043.00 0.2707 3621.71 3043.00

Table D3: Shear bevameter results for tests at medium pressure and low density.

Medium Pressure (approximately 10 kPa) 1.64 g/cc Density

Grousers: Sandpaper: Shear Shear Calculated Shear Shear Calculated Displacement Stress Shear Stress Displacement Stress Shear Stress

-0.0009 253.42 -240.42 -0.0006 267.18 -145.26 -0.0015 312.07 -405.20 -0.0002 249.07 -48.08 -0.0014 298.31 -377.48 -0.0005 312.07 -120.84 -0.0005 339.58 -132.58 0.0003 307.72 71.50 -0.0006 321.48 -159.39 0.0011 330.17 258.57 -0.0005 303.38 -132.58 0.0007 357.68 165.69 -0.0007 325.82 -186.31 0.0016 325.82 372.87 -0.0005 293.97 -132.58 0.0003 352.61 71.50 0.0001 298.31 26.22 0 303.38 0.00 -0.0011 257.76 -294.94 0.0011 289.62 258.57 -0.0003 262.11 -79.26 0.0012 285.28 281.59 0.0001 267.18 26.22 0.0007 235.32 165.69 -0.0005 253.42 -132.58 0.0003 257.76 71.50 -0.0009 280.21 -240.42 0.0008 230.97 189.03 -0.0013 257.76 -349.87 0.001 225.90 235.47 -0.0002 257.76 -52.74 0.0006 230.97 142.26 -0.0005 289.62 -132.58 0.0015 176.67 350.17 -0.0005 262.11 -132.58 0.0014 199.11 327.39 -0.0011 293.97 -294.94 0.0008 171.60 189.03 -0.0006 285.28 -159.39 0.0016 162.91 372.87 0.0001 275.86 26.22 0.001 158.57 235.47 -0.0006 312.07 -159.39 0.0012 112.95 281.59 -0.0005 275.86 -132.58 0.0003 162.91 71.50 -0.0001 303.38 -26.32 0.0006 108.61 142.26 -0.0006 271.52 -159.39 0.0007 117.30 165.69 -0.0003 257.76 -79.26 0.0014 131.05 327.39 -0.0009 271.52 -240.42 0.0006 104.26 142.26 -0.0013 225.90 -349.87 0.0007 126.71 165.69 -0.0005 249.07 -132.58 0.0006 86.16 142.26 -0.0011 230.97 -294.94 0.0003 108.61 71.50 -0.0006 212.87 -159.39 0.0003 112.95 71.50 -0.0001 230.97 -26.32 0.0003 81.09 71.50

568

-0.0009 203.46 -240.42 0.0004 117.30 95.17 -0.0009 207.80 -240.42 0.0008 81.09 189.03 -0.0003 176.67 -79.26 0.0008 86.16 189.03 -0.0006 176.67 -159.39 0.0006 90.51 142.26 -0.0006 199.11 -159.39 0.0011 62.99 258.57 -0.0005 185.36 -132.58 0.0015 94.85 350.17 -0.0007 217.22 -186.31 -0.0005 72.41 -120.84 0.0002 199.11 52.35 0.0014 90.51 327.39 -0.001 181.01 -267.63 0.0015 104.26 350.17 0.0001 194.77 26.22 0.0011 81.09 258.57 -0.0006 158.57 -159.39 0.0007 117.30 165.69 -0.0002 176.67 -52.74 0.0011 81.09 258.57 0.0002 158.57 52.35 0.0004 76.75 95.17 -0.0003 158.57 -79.26 0.0012 104.26 281.59 -0.0006 171.60 -159.39 0.001 68.06 235.47 -0.0011 149.15 -294.94 0.0011 112.95 258.57 -0.0006 189.70 -159.39 0.0008 99.20 189.03 0.0001 207.80 26.22 0 112.95 0.00 -0.0009 212.87 -240.42 0.0014 108.61 327.39 0.0002 275.86 52.35 0.001 58.65 235.47 -0.0014 253.42 -377.48 0.001 86.16 235.47 -0.0006 293.97 -159.39 0.001 40.55 235.47 -0.0006 253.42 -159.39 0.0008 54.30 189.03 -0.0007 253.42 -186.31 0.0011 68.06 258.57 -0.0007 253.42 -186.31 -0.0002 40.55 -48.08 -0.0014 225.90 -377.48 0.0007 68.06 165.69 -0.0002 267.18 -52.74 0.001 26.79 235.47 -0.0009 239.66 -240.42 0.0003 40.55 71.50 -0.0003 235.32 -79.26 -0.0002 62.99 -48.08 -0.0003 249.07 -79.26 0.0011 22.45 258.57 -0.0013 203.46 -349.87 0.0007 62.99 165.69 -0.0005 230.97 -132.58 0 26.79 0.00 -0.0001 212.87 -26.32 -0.0005 40.55 -120.84 -0.0013 217.22 -349.87 0.0004 40.55 95.17 -0.0006 253.42 -159.39 0.001 8.69 235.47 -0.0014 257.76 -377.48 0.0003 26.79 71.50 -0.0011 321.48 -294.94 0.0007 0.00 165.69 -0.0007 339.58 -186.31 0.0004 18.10 95.17 0.0001 380.13 26.22 0 31.86 0.00 -0.0006 425.02 -159.39 0.0006 4.34 142.26 -0.0013 398.23 -349.87 0 31.86 0.00 -0.0003 425.02 -79.26 0.0008 22.45 189.03 -0.0009 398.23 -240.42 0.001 36.20 235.47 -0.0005 393.88 -132.58 0.0014 62.99 327.39 -0.0003 406.92 -79.26 0.0008 26.79 189.03 -0.0005 375.78 -132.58 0 81.09 0.00 -0.0002 398.23 -52.74 0.0007 62.99 165.69 -0.0007 380.13 -186.31 0.0003 86.16 71.50 -0.0006 384.47 -159.39 0.0008 140.47 189.03 -0.001 425.02 -267.63 0.0008 108.61 189.03 -0.0007 416.33 -186.31 0.0003 185.36 71.50

569

-0.0003 461.22 -79.26 0.0012 199.11 281.59 -0.0014 484.39 -377.48 0.001 285.28 235.47 -0.0007 520.59 -186.31 0.0008 411.99 189.03 -0.0003 565.48 -79.26 0.0014 515.52 327.39 -0.0005 556.80 -132.58 0.0018 696.54 418.04 0.0001 597.34 26.22 0.0011 805.15 258.57 0.0002 593.00 52.35 0.001 931.85 235.47 -0.0011 611.10 -294.94 0.0006 1022.36 142.26 -0.0007 669.75 -186.31 0.0008 1094.77 189.03 -0.0007 705.95 -186.31 -0.0002 1248.99 -48.08 -0.0009 800.80 -240.42 0.0006 1438.69 142.26 -0.0006 846.42 -159.39 0.001 1737.72 235.47 -0.0003 900.72 -79.26 0.0006 2072.24 142.26 -0.0001 991.23 -26.32 0.0015 2361.86 350.17 -0.0009 1022.36 -240.42 0.001 2642.79 235.47 -0.0001 1108.52 -26.32 0.0012 2805.70 281.59 -0.0009 1144.73 -240.42 0.0016 2950.51 372.87 -0.0005 1185.27 -132.58 0.0014 3090.98 327.39 -0.0003 1271.43 -79.26 0.0016 3163.38 372.87 -0.0006 1303.29 -159.39 0.001 3334.98 235.47 -0.001 1407.56 -267.63 0.001 3434.90 235.47 0.0003 1448.10 78.38 0.0022 3538.44 507.44 -0.0006 1529.20 -159.39 0.0022 3597.81 507.44 -0.0007 1651.56 -186.31 0.0019 3656.46 440.51 0.0001 1751.48 26.22 0.001 3828.06 235.47 -0.0002 1914.39 -52.74 0.0022 3977.94 507.44 -0.0006 2077.30 -159.39 0.0027 4145.20 617.45 -0.0005 2316.97 -132.58 0.0025 4231.36 573.68 0.0009 2588.48 232.58 0.0032 4244.39 725.57 0.0018 2805.70 457.56 0.0039 4321.86 873.81 0.0006 3059.12 155.91 0.0043 4308.11 956.91 0.0002 3258.23 52.35 0.0044 4267.56 977.51 0.0015 3461.69 383.39 0.0051 4171.99 1119.69 0.0012 3715.11 308.40 0.0057 4072.79 1238.84 0.002 3932.32 506.55 0.0055 4072.79 1199.40 0.0026 4145.20 651.37 0.0068 4090.89 1450.93 0.0024 4231.36 603.46 0.0068 4127.09 1450.93 0.0038 4235.70 931.58 0.0065 4145.20 1393.89 0.0035 4213.26 862.69 0.0078 4090.89 1636.82 0.0038 4149.54 931.58 0.0088 4063.38 1816.36 0.0054 4163.30 1286.42 0.0096 3990.97 1955.56 0.0047 4122.75 1133.75 0.0101 3936.67 2040.62 0.0057 4131.44 1350.65 0.0116 3946.08 2287.09 0.0068 4185.74 1580.18 0.0113 3936.67 2238.82 0.0079 4231.36 1800.59 0.0126 3977.94 2444.41 0.0081 4321.86 1839.71 0.0146 4000.39 2743.11 0.0089 4362.41 1993.35 0.0151 4068.45 2814.59 0.0104 4376.17 2269.48 0.0155 4104.65 2870.89 0.0116 4380.51 2479.65 0.0174 4059.03 3127.87 0.0122 4339.97 2581.30 0.0178 4086.55 3179.85 0.0138 4394.27 2841.62 0.0198 4068.45 3429.14

570

0.0145 4484.78 2950.76 0.0206 4104.65 3524.10 0.0153 4611.48 3072.10 0.0215 4145.20 3627.83 0.0167 4688.23 3276.02 0.0227 4135.78 3761.17 0.0185 4652.03 3523.20 0.0241 4226.29 3909.87 0.019 4611.48 3589.00 0.0253 4253.80 4031.69 0.0208 4534.01 3816.08 0.0277 4285.66 4260.60 0.021 4457.26 3840.39 0.0284 4358.07 4323.84 0.0227 4507.22 4039.97 0.0301 4407.30 4471.18 0.024 4602.07 4184.37 0.0312 4452.92 4561.98 0.0251 4769.33 4301.26 0.032 4394.27 4625.86 0.026 4841.73 4393.43 0.0325 4412.37 4664.90 0.0271 4909.79 4502.01 0.035 4475.36 4850.22 0.0293 5000.30 4706.40 0.0355 4502.88 4885.39 0.0301 4946.00 4776.70 0.0372 4597.73 5000.50 0.0313 4883.00 4878.35 0.0387 4606.42 5096.57 0.031 4756.30 4853.36 0.0406 4638.27 5211.28 0.0328 4760.64 4999.24 0.0419 4597.73 5285.51 0.0336 4846.80 5061.03 0.044 4515.91 5398.55 0.0355 4869.25 5200.69 0.0445 4575.28 5424.27 0.0365 4959.75 5270.35 0.0464 4561.53 5518.03 0.0375 5054.60 5337.50 0.0482 4629.59 5601.33 0.0383 5154.52 5389.46 0.0494 4733.13 5654.03 0.0399 5172.62 5488.89 0.0508 4760.64 5712.79 0.0402 5136.42 5506.89 0.0531 4823.63 5803.34 0.0418 5158.87 5599.59 0.0546 4805.53 5858.61 0.0412 5176.97 5565.47 0.0554 4859.83 5886.93 0.0439 5158.87 5713.26 0.0578 4914.14 5967.32 0.044 5172.62 5718.45 0.0587 4923.55 5995.77 0.0459 5140.77 5813.63 0.0603 5022.75 6044.21 0.0468 5195.07 5856.43 0.0612 5064.02 6070.30 0.0476 5226.93 5893.31 0.0632 5104.56 6125.43 0.0497 5249.37 5985.09 0.0655 5154.52 6184.26 0.0509 5308.02 6034.43 0.0657 5167.56 6189.16 0.0513 5376.08 6050.39 0.0674 5285.58 6229.44 0.0524 5498.45 6093.11 0.069 5344.23 6265.24 0.0544 5552.75 6166.47 0.0705 5444.14 6297.04 0.0547 5593.30 6177.02 0.0718 5493.38 6323.29 0.0557 5607.06 6211.34 0.0738 5480.35 6361.42 0.0579 5588.95 6282.53 0.0749 5543.34 6381.29 0.0586 5629.50 6304.00 0.0759 5593.30 6398.71 0.0593 5579.54 6324.92 0.077 5710.60 6417.18 0.0618 5570.85 6395.38 0.0772 5824.27 6420.47 0.0619 5647.60 6398.06 0.0791 5842.37 6450.54 0.063 5665.70 6426.96 0.082 5891.61 6492.79 0.0644 5701.91 6462.08 0.0825 5837.30 6499.65 0.066 5697.56 6500.06 0.084 5869.16 6519.54 0.0681 5746.80 6546.63 0.0853 5955.32 6535.95 0.0677 5819.20 6538.03 0.0861 6036.42 6545.69 0.0696 5851.06 6577.75 0.0865 6136.34 6550.46 0.071 5901.02 6605.28 0.088 6136.34 6567.77 0.072 5878.58 6624.10 0.09 6145.03 6589.48

571

0.0741 5878.58 6661.42 0.091 6145.03 6599.78 0.0753 5878.58 6681.49 0.0921 6131.99 6610.71 0.0759 5783.00 6691.19 0.0939 6240.60 6627.71 0.0781 5783.00 6725.00 0.0937 6276.80 6625.88 0.0795 5774.31 6745.12 0.0961 6321.69 6647.10 0.0808 5810.51 6762.90 0.0971 6326.04 6655.44 0.0823 5905.37 6782.39 0.0987 6285.49 6668.18 0.0839 5973.43 6802.02 0.0998 6313.01 6676.54 0.0849 6050.18 6813.71 0.1004 6331.11 6680.97 0.0869 6122.58 6835.84 0.1012 6434.65 6686.73 0.0872 6172.54 6839.02 0.1035 6494.02 6702.43 0.0892 6190.64 6859.35 0.1047 6480.26 6710.14 0.0905 6113.89 6871.79 0.1053 6480.26 6713.87 0.0921 6104.48 6886.29 0.1065 6444.06 6721.11 0.0938 6032.07 6900.80 0.1078 6502.71 6728.62 0.0947 6032.07 6908.12 0.109 6620.73 6735.25 0.0969 6104.48 6925.02 0.1104 6665.62 6742.65 0.0974 6095.79 6928.67 0.1121 6751.78 6751.17 0.0986 6186.30 6937.17 0.1138 6701.82 6759.19 0.0996 6240.60 6943.97 0.1155 6688.06 6766.76 0.101 6263.05 6953.08 0.1166 6665.62 6771.42 0.1027 6294.90 6963.52 0.1174 6651.86 6774.70 0.1045 6281.15 6973.89 0.1183 6697.48 6778.28 0.1063 6267.39 6983.60 0.121 6701.82 6788.38 0.1077 6240.60 6990.71 0.1216 6724.27 6790.50 0.1087 6281.15 6995.57 0.1229 6733.68 6794.94 0.1106 6344.14 7004.33 0.1251 6706.17 6802.01 0.1108 6367.31 7005.22 0.1272 6729.34 6808.28 0.1122 6439.72 7011.24 0.1284 6733.68 6811.66 0.1141 6452.75 7018.94 0.1296 6801.74 6814.90 0.1157 6494.02 7025.02 0.1312 6856.04 6819.02 0.1171 6557.01 7030.05 0.1327 6828.53 6822.68 0.1182 6566.42 7033.82 0.1343 6837.94 6826.37 0.1202 6638.83 7040.30 0.1359 6783.64 6829.87 0.1216 6679.38 7044.57 0.1383 6787.98 6834.77 0.1218 6683.72 7045.16 0.139 6819.84 6836.12 0.1236 6724.27 7050.28 0.1409 6837.94 6839.63 0.1256 6711.23 7055.60 0.1423 6932.79 6842.07 0.1259 6729.34 7056.36 0.1441 6923.38 6845.04 0.1267 6706.17 7058.35 0.1457 6919.04 6847.52 0.1283 6724.27 7062.17 0.1474 6905.28 6850.02 0.1294 6756.13 7064.67 0.1485 6842.29 6851.56 0.1314 6733.68 7068.96 0.1504 6874.15 6854.08 0.132 6856.04 7070.19 0.1514 6869.08 6855.34 0.1335 6896.59 7073.14 0.1526 6896.59 6856.80 0.1351 6914.69 7076.11 0.1545 6919.04 6858.98 0.1357 6995.79 7077.18 0.1555 6869.08 6860.08 0.1374 6964.65 7080.08 0.1576 6900.94 6862.25 0.1381 6955.24 7081.23 0.1586 6878.49 6863.24 0.1394 6950.90 7083.28 0.16 6896.59 6864.56 0.1403 6946.55 7084.64 0.1612 6964.65 6865.64

572

0.142 6932.79 7087.09 0.1629 6977.69 6867.09 0.1433 6910.35 7088.86 0.1629 7037.06 6867.09 0.1447 6964.65 7090.68 0.166 6995.79 6869.53 0.1452 6973.34 7091.31 0.167 6969.00 6870.27 0.1469 7005.20 7093.36 0.169 6959.58 6871.66 0.1477 7055.16 7094.28 0.1696 6928.45 6872.06 0.1484 7000.86 7095.06 0.1714 6959.58 6873.21 0.1512 7050.09 7098.00 0.1729 6928.45 6874.11 0.1505 7037.06 7097.29 0.1739 6919.04 6874.69 0.1524 7037.06 7099.17 0.1754 6932.79 6875.52 0.155 7104.39 7101.53 0.1775 6874.15 6876.61 0.1558 7100.05 7102.21 0.1783 6928.45 6877.00 0.1567 7118.15 7102.95 0.1798 6923.38 6877.71 0.1584 7095.71 7104.29 0.1812 6959.58 6878.35 0.1596 7100.05 7105.19 0.1833 6964.65 6879.24 0.1595 7095.71 7105.12 0.1849 6937.14 6879.87 0.1627 7045.75 7107.33 0.1854 6946.55 6880.07 0.164 7091.36 7108.16 0.1882 6905.28 6881.08 0.1655 7068.19 7109.06 0.1893 6955.24 6881.45 0.1667 7100.05 7109.75 0.1913 7037.06 6882.09 0.1681 7172.46 7110.52 0.1922 7068.19 6882.37 0.1697 7145.67 7111.35 0.1939 7113.81 6882.86 0.1713 7181.87 7112.13 0.1964 7073.26 6883.54 0.1713 7190.56 7112.13 0.1968 7077.60 6883.64 0.1735 7181.87 7113.13 0.1984 7127.56 6884.04 0.1745 7226.76 7113.56 0.2015 7127.56 6884.75 0.1765 7236.17 7114.38 0.202 7168.11 6884.86 0.179 7262.96 7115.31 0.204 7140.60 6885.27 0.1799 7244.86 7115.63 0.2048 7127.56 6885.43 0.182 7272.37 7116.33 0.2068 7140.60 6885.80 0.1819 7290.48 7116.29 0.208 7118.15 6886.02 0.184 7236.17 7116.94 0.2094 7176.80 6886.25 0.1859 7258.62 7117.49 0.2109 7168.11 6886.49 0.1876 7218.07 7117.95 0.2121 7176.80 6886.68 0.1894 7222.42 7118.40 0.2138 7176.80 6886.93 0.1909 7281.06 7118.75 0.2146 7131.91 6887.04 0.1918 7299.16 7118.96 0.2164 7140.60 6887.28 0.1938 7385.33 7119.39 0.2172 7068.19 6887.38 0.195 7403.43 7119.63 0.218 7059.50 6887.48 0.1974 7407.77 7120.08 0.2198 7059.50 6887.69 0.1982 7389.67 7120.23 0.2207 7031.99 6887.80 0.2006 7299.16 7120.63 0.2217 7068.19 6887.90 0.2027 7308.58 7120.96 0.2227 7068.19 6888.01 0.2032 7272.37 7121.03 0.224 7109.46 6888.14 0.2043 7290.48 7121.19 0.2239 7172.46 6888.13 0.2061 7317.27 7121.43 0.2264 7168.11 6888.37 0.2074 7294.82 7121.60 0.2265 7213.00 6888.38 0.2096 7367.23 7121.87 0.2274 7176.80 6888.46 0.2114 7371.57 7122.07 0.2288 7158.70 6888.58 0.2129 7389.67 7122.22 0.2294 7181.87 6888.63 0.2141 7425.87 7122.34 0.2302 7181.87 6888.70

573

0.2163 7421.53 7122.55 0.231 7249.20 6888.76 0.2184 7448.32 7122.73 0.2325 7240.52 6888.87 0.2204 7448.32 7122.90 0.2327 7254.27 6888.89 0.2211 7471.49 7122.95 0.2342 7272.37 6889.00 0.2233 7516.38 7123.11 0.2341 7258.62 6888.99 0.2247 7512.04 7123.20 0.2358 7321.61 6889.10 0.2266 7570.68 7123.33 0.2374 7285.41 6889.21 0.228 7566.34 7123.41 0.2386 7290.48 6889.28 0.229 7562.00 7123.47 0.2386 7285.41 6889.28 0.2302 7588.79 7123.53 0.2396 7254.27 6889.34 0.2319 7575.03 7123.62 0.2403 7290.48 6889.38 0.2341 7624.99 7123.73 0.2397 7267.31 6889.34 0.2357 7643.09 7123.80 0.2416 7294.82 6889.45 0.2376 7679.29 7123.88 0.2425 7317.27 6889.50 0.2382 7733.60 7123.91 0.2435 7299.16 6889.55 0.2392 7724.91 7123.95 0.2444 7357.81 6889.59 0.2412 7761.11 7124.02 0.2447 7349.12 6889.61 0.2431 7761.11 7124.09 0.2462 7367.23 6889.68 0.2445 7779.21 7124.13 0.2465 7385.33 6889.69 0.2452 7833.51 7124.16 0.2469 7317.2658 6889.711203 0.2469 7833.51 7124.21 0.2481 7344.7797 6889.763868 0.2478 7887.82 7124.23 0.2488 7317.2658 6889.793589 0.2485 7896.51 7124.25 0.2494 7331.0227 6889.818495 0.25 7942.12 7124.29 0.2498 7367.2253 6889.834813 0.2505 7996.43 7124.31 0.2503 7353.4683 6889.854894 0.2519 7978.32 7124.34 0.2505 7403.4279 6889.862829 0.253 8018.87 7124.37 0.2521 7385.3266 6889.924361 0.255 7996.43 7124.41 0.2523 7380.9823 6889.931815 0.2567 7987.01 7124.45 0.2537 7371.5696 6889.982564 0.257 8032.63 7124.45 0.2542 7331.0227 6890.000099 0.2583 8014.53 7124.48 0.2551 7335.367 6890.030902 0.2598 8036.97 7124.51 0.2558 7321.6101 6890.054203 0.2603 8045.66 7124.52 0.2555 7317.2658 6890.044287 0.2616 8036.97 7124.54 0.2572 7317.2658 6890.099138 0.2631 8036.97 7124.56 0.2583 7262.9619 6890.132941 0.2635 8009.46 7124.57 0.2594 7290.4758 6890.165475 0.2648 8059.42 7124.59 0.2599 7254.2733 6890.179858 0.2653 8055.07 7124.60 0.2605 7258.6176 6890.196789 0.266 8059.42 7124.61 0.2619 7258.6176 6890.23495 0.2685 8123.14 7124.64 0.2688 8123.14 7124.65 0.27 8136.17 7124.66 0.2707 8105.03 7124.67 0.2714 8105.03 7124.68 0.2721 8131.82 7124.69

574

Table D4: Shear bevameter results for tests at medium pressure and high density.

Medium Pressure (approximately 10 kPa) 1.75 g/cc Density

Grousers: Sandpaper: Calculated Calculated Shear Shear Shear Shear Shear Shear Displacement Stress Stress Displacement Stress Stress -0.0011 189.70 -416.84 -0.0001 117.30 -68.98 -0.0003 221.56 -111.14 0.0005 122.36 333.45 -0.0001 185.36 -36.84 -0.0005 58.65 -352.81 -0.0007 203.46 -262.27 -0.0003 72.41 -209.29 -0.0004 199.11 -148.60 0 90.51 0.00 -0.0005 171.60 -186.28 0.0002 99.20 135.64 -0.0005 199.11 -186.28 0 153.50 0.00 -0.0004 158.57 -148.60 0.0001 112.95 68.20 -0.0008 185.36 -300.59 0.0006 108.61 397.91 -0.0013 185.36 -495.43 0 90.51 0.00 -0.0001 176.67 -36.84 0.0009 72.41 586.99 -0.0005 203.46 -186.28 0.0001 104.26 68.20 -0.0015 176.67 -574.92 0.0001 117.30 68.20 0 199.11 0.00 0.0004 144.81 268.26 -0.0007 199.11 -262.27 0.0002 135.40 135.64 -0.0011 185.36 -416.84 -0.0005 76.75 -352.81 -0.0001 221.56 -36.84 0.0006 94.85 397.91 -0.0011 185.36 -416.84 0 68.06 0.00 -0.0012 217.22 -456.02 0.0004 108.61 268.26 -0.0005 199.11 -186.28 0.0001 131.05 68.20 -0.0008 194.77 -300.59 0.0002 104.26 135.64 0.0004 230.97 145.30 0.0001 99.20 68.20 0.0005 217.22 181.12 0.0002 58.65 135.64 -0.0001 225.90 -36.84 0.0002 58.65 135.64 -0.0007 221.56 -262.27 -0.0008 -108.61 -574.24 -0.0009 194.77 -339.12 -0.0004 -94.85 -280.64 -0.0009 239.66 -339.12 -0.0007 40.55 -499.60 -0.0005 203.46 -186.28 0 62.99 0.00 -0.0012 217.22 -456.02 -0.0001 126.71 -68.98 -0.0003 212.87 -111.14 -0.0005 189.70 -352.81 0.0005 194.77 181.12 0.0005 199.11 333.45 -0.0007 235.32 -262.27 0.0009 307.72 586.99

575

-0.0001 203.46 -36.84 -0.0001 316.41 -68.98 0.0002 212.87 73.06 0.0002 352.61 135.64 -0.0005 207.80 -186.28 0 343.92 0.00 -0.0009 189.70 -339.12 -0.0007 303.38 -499.60 -0.0001 217.22 -36.84 0.0002 334.51 135.64 -0.0004 185.36 -148.60 -0.0011 325.82 -803.31 -0.0003 203.46 -111.14 0 380.13 0.00 -0.0003 185.36 -111.14 0.0005 380.13 333.45 0.0002 176.67 73.06 -0.0005 325.82 -352.81 -0.0004 217.22 -148.60 0.0004 312.07 268.26 -0.0001 181.01 -36.84 0 262.11 0.00 0.0001 221.56 36.63 0.0005 280.21 333.45 -0.0001 217.22 -36.84 -0.0011 293.97 -803.31 -0.0008 189.70 -300.59 0.0008 257.76 524.67 -0.0011 221.56 -416.84 -0.0005 267.18 -352.81 -0.0001 181.01 -36.84 0.0004 207.80 268.26 -0.0003 207.80 -111.14 0 225.90 0.00 0.0001 203.46 36.63 -0.0003 235.32 -209.29 -0.0004 189.70 -148.60 -0.0001 235.32 -68.98 0 225.90 0.00 -0.0004 298.31 -280.64 -0.0007 185.36 -262.27 0.0005 244.01 333.45 -0.0009 212.87 -339.12 -0.0003 235.32 -209.29 -0.0009 212.87 -339.12 0.0002 221.56 135.64 -0.0001 203.46 -36.84 -0.0008 199.11 -574.24 0.0004 217.22 145.30 0.0001 253.42 68.20 0 185.36 0.00 0.0004 257.76 268.26 -0.0003 212.87 -111.14 0.0005 298.31 333.45 0 207.80 0.00 -0.0001 275.86 -68.98 -0.0001 189.70 -36.84 -0.0001 207.80 -68.98 -0.0012 212.87 -456.02 0.0001 217.22 68.20 -0.0012 189.70 -456.02 0.0009 185.36 586.99 -0.0008 225.90 -300.59 0.0004 221.56 268.26 -0.0005 221.56 -186.28 -0.0004 253.42 -280.64 0.0002 199.11 73.06 0.0016 271.52 1004.05 -0.0004 225.90 -148.60 -0.0004 298.31 -280.64 -0.0005 185.36 -186.28 -0.0003 244.01 -209.29 -0.0003 207.80 -111.14 0 221.56 0.00 -0.0004 207.80 -148.60 0.0001 235.32 68.20 -0.0003 185.36 -111.14 -0.0004 217.22 -280.64 0.0001 212.87 36.63 -0.0003 271.52 -209.29 -0.0005 189.70 -186.28 -0.0001 217.22 -68.98 -0.0007 221.56 -262.27 0.0004 221.56 268.26 0.0005 203.46 181.12 0.0005 212.87 333.45 0 189.70 0.00 0.0002 185.36 135.64 0.0001 221.56 36.63 0.0002 225.90 135.64 -0.0011 203.46 -416.84 0.001 207.80 648.61 -0.0004 225.90 -148.60 -0.0005 203.46 -352.81 -0.0001 235.32 -36.84 0.0002 212.87 135.64 -0.0007 225.90 -262.27 0.0009 189.70 586.99 -0.0011 280.21 -416.84 0.0002 257.76 135.64

576

0.0002 267.18 73.06 0.0013 257.76 829.34 -0.0004 303.38 -148.60 0.0002 271.52 135.64 -0.0011 312.07 -416.84 0.0001 239.66 68.20 0 330.17 0.00 -0.0009 203.46 -649.74 -0.0008 388.82 -300.59 0.001 249.07 648.61 -0.0001 384.47 -36.84 0 262.11 0.00 -0.0008 443.12 -300.59 0.0002 325.82 135.64 -0.0004 502.49 -148.60 0.0002 357.68 135.64 -0.0008 556.80 -300.59 0.0005 330.17 333.45 0.0009 642.23 322.39 0.0004 380.13 268.26 0 655.99 0.00 -0.0003 398.23 -209.29 -0.0009 714.64 -339.12 -0.0001 493.08 -68.98 -0.0003 746.50 -111.14 0.0002 565.48 135.64 -0.0004 782.70 -148.60 -0.0001 611.10 -68.98 -0.0005 905.06 -186.28 0.0005 687.85 333.45 -0.0001 963.71 -36.84 -0.0007 724.05 -499.60 0.0001 1122.28 36.63 0.0005 841.35 333.45 -0.0004 1275.78 -148.60 0.0006 991.23 397.91 -0.0007 1416.25 -262.27 0.0001 1122.28 68.20 -0.0003 1611.01 -111.14 -0.0009 1285.19 -649.74 -0.0001 1733.38 -36.84 0.0004 1353.25 268.26 0.0001 1896.29 36.63 -0.0003 1479.96 -209.29 0 1995.49 0.00 -0.0004 1669.66 -280.64 -0.0001 2104.09 -36.84 0.0006 1909.32 397.91 0.0004 2289.45 145.30 0.0016 2258.32 1004.05 0.0005 2484.22 181.12 0.0004 2570.38 268.26 0.0001 2765.15 36.63 0.0001 2886.79 68.20 0.0013 3045.36 460.53 0.0006 3145.28 397.91 0.0012 3334.98 426.29 0.0004 3357.43 268.26 0.0008 3678.91 287.37 0.0006 3638.36 397.91 0.0006 3932.32 216.74 0.0013 3809.96 829.34 0.0018 4190.09 628.89 0.0004 3986.63 268.26 0.0018 4380.51 628.89 0.0018 4195.16 1117.29 0.0017 4461.61 595.59 0.0021 4384.86 1282.42 0.0026 4543.42 888.61 0.0012 4665.79 769.77 0.002 4515.91 694.92 0.0022 4828.70 1336.23 0.003 4493.46 1014.16 0.002 4964.10 1228.00 0.0032 4448.57 1075.89 0.0022 5036.50 1336.23 0.0022 4434.82 760.21 0.0033 5050.26 1889.78 0.0028 4557.18 951.74 0.0033 5167.56 1889.78 0.003 4629.59 1014.16 0.003 5221.86 1745.56 0.0045 4678.82 1460.62 0.0034 5339.88 1936.77 0.0049 4674.48 1573.45 0.0034 5430.39 1936.77 0.0033 4620.17 1106.49 0.0037 5448.49 2074.63 0.0053 4565.87 1683.78 0.0048 5475.28 2541.97 0.0048 4425.40 1545.48 0.005 5416.63 2620.88 0.0053 4402.96 1683.78 0.0053 5420.97 2735.96 0.0061 4434.82 1897.13 0.0046 5457.18 2461.26 0.0073 4493.46 2199.70 0.0049 5511.48 2581.65 0.0079 4638.27 2343.51 0.0059 5593.30 2954.76

577

0.0081 4647.69 2390.37 0.0065 5543.34 3159.23 0.0086 4701.99 2505.26 0.0058 5629.50 2919.31 0.0095 4710.68 2704.10 0.0074 5575.20 3441.11 0.0094 4746.88 2682.50 0.0079 5448.49 3585.78 0.0104 4919.21 2893.13 0.0081 5426.04 3641.39 0.0118 5040.85 3168.82 0.0091 5362.33 3901.41 0.0124 5127.01 3280.50 0.0097 5326.12 4043.91 0.0127 5082.12 3334.94 0.0091 5276.16 3901.41 0.0139 4941.65 3543.75 0.0103 5203.76 4177.08 0.0139 4828.70 3543.75 0.0114 5231.27 4398.99 0.0147 4728.78 3675.33 0.0123 5203.76 4561.14 0.0159 4810.60 3861.94 0.0138 5231.27 4797.35 0.016 4932.24 3876.93 0.0146 5249.37 4907.90 0.0168 5018.40 3993.87 0.0149 5258.06 4946.85 0.0177 5181.31 4119.30 0.0169 5348.57 5175.38 0.0184 5190.73 4212.55 0.0175 5366.67 5234.48 0.0195 5172.62 4351.89 0.0188 5439.08 5349.57 0.02 5140.77 4412.43 0.0196 5507.14 5412.45 0.0208 5077.05 4505.83 0.0216 5493.38 5546.92 0.0212 5077.05 4550.98 0.022 5525.24 5570.36 0.0222 5054.60 4659.50 0.0245 5475.28 5695.15 0.0228 5064.02 4721.75 0.0254 5452.83 5732.12 0.0241 5077.05 4849.64 0.0269 5466.59 5785.98 0.0245 5113.25 4887.14 0.0289 5529.58 5844.98 0.0254 5226.93 4968.51 0.0289 5692.49 5844.98 0.0263 5253.72 5045.87 0.0308 5701.91 5889.95 0.0274 5312.37 5135.25 0.0316 5715.66 5906.18 0.0271 5348.57 5111.42 0.0348 5675.12 5958.26 0.0281 5357.98 5189.32 0.0351 5607.06 5962.25 0.0289 5402.87 5248.56 0.0361 5710.60 5974.60 0.0298 5312.37 5312.11 0.0377 5810.51 5991.68 0.0311 5299.33 5398.40 0.0398 5896.68 6009.89 0.0315 5317.44 5423.71 0.0413 5905.37 6020.50 0.0319 5294.27 5448.45 0.0433 5869.16 6032.12 0.0332 5294.27 5525.14 0.0441 5882.92 6036.08 0.0336 5271.82 5547.63 0.0453 5864.82 6041.39 0.0346 5281.23 5601.70 0.0473 5937.22 6048.78 0.0357 5276.16 5657.76 0.0477 5991.53 6050.07 0.0368 5303.68 5710.47 0.05 5973.43 6056.46 0.0367 5434.73 5705.81 0.0512 5964.01 6059.19 0.0375 5493.38 5742.35 0.0528 5901.02 6062.29 0.0385 5579.54 5785.77 0.0547 5882.92 6065.32 0.0394 5579.54 5822.82 0.0563 5937.22 6067.42 0.0409 5457.18 5880.56 0.0579 5959.67 6069.17 0.0416 5416.63 5905.88 0.0588 6045.83 6070.02 0.0426 5353.64 5940.36 0.0608 6000.22 6071.63 0.044 5308.02 5985.50 0.0625 5995.87 6072.74 0.0442 5276.16 5991.67 0.0642 5995.87 6073.66 0.0455 5308.02 6030.09 0.0654 6023.39 6074.21 0.0462 5457.18 6049.64 0.0666 6131.99 6074.69

578

0.0477 5507.14 6089.04 0.0665 6150.09 6074.65 0.0487 5579.54 6113.52 0.07 6118.24 6075.75 0.0499 5565.78 6141.13 0.0699 6054.52 6075.72 0.0507 5493.38 6158.54 0.072 5964.01 6076.20 0.0518 5493.38 6181.22 0.0732 5991.53 6076.43 0.0534 5407.94 6211.81 0.074 6054.52 6076.56 0.0534 5389.84 6211.81 0.0757 6181.23 6076.81 0.0548 5412.29 6236.42 0.0773 6226.84 6077.01 0.0565 5502.79 6263.80 0.0779 6100.14 6077.08 0.0568 5593.30 6268.37 0.0793 6082.03 6077.21 0.059 5565.78 6299.61 0.0806 6068.28 6077.32 0.0602 5543.34 6315.09 0.0809 6136.34 6077.34 0.0604 5498.45 6317.57 0.0822 6249.29 6077.43 0.062 5416.63 6336.44 0.0834 6281.15 6077.50 0.0637 5398.53 6354.71 0.0843 6249.29 6077.55 0.0641 5362.33 6358.76 0.0853 6176.88 6077.60 0.0661 5407.94 6377.71 0.0865 6199.33 6077.65 0.0675 5480.35 6389.76 0.0878 6326.04 6077.70 0.0685 5489.04 6397.81 0.0902 6430.30 6077.77 0.0691 5480.35 6402.42 0.0904 6557.01 6077.77 0.071 5398.53 6416.05 0.0918 6520.81 6077.81 0.0734 5394.18 6431.31 0.0927 6434.65 6077.83 0.0741 5353.64 6435.39 0.0941 6448.40 6077.85 0.0751 5289.92 6440.94 0.0943 6462.16 6077.85 0.0765 5348.57 6448.21 0.0953 6584.53 6077.87 0.078 5380.43 6455.39 0.0961 6629.42 6077.88 0.0784 5452.83 6457.20 0.0988 6643.17 6077.91 0.08 5480.35 6464.06 0.0993 6615.66 6077.92 0.0814 5470.93 6469.58 0.1005 6588.87 6077.93 0.0828 5475.28 6474.68 0.1018 6611.32 6077.94 0.0847 5439.08 6480.99 0.1033 6625.07 6077.95 0.0857 5452.83 6484.05 0.1034 6651.86 6077.95 0.0874 5462.25 6488.88 0.1055 6679.38 6077.96 0.0879 5448.49 6490.21 0.107 6575.11 6077.97 0.0891 5561.44 6493.26 0.1075 6570.77 6077.97 0.0915 5629.50 6498.78 0.1091 6534.57 6077.97 0.0919 5674.39 6499.63 0.1102 6552.67 6077.98 0.0933 5661.36 6502.46 0.1118 6557.01 6077.98 0.0955 5620.09 6506.47 0.1137 6525.15 6077.98 0.0967 5597.64 6508.46 0.1137 6502.71 6077.98 0.0976 5534.65 6509.87 0.1157 6462.16 6077.99 0.0985 5565.78 6511.21 0.1174 6462.16 6077.99 0.1005 5607.06 6513.95 0.1182 6543.25 6077.99 0.102 5661.36 6515.81 0.1202 6575.11 6077.99 0.1029 5819.20 6516.86 0.1224 6647.52 6077.99 0.1047 5842.37 6518.80 0.1229 6561.36 6077.99 0.1054 5851.06 6519.50 0.1257 6488.95 6078.00 0.1074 5882.92 6521.36 0.1259 6462.16 6078.00 0.1092 5887.26 6522.86 0.1283 6439.72 6078.00 0.1108 5941.57 6524.08 0.1295 6538.91 6078.00

579

0.1122 5955.32 6525.06 0.1315 6570.77 6078.00 0.1127 6045.83 6525.39 0.1333 6570.77 6078.00 0.1137 6072.62 6526.02 0.1335 6530.22 6078.00 0.1156 6086.38 6527.13 0.1353 6462.16 6078.00 0.1173 6145.03 6528.03 0.1364 6516.46 6078.00 0.1196 6104.48 6529.12 0.1377 6552.67 6078.00 0.1213 6113.89 6529.84 0.1392 6579.46 6078.00 0.1221 6126.92 6530.15 0.1419 6606.97 6078.00 0.1235 6104.48 6530.67 0.1423 6552.67 6078.00 0.1253 6145.03 6531.28 0.1451 6552.67 6078.00 0.1262 6168.20 6531.56 0.1457 6525.15 6078.00 0.1282 6213.09 6532.14 0.1468 6543.25 6078.00 0.1295 6235.53 6532.48 0.1487 6606.97 6078.00 0.131 6213.09 6532.85 0.1498 6593.21 6078.00 0.1318 6258.70 6533.03 0.1513 6611.32 6078.00 0.1333 6204.40 6533.35 0.1531 6520.81 6078.00 0.1349 6244.95 6533.67 0.1549 6525.15 6078.00 0.1376 6289.84 6534.13 0.1552 6561.36 6078.00 0.1382 6285.49 6534.23 0.1569 6570.77 6078.00 0.1393 6331.11 6534.40 0.1578 6615.66 6078.00 0.1412 6317.35 6534.66 0.1589 6557.01 6078.00 0.1426 6307.94 6534.84 0.1613 6530.22 6078.00 0.1434 6349.21 6534.93 0.1613 6561.36 6078.00 0.1453 6344.14 6535.14 0.1635 6557.01 6078.00 0.1473 6362.24 6535.34 0.1647 6625.07 6078.00 0.1478 6321.69 6535.38 0.1657 6643.17 6078.00 0.1499 6353.55 6535.56 0.1653 6675.03 6078.00 0.1529 6357.90 6535.79 0.1672 6711.23 6078.00 0.1527 6344.14 6535.77 0.1696 6647.52 6078.00 0.1541 6448.40 6535.87 0.1708 6661.28 6078.00 0.157 6439.72 6536.04 0.1715 6615.66 6078.00 0.1578 6452.75 6536.08 0.1729 6633.76 6078.00 0.1594 6502.71 6536.16 0.1748 6675.03 6078.00 0.1613 6470.85 6536.24 0.1764 6675.03 6078.00 0.1626 6516.46 6536.30 0.1782 6733.68 6078.00 0.1651 6534.57 6536.39 0.1782 6729.34 6078.00 0.1665 6557.01 6536.44 0.1796 6760.47 6078.00 0.1682 6557.01 6536.49 0.1805 6742.37 6078.00 0.1686 6561.36 6536.50 0.1827 6679.38 6078.00 0.1708 6620.73 6536.56 0.1839 6738.02 6078.00 0.1716 6588.87 6536.58 0.186 6751.78 6078.00 0.1735 6633.76 6536.62 0.1872 6792.33 6078.00 0.1755 6661.28 6536.66 0.1883 6769.88 6078.00 0.1764 6629.42 6536.68 0.1894 6665.62 6078.00 0.1781 6697.48 6536.71 0.1912 6629.42 6078.00 0.179 6706.17 6536.72 0.1924 6588.87 6078.00 0.1804 6724.27 6536.74 0.1937 6615.66 6078.00 0.1809 6765.54 6536.75 0.1949 6625.07 6078.00 0.1823 6756.13 6536.77 0.1965 6593.21 6078.00 0.1843 6792.33 6536.79 0.1977 6615.66 6078.00

580

0.1855 6792.33 6536.81 0.2001 6593.21 6078.00 0.187 6846.63 6536.82 0.2011 6647.52 6078.00 0.1875 6878.49 6536.83 0.2035 6706.17 6078.00 0.1887 6864.73 6536.84 0.2046 6715.58 6078.00 0.1899 6937.14 6536.85 0.2058 6747.44 6078.00 0.1915 6900.94 6536.86 0.2071 6733.68 6078.00 0.192 6937.14 6536.87 0.2086 6738.02 6078.00 0.194 6950.90 6536.88 0.2095 6697.48 6078.00 0.1948 6914.69 6536.88 0.2123 6615.66 6078.00 0.1952 6969.00 6536.89 0.2135 6588.87 6078.00 0.1968 6959.58 6536.90 0.214 6552.67 6078.00 0.1974 6959.58 6536.90 0.217 6566.42 6078.00 0.1985 6964.65 6536.91 0.2186 6593.21 6078.00 0.1989 6995.79 6536.91 0.2185 6570.77 6078.00 0.1996 7027.65 6536.91 0.2207 6570.77 6078.00 0.2009 7009.54 6536.92 0.2225 6552.67 6078.00 0.2017 7045.75 6536.92 0.2235 6588.87 6078.00 0.2035 7063.85 6536.93 0.2238 6656.93 6078.00 0.2037 7045.75 6536.93 0.2259 6647.52 6078.00 0.2059 7091.36 6536.94 0.2272 6679.38 6078.00 0.2054 7086.29 6536.94 0.2287 6625.07 6078.00 0.207 7081.95 6536.94 0.2278 6647.52 6078.00 0.2075 7077.60 6536.94 0.2297 6679.38 6078.00 0.2092 7013.89 6536.95 0.2311 6665.62 6078.00 0.2088 7045.75 6536.95 0.232 6719.9232 6078 0.2115 7037.06 6536.95 0.2331 6656.9307 6078 0.2129 7086.29 6536.96 0.2352 6625.0724 6078 0.2139 7081.95 6536.96 0.2358 6625.0724 6078 0.2143 7068.19 6536.96 0.2374 6633.761 6078 0.2164 7109.46 6536.97 0.2382 6693.1333 6078 0.2172 7091.36 6536.97 0.2391 6669.9636 6078 0.2176 7100.05 6536.97 0.2402 6683.7206 6078 0.2193 7104.39 6536.97 0.2417 6706.1662 6078 0.2215 7050.09 6536.97 0.2439 6661.275 6078 0.2229 7118.15 6536.98 0.2435 6679.3763 6078 0.2242 7127.56 6536.98 0.2454 6643.1737 6078 0.226 7136.25 6536.98 0.2462 6643.1737 6078 0.2274 7140.60 6536.98 0.2476 6647.518 6078 0.2291 7095.71 6536.98 0.2491 6625.0724 6078 0.2299 7127.56 6536.98 0.2496 6675.032 6078 0.2307 7118.15 6536.98 0.2509 6679.3763 6078 0.2312 7163.77 6536.99 0.252 6643.1737 6078 0.2324 7208.66 6536.99 0.2533 6625.0724 6078 0.2336 7181.87 6536.99 0.2554 6552.6672 6078 0.2344 7240.52 6536.99 0.2558 6584.5255 6078 0.2354 7240.52 6536.99 0.2573 6629.4167 6078 0.2365 7267.31 6536.99 0.2582 6693.1333 6078 0.2366 7281.06 6536.99 0.2603 6756.1257 6078 0.2377 7258.62 6536.99 0.2615 6729.3358 6078 0.239 7303.51 6536.99 0.2615 6575.1128 6078

581

0.2394 7308.58 6536.99 0.2634 6317.3505 6078 0.24 7335.37 6536.99 0.2642 6226.844 6078 0.2409 7367.23 6536.99 0.2655 6271.7352 6078 0.2423 7362.88 6536.99 0.2658 6321.6948 6078 0.2429 7407.77 6536.99 0.2676 6425.9582 6078 0.2439 7394.02 6536.99 0.2688 6434.6468 6078 0.2443 7425.87 6536.99 0.2693 6470.8494 6078 0.2454 7435.29 6536.99 0.2705 6494.0191 6078 0.2458 7389.67 6536.99 0.2712 6466.5051 6078 0.2467 7412.12 6536.99 0.2723 6498.3634 6078 0.2479 7357.81 6536.99 0.2725 6470.8494 6078 0.2483 7367.23 6536.99 0.2741 6466.5051 6078 0.2499 7371.57 6536.99 0.2742 6480.2621 6078 0.2503 7353.47 6536.99 0.2742 6412.2012 6078 0.2501 7399.08 6536.99 0.2744 6412.2012 6078 0.2513 7353.47 6537.00 0.2528 7339.71 6537.00 0.2532 7331.02 6537.00 0.2541 7285.41 6537.00 0.2554 7308.58 6537.00 0.2556 7285.41 6537.00 0.2569 7285.41 6537.00 0.2574 7290.48 6537.00 0.2586 7249.20 6537.00 0.259 7281.06 6537.00 0.2606 7267.31 6537.00 0.261 7272.37 6537.00 0.2617 7308.58 6537.00 0.2629 7299.16 6537.00 0.2642 7344.78 6537.00 0.2637 7335.37 6537.00 0.2642 7371.57 6537.00 0.2658 7394.02 6537.00 0.266 7349.12 6537.00 0.2668 7399.08 6537.00 0.2675 7412.12 6537.00 0.2686 7443.97 6537.00 0.2678 7498.28 6537.00 0.2686 7471.49 6537.00 0.2694 7448.32 6537.00 0.2707 7371.57 6537.00 0.2717 7344.78 6537.00 0.2724 7349.12 6537.00 0.2732 7344.78 6537.00 0.2741 7380.98 6537.00 0.2745 7394.02 6537.00 0.2754 7462.08 6537.00 0.2762 7516.38 6537.00 0.2769 7498.28 6537.00 0.2761 7498.279 6537.00

582

0.2773 7430.22 6537.00 0.2782 7389.67 6537.00 0.2788 7385.33 6537.00 0.2793 7335.37 6537.00 0.2788 7353.47 6537.00

Table D5: Shear bevameter results for tests at high pressure and low density.

High Pressure (approximately 30 kPa) 1.64 g/cc Density

Grousers: Sandpaper: Calculated Calculated Shear Shear Shear Shear Shear Shear Displacement Stress Stress Displacement Stress Stress -0.0005 -144.81 -392.53 -0.0042 579.24 -2217.70 0.0003 -122.36 231.82 -0.0053 561.14 -2839.96 -0.0008 -131.05 -631.80 -0.0037 569.83 -1940.73 -0.0008 -149.15 -631.80 -0.005 597.34 -2668.47 -0.0005 -131.05 -392.53 -0.0041 565.48 -2162.02 -0.0008 -158.57 -631.80 -0.0049 597.34 -2611.61 -0.0006 -112.95 -471.97 -0.0042 569.83 -2217.70 0.0004 -126.71 308.49 -0.004 587.93 -2106.48 -0.0004 -144.81 -313.40 -0.0054 597.34 -2897.42 -0.0005 -122.36 -392.53 -0.0044 587.93 -2329.51 -0.0004 -149.15 -313.40 -0.0046 633.55 -2441.91 -0.0002 -122.36 -156.08 -0.004 615.44 -2106.48 -0.0005 -112.95 -392.53 -0.0052 629.20 -2782.65 -0.0004 -131.05 -313.40 -0.0052 647.30 -2782.65 0 -86.16 0.00 -0.0045 629.20 -2385.64 -0.0005 -131.05 -392.53 -0.0054 651.65 -2897.42 -0.0001 -94.85 -77.89 -0.0052 624.13 -2782.65 -0.0005 -99.20 -392.53 -0.004 647.30 -2106.48 0.0002 -112.95 154.85 -0.0045 665.40 -2385.64 -0.0009 -76.75 -712.18 -0.0045 642.23 -2385.64 -0.0006 -122.36 -471.97 -0.0046 683.50 -2441.91 -0.0002 -94.85 -156.08 -0.0038 651.65 -1995.83 -0.0022 -112.95 -1786.64 -0.0044 647.30 -2329.51 0.0005 -122.36 384.85 -0.0037 665.40 -1940.73 -0.0001 -81.09 -77.89 -0.0046 629.20 -2441.91 -0.0002 -90.51 -156.08 -0.0049 651.65 -2611.61 0.0007 -54.30 536.68 -0.0044 619.79 -2329.51 -0.0004 -36.20 -313.40 -0.004 633.55 -2106.48 -0.0002 -44.89 -156.08 -0.0044 637.89 -2329.51 -0.0002 -4.34 -156.08 -0.0041 615.44 -2162.02 -0.0005 -44.89 -392.53 -0.0049 647.30 -2611.61 -0.0006 -18.10 -471.97 -0.0042 606.03 -2217.70

583

0.0003 -27.51 231.82 -0.0046 624.13 -2441.91 0.0007 -49.96 536.68 -0.0042 637.89 -2217.70 -0.0001 0.00 -77.89 -0.0038 611.10 -1995.83 -0.0001 -36.20 -77.89 -0.0045 629.20 -2385.64 0.0008 -9.41 612.14 -0.004 597.34 -2106.48 0.0008 -13.76 612.14 -0.0045 597.34 -2385.64 0.0003 -40.55 231.82 -0.0045 611.10 -2385.64 -0.0001 -9.41 -77.89 -0.005 579.24 -2668.47 -0.0012 -44.89 -955.26 -0.0046 615.44 -2441.91 -0.0009 -18.10 -712.18 -0.0042 579.24 -2217.70 -0.0002 -18.10 -156.08 -0.0044 597.34 -2329.51 -0.001 -40.55 -792.89 -0.0044 633.55 -2329.51 -0.0005 -9.41 -392.53 -0.0037 574.90 -1940.73 0 -40.55 0.00 -0.004 611.10 -2106.48 -0.0012 -18.10 -955.26 -0.0046 587.93 -2441.91 -0.0013 -18.10 -1036.93 -0.0042 601.69 -2217.70 -0.0005 -31.86 -392.53 -0.0042 624.13 -2217.70 0.0008 -9.41 612.14 -0.0053 597.34 -2839.96 -0.0002 -31.86 -156.08 -0.0034 629.20 -1776.27 0 -4.34 0.00 -0.005 606.03 -2668.47 -0.0001 -18.10 -77.89 -0.0042 624.13 -2217.70 -0.0001 -36.20 -77.89 -0.0048 642.23 -2554.89 -0.0004 13.76 -313.40 -0.0048 619.79 -2554.89 -0.0006 -27.51 -471.97 -0.0042 669.75 -2217.70 -0.0005 4.34 -392.53 -0.0044 633.55 -2329.51 -0.0001 13.76 -77.89 -0.0045 647.30 -2385.64 -0.0005 -27.51 -392.53 -0.0048 655.99 -2554.89 0.0007 8.69 536.68 -0.0041 624.13 -2162.02 -0.0002 -27.51 -156.08 -0.0046 642.23 -2441.91 -0.0008 -9.41 -631.80 -0.0041 611.10 -2162.02 -0.0005 -13.76 -392.53 -0.0044 619.79 -2329.51 -0.0001 0.00 -77.89 -0.0046 624.13 -2441.91 -0.0002 31.86 -156.08 -0.0049 601.69 -2611.61 -0.0001 18.10 -77.89 -0.0044 624.13 -2329.51 0.0004 54.30 308.49 -0.0042 611.10 -2217.70 0.0002 62.99 154.85 -0.0044 624.13 -2329.51 -0.0001 44.89 -77.89 -0.004 660.34 -2106.48 -0.0006 86.16 -471.97 -0.0045 633.55 -2385.64 0.0007 49.96 536.68 -0.0044 665.40 -2329.51 -0.0008 86.16 -631.80 -0.0045 669.75 -2385.64 -0.0004 90.51 -313.40 -0.0045 678.44 -2385.64 0.0002 76.75 154.85 -0.0044 724.05 -2329.51 -0.0005 99.20 -392.53 -0.0046 701.61 -2441.91 0.0003 76.75 231.82 -0.0037 724.05 -1940.73 -0.0002 86.16 -156.08 -0.0044 696.54 -2329.51 -0.0005 72.41 -392.53 -0.004 696.54 -2106.48 -0.0002 54.30 -156.08 -0.0041 719.71 -2162.02 -0.0004 90.51 -313.40 -0.0053 692.19 -2839.96 -0.0006 54.30 -471.97 -0.0048 732.74 -2554.89 -0.0004 94.85 -313.40 -0.0042 728.40 -2217.70

584

0 90.51 0.00 -0.0042 732.74 -2217.70 0.0002 86.16 154.85 -0.0046 760.25 -2441.91 -0.0008 112.95 -631.80 -0.0042 737.81 -2217.70 -0.0002 99.20 -156.08 -0.0048 774.01 -2554.89 -0.0009 126.71 -712.18 -0.0046 768.94 -2441.91 -0.0004 140.47 -313.40 -0.0041 814.56 -2162.02 -0.0002 140.47 -156.08 -0.0049 846.42 -2611.61 0.0002 199.11 154.85 -0.0045 864.52 -2385.64 0.0004 199.11 308.49 -0.0041 949.96 -2162.02 -0.0009 257.76 -712.18 -0.0042 995.57 -2217.70 -0.0001 275.86 -77.89 -0.0044 1108.52 -2329.51 0 289.62 0.00 -0.0044 1239.58 -2329.51 -0.0001 348.27 -77.89 -0.0038 1339.50 -1995.83 -0.0005 380.13 -392.53 -0.004 1506.75 -2106.48 -0.0004 493.08 -313.40 -0.0044 1624.77 -2329.51 -0.0008 574.90 -631.80 -0.0036 1778.27 -1885.77 -0.0004 647.30 -313.40 -0.0046 1973.04 -2441.91 0.0004 782.70 308.49 -0.0053 2140.30 -2839.96 -0.0005 868.86 -392.53 -0.0042 2403.13 -2217.70 -0.0002 1018.02 -156.08 -0.0042 2620.34 -2217.70 -0.0002 1172.24 -156.08 -0.0042 2886.79 -2217.70 -0.0005 1317.05 -392.53 -0.0046 3153.97 -2441.91 -0.0004 1506.75 -313.40 -0.0048 3398.70 -2554.89 -0.0012 1619.70 -955.26 -0.0052 3710.76 -2782.65 0 1773.93 0.00 -0.0049 3982.28 -2611.61 0.0002 1878.19 154.85 -0.0048 4326.21 -2554.89 -0.0006 1977.39 -471.97 -0.0042 4660.72 -2217.70 0.0002 2117.85 154.85 -0.0049 4937.31 -2611.61 0.0008 2208.36 612.14 -0.0054 5245.03 -2897.42 -0.0006 2375.61 -471.97 -0.0045 5470.93 -2385.64 -0.0002 2506.67 -156.08 -0.0042 5746.80 -2217.70 -0.0004 2629.03 -313.40 -0.0037 6023.39 -1940.73 -0.0008 2805.70 -631.80 -0.0044 6267.39 -2329.51 0.0004 2932.41 308.49 -0.0038 6575.11 -1995.83 -0.001 3109.08 -792.89 -0.0041 6824.19 -2162.02 -0.0009 3226.37 -712.18 -0.0044 7086.29 -2329.51 -0.0004 3308.19 -313.40 -0.0046 7394.02 -2441.91 0.0004 3403.04 308.49 -0.0037 7638.74 -1940.73 0.0002 3380.60 154.85 -0.0034 7960.22 -1776.27 0.0002 3290.09 154.85 -0.0042 8204.23 -2217.70 -0.0002 3226.37 -156.08 -0.0041 8407.69 -2162.02 -0.0002 3298.78 -156.08 -0.0042 8557.57 -2217.70 0.0012 3457.35 911.03 -0.0036 8521.36 -1885.77 0 3547.85 0.00 -0.0038 8362.80 -1995.83 0.0004 3688.32 308.49 -0.003 7914.61 -1559.00 0.0008 3783.17 612.14 -0.0023 7367.23 -1184.21 0.0011 3859.92 836.75 -0.0017 6828.53 -868.38 0.0011 4009.07 836.75 -0.0008 6398.44 -403.84 0.0028 4072.79 2060.47 -0.0003 6263.05 -150.45 0.0015 4231.36 1132.12 0.0004 6258.70 198.77

585

0.0025 4421.06 1850.45 0.0009 6353.55 444.32 0.0021 4652.03 1566.52 0.0026 6394.10 1255.56 0.0024 4964.10 1779.89 0.003 6444.06 1441.25 0.0027 5154.52 1990.74 0.0045 6693.13 2120.53 0.0036 5285.58 2608.51 0.0058 7059.50 2688.04 0.0047 5344.23 3334.34 0.0073 7534.48 3319.31 0.0044 5380.43 3139.50 0.0085 7928.37 3806.77 0.0043 5516.55 3074.04 0.0098 8131.82 4317.86 0.0052 5656.29 3653.98 0.0101 8290.39 4433.36 0.0058 5851.06 4029.30 0.0109 8435.20 4736.95 0.0064 5969.08 4395.83 0.0118 8742.92 5070.97 0.0057 6113.89 3967.36 0.0138 9041.23 5785.66 0.006 6389.76 4152.44 0.0144 9159.25 5992.87 0.0068 6679.38 4635.41 0.016 9254.10 6529.78 0.0068 7104.39 4635.41 0.0175 9367.06 7013.12 0.0069 7562.00 4694.71 0.0189 9539.38 7447.43 0.007 8000.77 4753.78 0.0197 9747.18 7688.55 0.0065 8349.04 4456.08 0.0207 9860.86 7982.94 0.0078 8362.80 5218.03 0.022 10104.86 8354.30 0.0076 8236.09 5103.34 0.0226 10448.79 8521.48 0.0074 7982.67 4987.74 0.0242 10910.73 8954.67 0.007 7765.45 4753.78 0.0258 11421.91 9370.09 0.0073 7688.70 4929.60 0.026 11783.94 9420.81 0.0066 7656.85 4516.09 0.0274 11856.35 9768.47 0.0068 7896.51 4635.41 0.029 11693.43 10150.51 0.007 8267.95 4753.78 0.0299 11679.68 10358.48 0.007 8702.38 4753.78 0.0306 11788.28 10516.88 0.007 9104.95 4753.78 0.0317 11842.59 10760.00 0.007 9290.31 4753.78 0.033 11983.05 11038.45 0.0076 9448.87 5103.34 0.0331 12182.17 11059.47 0.0068 9543.72 4635.41 0.0347 12544.19 11388.56 0.0061 9638.58 4213.65 0.0351 12987.31 11468.70 0.007 9792.80 4753.78 0.0358 13286.35 11606.94 0.0077 9792.80 5160.80 0.0368 13358.75 11800.08 0.0069 9584.27 4694.71 0.0372 13250.14 11875.93 0.0072 9073.09 4871.22 0.0379 13272.59 12006.78 0.0073 8543.81 4929.60 0.0388 13467.36 12171.52 0.0076 8217.99 5103.34 0.0393 13625.93 12261.38 0.0084 8136.17 5556.72 0.0405 13688.92 12472.31 0.0085 8358.45 5612.39 0.04 13670.82 12385.23 0.0081 8706.72 5388.38 0.0417 13847.49 12676.72 0.0093 9136.81 6049.93 0.0407 14145.80 12506.83 0.0092 9634.23 5995.99 0.0413 14394.87 12609.30 0.0107 10005.67 6783.14 0.0415 14507.82 12643.10 0.011 10267.78 6935.04 0.0428 14250.06 12858.54 0.0107 10259.09 6783.14 0.0432 13987.95 12923.36 0.0114 10122.97 7134.81 0.044 13901.79 13051.00 0.0123 10109.21 7572.90 0.0437 13865.59 13003.45 0.0121 10132.38 7476.89 0.0448 13797.53 13175.99 0.0129 10249.67 7856.43 0.0448 13662.13 13175.99

586

0.013 10376.38 7903.03 0.0454 13725.12 13268.03 0.0134 10571.15 8087.62 0.0457 13996.64 13313.51 0.0134 10896.98 8087.62 0.047 14141.45 13506.52 0.0139 11096.09 8314.29 0.0475 14069.05 13579.02 0.0143 11136.64 8492.43 0.0482 14100.91 13678.94 0.0141 11037.44 8403.71 0.049 14431.07 13790.92 0.015 10996.17 8797.48 0.0495 14571.54 13859.72 0.0158 11100.44 9135.94 0.0505 14408.63 13994.66 0.0155 11168.50 9010.27 0.0503 14336.22 13967.95 0.017 11327.06 9623.98 0.0523 14481.03 14228.81 0.0167 11399.47 9504.13 0.0524 14829.30 14241.50 0.0168 11358.20 9544.24 0.0539 15024.07 14427.89 0.0174 11417.57 9781.59 0.0544 15019.73 14488.41 0.0172 11584.83 9703.10 0.0558 15078.38 14653.71 0.0191 11770.18 10424.32 0.0564 15060.27 14722.73 0.018 11774.53 10013.38 0.0564 15064.62 14722.73 0.019 11860.69 10387.70 0.0584 14996.56 14945.09 0.0195 12114.11 10569.38 0.0593 14996.56 15041.42 0.02 11906.31 10747.51 0.0599 15150.78 15104.38 0.0204 11566.72 10887.51 0.0617 15249.98 15287.46 0.0211 11598.58 11127.23 0.0632 15277.49 15433.58 0.0223 12033.01 11523.08 0.0638 15241.29 15490.43 0.0229 12503.65 11714.08 0.0649 15186.98 15592.38 0.0233 12779.51 11838.92 0.0666 15295.59 15744.27 0.0233 13132.12 11838.92 0.0678 15390.44 15847.49 0.0245 13240.73 12201.82 0.0686 15386.10 15914.53 0.0252 12892.46 12405.70 0.0699 15327.45 16020.51 0.0253 12467.45 12434.37 0.0718 15263.73 16169.06 0.026 12232.13 12631.91 0.0731 15454.16 16266.52 0.0266 12367.53 12796.93 0.075 15684.41 16403.13 0.0272 12516.68 12958.09 0.0758 15793.01 16458.65 0.0272 12675.25 12958.09 0.0765 15698.16 16506.28 0.0284 12956.18 13269.17 0.0776 15675.72 16579.40 0.0292 13055.37 13468.51 0.0793 15951.58 16688.33 0.0296 13028.59 13565.85 0.0807 16082.63 16774.46 0.0301 12982.97 13685.37 0.0817 16087.70 16834.09 0.0315 13005.42 14007.75 0.0832 16128.25 16920.65 0.0306 12938.08 13802.56 0.0842 16236.86 16976.49 0.0323 12783.86 14184.12 0.0853 16440.32 17036.26 0.0319 12919.98 14096.63 0.0862 16526.48 17083.89 0.0329 13209.60 14312.78 0.0873 16512.72 17140.61 0.0342 13358.75 14581.31 0.0883 16526.48 17190.77 0.0342 13499.22 14581.31 0.0894 16612.64 17244.45 0.0351 13584.66 14759.30 0.0909 16757.45 17315.21 0.0351 13557.87 14759.30 0.0919 16707.49 17360.86 0.0366 13376.85 15042.25 0.0922 16643.77 17374.32 0.0375 13340.65 15204.14 0.0938 16612.64 17444.37 0.039 13444.91 15461.48 0.0955 16526.48 17515.65 0.0383 13313.14 15343.28 0.096 16535.17 17536.02 0.0403 13399.30 15672.51 0.0979 16522.13 17611.04

587

0.0403 13598.41 15672.51 0.0983 16589.47 17626.36 0.0408 13602.76 15750.83 0.0993 16743.69 17663.97 0.042 13657.06 15932.61 0.1011 16892.85 17729.24 0.0423 13996.64 15976.73 0.1017 17005.80 17750.32 0.0437 14300.02 16175.82 0.1037 16902.26 17818.25 0.0452 14078.46 16377.26 0.1052 16866.06 17866.91 0.046 13888.03 16479.91 0.1062 16924.71 17898.31 0.0466 13956.10 16554.80 0.1071 16942.81 17925.87 0.0476 13788.84 16675.74 0.1082 16987.70 17958.68 0.0486 13711.37 16791.99 0.1102 16997.11 18015.98 0.0497 14100.91 16914.67 0.1122 17123.82 18070.36 0.0502 14422.38 16968.70 0.112 17359.14 18065.05 0.0509 14422.38 17042.57 0.1136 17540.15 18106.76 0.0521 14507.82 17164.54 0.1148 17703.06 18136.92 0.0527 14824.96 17223.39 0.1163 17775.47 18173.32 0.0537 14621.50 17318.43 0.1173 17852.22 18196.79 0.0543 14295.68 17373.68 0.1201 17856.56 18259.36 0.0566 14512.89 17573.73 0.1197 17721.16 18250.70 0.057 14666.39 17606.71 0.1209 17639.35 18276.41 0.0574 14444.83 17639.16 0.1228 17621.24 18315.50 0.0583 14399.21 17710.35 0.1248 17729.85 18354.59 0.0594 14756.90 17793.98 0.1249 17902.18 18356.50 0.0603 15074.03 17859.75 0.1259 17992.68 18375.24 0.0612 15218.84 17923.22 0.127 18155.59 18395.30 0.0625 15671.37 18011.02 0.1293 18209.90 18435.43 0.0636 15979.10 18081.86 0.1295 18264.20 18438.80 0.065 15784.33 18167.69 0.1312 18290.99 18466.80 0.066 15635.17 18226.15 0.1324 18277.96 18485.83 0.0664 15508.46 18248.90 0.1343 18354.71 18514.75 0.0672 15227.53 18293.32 0.1357 18350.36 18535.17 0.0685 15087.06 18362.59 0.1364 18517.62 18545.10 0.0695 15621.41 18413.50 0.1369 18634.92 18552.08 0.0699 16341.12 18433.31 0.1388 18616.82 18577.79 0.0711 16612.64 18490.89 0.1383 18752.94 18571.15 0.0725 16784.24 18554.71 0.1399 18802.90 18592.10 0.073 16956.57 18576.66 0.1409 18807.24 18604.76 0.0744 16829.86 18635.87 0.1417 18730.49 18614.65 0.0747 16544.58 18648.13 0.1428 18576.27 18627.92 0.0775 16354.15 18755.87 0.144 18580.61 18641.96 0.0774 16254.96 18752.22 0.1444 18608.13 18646.54 0.0783 16069.60 18784.53 0.1469 18694.29 18674.13 0.0789 16092.05 18805.43 0.147 18857.20 18675.20 0.0805 16390.36 18858.82 0.1485 19078.76 18690.86 0.082 16472.17 18905.89 0.1506 19209.81 18711.78 0.0821 16508.38 18908.93 0.1506 19191.71 18711.78 0.0836 16739.35 18953.12 0.1522 19128.72 18726.97 0.085 16866.06 18992.07 0.1531 18952.05 18735.23 0.086 16798.00 19018.60 0.1548 18752.94 18750.33 0.0868 16752.38 19039.08 0.1565 18752.94 18764.77 0.0872 16779.90 19049.08 0.1575 18771.04 18772.96

588

0.0889 16661.88 19089.87 0.1584 18857.20 18780.16 0.0902 16679.98 19119.26 0.1607 18952.05 18797.80 0.0921 16960.91 19159.59 0.1618 19033.15 18805.86 0.0927 16979.01 19171.71 0.1633 19137.41 18816.50 0.0935 16938.46 19187.43 0.1659 19110.62 18833.97 0.0951 17010.87 19217.42 0.1667 18988.25 18839.11 0.097 16992.77 19250.65 0.1687 18815.93 18851.50 0.0993 16811.75 19287.68 0.1698 18571.92 18858.04 0.1001 16761.80 19299.79 0.1708 18350.36 18863.83 0.1001 17028.97 19299.79 0.172 18141.84 18870.57 0.1025 17141.92 19333.91 0.1736 18087.53 18879.25 0.1028 17250.53 19337.95 0.175 18209.90 18886.54 0.105 17535.81 19366.18 0.1763 18336.61 18893.08 0.1057 17503.95 19374.65 0.1776 18535.72 18899.40 0.1066 17318.59 19385.21 0.1784 18671.12 18903.19 0.1087 17191.88 19408.44 0.1801 18807.24 18910.97 0.1095 17019.56 19416.80 0.1814 18902.09 18916.69 0.1109 16757.45 19430.80 0.1828 18938.29 18922.64 0.1127 16666.94 19447.70 0.1837 18974.50 18926.35 0.1139 16811.75 19458.31 0.1854 18956.40 18933.13 0.1142 16748.04 19460.89 0.1862 19015.04 18936.21 0.1158 16834.20 19474.13 0.1865 19096.86 18937.35 0.1174 17286.73 19486.55 0.1894 19101.21 18947.93 0.1188 17512.64 19496.80 0.1902 19155.51 18950.71 0.1191 17590.11 19498.92 0.19 19096.862 18950.02 0.1208 17811.67 19510.49 0.1916 19006.355 18955.43 0.122 17924.62 19518.20 0.1943 18915.849 18964.07 0.1228 17789.22 19523.14 0.1949 18815.93 18965.91 0.1241 17693.65 19530.84 0.1953 18807.241 18967.11 0.1246 17761.71 19533.70 0.1967 18807.241 18971.25 0.126 17472.09 19541.41 0.1977 18924.537 18974.11 0.1269 17146.27 19546.15 0.1996 19046.902 18979.35 0.1282 17123.82 19552.70 0.1998 19105.55 18979.88 0.1295 16938.46 19558.92 0.2024 19255.429 18986.60 0.1299 16666.94 19560.77 0.2028 19358.968 18987.59 0.1317 16757.45 19568.75 0.204 19458.888 18990.51 0.1323 16974.67 19571.28 0.2054 19549.394 18993.81 0.1339 17069.52 19577.76 0.2059 19567.495 18994.95 0.1346 17372.89 19580.47 0.2079 19630.488 18999.39 0.1359 17938.38 19585.30 0.2087 19666.69 19001.11 0.1367 18096.95 19588.15 0.2102 19739.096 19004.22 0.1375 18024.54 19590.92 0.2107 19843.359 19005.23 0.1399 18169.35 19598.70 0.2124 19865.805 19008.57 0.1403 18024.54 19599.93 0.2136 19857.116 19010.84 0.142 17766.05 19604.94 0.2143 19766.61 19012.14 0.1423 17753.02 19605.78 0.2153 19635.556 19013.94 0.144 17775.47 19610.41 0.2164 19481.333 19015.87 0.1452 17562.60 19613.49 0.2181 19286.563 19018.75 0.1469 17544.50 19617.62 0.2193 19205.469 19020.71 0.1474 17793.57 19618.78 0.2206 19105.55 19022.76

589

0.1478 17703.06 19619.69 0.2212 19119.307 19023.68 0.1498 17662.52 19624.05 0.2225 19151.166 19025.63 0.1502 17956.48 19624.88 0.2238 19137.409 19027.52 0.1522 18001.37 19628.84 0.2243 19277.875 19028.23 0.153 18024.54 19630.33 0.2262 19332.179 19030.84 0.1547 18340.95 19633.37 0.2269 19431.374 19031.77 0.155 18535.72 19633.88 0.2286 19499.434 19033.95 0.1563 18503.86 19636.04 0.2286 19539.981 19033.95 0.1572 18644.33 19637.47 0.2302 19626.143 19035.92 0.1579 18875.30 19638.55 0.2303 19639.9 19036.04 0.1604 18716.73 19642.16 0.2312 19694.204 19037.11 0.1605 18639.99 19642.30 0.2327 19820.913 19038.84 0.1624 18771.04 19644.81 0.2344 19902.007 19040.72 0.1628 18521.96 19645.31 0.2353 20010.615 19041.68 0.164 18381.50 19646.78 0.2356 20010.615 19042.00 0.1653 18621.88 19648.29 0.2363 20028.716 19042.72 0.1673 18766.69 19650.47 0.2373 20051.886 19043.74 0.1675 18843.44 19650.68 0.2392 19997.582 19045.59 0.1681 19164.92 19651.30 0.2392 19965.724 19045.59 0.1695 19545.05 19652.68 0.241 19947.622 19047.27 0.1699 19567.50 19653.06 0.2409 19929.521 19047.18 0.1711 19720.99 19654.17 0.2422 19920.108 19048.34 0.1723 19997.58 19655.23 0.2433 19915.764 19049.30 0.172 19893.32 19654.97 0.2442 19965.724 19050.06 0.174 19861.46 19656.64 0.2445 19961.379 19050.31 0.1758 20060.57 19658.04 0.2459 19947.622 19051.45 0.1751 20015.68 19657.51 0.2474 19870.873 19052.63 0.176 19902.01 19658.19 0.2474 19807.156 19052.63 0.1764 19983.82 19658.48 0.2494 19852.772 19054.13 0.1775 20010.61 19659.27 0.2503 19825.258 19054.77 0.1779 19766.61 19659.55 0.2507 19802.812 19055.06 0.1795 19870.87 19660.62 0.2526 19825.258 19056.37 0.1792 20151.08 19660.42 0.2523 19762.265 19056.16 0.1809 20132.98 19661.50 0.2545 19784.711 19057.61 0.1813 20282.13 19661.74 0.2565 19748.508 19058.85 0.1829 20495.01 19662.68 0.2572 19726.063 19059.27 0.1833 20323.41 19662.90 0.2579 19793.399 19059.69 0.1852 20182.94 19663.92 0.2583 19784.711 19059.92 0.1848 20291.55 19663.71 0.259 19857.116 19060.32 0.1858 20251.00 19664.23 0.2608 19925.177 19061.32 0.1866 20106.19 19664.63 0.2614 19983.825 19061.64 0.1877 20196.70 19665.15 0.263 19938.21 19062.48 0.1897 20264.03 19666.05 0.2629 19920.108 19062.42 0.1883 20187.28 19665.43 0.2642 20001.926 19063.08 0.1907 20400.15 19666.48 0.2651 19974.412 19063.52 0.1916 20581.17 19666.84 0.2663 19997.582 19064.09 0.1926 20626.06 19667.24 0.2678 20028.716 19064.78 0.1932 20848.34 19667.47 0.2681 20069.987 19064.92 0.195 20975.05 19668.12 0.269 20169.182 19065.31 0.1959 20979.4 19668.43 0.2692 20178.595 19065.40

590

0.1952 20975.05 19668.19 0.2712 20219.142 19066.25 0.1961 20983.74 19668.50 0.2723 20237.243 19066.69 0.1981 20920.75 19669.14 0.2728 20191.628 19066.89 0.1991 20807.07 19669.45 0.2732 20196.696 19067.05 0.1996 20897.58 19669.60 0.2739 20137.324 19067.32 0.201 20915.68 19669.99 0.2745 20096.777 19067.55 0.2017 20906.99 19670.18 0.2756 20046.817 19067.96 0.2026 20965.64 19670.42 0.2038 20888.89 19670.73 0.2036 20834.59 19670.68 0.2046 20830.24 19670.92 0.2049 20807.07 19670.99 0.2067 20807.07 19671.41 0.2057 20788.97 19671.18 0.2079 20933.78 19671.67 0.2086 20979.40 19671.81 0.2093 20988.08 19671.95 0.2105 21056.15 19672.19 0.2116 21015.60 19672.39 0.2112 20975.05 19672.32 0.2122 20911.34 19672.50 0.214 20838.93 19672.81 0.2138 20757.84 19672.77 0.2155 20667.33 19673.05 0.216 20662.26 19673.13 0.2161 20613.03 19673.14 0.2163 20639.82 19673.17 0.2187 20712.22 19673.52 0.2192 20721.63 19673.59 0.2201 20843.27 19673.71 0.221 20920.75 19673.82 0.2213 20920.75 19673.86 0.2229 20997.50 19674.05 0.223 20997.50 19674.06 0.2242 20997.5 19674.20 0.2252 20965.64 19674.31 0.2258 20920.75 19674.37 0.2267 20915.68 19674.46 0.2282 20893.23 19674.61 0.229 20979.4 19674.68 0.2282 21019.94 19674.61 0.2299 21069.9 19674.76 0.2304 21187.2 19674.81 0.2312 21223.4 19674.88 0.2316 21287.12 19674.91 0.2326 21291.46 19674.99 0.2339 21273.36 19675.09 0.2344 21282.77 19675.13 0.2352 21228.47 19675.19 0.235 21250.92 19675.17

591

0.236 21214.71 19675.24 0.2364 21200.96 19675.27 0.2369 21305.22 19675.30 0.2381 21436.27 19675.38 0.2384 21572.39 19675.40 0.2395 21599.18 19675.47 0.2396 21558.64 19675.48 0.2402 21540.54 19675.51 0.2412 21440.62 19675.57 0.2416 21418.17 19675.59 0.2417 21418.17 19675.60 0.2429 21445.69 19675.66 0.2428 21540.54 19675.66 0.2429 21544.88 19675.66 0.2441 21554.29 19675.72 0.2436 21518.09 19675.70 0.2454 21450.03 19675.79 0.2446 21413.83 19675.75 0.2462 21373.28 19675.83 0.2465 21395.73 19675.84 0.2477 21409.48 19675.89 0.2474 21431.93 19675.88 0.249 21526.78 19675.95 0.2486 21522.43 19675.93 0.2494 21518.09 19675.96 0.2498 21431.93 19675.98 0.251 21327.66 19676.03 0.2518 21295.81 19676.06 0.2527 21223.4 19676.09 0.2536 21309.56 19676.12 0.2542 21337.08 19676.14 0.2549 21345.77 19676.17 0.2557 21377.62 19676.19 0.2565 21318.98 19676.22 0.2576 21300.87 19676.25 0.2581 21282.77 19676.27 0.2589 21282.77 19676.29 0.2609 21368.21 19676.34 0.261 21431.93 19676.35 0.2629 21572.39 19676.39 0.2628 21626.7 19676.39 0.2628 21649.14 19676.39 0.2646 21735.31 19676.43 0.2653 21707.79 19676.45 0.2662 21753.41 19676.47 0.2666 21807.71 19676.48 0.2687 21906.91 19676.52 0.2696 22011.17 19676.53 0.2691 22006.83 19676.52 0.271 22029.27 19676.56

592

0.2707 22015.51 19676.55 0.2703 22024.93 19676.55 0.2715 22151.64 19676.57 0.2728 22242.14 19676.59 0.2727 22395.64 19676.59 0.273 22477.46 19676.59 0.2738 22477.46 19676.61 0.2736 22504.25 19676.60 0.2739 22477.46 19676.61 0.2749 22526.69 19676.62 0.2744 22630.96 19676.61 0.2755 22793.87 19676.63 0.2755 22952.44 19676.63 0.2756 22952.44 19676.63 0.2753 22974.88 19676.63 0.2757 22717.12 19676.63

593

Table D6: Shear bevameter results for tests at high pressure and high density.

High Pressure (approximately 30 kPa) 1.75 g/cc Density

Grousers: Sandpaper: Shear Shear Calculated Shear Shear Calculated Displacement Stress Shear Stress Displacement Stress Shear Stress

0.0001 131.05 78.12 -0.0009 343.92 -601.99 0.0004 185.36 310.51 -0.0006 312.07 -399.29 0.0003 153.50 233.37 -0.0002 312.07 -132.20 0.0004 185.36 310.51 -0.0003 253.42 -198.63 0.0003 181.01 233.37 -0.0006 207.80 -399.29 -0.0001 167.26 -78.45 0 162.91 0.00 0 194.77 0.00 0 62.99 0.00 0 181.01 0.00 0 62.99 0.00 0.0001 181.01 78.12 -0.0001 26.79 -65.99 -0.0003 176.67 -236.35 0.0012 26.79 774.69 0.0005 167.26 387.32 0 40.55 0.00 0.0003 203.46 233.37 -0.0002 22.45 -132.20 0 171.60 0.00 -0.0003 76.75 -198.63 0.0001 203.46 78.12 0.0007 76.75 455.72 0 221.56 0.00 0.0008 126.71 519.94 -0.0003 221.56 -236.35 -0.0003 171.60 -198.63 0 262.11 0.00 0.0007 171.60 455.72 -0.0004 244.01 -315.81 0.0002 239.66 131.31 0.0005 262.11 387.32 0.0002 244.01 131.31 0 267.18 0.00 -0.0001 262.11 -65.99 0 239.66 0.00 -0.0001 293.97 -65.99 0 271.52 0.00 0.001 271.52 647.75 0 257.76 0.00 0.0006 316.41 391.27 -0.0001 293.97 -78.45 0.001 293.97 647.75 0.0009 303.38 691.34 -0.0002 312.07 -132.20 0.0001 280.21 78.12 -0.0005 334.51 -332.18 -0.0006 330.17 -475.72 0 285.28 0.00 0 307.72 0.00 0 289.62 0.00 -0.0001 316.41 -78.45 -0.0003 267.18 -198.63 0.0001 307.72 78.12 0.001 249.07 647.75 -0.0003 285.28 -236.35 -0.0005 235.32 -332.18 0.0003 330.17 233.37 0.0002 189.70 131.31 0 285.28 0.00 0 221.56 0.00

594

-0.0004 312.07 -315.81 0 207.80 0.00 -0.0005 312.07 -395.60 -0.0002 212.87 -132.20 -0.0003 298.31 -236.35 -0.0001 253.42 -65.99 0.0001 348.27 78.12 0.0006 235.32 391.27 -0.0003 321.48 -236.35 0.0008 271.52 519.94 0.0009 366.37 691.34 0.0006 239.66 391.27 0 357.68 0.00 0.0002 253.42 131.31 0.0003 330.17 233.37 0 271.52 0.00 0.0003 362.03 233.37 -0.0001 235.32 -65.99 0.0001 330.17 78.12 0.0003 271.52 196.63 -0.0009 357.68 -718.15 0.0002 249.07 131.31 0 348.27 0.00 0.0007 262.11 455.72 -0.0004 312.07 -315.81 0.0006 298.31 391.27 0.0007 321.48 539.97 -0.0006 257.76 -399.29 -0.0001 293.97 -78.45 -0.0001 289.62 -65.99 0 330.17 0.00 -0.0005 262.11 -332.18 0.0001 334.51 78.12 -0.0001 280.21 -65.99 0.0001 312.07 78.12 0.0006 307.72 391.27 -0.0004 357.68 -315.81 0.0008 289.62 519.94 -0.001 348.27 -799.64 0.0006 366.37 391.27 0.0005 352.61 387.32 0 380.13 0.00 0.0007 357.68 539.97 -0.0007 398.23 -466.63 0 330.17 0.00 -0.0002 438.78 -132.20 0.0005 366.37 387.32 0 416.33 0.00 0.0009 330.17 691.34 -0.0001 443.12 -65.99 -0.0003 330.17 -236.35 0.0002 438.78 131.31 0.0003 321.48 233.37 -0.0006 434.43 -399.29 0.0004 280.21 310.51 -0.0001 452.53 -65.99 -0.0001 321.48 -78.45 0.0004 411.99 261.73 -0.0005 280.21 -395.60 0.0004 425.02 261.73 -0.0006 321.48 -475.72 -0.0006 393.88 -399.29 0 339.58 0.00 0.0006 388.82 391.27 0 321.48 0.00 -0.0005 402.57 -332.18 0.0003 384.47 233.37 -0.0001 343.92 -65.99 -0.0004 348.27 -315.81 0.0007 325.82 455.72 0.0003 375.78 233.37 0.0003 289.62 196.63 -0.0001 388.82 -78.45 0.0003 293.97 196.63 -0.0004 352.61 -315.81 -0.0005 343.92 -332.18 0.0001 366.37 78.12 -0.0005 343.92 -332.18 0.0008 325.82 615.82 -0.0006 416.33 -399.29 -0.0001 348.27 -78.45 0.0006 452.53 391.27 -0.0001 348.27 -78.45 -0.0003 543.04 -198.63 0.0001 330.17 78.12 0.0006 678.44 391.27 -0.0003 352.61 -236.35 0 787.04 0.00 -0.0003 321.48 -236.35 0.0004 1036.12 261.73 0.0007 352.61 539.97 -0.0002 1235.23 -132.20 0 375.78 0.00 0.0004 1456.79 261.73 -0.0005 357.68 -395.60 -0.0001 1674.01 -65.99 0.0001 420.67 78.12 -0.0001 1778.27 -65.99 0.0003 366.37 233.37 -0.0003 1891.22 -198.63 0 402.57 0.00 0.0008 1909.32 519.94

595

0 402.57 0.00 0.0002 1954.94 131.31 -0.0003 366.37 -236.35 -0.0002 2027.34 -132.20 0.0008 420.67 615.82 -0.0003 2108.44 -198.63 0.0003 388.82 233.37 -0.0003 2316.97 -198.63 0.0008 411.99 615.82 -0.0001 2497.98 -65.99 0.0001 425.02 78.12 0 2733.29 0.00 0.0001 406.92 78.12 0.0004 3013.50 261.73 -0.0013 461.22 -1046.20 -0.0001 3244.48 -65.99 -0.0009 434.43 -718.15 0.0007 3620.26 455.72 0.0005 466.29 387.32 0.0002 4014.14 131.31 0.0004 466.29 310.51 0.0007 4534.01 455.72 -0.0006 425.02 -475.72 0.0004 5131.35 261.73 0 443.12 0.00 -0.0003 5651.95 -198.63 -0.0006 384.47 -475.72 0.0008 6190.64 519.94 -0.0004 393.88 -315.81 -0.0005 6593.21 -332.18 0.0003 402.57 233.37 -0.0002 6977.69 -132.20 0.0008 406.92 615.82 0.0002 7335.37 131.31 -0.0005 479.32 -395.60 0.0006 7643.09 391.27 0.0001 493.08 78.12 0.0004 7991.36 261.73 0.0001 565.48 78.12 -0.0001 8294.74 -65.99 0 619.79 0.00 0.001 8606.80 647.75 0.0001 619.79 78.12 0 8910.18 0.00 0.0001 701.61 78.12 0.0016 9181.70 1026.01 -0.0004 724.05 -315.81 0.0004 9521.28 261.73 -0.0008 841.35 -637.00 0.0004 9847.10 261.73 0 986.16 0.00 -0.0003 10263.43 -198.63 0.0001 1117.94 78.12 0.0014 10724.65 900.77 -0.0001 1317.05 -78.45 0.0011 11082.33 711.32 0.0005 1470.55 387.32 0.0015 11403.81 963.50 0.0009 1697.18 691.34 0.0016 11484.91 1026.01 -0.0009 1896.29 -718.15 0.0016 11371.95 1026.01 0.0003 2095.41 233.37 0.0027 11077.99 1699.88 0.0003 2393.71 233.37 0.002 10543.64 1273.96 -0.0008 2620.34 -637.00 0.0022 9923.85 1396.68 0.0011 2882.45 841.43 0.0023 9195.46 1457.73 0.0007 3067.81 539.97 0.0043 8606.80 2636.39 0.0008 3163.38 615.82 0.0039 8217.99 2406.99 0.0011 3298.78 841.43 0.0056 8118.07 3360.87 0 3393.63 0.00 0.006 8222.33 3577.45 0.0001 3642.70 78.12 0.0069 8280.98 4054.20 0.0001 3982.28 78.12 0.0071 8403.34 4158.19 -0.0004 4339.97 -315.81 0.0089 8461.99 5063.10 0.0004 4733.13 310.51 0.0097 8380.90 5447.95 -0.0004 4950.34 -315.81 0.0104 8656.76 5776.25 0.0003 5090.81 233.37 0.0113 8950.73 6187.10 -0.0001 5127.01 -78.45 0.0129 9322.16 6887.34 -0.0003 5113.25 -236.35 0.0134 9756.60 7098.51 0.0001 5203.76 78.12 0.0163 9878.96 8255.33 0.0004 5294.27 310.51 0.017 10082.42 8517.98 -0.0004 5543.34 -315.81 0.0179 10362.63 8846.67 0.0003 5882.92 233.37 0.0196 10245.33 9440.89

596

0.0009 6231.19 691.34 0.0206 10272.12 9774.80 0.0001 6638.83 78.12 0.022 10788.37 10223.72 0 6850.98 0.00 0.0234 10838.33 10651.89 0.0004 6955.24 310.51 0.0248 10878.88 11060.26 0.0001 6987.10 78.12 0.0261 11376.30 11422.54 0.0007 6977.69 539.97 0.0275 11489.98 11795.29 0.0005 7150.01 387.32 0.0276 11738.33 11821.24 0.0005 7435.29 387.32 0.0293 12164.07 12249.33 0.0007 7896.51 539.97 0.0309 12150.31 12630.36 0.0015 8262.88 1137.83 0.0314 12385.63 12745.27 0.0019 8349.04 1429.26 0.0336 12552.88 13228.42 0.0019 8258.53 1429.26 0.0343 12620.94 13374.77 0.0019 8050.73 1429.26 0.0341 13028.59 13333.31 0.0024 7932.71 1786.69 0.0343 12933.01 13374.77 0.0029 7968.91 2136.64 0.0369 12896.81 13889.00 0.0031 8086.93 2274.56 0.0374 13236.39 13982.81 0.0043 8330.94 3078.04 0.0379 13358.75 14075.05 0.0052 8543.81 3654.46 0.0375 13652.72 14001.38 0.0064 8805.92 4389.68 0.0392 13793.18 14307.70 0.007 9041.23 4743.53 0.0394 13729.47 14342.60 0.0073 9199.80 4917.13 0.0403 13847.49 14496.74 0.0077 9435.12 5145.18 0.0408 14050.95 14580.36 0.0094 9706.64 6072.52 0.0411 14268.16 14629.86 0.0109 10086.76 6837.21 0.0419 14453.52 14759.44 0.0111 10349.59 6935.55 0.0424 14390.53 14838.66 0.0117 10494.40 7225.64 0.043 14109.59 14931.98 0.0119 10666.00 7320.71 0.0432 14105.25 14962.67 0.013 10815.16 7829.48 0.044 14399.21 15083.36 0.0143 11064.23 8401.03 0.0443 14607.74 15127.79 0.015 11263.35 8696.02 0.0441 14829.30 15098.22 0.0151 11308.96 8737.46 0.0457 14797.44 15329.25 0.0159 11317.65 9062.69 0.0452 14507.82 15258.39 0.0163 11303.89 9221.23 0.0464 14557.78 15426.47 0.0167 11394.40 9377.11 0.0456 14702.59 15315.18 0.0174 11548.62 9643.64 0.0471 14811.20 15521.41 0.0187 11697.78 10118.17 0.0472 14843.06 15534.79 0.0179 11914.99 9829.24 0.048 14680.15 15640.22 0.0183 12051.12 9974.93 0.0483 14648.29 15679.02 0.0187 12208.96 10118.17 0.0492 14720.69 15793.11 0.0186 12263.26 10082.59 0.0489 14861.16 15755.47 0.0191 12159.72 10259.01 0.0501 15024.07 15903.78 0.0203 12168.41 10667.52 0.0504 15028.42 15939.92 0.0201 12172.76 10600.86 0.051 14992.21 16011.13 0.0203 12277.02 10667.52 0.0508 15114.58 15987.55 0.0203 12345.08 10667.52 0.0532 15159.47 16260.19 0.0204 12421.83 10700.63 0.053 15155.12 16238.31 0.0209 12612.26 10864.13 0.0545 15186.98 16398.89 0.0216 12702.76 11087.29 0.0547 15137.02 16419.70 0.0207 12747.65 10799.14 0.0553 15137.02 16481.27 0.0219 12711.45 11180.93 0.0567 15309.35 16620.17 0.0233 12657.15 11602.55 0.0569 15394.79 16639.48

597

0.0242 12779.51 11860.70 0.0581 15485.29 16752.64 0.0237 12707.11 11718.49 0.0585 15526.56 16789.36 0.0264 12376.94 12451.89 0.0606 15390.44 16974.16 0.0276 12046.05 12751.92 0.0595 15458.50 16879.00 0.0281 11973.64 12872.51 0.062 15526.56 17090.28 0.0286 12195.93 12990.57 0.0622 15422.30 17106.42 0.0297 12381.28 13241.70 0.0645 15549.01 17284.44 0.031 12620.94 13523.81 0.064 15571.45 17246.91 0.0326 13150.23 13850.41 0.0655 15454.16 17357.62 0.0344 13775.08 14192.36 0.0661 15589.56 17400.36 0.0351 13987.95 14318.47 0.0673 15571.45 17483.27 0.037 13562.21 14642.54 0.0681 15585.21 17536.71 0.0386 13023.52 14895.96 0.0697 15838.63 17639.35 0.0391 12516.68 14971.70 0.0704 15829.22 17682.54 0.0411 12177.82 15259.15 0.0709 15725.68 17712.77 0.0431 12345.08 15523.30 0.0726 15784.33 17811.80 0.044 12697.69 15635.07 0.0738 15730.02 17878.36 0.0453 13046.69 15789.19 0.0746 15911.03 17921.26 0.0461 13489.81 15879.90 0.0753 16281.75 17957.85 0.0481 14109.59 16093.72 0.0757 16349.81 17978.38 0.0507 14621.50 16345.97 0.0771 16367.91 18048.07 0.051 14738.79 16373.34 0.0782 16485.93 18100.56 0.0531 14712.01 16555.45 0.0794 16435.97 18155.64 0.0531 14562.13 16555.45 0.0799 16625.67 18177.94 0.055 14399.21 16706.86 0.0814 16852.30 18242.62 0.0572 14163.90 16867.63 0.0814 16824.79 18242.62 0.0575 13684.58 16888.42 0.0827 16897.19 18296.08 0.0587 13634.62 16968.98 0.0832 16951.50 18316.02 0.0596 14308.71 17026.78 0.0843 16947.15 18358.73 0.0617 15128.33 17153.38 0.0845 17069.52 18366.33 0.0619 15702.51 17164.86 0.0856 17254.87 18407.20 0.0627 15933.48 17209.83 0.0864 17363.48 18435.99 0.0648 16132.59 17320.88 0.0878 17490.19 18484.53 0.0649 16341.12 17325.93 0.088 17594.45 18491.27 0.0661 16467.83 17384.85 0.0881 17566.94 18494.63 0.0672 16259.30 17436.29 0.0902 17535.81 18562.57 0.0668 15630.10 17417.86 0.0898 17680.62 18550.00 0.0676 15273.15 17454.42 0.0909 17775.47 18584.17 0.0681 15363.65 17476.64 0.0921 17906.52 18620.02 0.069 15571.45 17515.48 0.092 18010.78 18617.09 0.0694 15734.37 17532.28 0.0934 17997.03 18657.26 0.0697 15929.14 17544.69 0.0935 18115.05 18660.05 0.0706 16372.26 17580.99 0.0951 18164.28 18703.54 0.071 16748.04 17596.69 0.0949 18155.59 18698.23 0.0726 16748.04 17656.88 0.0963 18155.59 18734.65 0.0723 16526.48 17645.90 0.097 18091.88 18752.22 0.0742 16186.90 17713.14 0.0975 18141.84 18764.52 0.0735 15924.79 17689.00 0.0992 18173.70 18804.82 0.0755 15630.10 17756.13 0.0994 18259.86 18809.41 0.0764 15381.75 17784.54 0.101 18372.81 18845.03 0.0774 15299.94 17814.86 0.1019 18449.56 18864.24

598

0.0784 15394.79 17843.92 0.1024 18549.48 18874.66 0.0792 15734.37 17866.31 0.1029 18562.51 18884.91 0.0801 16023.99 17890.60 0.1045 18608.13 18916.56 0.0813 16028.33 17921.59 0.1052 18684.88 18929.88 0.0825 15892.93 17951.04 0.1068 18648.67 18959.16 0.084 15730.02 17985.82 0.1076 18662.43 18973.21 0.0857 15748.12 18022.66 0.1088 18580.61 18993.60 0.0868 15698.16 18045.12 0.1093 18644.33 19001.85 0.0889 15508.46 18085.21 0.1113 18771.04 19033.51 0.0901 15462.85 18106.57 0.112 18847.79 19044.09 0.093 15575.80 18153.93 0.1134 18988.25 19064.52 0.0942 15847.32 18171.89 0.1146 19010.70 19081.27 0.0955 16005.89 18190.34 0.1158 19006.36 19097.36 0.0975 15915.38 18216.83 0.1167 18974.50 19109.01 0.0989 15842.97 18234.08 0.119 18897.75 19137.21 0.1011 15779.98 18259.21 0.1199 18897.75 19147.67 0.1033 15897.28 18282.11 0.1206 18843.44 19155.58 0.1045 15933.48 18293.73 0.1229 18861.54 19180.30 0.1057 15979.10 18304.77 0.124 18924.54 19191.46 0.1083 16323.02 18326.86 0.1256 18915.85 19206.96 0.1103 16716.18 18342.28 0.1264 18970.15 19214.41 0.1123 17047.07 18356.45 0.1286 18988.25 19233.88 0.1139 17182.47 18366.95 0.1292 19042.56 19238.94 0.1151 17209.98 18374.37 0.1309 19105.55 19252.74 0.1176 17291.08 18388.68 0.1314 19092.52 19256.65 0.1197 17146.27 18399.58 0.1338 19133.06 19274.52 0.1221 16874.75 18410.91 0.135 19114.96 19282.93 0.1233 16553.27 18416.16 0.1359 19133.06 19289.01 0.1246 16313.61 18421.55 0.1378 19227.92 19301.27 0.1273 16341.12 18431.85 0.1384 19295.98 19304.98 0.1293 16426.56 18438.75 0.1404 19404.58 19316.81 0.1302 16625.67 18441.67 0.1407 19427.03 19318.52 0.1326 16829.86 18448.94 0.1424 19485.68 19327.88 0.1354 17037.66 18456.54 0.1428 19476.99 19330.00 0.1371 17295.42 18460.73 0.1447 19427.03 19339.70 0.1384 17367.83 18463.74 0.1468 19458.89 19349.73 0.1396 17372.89 18466.37 0.148 19427.03 19355.15 0.1416 17259.22 18470.48 0.1482 19476.99 19356.03 0.1433 17182.47 18473.71 0.1496 19513.19 19362.04 0.145 17182.47 18476.71 0.1514 19485.68 19369.36 0.1467 17047.07 18479.50 0.1525 19521.88 19373.61 0.1491 16974.67 18483.12 0.1537 19513.19 19378.08 0.1509 16915.29 18485.60 0.1551 19539.98 19383.07 0.1522 16829.86 18487.28 0.1566 19630.49 19388.16 0.1535 16852.30 18488.87 0.1584 19658.00 19393.94 0.1551 16784.24 18490.71 0.1586 19752.85 19394.56 0.1575 16802.34 18493.25 0.1596 19766.61 19397.60 0.1584 16856.65 18494.13 0.1602 19802.81 19399.37 0.1607 16892.85 18496.25 0.1623 19825.26 19405.31 0.1624 16965.25 18497.69 0.1636 19857.12 19408.78 0.1629 16987.70 18498.10 0.1645 19902.01 19411.09

599

0.1654 17055.76 18499.99 0.166 19879.56 19414.80 0.1663 17119.48 18500.63 0.168 19938.21 19419.45 0.1675 17141.92 18501.44 0.1678 19992.51 19419.00 0.1702 17091.96 18503.12 0.17 19965.72 19423.80 0.1724 16956.57 18504.35 0.1708 19983.82 19425.46 0.1728 16902.26 18504.56 0.1726 19965.72 19429.04 0.1752 16884.16 18505.76 0.1729 20006.27 19429.61 0.1767 16888.50 18506.45 0.1735 20074.33 19430.74 0.1788 17047.07 18507.35 0.1755 20083.02 19434.36 0.1803 17259.22 18507.94 0.1766 20169.18 19436.24 0.181 17544.50 18508.21 0.1764 20146.74 19435.90 0.1837 17771.12 18509.15 0.1792 20182.94 19440.43 0.1849 17928.97 18509.54 0.1787 20196.70 19439.65 0.1869 18073.78 18510.15 0.1815 20191.63 19443.84 0.1881 18069.43 18510.49 0.1817 20273.45 19444.12 0.1903 18087.53 18511.06 0.1825 20245.93 19445.24 0.1918 18046.99 18511.43 0.1837 20269.10 19446.86 0.193 17974.58 18511.70 0.1849 20273.45 19448.42 0.1951 17952.14 18512.15 0.186 20255.34 19449.79 0.1977 17947.07 18512.66 0.187 20255.34 19450.99 0.198 18042.64 18512.71 0.1881 20219.14 19452.27 0.1995 18123.74 18512.98 0.1888 20205.38 19453.06 0.201 18196.14 18513.22 0.19 20164.84 19454.37 0.203 18399.60 18513.53 0.1909 20056.23 19455.32 0.2046 18562.51 18513.76 0.1914 20028.72 19455.83 0.2057 18702.98 18513.90 0.1933 19965.72 19457.71 0.2071 18802.90 18514.08 0.1943 19925.18 19458.65 0.2083 18924.54 18514.23 0.1947 19875.22 19459.01 0.2103 19151.17 18514.45 0.1952 19734.75 19459.47 0.2116 19291.63 18514.59 0.1967 19648.59 19460.78 0.2124 19463.23 18514.67 0.1983 19535.64 19462.11 0.2132 19539.98 18514.75 0.1988 19495.09 19462.51 0.214 19558.08 18514.82 0.2004 19422.68 19463.74 0.2148 19585.60 18514.89 0.2013 19295.98 19464.41 0.2165 19503.78 18515.04 0.2013 19282.22 19464.41 0.2179 19508.85 18515.15 0.2035 19205.47 19465.96 0.2187 19563.15 18515.21 0.2045 19159.85 19466.62 0.2204 19653.66 18515.34 0.2058 19141.75 19467.46 0.2213 19847.70 18515.40 0.2068 19042.56 19468.07 0.2217 19961.38 18515.43 0.2089 18974.50 19469.30 0.2222 20096.78 18515.46 0.2094 18883.99 19469.58 0.2233 20196.70 18515.53 0.2119 18834.03 19470.91 0.2245 20232.90 18515.60 0.2123 18847.79 19471.12 0.2254 20327.75 18515.65 0.2135 18834.03 19471.71 0.2259 20354.54 18515.68 0.2148 18888.33 19472.32 0.2265 20463.15 18515.72 0.216 18920.19 19472.87 0.2271 20563.07 18515.75 0.2176 18952.05 19473.56 0.2283 20607.96 18515.81 0.2187 18988.25 19474.01 0.2287 20694.12 18515.83 0.2187 19015.04 19474.01 0.2304 20631.13 18515.91 0.2205 19078.76 19474.72 0.2304 20626.06 18515.91 0.2216 19078.76 19475.13

600

0.2312 20589.86 18515.95 0.2233 19119.31 19475.74 0.2318 20476.90 18515.97 0.224 19191.71 19475.98 0.232 20490.66 18515.98 0.2256 19187.37 19476.51 0.2334 20450.11 18516.04 0.225 19268.46 19476.31 0.2339 20540.62 18516.06 0.227 19268.46 19476.94 0.2343 20649.23 18516.08 0.2282 19327.83 19477.30 0.2355 20734.67 18516.12 0.229 19368.38 19477.54 0.2364 20830.24 18516.15 0.2299 19350.28 19477.79 0.2372 20861.38 18516.18 0.2309 19422.68 19478.06 0.2375 20965.64 18516.19 0.2323 19440.79 19478.43 0.2379 20993.15 18516.21 0.2335 19521.88 19478.73 0.239 20920.75 18516.24 0.2342 19599.35 19478.90 0.2398 20911.34 18516.27 0.2347 19626.14 19479.02 0.2412 20770.87 18516.31 0.2366 19689.86 19479.45 0.2416 20744.08 18516.32 0.2372 19680.45 19479.59 0.2425 20766.52 18516.35 0.2375 19720.99 19479.65 0.2436 20784.63 18516.38 0.2389 19766.61 19479.94 0.2447 20875.13 18516.40 0.2395 19789.06 19480.07 0.2466 20897.58 18516.45 0.2405 19820.91 19480.26 0.2458 20911.34 18516.43 0.2409 19784.71 19480.34 0.2479 20857.03 18516.48 0.2424 19820.91 19480.62 0.2473 20812.14 18516.47 0.2436 19847.70 19480.83 0.25 20893.23 18516.52 0.2446 19816.57 19481.01 0.2508 20947.54 18516.54 0.2456 19829.60 19481.17 0.2519 21029.36 18516.56 0.246 19789.06 19481.24 0.2523 21110.45 18516.57 0.2472 19829.60 19481.43 0.2535 21174.17 18516.59 0.2478 19847.70 19481.52 0.254 21277.71 18516.60 0.2485 19811.50 19481.62 0.2552 21241.50 18516.62 0.2495 19825.26 19481.77 0.2561 21313.91 18516.63 0.2503 19820.91 19481.88 0.2563 21345.77 18516.64 0.2502 19843.36 19481.87 0.2567 21327.66 18516.64 0.2525 19911.42 19482.18 0.258 21409.48 18516.66 0.2527 19929.52 19482.20 0.2596 21427.58 18516.68 0.2534 20024.37 19482.29 0.26 21518.09 18516.69 0.2537 20083.02 19482.33 0.2606 21599.18 18516.70 0.2546 20146.74 19482.44 0.2612 21694.03 18516.70 0.2548 20237.24 19482.46 0.2633 21820.74 18516.73 0.2548 20264.03 19482.46 0.2629 21789.61 18516.72 0.2566 20336.44 19482.67 0.2637 21816.40 18516.73 0.2567 20291.55 19482.68 0.2649 21825.81 18516.75 0.2575 20255.34 19482.77 0.2659 21820.74 18516.76 0.2576 20255.34 19482.78 0.2659 21870.7 18516.76 0.2588 20187.28 19482.91 0.2662 21862.01 18516.76 0.2589 20205.38 19482.92 0.2674 21843.91 18516.77 0.2589 20201.04 19482.92 0.2679 21721.55 18516.78 0.2595 20245.93 19482.98 0.2687 21499.99 18516.78 0.2604 20313.99 19483.07 0.2694 21332.01 18516.79 0.2608 20309.65 19483.11 0.2703 21078.59 18516.80 0.2627 20336.44 19483.29 0.2616 20318.34 19483.19 0.2632 20318.34 19483.34

601

0.2627 20309.65 19483.29 0.2645 20277.79 19483.45 0.2658 20327.75 19483.56 0.2649 20305.30 19483.49 0.2661 20305.30 19483.59 0.267 20295.89 19483.66 0.2673 20269.10 19483.68 0.2674 20327.75 19483.69 0.2685 20287.20 19483.77 0.2678 20201.04 19483.72 0.2691 20164.84 19483.82 0.2698 20124.29 19483.87 0.2705 20201.04 19483.92 0.2701 20227.83 19483.89 0.271 20255.34 19483.95 0.2714 20282.13 19483.98 0.2718 20282.13 19484.01 0.2723 20354.54 19484.04 0.2719 20382.05 19484.02 0.2731 20404.50 19484.09 0.2735 20408.84 19484.12 0.2731 20345.85 19484.09 0.2743 20318.34 19484.17 0.2735 20209.73 19484.12 0.2739 20209.73 19484.15 0.274 20255.34 19484.15 0.2756 20259.69 19484.25 0.2742 20345.85 19484.16 0.2754 20408.84 19484.24 0.2746 20445.05 19484.19 0.275 20277.79 19484.21

602

APPENDIX E CONE PENETRATION TEST RESULTS FOR GRC-1 ______

Table E1: CPT Test 1 at 1.60 g/cc.

R (%) Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm d ,

Test G 1 11 18 29 44 58 73 85 97 114 119 132 140 158 162 166 195 197 1.19 0.00 2 9 18 29 45 57 78 99 115 129 142 154 163 173 187 194 209 212 1.35 0.00 3 0 0 4 15 32 66 82 94 117 146 153 159 180 194 197 223 228 1.59 0.00 4 0 12 17 36 62 81 102 133 135 157 162 176 187 200 204 217 227 1.50 0.00 5 11 25 41 59 81 102 120 132 150 173 182 202 216 232 236 259 310 1.73 0.00 6 0 0 2 10 21 38 59 93 100 121 131 170 168 199 202 224 265 1.71 0.00 ±kPa/mm

7 Penetration 1 10 49 60 82 104 129 145 156 183 184 195 223 241 278 276 308 1.86 0.00

8 kPa Resistance, 0 0 2 22 32 52 70 103 111 126 146 160 178 194 219 227 250 1.68 0.00 Standard Deviation of Deviation Standard 9 12 23 40 62 89 109 131 143 163 186 203 220 228 244 258 244 252 1.66 0.00 mean, kPa 4.9 12 24 39 57 78 97 117 131 150 161 176 190 206 217 230 250 1.59 0.21

Figure E1: CPT Test 1 at 1.60 g/cc.

603

350

300 y = -0.0011x2 + 1.7748x - 14.242

250

200

150

Penetration Resistance,kPa 100

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E2: CPT Test 2 at 1.63 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 0 3 17 49 97 117 140 169 177 190 216 244 255 289 288 294 341 2.15 10.34 2 18 46 61 82 106 134 148 171 183 209 240 277 294 317 354 351 431 2.40 10.34 3 0 6 38 59 89 122 147 167 194 215 238 263 283 316 321 331 346 2.32 10.34 4 18 39 59 79 106 127 150 175 203 221 242 257 280 308 324 341 360 2.18 10.34 5 23 41 59 84 109 128 151 178 198 217 239 269 297 325 347 379 429 2.44 10.34 6 0 1 10 25 45 67 88 114 138 157 176 202 229 252 279 306 321 2.16 10.34 ±kPa/mm

7 Penetration 0 4 21 51 90 121 145 170 200 222 234 250 277 304 325 364 410 2.51 10.34

8 kPa Resistance, 0 9 26 56 100 142 166 190 215 234 250 266 289 309 315 321 334 2.25 10.34 Standard Deviation Deviation of G, Standard 9 0 3 40 61 110 142 159 181 207 227 246 263 290 318 342 372 400 2.50 10.34 mean, kPa 6.6 17 37 61 95 122 144 168 191 210 231 255 277 304 322 340 375 2.32 0.14

Figure E2: CPT Test 2 at 1.63 g/cc.

604

500

450 y = -0.0007x2 + 2.448x - 15.456

400

350

300

250

200

Penetration Resistance, kPa Resistance, Penetration 150

100

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E3: CPT Test 3 at 1.65 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 23 48 75 114 145 186 207 243 272 306 342 387 413 450 475 515 533 3.29 17.24 2 0 0 7 36 55 91 131 184 236 270 288 316 352 425 435 440 494 3.38 17.24 3 25 54 84 114 140 167 210 253 283 314 351 378 419 448 483 510 533 3.29 17.24 4 12 33 53 110 128 153 186 233 245 302 344 344 371 395 412 431 430 2.85 17.24 5 26 48 67 93 128 151 187 229 250 281 316 353 394 421 464 516 572 3.34 17.24 6 0 1 12 27 71 87 118 155 181 222 265 280 309 335 384 402 548 3.15 17.24 ±kPa/mm

7 Penetration 0 4 19 82 120 170 212 237 281 334 365 400 437 456 498 552 570 3.80 17.24

8 kPa Resistance, 28 59 78 107 130 177 196 236 260 289 327 345 379 407 442 463 495 2.96 17.24 Standard Deviation Deviation of G, Standard 9 0 1 13 28 44 66 93 123 149 188 215 251 307 310 355 395 407 2.79 17.24 mean, kPa 13 28 45 79 107 139 171 210 240 278 313 339 376 405 439 469 509 3.21 0.31

Figure E3: CPT Test 3 at 1.65 g/cc.

605

700

y = 0.0024x2 + 2.7926x - 16.147 600

500

400

300

Penetration Resistance, kPa Resistance, Penetration 200

100

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E4: CPT Test 4 at 1.68 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 23 65 111 149 198 244 294 331 397 418 462 516 537 570 612 602 607 3.96 27.59 2 59 80 117 160 205 250 299 337 386 427 503 528 603 634 676 750 819 4.76 27.59 3 14 43 61 98 171 241 301 326 377 413 439 500 521 565 567 585 585 3.99 27.59 4 34 61 101 137 176 213 252 287 334 373 412 462 515 539 601 678 725 4.26 27.59 5 18 33 43 67 98 130 160 199 227 261 303 361 396 454 497 535 551 3.60 27.59 6 0 1 15 38 69 112 158 201 236 292 345 396 427 466 527 553 615 4.10 27.59 ±kPa/mm

7 Penetration 8 26 53 101 180 231 276 324 369 419 466 523 573 626 664 727 736 4.89 27.59

8 kPa Resistance, 0 10 32 62 95 131 166 206 239 284 354 425 467 505 532 543 553 3.97 27.59 Standard Deviation Deviation of G, Standard 9 0 1 14 31 55 95 142 186 226 276 332 464 478 514 553 578 605 4.36 27.59 mean, kPa 17 36 61 94 139 183 228 266 310 351 402 464 502 541 581 617 644 4.21 0.41

Figure E4: CPT Test 4 at 1.68 g/cc.

606

900

800 y = 0.0026x2 + 3.7629x - 25.377

700

600

500

400

300 Penetration Resistance, kPa Resistance, Penetration

200

100

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E5: CPT Test 5 at 1.70 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 3 29 77 130 167 210 260 297 354 403 428 482 533 570 613 668 665 4.39 34.48 2 24 47 79 120 151 191 226 263 316 372 412 460 514 531 576 605 619 4.03 34.48 3 0 4 20 40 67 98 130 175 306 327 401 423 438 474 488 521 559 3.98 34.48 4 35 56 72 83 109 164 229 272 329 357 405 434 469 499 520 532 527 3.61 34.48 5 28 51 81 108 141 168 200 246 277 332 394 429 484 523 587 686 693 4.29 34.48 6 0 2 17 36 60 95 134 170 213 251 283 331 366 408 447 505 530 3.56 34.48 ±kPa/mm

7 Penetration 0 4 29 70 124 204 285 328 392 422 472 517 573 629 688 751 804 5.30 34.48

8 kPa Resistance, 0 8 29 55 87 144 179 221 256 303 352 401 445 516 520 532 558 3.93 34.48 Standard Deviation Deviation of G, Standard 9 0 0 4 20 45 74 109 149 198 229 262 298 308 360 390 444 485 3.21 34.48 mean, kPa 10 22 45 74 106 150 195 236 293 333 379 419 459 501 537 583 604 4.03 0.60

Figure E5: CPT Test 5 at 1.70 g/cc.

607

900

800 y = 0.0034x2 + 3.458x - 35.531

700

600

500

400

300 Penetration Resistance, kPa Resistance, Penetration

200

100

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E6: CPT Test 6 at 1.71 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 0 15 40 88 173 264 327 347 400 457 502 551 603 620 664 665 676 4.76 37.93 2 48 78 114 149 197 236 281 338 355 415 462 511 558 621 648 718 726 4.45 37.93 3 0 1 15 40 74 118 178 340 388 432 490 535 558 582 609 607 602 4.71 37.93 4 0 5 19 42 82 124 174 221 260 317 368 420 442 510 544 587 603 4.22 37.93 5 40 65 99 167 188 221 250 279 318 366 414 464 517 575 623 691 771 4.38 37.93 6 0 2 18 44 94 149 210 257 406 454 503 554 609 640 674 716 747 5.38 37.93 ±kPa/mm

7 Penetration 1 19 51 116 187 222 246 280 325 367 390 452 515 543 593 619 631 4.17 37.93

8 kPa Resistance, 2 25 70 123 200 266 312 361 404 456 509 569 611 669 726 786 845 5.34 37.93 Standard Deviation Deviation of G, Standard 9 0 2 19 53 179 199 223 248 372 388 517 531 562 624 697 720 726 5.15 37.93 mean, kPa 10 24 49 91 153 200 245 297 359 406 462 510 553 598 642 679 703 4.73 0.47

Figure E6: CPT Test 6 at 1.71 g/cc.

608

900

800 y = -0.0001x2 + 4.7523x - 50.902

700

600

500

400

300 Penetration Resistance, kPa Resistance, Penetration

200

100

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E7: CPT Test 7 at 1.73 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 11 52 109 205 305 401 451 538 582 666 728 812 875 954 1047 1115 1201 7.48 44.83 2 50 94 139 194 260 315 367 430 495 554 600 657 722 749 755 773 750 4.97 44.83 3 35 95 149 200 262 341 428 483 559 606 646 733 741 746 770 772 749 5.04 44.83 4 58 94 137 176 235 282 338 395 451 541 632 657 739 817 907 1015 1067 6.43 44.83 5 10 31 78 94 138 204 301 426 454 552 591 663 706 764 998 1009 1169 7.19 44.83 6 0 4 22 59 150 206 336 367 447 501 570 638 664 704 724 733 719 5.45 44.83 ±kPa/mm

7 Penetration 3 22 50 107 303 402 424 537 593 643 708 728 782 790 832 837 842 5.90 44.83

8 kPa Resistance, 31 54 130 162 220 291 339 401 449 528 579 645 741 827 850 914 934 6.04 44.83 Standard Deviation Deviation of G, Standard 9 11 33 61 103 169 215 269 316 377 428 488 552 598 677 710 739 760 5.14 44.83 mean, kPa 23 53 97 144 227 295 361 433 490 558 616 676 730 781 844 879 910 5.96 0.92

Figure E7: CPT Test 7 at 1.73 g/cc.

609

1400

1200 y = -0.0045x2 + 6.7179x - 50.737

1000

800

600

Penetration Resistance, kPa Resistance, Penetration 400

200

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E8: CPT Test 8 at 1.75 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 40 86 143 202 256 327 400 479 550 620 708 766 859 909 950 988 954 6.49 51.72 2 41 72 113 174 221 298 378 437 512 558 627 713 767 855 875 912 936 6.14 51.72 3 50 85 115 133 278 297 383 463 510 593 641 697 716 726 751 775 743 5.09 51.72 4 0 19 53 92 236 243 384 411 431 449 517 558 637 753 755 757 733 5.25 51.72 5 48 81 124 172 231 279 319 379 433 492 551 627 694 750 915 945 983 6.04 51.72 6 8 28 57 90 128 193 265 317 366 415 550 567 666 718 800 878 934 6.10 51.72 ±kPa/mm

7 Penetration 56 106 161 230 279 341 415 479 574 621 721 768 868 931 1012 1079 1138 6.98 51.72

8 kPa Resistance, 5 27 56 95 133 195 269 324 367 422 489 564 680 725 742 784 801 5.58 51.72 Standard Deviation Deviation of G, Standard 9 0 4 22 44 74 115 207 216 262 302 360 390 465 552 616 760 770 4.98 51.72 mean, kPa 28 56 94 137 204 254 336 389 445 497 574 628 706 769 824 875 888 5.85 0.67

Figure E8: CPT Test 8 at 1.75 g/cc.

610

1200

1000 y = 0.0027x2 + 5.395x - 31.208

800

600

400 Penetration Resistance, kPa Resistance, Penetration

200

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E9: CPT Test 9 at 1.76 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 16 57 105 199 300 358 421 469 545 607 696 744 803 881 867 850 849 5.90 55.17 2 64 116 150 202 260 331 401 466 546 613 711 760 826 893 1005 1044 1113 6.81 55.17 3 2 21 58 135 246 353 414 464 537 591 687 753 808 846 852 845 828 6.08 55.17 4 4 26 55 87 139 190 296 314 375 428 495 566 643 839 836 925 909 6.28 55.17 5 54 81 114 153 208 265 320 368 420 498 559 626 730 775 866 975 1047 6.28 55.17 6 49 81 103 131 234 270 333 392 452 490 546 611 662 742 795 812 804 5.30 55.17 ±kPa/mm

7 Penetration 7 23 53 86 122 161 207 243 277 319 399 457 553 630 700 748 766 5.10 55.17

8 kPa Resistance, 15 41 87 152 225 294 367 427 495 557 625 694 775 833 891 949 990 6.48 55.17 Standard Deviation Deviation of G, Standard 9 0 10 30 58 91 131 176 218 272 313 369 443 494 565 643 725 800 5.06 55.17 mean, kPa 23 51 84 134 203 261 326 373 435 491 565 628 699 778 828 875 901 5.92 0.63

Figure E9: CPT Test 9 at 1.76 g/cc.

611

1200 y = 0.0042x2 + 5.2094x - 32.72

1000

800

600

400 Penetration Resistance, kPa Resistance, Penetration

200

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E10: CPT Test 10 at 1.78 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 67 120 173 219 293 357 425 474 562 599 694 800 833 938 1027 1103 1166 7.00 62.07 2 43 91 158 219 272 327 393 433 494 562 658 717 766 836 853 883 839 5.63 62.07 3 0 12 44 91 151 227 293 353 403 483 574 635 726 777 771 786 765 5.77 62.07 4 50 82 129 188 236 280 337 382 435 487 564 633 728 783 867 958 1031 6.12 62.07 5 8 35 64 109 150 221 283 354 425 490 564 684 705 735 822 851 1071 6.42 62.07 6 40 69 100 141 197 249 311 370 460 524 610 685 757 797 905 971 1024 6.52 62.07 ±kPa/mm

7 Penetration 0 8 36 69 112 162 215 273 319 383 432 492 564 650 718 766 846 5.49 62.07

8 kPa Resistance, 0 6 29 59 107 151 184 225 273 315 368 423 493 539 593 668 764 4.74 62.07 Standard Deviation Deviation of G, Standard 9 0 9 31 60 96 136 180 221 263 311 374 454 514 580 606 698 809 5.01 62.07 mean, kPa 23 48 85 128 179 234 291 343 404 462 538 614 676 737 796 854 924 5.86 0.73

Figure E10: CPT Test 10 at 1.78 g/cc.

612

1400

1200 y = 0.0097x2 + 4.2057x - 19.427

1000

800

600

Penetration Resistance, kPa Resistance, Penetration 400

200

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E11: CPT Test 11 at 1.80 g/cc.

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 G , kPa/mm R d (%) Test 1 16 50 152 196 302 433 554 678 780 905 1016 1094 1093 1389 815 1447 1470 9.23 68.97 2 21 63 118 222 281 375 449 540 661 765 737 8.02 68.97 3 0 8 32 62 113 196 290 382 486 565 820 1075 1213 1287 1341 1291 1243 10.09 68.97 4 66 95 126 203 237 300 405 517 601 698 787 879 984 1115 1162 1222 1251 8.29 68.97 5 54 93 136 191 245 306 382 490 597 698 807 865 1041 1100 1331 1388 1525 9.43 68.97 6 7 34 81 306 347 418 508 630 723 816 950 1026 1163 9.82 68.97 ±kPa/mm

7 Penetration 26 54 84 139 220 329 368 488 600 716 854 985 8.85 68.97

8 kPa Resistance, 46 88 119 181 243 309 379 436 565 676 823 857 974 1088 1171 990 1334 8.13 68.97 Standard Deviation Deviation of G, Standard 9 0 10 78 226 262 341 445 506 580 634 664 699 813 1240 1304 1337 1394 9.00 68.97 mean, kPa 34 68 117 205 268 353 435 540 647 753 853 935 1040 1203 1187 1279 1370 8.98 0.74

Figure E11: CPT Test 11 at 1.80 g/cc.

613

1800

1600 y = 0.0078x2 + 7.6103x - 58.026

1400

1200

1000

800

600 Penetration Resistance, kPa Resistance, Penetration

400

200

0 0 20 40 60 80 100 120 140 160 180 Depth, mm Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Mean Poly. (Mean)

Table E12: CPT test results corresponding to soil preparations for bevameter tests.

614

Depth, mm 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155 165 175 185 G , kPa/mm R d , % Test 2 31 66 106 150 204 267 312 363 399 449 482 526 568 572 593 652 659 742 741 4.04 24.14 3 0 7 32 77 115 163 216 257 295 325 364 369 460 455 499 529 544 629 626 3.69 24.14 4 0 49 75 135 199 271 343 385 424 475 540 553 551 571 609 656 735 733 749 4.26 24.14 5 0 0 24 68 102 148 197 246 287 319 355 398 454 484 494 523 581 674 684 3.97 24.14 6 50 96 141 197 257 327 368 429 515 549 631 672 754 785 862 862 992 961 1055 5.71 51.72 7 16 64 129 202 284 385 485 590 656 807 919 1042 1057 1191 1195 1259 1319 1285 1417 8.37 51.72 8 1 29 69 141 221 271 317 378 428 469 528 608 633 671 731 798 869 932 956 5.44 51.72 9 4 37 79 155 203 301 362 439 510 552 599 682 729 752 795 890 916 908 968 5.68 51.72 10 24 62 109 174 232 277 342 412 438 530 573 626 656 737 772 783 858 922 951 5.29 51.72 11 1 30 88 158 296 374 455 538 622 665 760 798 882 882 981 1018 1023 1095 1074 6.54 51.72 12 42 89 148 205 275 336 388 451 534 602 646 690 776 794 832 929 991 996 1021 5.73 51.72 13 33 82 133 215 288 360 447 532 629 666 789 844 927 999 1063 1136 1168 1262 1251 7.34 51.72 14 30 79 147 258 297 384 450 517 549 663 674 688 745 798 823 876 926 926 1025 5.36 51.72 15 48 96 141 218 277 372 482 546 608 697 760 842 869 933 1016 1033 1128 1121 1286 6.84 51.72 16 15 46 65 86 114 137 162 186 212 226 237 263 283 283 321 355 388 389 418 2.18 13.79 17 0 1 18 41 69 98 147 168 200 236 240 255 288 327 330 359 404 393 447 2.57 13.79 18 1 23 58 101 141 189 216 250 295 308 318 338 383 389 386 419 493 508 491 2.80 13.79 19 13 37 61 91 123 160 198 226 252 278 296 330 372 379 421 449 497 510 493 2.88 13.79 20 3 22 46 72 103 137 164 191 223 300 315 320 330 352 363 390 414 457 518 2.74 13.79 21 8 36 72 119 168 210 243 276 303 329 344 355 364 383 409 482 475 478 482 2.68 13.79 22 11 42 81 151 167 190 212 237 271 281 306 337 366 406 446 473 533 547 614 3.07 13.79 23 41 75 120 156 199 231 299 304 339 368 388 431 468 518 517 541 587 611 629 3.28 13.79 24 12 46 80 109 147 178 198 236 257 279 315 322 327 343 405 419 431 506 533 2.68 13.79 25 35 88 124 159 193 231 272 305 346 372 375 386 401 433 459 503 546 538 559 2.82 13.79 26 0 8 27 54 83 115 148 179 209 245 259 301 316 373 382 438 440 474 536 3.00 13.79 27 0 0 5 35 66 90 112 136 157 181 212 244 273 294 314 359 388 412 462 2.61 13.79 28 3 34 96 148 192 239 264 283 316 353 376 399 445 425 431 459 492 569 593 2.98 13.79 29 0 1 21 49 88 126 160 206 233 275 316 324 343 360 396 444 451 434 464 2.87 13.79 30 36 75 130 182 223 263 306 338 373 399 427 468 549 552 529 555 613 721 723 3.63 24.14 31 kPa Resistance, Penetration 32 62 110 168 208 277 351 372 404 445 510 504 542 588 610 608 622 647 698 3.70 24.14 32 15 67 162 235 341 441 503 570 619 675 746 776 828 914 943 1004 1103 1095 1131 6.30 51.72 33 43 101 171 246 328 423 502 567 674 766 868 884 1028 1057 1075 1130 1184 1272 1330 7.37 51.72 34 40 117 186 235 283 329 378 425 482 526 560 599 649 694 747 783 842 912 957 4.83 51.72 35 1 34 98 176 271 364 457 535 592 655 744 798 859 952 983 1042 1135 1154 1196 7.01 51.72 36 4 30 68 126 179 240 293 341 380 417 450 485 522 571 566 569 569 585 626 3.60 24.14 37 0 19 51 79 116 152 182 195 222 254 0 275 292 310 331 364 402 424 454 2.36 24.14 38 12 41 74 100 123 148 173 199 215 239 271 323 331 349 393 443 451 487 570 2.85 13.79 39 13 49 94 137 201 256 294 339 359 396 446 458 481 518 577 569 647 661 668 3.70 13.79 40 2 20 41 72 112 158 188 213 249 0 278 308 337 357 0 399 447 501 566 2.57 13.79 41 10 41 82 170 189 218 246 265 293 323 341 373 407 434 468 497 526 576 585 3.08 13.79 42 1 15 46 85 137 185 219 240 271 304 0 346 392 429 469 489 483 484 510 2.97 13.79 43 6 29 60 95 134 187 213 250 291 327 351 371 385 401 425 447 465 495 543 2.92 13.79 44 5 29 63 102 132 157 180 204 229 263 294 312 332 347 365 386 413 433 480 2.51 13.79 45 16 41 72 111 155 191 226 257 273 297 322 346 372 397 423 443 460 482 546 2.78 13.79 46 1 34 78 137 194 275 342 390 439 475 515 538 550 583 606 629 647 689 776 4.11 24.14 47 20 52 112 158 199 243 278 321 365 398 443 476 489 505 519 549 601 677 680 3.58 24.14 48 0 26 82 161 252 343 403 477 568 631 693 783 797 848 977 977 1020 1079 1155 6.64 51.72 49 29 83 145 217 288 342 405 474 538 586 634 695 744 777 810 855 905 943 1006 5.39 51.72

BIBLIOGRAPHY

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