An Abstract of the Thesis Of

AN ABSTRACT OF THE THESIS OF

Youssef Bougataya for the degree of Master of Science in Civil Engineering presented on June 16, 2016.

Title: Static and Wave Equation Analyses and Development of Region-specific Resistance Factors for Driven Piles

Abstract approved: ______Armin W. Stuedlein

This study uses an existing database of dynamic loading tests of driven piles

installed in the Puget Sound Lowlands to improve the reliability of axial performance.

First, the unit shaft resistances developed from stress wave signal matching to dynamic

records of pile installation are used to develop an effective stress-based shaft resistance

model. New, statistically unbiased unit shaft resistance models are proposed for piles

driven at End-of-Drive (EOD) and Beginning-of-Restrike (BOR) and for a range of

specific soil types and relative densities and consistencies. The accuracy and

uncertainty of each model is quantified and compared. Then, the observed unit shaft

resistances and proposed design models are used to characterize the magnitude of time- dependent capacity gain. Although these models allow estimation of the range of capacity gain anticipated following pile installation, no reliable time-dependent relationship could be proposed. The study concludes with the quantification of accuracy and uncertainty in dynamic wave equation-based and existing static analysis procedures and calibration of resistance factors for use with load and resistance factor

design (LRFD). These resistance factors indicate, in some cases, dramatic

improvement in the useable pile capacity at a given reliability owing to the use of a database from a specific region. The results from this work may be immediately applied in practice in the Puget Sound Lowlands.

Static and Wave Equation Analyses and Development of Region-specific Resistance Factors for Driven Piles

by Youssef Bougataya

A THESIS

submitted to

Oregon State University

in partial fulfillment of the requirements for the degree of

Master of Science

Presented June 16, 2016 Commencement June 2017

Master of Science thesis of Youssef Bougataya presented on June 16, 2016

APPROVED:

Major Professor, representing Civil Engineering

Head of the School of Civil and Construction Engineering

Dean of the Graduate School

I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request.

Youssef Bougataya, Author

ACKNOWLEDGEMENTS

My experience with Dr. Armin Stuedlein was a true highlight. Your vision and acute attention to make every day so visceral is unparalleled. Your responsiveness, nonpareil follow up, constant support and endorsement, have been pillars for my growth and success. Your dedication to sharpen the geotechnical program at OSU is unfathomable and can only put the school in the front lead of our specialization. I look forward to keep working with you in the future and ultimately making impactful differences toward improving and shaping our field to the best.

My sincere appreciation and thanks are forwarded to Dr. Matt Evans. Your extreme humbleness taught me how knowledge can be transferred in a friendly and joyful atmosphere. Your availability to answer my questions was influential in shaping my geotechnical knowledge. The accuracy of your thought process and clarity of your presentations and explanations were hallmarks of all your classes. Your careful consideration to the geotechnical program in OSU made my stay in school smooth, enjoyable and an opportunity to learn and grow.

I want to thank my other two geotechnical professors Dr. Ben Leshchcinsky and

Dr. Ben Mason for their advices and the numerous fruitful discussions I had with them.

The energy you show everyday make working with you a delightful experience. Your dedication to teaching and vivid interaction with students was inspiring not only to me but many of your other students as well.

I would like to acknowledge Dr. Seth Reddy for his visit to present the existing pile database, and also for laying the infrastructure used to perform the reliability calibrations.

I would like to extend my appreciation to the quality of service offered at OSU. I

would like to express my gratitude specifically to the school of Civil and Construction

Engineering (CCE), in particular Cindy Olson, as well as the Graduate School in the

name of Michelle LaCrosse for answering my requests with diligence and friendliness.

Your commitment to help graduate students reach their full potential cannot be undervalued in any way.

I want to thank the students that I stayed shoulder to shoulder with in office or shared the classroom with. I wish to thank all my friends here in Oregon, especially,

David Bailey, Josiah Baker, and Maggie Exton, your friendship has provided me with

life experiences I could not have gained elsewhere. A great thanks go to fellow

geotechnical students Michael Bunn, Andrew Strahler, Danny Hess, Nan Zhang, Qiang

Li, Stephie Lange, Ali Khoubani ,Nan Zhang, and Abbas Abdoullahi with whom I

shared my everyday experience at OSU.

Finally, establishing my career plan and investing independently into my growth

and learning wouldn’t be possible without the matchless support of my brother Hicham, the most influential person in my life. Helping me sponsor expensive endeavors was

key for me to be able to focus in my studies and career. Your love is beyond

comprehension and made me think every day of how special you are. I thank my family

and especially my parents for their constant support, encouragement and love. I look

forward to see my very young nephews, Adam, Maria and Ziad, to whom I dedicate

this work.

TABLE OF CONTENTS Page

1 Introduction ...... 1

1.1 Background ...... 1 1.2 Statement of Problem ...... 2 1.3 Purpose of Research ...... 4 1.4 Organization of this Thesis ...... 4

2 Litterature Review ...... 6

2.1 Introduction ...... 6 2.2 Use of Dynamic Formulas to Estimate Pile Axial Capacity ...... 6 2.3 Wave Equation Analysis of Pile Driving ...... 9 2.3.1 Wave Equation Approach History...... 10 2.3.2 Wave Equation for a Free Pile ...... 12 2.3.3 Wave Equation Theory in GRLWEAP ...... 17 2.4 Dynamic Testing of Driven Piles ...... 22 2.4.1 Dynamic Testing Setup ...... 22 2.4.2 Advantages of Dynamic Testing ...... 24 2.5 Static Analysis Using Standard Penetration Test Correlations ...... 26 2.6 LRFD Reliability Theory ...... 30 2.6.1 First Order Second Moment (FOSM) ...... 33 2.6.2 Statistics Necessary for Reliability Calibrations ...... 38 2.7 Development of Recommended Resistance Factors for Driven Piles...... 42 2.8 Summary ...... 44

3 Research Objectives and Program ...... 45

3.1 Research Objectives ...... 45 3.2 Research Program ...... 45

4 Development of New Shaft Resistance Models for Piles Driven in the Puget Sound Lowlands…...... 48

TABLE OF CONTENTS (Continued) Page

4.1 Introduction ...... 48 4.2 Selection of the Reference Capacity: CAse Pile Wave Analysis Program (CAPWAP) Technique… ...... 49 4.3 Database of CAPWAP Dynamic Analysis Records ...... 51 4.4 Typical Subsurface Conditions of Puget Sound Lowlands ...... 52 4.5 Methodology for the Development of the New β-Models ...... 52 4.6 Estimation of Axial Capacity Using the β-coefficient and Toe Bearing Capacity Coefficient . 57 4.6.1 Estimation of β-coefficient in the literature...... 57 4.6.2 Estimation of Toe Bearing Capacity Coefficient ...... 60 4.7 New developed Models for β-Coefficient Specific to the Puget Sound Lowlands ...... 61 4.7.1 β-Coefficient Models Based on USCS Classification ...... 63 4.7.2 Observations ...... 87 4.7.3 β-coefficient Based on Density or Consistency ...... 88 4.8 Summary ...... 90

5 Assessment of Time Dependent Capacity Gain for Piles Driven in the Puger Sound Lowlands ...... 91

5.1 Background ...... 91 5.2 Mechanisms of Setup ...... 93 5.3 Empirical Relationships for estimate of Setup ...... 96 5.3.1 Existing empirical relationships for estimate of setup ...... 96 5.3.2 Observations and Discussion of existing methods ...... 100 5.3.3 Current practices for estimating Setup: State of the practice ...... 101 5.4 Development of Setup Estimation Methods ...... 103 5.4.1 Example 1: Setup in all layers ...... 104 5.4.2 Example 2: Inferred Liquefaction in Response to Driving...... 105 5.4.3 Example 3: Relaxation in some soil layers ...... 110 5.5 Quantification of Setup using the Proposed β-Coefficient Models ...... 114 5.6 Summary ...... 123

TABLE OF CONTENTS (Continued) Page

6 Development of Calibrated Resistance Factors for Static Axial Capacity of Piles Driven in the Puget Sound Lowlands...... 125

6.1 Introduction ...... 125 6.2 Selected Static Axial Capacity Estimation Methods ...... 126 6.2.1 Static Analysis using Standard Penetration Test Correlations ...... 126 6.2.2 Wave Equation-based Bearing Graph Static Axial Capacity ...... 126 6.3 Assessment of Static Axial Capacity Methods at EOD...... 129 6.4 Accuracy of and Uncertainty in Selected Static Analysis Methods at EOD ...... 131 6.4.1 Accuracy and Uncertainty of Case WEAP 1 at EOD ...... 132 6.4.2 Accuracy and Uncertainty of Case WEAP 2 at EOD ...... 133 6.4.3 Accuracy and Uncertainty of Case FHWA-SA Compared to CAPWAP EOD Resistance…...... 134 6.4.4 Accuracy and Uncertainty of Case PSL-SA at EOD ...... 135 6.4.5 Comparison between the Selected Static Capacity Analysis Methods ...... 136 6.4.6 Effect of Pile Material Type on Accuracy and Uncertainty in Static Capacity at EOD .. 138 6.4.7 Effect of Pile Shape and Condition on Accuracy and Uncertainty in Static Capacity at EOD: 141 6.4.8 Effect of Driving Resistance on Accuracy and Uncertainty in Static Capacity at EOD .. 146 6.5 Assessment of Static Axial Capacity Methods at BOR...... 151 6.6 LRFD Reliability Theory and Resistance Factors Calibration in Selected Static Capacity Methods...... 167 6.7 Summary ...... 181

7 Summary and Conclusions ...... 182

7.1 Summary of Research ...... 182 7.2 Conclusions ...... 183 7.3 Recommendations for Future Work ...... 185

8 Bibliography...... 185 9 Appendices...... 191

LIST OF FIGURES

Figure Page

Figure 2.1. Example boundary condition for a free pile and illustration of methods of characteristics geometrically ...... 17

Figure 2.2. Driving system- pile- soil discrete model used in WEAP analysis for a Diesel hammer (Modified after GRLWEAP Background Manual 2010) ...... 19

Figure 2.3. Static and dynamic resistance force models ...... 19

Figure 2.4. Example of calculated force and reflected velocity from wave equation theory (GRLWEAP 2010 version Program was used to generate it)...... 20

Figure 2.5. Example of GRLWEAP bearing capacity results (capacity, stroke and compressive and tensile stresses as a function of blow count) ...... 21

Figure 2.6. Drivability study flow chart in WEAP analysis ...... 22

Figure 2.7. Dynamic testing main logistics and setup ...... 24

Figure 2.8. Simplified comparison between dynamic testing and static testing Note that static testing is irreplaceable for highly reliable measurements...... 26

Figure 2.9. Unit shaft resistance methodology determination based on the SA method for silty soils ...... 28

Figure 2.10. Unit shaft resistance methodology determination based on the SA method for sand, gravel, and clay ...... 29

Figure 2.11. Unit toe resistance determination for the SA method ...... 30

Figure 2.12. General concepts of load and resistance distribution in reliability theory...... 31

Figure 2.13. Probability of failure and reliability index ...... 32

Figure 4.1. Chart for Estimating β-coefficient versus Soil Type ϕ’ (after Fellenius 1991) ...... 59

Figure 4.2. Chart for estimating Nt Coefficients versus Soil Type ϕ' Angle (after Fellenius, 1991) ...... 60

Figure 4.3. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for clayey USCS soils (CH, CL, and CL-ML) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 65

Figure 4.4. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for clayey USCS soils (CH, CL, and CL-ML) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 66

LIST OF FIGURES (Continued)

Figure Page

Figure 4.5. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for gravelly USCS soils (GP, GW, GW-GM, and GP-GM) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 68

Figure 4.6. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for gravelly USCS soils (GP, GW, GW-GM, and GP-GM) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 69

Figure 4.7. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for silty USCS soils (ML) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 71

Figure 4.8. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for silty USCS soils (ML) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 72

Figure 4.9. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for organic USCS soils (OH, OL, and PT) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 74

Figure 4.10. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for organic USCS soils (OH, OL, and PT) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 75

Figure 4.11. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for sandy USCS soils (SM and SC) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 77

Figure 4.12. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for sandy USCS soils (SM and SC) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 78

Figure 4.13. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for USCS intermixed soils SM and ML at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 80

Figure 4.14. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for USCS intermixed soils SM and ML at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 81

Figure 4.15. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for clean sandy USCS soils (SW and SP) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 83

LIST OF FIGURES (Continued)

Figure Page

Figure 4.16. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for clean sandy USCS soils (SW and SP) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 84

Figure 4.17. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for silty sandy USCS soils (SW-SM and SP-SM) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 85

Figure 4.18. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for silty sandy USCS soils (SW-SM and SP-SM) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient...... 86

Figure 5.1. Theoretical idealization scheme of setup phases (modified from Komurka 2003) .... 95

Figure 5.2. Pile ID: RI-001&WSP6. Unit shaft resistance and Setup ratio variation as a function of depth .Example 1 illustrating setup in all soil layers ...... 107

Figure 5.3. Pile ID: RI-007&TP19. Unit shaft resistance and Setup ratio variation as a function of depth .Example 2 illustrating liquefaction at low depths in loose sandy silty soils ...... 109

Figure 5.4. Pile ID: RI-002&T1. Unit shaft resistance and Setup ratio variation as a function of depth .Example 3 illustrating relaxation in some layers ...... 113

Figure 5.5. Soil layering along the shaft of a driven pile ...... 115

Figure 5.6. Back-calculated setup ratio and the corresponding model based on the new β-models for four soil groups (Model No. 1 to Model No. 4): (a) CH, CL, and CL-ML (b) GP, GW, GM, GW-GM, and GP-GM (c) ML (d) OH, OL, and PT...... 118

Figure 5.7. Back-calculated setup ratio and the corresponding model based on the new β-models for four soil groups (Model No. 5 to Model No. 8): (a) SM and SC (b) SM/ML (c) SW and SP (d) SW-SM and SP-SM...... 119

Figure 5.8. (a) Predicted setup using β-coefficient models versus CAPWAP measured setup of shaft resistance (b) Bias as a function of nominal setup...... 121

Figure 5.9. Setup ratio as a function time for all studied soil segments ...... 122

Figure 5.10. Setup ratio versus EOD resistance for all soil segments used in this study ...... 123

Figure 6.1. Flow chart for the development of bearing graph in WEAP analysis ...... 128

Figure 6.2. Summary of pile database used in EOD WEAP analysis by material, shape and hammer type...... 130

LIST OF FIGURES (Continued)

Figure Page

Figure 6.3. Predicted capacity of case WEAP 1 versus CAPWAP measured capacity at End of Driving (EOD) for all piles ...... 133

Figure 6.4. Predicted capacity of case WEAP 2 versus CAPWAP measured capacity at End of Driving (EOD) for all piles ...... 134

Figure 6.5. Predicted capacity of case FHWA-SA versus CAPWAP measured capacity at End of Driving (EOD) for all piles ...... 135

Figure 6.6. Predicted shaft resistance of case PSL-SA versus CAPWAP measured shaft resistance at EOD 85 piles ...... 136

Figure 6.7. Predicted capacity for different predictive methods versus CAPWAP measured capacity at EOD for concrete piles ...... 139

Figure 6.8. Predicted capacity for different predictive methods versus CAPWAP measured capacity at EOD for steel piles...... 141

Figure 6.9. Comparison of measured and predicted capacity at End of Driving (EOD) and for closed octagonal pre-stressed concrete piles...... 143

Figure 6.10. Comparison of measured and predicted capacity at End of Driving (EOD) and for concrete cylindrical open piles...... 144

Figure 6.11. Predicted capacity for different predictive methods versus CAPWAP measured capacity at EOD for steel closed pipe piles ...... 145

Figure 6.12. Predicted capacity for different predictive methods versus CAPWAP measured capacity at EOD for steel open pipe piles ...... 146

Figure 6.13. Variation in prediction bias for case WEAP 1 at the end of driving condition as a function of the terminal pile set...... 147

Figure 6.14. Variation in prediction bias for case WEAP 2 at the end of driving condition as a function of the terminal pile set...... 148

Figure 6.15. Variation in prediction bias for case FHWA-SA at the end of driving condition as a function of the terminal pile set...... 148

Figure 6.16. Histogram and frequency distributions of sample bias based on WEAP 1 methods at End of Driving (EOD) grouped in 0.1 sized bins ...... 149

Figure 6.17. Histogram and frequency distributions of sample bias based on WEAP 2 methods at End of Driving (EOD) grouped in 0.1 sized bins ...... 150

LIST OF FIGURES (Continued)

Figure Page

Figure 6.18. Histogram and frequency distributions of sample bias based on FHWA-SA method grouped in 0.1 sized bins ...... 150

Figure 6.19. Histogram and frequency distributions of sample bias based on PSL-SA method grouped in 0.1 sized bins ...... 151

Figure 6.20. Summary of pile database used in BOR WEAP analysis by material, shape and hammer type...... 152

Figure 6.21. Comparison of measured and predicted capacity using WEAP 1 at BOR, assuming that BOR capacity is the sum of BOR shaft resistance and EOD toe resistance...... 153

Figure 6.22. Comparison of measured and predicted capacity using WEAP 2 at BOR, assuming that BOR capacity is the sum of BOR shaft resistance and EOD toe resistance...... 154

Figure 6.23. Comparison of measured and predicted capacity using FHWA-SA at BOR, assuming that BOR capacity is the sum of BOR shaft resistance and EOD toe resistance...... 155

Figure 6.24. Comparison of measured and predicted shaft resistance using PSL-SA at BOR... 156

Figure 6.25. Comparison of measured and predicted capacity at BOR for concrete piles. Note that PSL-SA estimate shaft resistance only...... 157

Figure 6.26. Comparison of measured and predicted capacity at BOR for concrete piles. Note that PSL-SA estimate shaft resistance only...... 158

Figure 6.27. Comparison of measured and predicted capacity at BOR and for closed octagonal pre-stressed concrete piles ...... 159

Figure 6.28. Comparison of measured and predicted capacity at BOR and for concrete cylindrical open piles ...... 160

Figure 6.29. Predicted capacity for different predictive methods versus CAPWAP measured capacity at BOR for steel open pipe piles ...... 161

Figure 6.30. Predicted capacity for different predictive methods versus CAPWAP measured capacity at BOR for steel closed pipe piles ...... 162

Figure 6.31. Variation in prediction bias for case (a) WEAP 1 and (b) WEAP 2 at BOR as a function of the terminal pile set...... 163

Figure 6.32. Variation in prediction bias for case FHWA-SA at BOR as a function of the terminal pile set ...... 164

LIST OF FIGURES (Continued)

Figure Page

Figure 6.33. Histogram and frequency distributions of sample bias grouped in 0.1 sized bins for case (a) WEAP 1 and (b) WEAP 2...... 165

Figure 6.34. Histogram and frequency distributions of sample bias grouped in 0.1 sized bins for case FHWA-SA...... 166

Figure 6.35. Histogram and frequency distributions of sample bias grouped in 0.1 sized bins for case PSL-SA...... 166

Figure 6.36. Cumulative distribution functions of the sample biases for the selected capacity estimation methods for EOD with summary statistics for fitted lognormal distributions...... 169

Figure 6.37. Cumulative distribution functions of the sample biases for the β-coefficient models used in the PSL-SA method at EOD with summary statistics for fitted lognormal distributions...... 170

Figure 6.38. Cumulative distribution functions of the sample biases for the selected capacity estimation methods for BOR with summary statistics for fitted lognormal distributions...... 171

Figure 6.39. Cumulative distribution functions of the sample biases for the β-coefficient models used in the PSL-SA method at BOR with summary statistics for fitted lognormal distributions...... 172

Figure 6.40. Variation in resistance factors as a function of dead to live load ratio for different predictive methods based on driving resistance at EOD ...... 174

Figure 6.41. Variation in resistance factors as a function of dead to live load ratio for the seven unbiased β-coefficient models at EOD ...... 175

Figure 6.42. Variation in resistance factors as a function of dead to live load ratio for different predictive methods based on driving resistance at BOR ...... 176

Figure 6.43. Variation in resistance factors as a function of dead to live load ratio for the eight β-coefficient models at BOR...... 177

Figure 6.44. Trevor Smith (2011) collected database in his report to Oregon Department of Transportation (ODOT) by state: (a) states with a number of piles equal or more than 4 (b) States with a number of piles strictly less than 4...... 180

LIST OF TABLES

Table Page

Table 2.1. Calibration results for different strength limits of driven piles using different methods of calibration (After Allen (2005)) ...... 43

Table 4.1. Example of a soil profile of one of the piles in the database...... 53

Table 4.2. Geologic units and their abbreviation as encountered in the database of soil profiles. 54

Table 4.3. Correlation between SPT N-value, relative density and unit weight for granular soils (after Peck et al. 1974)...... 56

Table 4.4. Correlation between SPT N-value, relative density and unit weight for cohesive soils (after Peck et al. 1974)...... 56

Table 4.5. Approximate ranges of β-coefficients based on case histories compiled by Fellenius (2008) ...... 59

Table 4.6. Number of soil segments per chosen USCS group ...... 64

Table 4.7. Fitting parameters for proposed β-coefficient models per USCS group ...... 87

Table 4.8. Number of soil segments per density (consistency) group ...... 89

Table 4.9. Fitting parameters for proposed β−coefficient models per density group ...... 89

Table 5.1. Proposed values for t0 from different authors in the literature ...... 97

Table 5.2. Proposed values for empirical constant A in the Skov and Denver (1988) equation by different authors from the literature ...... 97

Table 5.3. Soil setup factors (After Rausche et al, 1996) ...... 103

Table 5.4. Descriptive statistics of time (in hours) for different soil groups ...... 123

Table 6.1. Resistance factors using the WEAP method at EOD from the literature ...... 179

LIST OF APPENDIX FIGURES

Figure Page

Figure A-1. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for loose granular soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 194

Figure A-2. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for loose granular soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 195

Figure A-3. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for medium dense granular soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 196

Figure A-4. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for medium dense granular soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 197

Figure A-5. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for dense granular soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 198

Figure A-6. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for dense granular soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 199

Figure A-7. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for very dense granular soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 200

Figure A-8. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for very dense granular soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 201

Figure A-9. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for soft plastic soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 202

Figure A-10. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for soft plastic soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 203

Figure A-11. Determined β-coefficient values from CAPWAP records and effective normal stress filtered for medium stiff plastic soils at EOD ...... 204

LIST OF APPENDIX FIGURES (Continued)

Figure Page

Figure A-12. Determined β-coefficient values from CAPWAP records and effective normal stress filtered for medium stiff plastic soils at BOR ...... 205

Figure A-13. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for very stiff plastic soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 206

Figure A-14. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β- coefficient model for very stiff plastic soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient ...... 207

Figure A-15. Determined β-coefficient values from CAPWAP records and effective normal stress filtered for hard plastic soils at EOD ...... 208

Figure A-16. Determined β-coefficient values from CAPWAP records and effective normal stress filtered for hard plastic soils at BOR ...... 209

Figure B-1. Pile 1: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 211

Figure B-2. Pile 2: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 212

Figure B-3. Pile 3: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 213

Figure B-4. Pile 4: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 214

Figure B-5. Pile 5: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 215

Figure B-6. Pile 6: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 216

Figure B-7. Pile 7: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 217

Figure B-8. Pile 8: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 218

Figure B-9. Pile 9: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 219

LIST OF APPENDIX FIGURES (Continued)

Figure Page

Figure B-10. Pile 10: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 220

Figure B-11. Pile 11: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 221

Figure B-12. Pile 12: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 222

Figure B-13. Pile 13: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 223

Figure B-14. Pile 14: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 224

Figure B-15. Pile 15: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 225

Figure B-16. Pile 16: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 226

Figure B-17. Pile 17: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 227

Figure B-18. Pile 18: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 228

Figure B-19. Pile 19: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 229

Figure B-20. Pile 20: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 230

Figure B-21. Pile 21: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 231

Figure B-22. Pile 22: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 232

Figure B-23. Pile 23: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 233

Figure B-24. Pile 24: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 234

LIST OF APPENDIX FIGURES (Continued)

Figure Page

Figure B-25. Pile 25: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 235

Figure B-26. Pile 26: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 236

Figure B-27. Pile 27: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 237

Figure B-28. Pile 28: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 238

Figure B-29. Pile 29: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 239

Figure B-30. Pile 30: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 240

Figure B-31. Pile 31: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 241

Figure B-32. Pile 32: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 242

Figure B-33. Pile 33: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 243

Figure B-34. Pile 34: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 244

Figure B-35. Pile 35: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 245

Figure B-36. Pile 36: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 246

Figure B-37. Pile 37: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 247

Figure B-38. Pile 38: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 248

Figure B-39. Pile 39: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 249

LIST OF APPENDIX FIGURES (Continued)

Figure Page

Figure B-40. Pile 40: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 250

Figure B-41. Pile 41: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 251

Figure B-42. Pile 42: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 252

Figure B-43. Pile 43: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 253

Figure B-44. Pile 44: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 254

Figure B-45. Pile 45: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 255

Figure B-46. Pile 46: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 256

Figure B-47. Pile 47: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 257

Figure B-48. Pile 48: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 258

Figure B-49. Pile 49: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 259

Figure B-50. Pile 50: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 260

Figure B-51. Pile 51: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 261

Figure B-52. Pile 52: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 262

Figure B-53. Pile 53: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 263

Figure B-54. Pile 54: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 264

LIST OF APPENDIX FIGURES (Continued)

Figure Page

Figure B-55. Pile 55: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 265

Figure B-56. Pile 56: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 266

Figure B-57. Pile 57: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 267

Figure B-58. Pile 58: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 268

Figure B-59. Pile 59: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 269

Figure B-60. Pile 60: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 270

Figure B-61. Pile 61: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 271

Figure B-62. Pile 62: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 272

Figure B-63. Pile 63: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 273

Figure B-64. Pile 64: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 274

Figure B-65. Pile 65: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 275

Figure B-66. Pile 66: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 276

Figure B-67. Pile 67: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 277

Figure B-68. Pile 68: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 278

Figure B-69. Pile 69: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 279

LIST OF APPENDIX FIGURES (Continued)

Figure Page

Figure B-70. Pile 70: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 280

Figure B-71. Pile 71: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 281

Figure B-72. Pile 72: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 282

Figure B-73. Pile 73: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 283

Figure B-74. Pile 74: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 284

Figure B-75. Pile 75: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 285

Figure B-76. Pile 76: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 286

Figure B-77. Pile 77: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 287

Figure B-78. Pile 78: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 288

Figure B-79. Pile 79: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio...... 289

Chapter 1 Introduction

1.1 Background

Driven piles are a common deep foundation alternative used to support heavy loads when soils

near ground surface are too weak or compressible to support the superstructure. They are typically used to support major structures such as port facilities (piers and wharves), bridges, and high-rise

buildings. The estimation of the axial capacity is a significant task in pile foundation design. Proper

evaluation ensures that the foundation system has adequate capacity to sustain the design loads at

the ultimate limit state (ULS), corresponding to the exceedance of capacity, and the serviceability

limit state (SLS), which corresponds to the loss of function.

The geotechnical engineering field is moving toward reliability based design (Huffman et al.

2016, Stuedlein et al. 2012, Whitman 2000) where sources of uncertainty are assessed rationally

resulting in improved conformity with structural design codes and providing a uniform degree of

the probability of failure (for ULS) or probability of exceeding a given limit state. The American

Association of State Highway and Transportation Officials (AASHTO) and the Federal Highway

Administration (FHWA) initiated reliability based design requirements in 2007 by mandating

usage of resistance factors for bridge foundation design. National calibrations of Load and

Resistance Factor Design (LRFD) reliability-based have exhibited some limitations, particularly

in its implementation in design of driven piles. This has necessitated numerous revisions of the

code as well as recommendations for the development and use of region-based deep foundation

performance data. While substantial efforts has been made by some states to determine

representative resistance factors specific to their geologic regions, there remains a significant need to develop large, representative, high-quality performance data to supplement on-going efforts.

1.2 Statement of Problem

Although several studies have been conducted to evaluate the accuracy and variability of

predicted capacity of driven piles using dynamic formulas, static methods, and wave equation

analysis based methods, most of them, if not all, have suffered from some drawbacks.

Calibrations based on national databases (e.g., Paikowsky et al. 2004, Smith 2011) ensure

statistical randomness and statistical significance because of their large sample size (Paikowsky et

al. (2004): 99 Piles; Smith 2011: 175 piles), causal statistical inferences are still affected by two

major components. Uniformity of geotechnical engineering practice can rarely be accommodated

by national standards, since rational incorporation of inherent soil variability and local construction

practice dictates much of the design. Because soil is not randomly deposited but dictated by auto-

correlated geologic processes, region-specific calibration present a more appropriate approach for capturing these sources of variability. It has also been observed that some national databases

include a considerable amount of error (Smith 2011). In fact, even with an experienced

investigator, it is difficult to ensure that high quality data from multiple sources can be obtained.

Recently, regionally-based calibrations, were developed by several researchers (Kam et al.

2010, Long et al. 2010). However, the lack of a large set of data affects the randomness and statistical significance of the design methods assessed. Developing resistance factors requires assumption about the distribution of the resistance population, small size samples (less than about

40, Reddy and Stuedlein 2012), do not support this essential requirement.

This study resolves the aforementioned limitations by using a region-specific database with an extensive set of information from which sample subsets can be developed and used to assess specific scenarios with representative sample sizes to achieve the following objectives:

• Region specific calibration of resistance factors for use with axial static capacities

calculated using wave equation bearing graph type analysis of driven piles at the End-of-

Driving (EOD) and Begin-of-Restrike (BOR) conditions in accordance with AASHTO

loading statistics.

• Region specific calibration of resistance factors for the FHWA (2006) static analysis

method for the same set of piles as for the Wave Equation Analysis Program (WEAP)

calibrations.

Axial capacity predictions can be based either on methods that require actual driving information, namely pile driving resistance (bpf / blows per 0.3 m), or on methods that only require field investigation and pile properties (geometrical and material properties). The former group of methods include dynamic formulas, and wave equation based methods. The latter set of methods are predictive methods and called static analyses (α-method (Tomlinson, 1987), β-method (Esrig and Kirby, 1979; Fellenius 1991), Schmertmann’s method (1987), Meyerhof’s method (1976)). It is expected in general that dynamic based methods are more accurate than static analysis methods because of the additional information they typically require. While a multitude of approaches based on Standard Penetration Test (SPT) and Cone Penetration Test (CPT) explorations exist, they are based on general soil categorization (sandy versus clayey soils) and developed empirically from correlations to static axial loading test data without consideration of other important insights such as geology, depth, or specific information about the soil type and its density/consistency.

1.3 Purpose of Research

This research focused on the development of new models based on shaft resistance

distributions back-calculated from signal matching to observed stress waves for piles driven in the

Puget Sound Lowlands. The product of this research captures the performance of piles in a given

geologic unit and the effect of local practice, making it suitable for application in this region..

Owing to the consideration of capacity observed at both EOD and BOR, a robust assessment of

the time-dependent gain in capacity (known as setup) was developed.

The findings of this research are expected to help practitioners evaluate the probability of

exceeding allowable shaft interface resistance stresses given selected equipment and model

parameters. Because it is focused on one geological region, the statistics of resistance are expected

to be most suitable for practice in this region. The framework presented herein can serve as a basis

for others to follow for development of region-specific calibrations in other geological regions.

1.4 Organization of this Thesis

This thesis is organized into seven chapters with additional data and details included in

appendices. Following this introductory chapter, Chapter 2 presents a literature review specific to

the state of knowledge of driven piles capacity assessment. Emphasis on wave equation based prediction of pile capacity is made. Also, a description of the well-known wave equation program software GRLWEAP is presented. Chapter 3 describes the research objectives and program developed to accomplish the objectives. Chapter 4 describes the development of effective stress- based shaft resistance models and their use to predict shaft resistance at EOD and BOR. The methodology used to achieve the proposed shaft resistance models is described in detail. Chapter

5 follows up on the work in Chapter 4 to provide a methodology for estimating the time-dependent

gain in capacity using the observed shaft resistance data. Chapter 5 also describes three examples

that show how to use the new approach estimates of setup and relaxation by considering shaft resistance distribution along the pile at EOD and BOR. Chapter 6 evaluates the accuracy and variability of different pile capacity estimation methods. The methodology of the different approaches used to predict the axial capacity of driven piles is described (WEAP based method and FHWA (2006) static method). The subset of data used at EOD and BOR, including differences in the pile geometry, materials, and driving systems is described. Calibrated resistance factors based on Monte Carlo simulations and AASHTO specifications at both driving conditions are presented. Chapter 7 provides a summary of the main findings, the conclusions of this research, and suggestions for future study. Following Chapter 7 is a bibliography of references cited in this research. A set of appendices relevant to the development of the findings follows the bibliography.

Chapter 2 Literature Review 2.1 Introduction

Assessment of axial capacity of driven piles is based on preliminary analysis or actual testing.

The former group include dynamic formulas based on energy balance, wave equation based methods that accounts for the full interaction between pile-driving system-soil, and static analysis methods based on total stress or effective stress. The latter group of methods is based on a direct

verification or determination of the true capacity, either by use of static or dynamic testing. In this

chapter, the focus will be on wave equations analysis of pile driving. After shortly presenting

dynamic formulas, wave equation theory and its applications are emphasized. Then, a short

overview of reliability based design for driven piles is presented.

2.2 Use of Dynamic Formulas to Estimate Pile Axial Capacity

The guiding principle behind all dynamic formulae is that the pile dynamic capacity is related

to the measured permanent displacement of the pile at each hammer impact. The height of the

hammer reflects its potential energy. As the hammer is lowered, this energy is translated to a

kinetic energy and transferred to the pile during impact. The pile then translates this energy into a

penetration into the soil. Based on the balance of the energy given to the pile and the work

produced by the pile to settle permanently, several equations were proposed (Holeyman 1984).

Since the mid-1800s, over 450 dynamic formulas for pile driving monitoring have been suggested

(Hannigan 1990). They are based on the balance of the energy produced by the hammer and the work of soil resistance.

The following four relationships are examples of well-known dynamic formulas used to estimate capacity of driven piles:

Modified Engineering News Record Formula:

eW⋅ ⋅ H W +⋅ n2 W R = RR P (2.1) sc++ WRP W

where: e = Hammer efficiency, WR = Weight of the ram, WP = Weight of the pile, H = Ram drop height or stroke, s = Pile penetration per blow or “set”, c = Elastic compression, and n = Coefficient of restitution

Danish Formula: eE⋅ R = H (2.2) ss+ 0

where: EHR= WH ⋅ (2.3)

and e = Hammer efficiency, WR = Weight of the ram, H = Ram drop height or stroke, s = Pile penetration per blow or “set”, and s0 is defined by the following equation:

eE⋅⋅HP L s0 = (2.4) 2⋅⋅AEPP

where LP = Length of pile, AP = Pile cross section area, EP = Elastic modulus (Young’s modulus) of pile material.

Modified Gates formula:

R=⋅⋅⋅ a eEHblog(10 ⋅ N ) −b (2.5)

where a and b are fitting coefficients. If English units are used, suggested values are:

a =1.75 (2.6)

b=100 kips (2.7)

And NB = Number of blows per inch, EH = Rated energy delivered by the hammer, lb.ft

Janbu formula: eE⋅ R = H (2.8) Ksu ⋅ where

λ = ⋅+ + KCud11 (2.9) C d

and

WP Cd =0.75 + 0.15 (2.10) WR

eE⋅⋅ L λ = HP 2 (2.11) AEsPP⋅⋅

where e, WR , WP , H , EH , s are defined earlier.

Dynamic formulas misrepresent the energy transfer from the hammer to the pile and only consider the energy transfer at impact. Energy losses in the driving system, before hitting the anvil, are due

to friction on ram guides, helmet, and pile and hammer cushions (Hannigan 1990 and Hannigan et

al. 2006). Analysis based on wave propagation was introduced to pile driving by Smith (1960) and

Rausche et al. (1970) to overcome those shortcomings. This method is named Wave Equation

Analysis of Pile (WEAP) driving.

2.3 Wave Equation Analysis of Pile Driving

Smith (1960) developed the first practical model of hammer pile-pile-soil system to predict the drivability and the bearing capacity of driven piles. To account for the dynamic behavior induced by the hammer impact, Smith introduced the so called Smith damping factor. This factor is linearly dependent upon pile velocity. The Smith damping factor is a global parameter intended to account for pile-soil interaction during impact.

Some of the well documented components of the dynamic behavior of pile-soil reaction are:

• Radiation damping: As the pile is driven into the soil, the soil react against the pile

penetration. During this process, energy is transferred to the surrounding soil. Radiation

damping is term that reflects this energy loss due to soil mobilization.

• Hysteretic and viscous damping: Those terms represent the intrinsic behavior of soil as a

plastic, non linear, dissipative material. The viscous damping presents the soil behavior as

a visco-elastic material or dashpot.

• Residual stress analysis: The pile’s shaft resistance tends to restrict the pile’s rebound at

the end of the impact. At least in part, residual stress analysis explains why often blow

counts remain relatively constant as piles are driven to great penetrations. Many authors

(Meyerhof 1976, Vesic 1977) attributed this to the existence of a depth where shaft

resistance reaches a plateau. This explanation is inaccurate as the shaft resistance does

increase with depth. Rausche et al. 2004) presented the case of an open ended pipe 100 m

length where shaft resistance increased along the full length of the pile.

2.3.1 Wave Equation Approach History

The wave equation approach emergence to the geotechnical field, specifically deep foundation practice, is relatively recent. Prior to 1950, usage of wave equation methods to predict pile capacities or optimize driving system was unheard of. The following steps summarizes the major leaps in the development of the WEAP method leading to the most update version of GRLWEAP

(GRLWEAP Background Manual (2010)):

• In the early 1950’s, Smith introduced the wave equation concept.

• Algorithms incorporating wave approach were developed in the USA by Drs. G.G. Goble

and Frank Rausche and co-workers at Case Western University in Cleveland, Ohio in the

late 1960’s and early 1970’s (GRLWEAP 2010).

• In the 1970’s, Federal Highway Administration (FHWA) and Texas Transportation

Institute (TTI) released the WEAP programs (Hirsch et al. (1976) and Goble et al. (1976))

• The software was updated for the first time in 1981, in a cooperation between GRL and

FHWA and New York Department of Transportation (NYDT) (GRLWEAP 2010).

• In 1986, major enhancements to the program, such as the residual stress analysis ( Hery

1983) included in this new version named WEAP 1986 and applicable to both mainframe

and personal computers. At that time the WEAP program moved from research and trial

phases to an established phase where it was accepted all over the world as viable tool in

deep foundation practice.

• From 1986 to this day, continuous improvements have been implemented to several

updated versions: WEAP87 was the last version sponsored by FHWA. After that GRL

became an independently supported company with sufficient income to sponsor their

research. All new versions since then were made under the GRLWEAP version.

GRLWEAP 1993 incorporated a menu driven graphics interface. GRLWEAP released a

1998 Windows version. After that, many enhancements such as static analysis methods

(ST and SA) were included in 2003-2005 versions. The program was lastly updated in 2010

with a new module specific to offshore analysis called “offshore wave”. This new version

includes two additional static analysis methods: a CPT based method using the

Schmertmann procedure and an API based method.

The developed theory was based on wave propagation in slender mediums assuming lateral

friction. Before presenting the numerical developed by Smith (1960), Rausche et al. (1972) to simulate pile driving, the case of wave propagation in a free pile is presented to familiarize with the assumptions, physics and mathematics involved in the development of the wave equation approach to simulate the driving process of piles.

2.3.2 Wave Equation for a Free Pile

The case of a free vertical pile without interaction with soil will be studied because of its simplicity. Afterwards, pile in interaction with soil laterally and at the base will be considered.

Considering an elastic, homogeneous and of constant section pile. Consider a section A ,

positioned at depth z. Its displacement uz due to the compression induced by the hammer impact is defined by:

u= u( zt, ) (2.12) in function of time and of the main spatial dimension z. Newton’s second law applied to an infinitesimal volume of the pile gives:

∂σ  ∂2u ⋅−σσ ⋅ + ⋅ = ρ ⋅ ⋅ ⋅ AAPPdzPP A dz 2 (2.13) ∂∂zt

where AP = pile section area, ρp = Density of the pile material, σ = Axial stress, positive for

∂2u compression, dz = An infinitesimal thickness of the pile = Acceleration of the considered ∂t 2 section. Hooke’s law applied to the considered pile section gives:

σε=EP ⋅ (2.14)

where EP = Elastic (Young’s) modulus of the pile material.

By definition of u as the displacement of the pile section at depth z, it relates to axial strain as following:

∂u ε = (2.15) ∂z By substituting ε in Equation (2.14) by its expression in Equation (2.15), the axial stress became:

∂u σ =E ⋅ (2.16) P ∂z Thus Equation (2.13) became:

∂∂uu22∂u ∂ u + ⋅ − ⋅ ⋅ =ρ ⋅ ⋅⋅ 22dz APP E A PP E PP A dz (2.17) ∂∂zz ∂z ∂ t

Simplification and rearrangement of Equation (2.17) leads to:

∂∂22uuρ =P ⋅ 22 (2.18) ∂∂zEtP

And by defining the wave propagation velocity as:

E c = P (2.19) ρP

Equation (2.18) becomes:

∂∂22uu1 = ⋅ (2.20) ∂∂zct2 22 Equation (2.20) represents the fundamental wave equation of the propagation of an elastic compression wave in a unidimensional elastic medium.

Solution to the one dimensional wave equation:

The wave equation for one dimensional wave propagation in a finite pile can be solved using different methods: (1) Analytically by using Laplace transform method, the method of

characteristics or by separation of variables (2) Numerically by using a finite difference approach

summing elements in space and time. In both cases, initial and boundary conditions are necessary

to provide a unique solution. Convergence of the solution depends on those conditions. In the more

general case, where skin or toe friction exists, convergence of the solution is not guaranteed and

calculations become more expensive with regards to time and sophistication of the solution. One

of the powerful and short solutions for one dimensional wave propagation is the method of

characteristics. This method will be considered herein to illustrate some of the methodologies that

can be used to solve one dimension wave equation in free piles.

According to the method of characteristics, the solution for the wave equation can be written

as follow:

uzt( , ) = uzct12( −+) uzct( +) (2.21)

where u1 and u2 define the form of the waves. They are determined by the initial and boundary

conditions. The directions z= ct and z= − ct are called the characteristics. The main parameters that are required when analyzing the pile movements are stress and velocity and their variation with respect to time and location. Using Equation (2.16) to express the derivative of stress σ with regards to time t and position z:

∂σ ∂ ∂uu  ∂∂  = EEpp =  (2.22) ∂z ∂ z ∂ t  ∂∂ zt 

Or by definition of velocity:

∂u v = (2.23) ∂t

Inserting this into Equation (2.22) gives:

∂∂σ v = E (2.24) ∂∂zzp With respect to time:

∂∂σ  ∂uu ∂2 = = EEpp2 (2.25) ∂∂tt ∂ t ∂ t

∂∂σ v = E (2.26) ∂∂ttp

∂∂σ v = ρ (2.27) ∂∂zt

Let’s construct two variables coinciding with the characteristics z= ct and z= − ct at z = 0 :

ξ =z − ct and η =z + ct

Equations (2.26) and (2.27) can be transformed into:

∂∂σσ  ∂∂vv + =ρc −+ (2.28) ∂∂ξη ∂∂ ξη

∂∂σσ  ∂∂vv −=ρc + (2.29) ∂∂ξη ∂∂ ξη

By adding and subtracting if these two equations:

∂−(σρcv) = 0 (2.30) ∂η

∂+(σρcv) = 0 (2.31) ∂η

Or, impedance is defined as:

Jc= ρ (2.32)

Therefore Equations (2.31) and (2.32) can be written as:

∂−(σ Jv) = 0 (2.33) ∂η

∂+(σ Jv) = 0 (2.34) ∂η

In terms of the original variables z and t, the equations become:

∂−(σ Jv) = 0 (2.35) ∂+( z ct)

∂+(σ Jv) = 0 (2.36) ∂−( z ct)

The last equations means that the term σ − Jv is independent of z+ ct , and σ + Jv is independent of z− ct . Therefore:

σ −=Jv f1(z − ct) (2.37)

σ +=Jv f1(z + ct) (2.38)

These equations means that σ − Jv is a function of z− ct only, and that σ + Jv is a function of z+ ct only. Consequently, if z− ct is constant so is σ − Jv and that σ + Jv is constant when

z+ ct is constant. These properties relating stress and velocity to time and space helps construct

solution either analytically or graphically by mapping the solution in z and ct planes.

In the case of a free pile that is impacted at the top z = 0 at time t = 0 resulting in a stress

− p . The toe of the pile zh= is considered free with a stress equal to zero. This is illustrated in

Figure 2.1. The solution by mapping will be used here to illustrate the method of characteristics for solving the one dimensional wave equation. The solution is shown in Figure 2.1. In the upper figure, lines of constant z− ct and z+ ct are drawn in z , ct space.

Figure 2.1. Example boundary condition for a free pile and illustration of methods of characteristics geometrically 2.3.3 Wave Equation Theory in GRLWEAP

In GRLWEAP (2010), the pile and driving system including hammer, helmet, and cushions

are modeled by a set of segments consisting of a point mass and a spring. In GRLWEAP (2010),

default pile segments length is one meter. Specified lengths are possible, they can improve the accuracy of the solution but usually require longer computational time. Stiffness of attached springs is computed from modulus of elasticity, unit weight and cross sectional area. The mass is calculated by simply multiplying unit weight of the pile with cross sectional area and segment length.

Hammer and pile cushions are typically used for concrete piles, and only hammer cushions for steel piles because steel piles are not as prone to driving stresses as concrete piles. In addition to geometrical and material parameters, coefficients of restitution (COR) can be specified to model energy losses in cushion materials. COR is a parameter representing the remaining kinetic energy for one object after collision with a second object. It is equal of less than unity. A value of one means that no energy was lost after the impact. A value less than one means that work was lost in deforming the impacted object.

The soil is represented by static and dynamic components along the pile shaft and toe. Every embedded pile segment is connected to a soil element applying static and dynamic forces. The static soil resistance is modeled by an elasto-plastic spring and the dynamic soil resistance by a dashpot. Figure 2.2 illustrates the hammer-cushion-pile-soil model in the wave equation model while Figure 2.3 illustrates the static resistance where soil behave elastically until a limit value referred to as quake where soil become plastic and further displacement do not result in a larger resistance. The dynamic soil resistance is proportional to the pile velocity through a damping factor

(Smith 1960).

Figure 2.2. Driving system- pile- soil discrete model used in WEAP analysis for a Diesel hammer (Modified after GRLWEAP Background Manual 2010)

Figure 2.3. Static and dynamic resistance force models

2.3.3.1 Bearing capacity analysis

One of the most common application of WEAP based analysis is the bearing graph calculation

(GRLWEAP 2010). This analysis simulates pile resistance to driving and produces a relationship between driving resistance (blow count) and pile static capacity. Several total capacities are assumed and distributed on shaft and toe resistance as well their percentage from total capacity.

After assuming driving system (Hammer type, cushion thickness, Coefficient of restitution), the dynamic analysis is launched. Figure 2.4 shows two waves corresponding to a propagated wave and a reflected one. It was produced using GRLWEAP program. Figure 2.5 shows an example of a bearing graph produced using GRLWEAP. In addition to bearing graph analysis, other types of analyses may be conducted, of major importance is drivability analysis.

Figure 2.4. Example of calculated force and reflected velocity from wave equation theory (GRLWEAP 2010 version Program was used to generate it)

Figure 2.5. Example of GRLWEAP bearing capacity results (capacity, stroke and compressive and tensile stresses as a function of blow count)

2.3.3.2 Drivability Analysis of Driven Piles

This analysis is similar to bearing graph analysis but for several depths whereas the bearing graph is used only to estimate capacity at the depth of penetration. This analysis calculates also stresses and transferred energy versus the pile penetration. Figure 2.6 presents a flow chart for running a typical driveability analysis. First the driving system, including hammer type and cushion thickness are entered. After that, the pile material and geometrical properties are identified. Soil static and dynamic properties are then entered or typically recommended values are used. Then static resistance for the selected depths should be estimated. This is typically done by running static analysis. Finally a graph relating driving resistance to depth is generated.

Figure 2.6. Drivability study flow chart in WEAP analysis

2.4 Dynamic Testing of Driven Piles 2.4.1 Dynamic Testing Setup

Dynamic testing of driven piles is a common tool to determine or verify their axial capacity.

Figure 2.7 shows a typical setup for dynamic testing with a PDA. The major steps in a dynamic

test calculation can be summarized as follow:

1- Two strain transducers and two accelerometers are bolted two widths below the pile top

2- A computer with a data logger (data acquisition system) digitizes the information signals ( A data logger is a device equipped with a microprocessor and sensors, the data logger interface with

a computer that has a built in software to activate the data logger and view and analyze the collected

data).

After each blow, a signal of pile strain and acceleration is recorded. Multiplying the pile strain by the pile area and the dynamic elastic modulus results in a force; Integrates the acceleration with time gives the velocity. The result is a plot of pile top force and velocity versus time. As the hammer impacts the pile, a downward-travelling force is initiated and travels down the pile, the changes in pile impedance combined with the mobilized side and toe resistance from the surrounding soil (or rock) reflect an upward-travelling wave. So now there are two waves, a downward wave and an upward wave. The downward wave is calculated as the average of the sum of the pile top force and the particle velocity times impedance. The upward wave is calculated as the difference of the pile top force and of the pile particle velocity impedance. The impedance Z is equal to EA/c which is equal to the product of ρ , c and A , where E is the pile material modulus of elasticity (Dynamic elastic modulus), A is the pile cross-sectional area, c is the speed of the wave in the pile, and ρ is the mass density of the pile. The parameter c can be determined from the

time (2L/c) required for the wave to travel up and down the pile length. This is determined from

the observed reflection of the impact wave returning from the toe.

Figure 2.7. Dynamic testing main logistics and setup

2.4.2 Advantages of Dynamic Testing

Bullock (2012) has written a comprehensive paper describing the advantages of dynamic pile testing. Static load testing is the most accurate method for predicting static capacity, however routine test do not include static loading tests in their programs due to cost and time prohibitions.

Dynamic testing represent a much more feasible alternative with many advantages and applications. Dynamic testing can be used for one or more of the following purposes (Salgado

2009, Bullock 2012):

• Predict how hard it is to drive a pile to some given static resistance and what stresses

develop in the pile during driving.

• Detect pile anomalies due to pile installation based on measurements of force and velocity

near the pile head during driving.

• Estimate static bearing capacity based on measurements of force and velocity near the pile

head during driving.

Comparison between static loading test and dynamic loading testing shows that dynamic

testing offers unique advantages. The following points present some of the main advantages of

dynamic testing when compared to static testing:

• Dynamic tests are relatively inexpensive.

• Dynamic tests cause only minor delays to the project. It takes only 30 minutes to install the

sensors. Static testing may require more than two weeks to install the loading frame.

• Dynamic tests can be performed on onshore as well as offshore sites. They can be easily

performed on any accessible pile. In offshore piling, static tests may require mobile

platforms to ensure proper transfer of loads to the pile.

• An impact weight of 1.5% of the desired static resistance is sufficient when using dynamic

tests. This is a significant advantage when testing high-capacity piles (Bullock 2005).

• Static tests may or may not measure the load distribution, dynamic test results with signal

matching (CAPWAP) always compute shaft resistance distribution

• Dynamic tests provide an easy means for evaluating gain in capacity as a function of time.

Subsequent delayed pile driving can be conducted to study effects of time in capacity

changes.

A brief comparison between both tests with regards to price, time, site accessibility, impact weight, shaft distribution determination and reliability is sketched in Figure 2.8. A green check mark is attributed to the optimal test with regards to a specific property exclusively assuming all others are equal or insignificant to the design decision.

It is clear that dynamic testing is a very appealing alternative for assessing ultimate resistance.

However, it is still an indirect measurement method where analytical procedures, pile parameters

and soil properties are assumed. Only a static tests can verify the actual true resistance, especially

if full mobilization is reached. For this reason, it is advisable for large projects and unusual sites to use a static load test as a means to verify dynamic testing results. Static loading tests are clearly more reliable especially in unknown sites where no previous experience. Static loading test requires little interpretation compared to dynamic testing where many assumptions and simplifications are required. Reliability of dynamic testing improves with consideration of site stratigraphy. Calibration to static resistance therefore would assure more accurate and reliable dynamic testing results.

Figure 2.8. Simplified comparison between dynamic testing and static testing Note that static testing is irreplaceable for highly reliable measurements.

2.5 Static Analysis Using Standard Penetration Test Correlations

Early stage design of driven piles use correlations based on soil properties. Those methods are

referred to as static analysis approaches. In this section, one static analysis method named FHWA-

SA herein will be presented. Its accuracy will be assessed in Chapter 6. This method is a static

analysis method using in situ SPT results. This method is implemented in GRLWEAP within the

Variable Resistance Distribution option. The SA method is inspired from the FHWA (Hannigan

et al. 2006) recommendation with minor modifications. The SA method can be used for cohesive

as well as granular soils to predict either shaft or toe resistance. It can be used for both bearing

graph and drivability Analyses.

The user can input either friction angle or relative density for granular soils. For cohesive soils,

undrained shear strength or friction angle can be used. Also the user is allowed to enter unit shaft

resistances directly and toe bearing values.

The SA method as implemented in GRLWEAP suffers from three limitations:

• It is not applicable to rock

• Blow count values N are limited to 60

• SPT N-value is not adjusted to N60 thus not accounting for the transfer efficiency of SPT

hammers

If rock is encountered, it is always possible to compute the corresponding unit shaft or toe

resistance using other methods from the literature, then enter those values into the program.

Shaft resistance is computed using formulas from the literature relating SPT N-values to relative density Dr (Kulhawy 1989 and 1991) and effective friction angle (Schmertmann (1975

and 1978), and earth pressure coefficient (Robertson and Campanella 1983). The calculation of

unit shaft toe resistance is different for sands and gravels, clays, and silts. Figure 2.9 and Figure

2.10 summarize the procedure used to obtain unit shaft resistance for different soil types. Note, the

only necessary data are SPT N-values and basic soil type classification to initiate the procedure.

Toe resistance is mainly based on empirical correlations between SPT N-value and unit toe

resistance. Figure 2.11 illustrates the different steps used to compute unit toe resistance for the

different soil types.

Silt

Find soil unit weight γ based on Bowles

’ Determine vertical effective stress σ v based on mid-layer location and ground water table

Cohesionless Cohesive

Use ’ φ’for sands Use ’φ’ for clays and gravels φ φ

Estimate Bjerrum-Borland β coefficient: 28 = + 0.27 ′0.23 𝜑𝜑 −6 𝛽𝛽

Calculate unit ’shaft resistance: σ v , = ’

𝑞𝑞𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝛽𝛽σ 𝑣𝑣 = min( , , 250 ) = min( , , 250 )

𝑞𝑞𝑠𝑠 𝑞𝑞𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑘𝑘𝑘𝑘𝑘𝑘 𝑞𝑞𝑠𝑠 𝑞𝑞𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑘𝑘𝑘𝑘𝑘𝑘 Figure 2.9. Unit shaft resistance methodology determination based on the SA method for silty soils

Establish soil profile based on SPT N-value result and soil type classification

Find soil unit weight γ based on Bowles (1977)

’ Determine vertical effective stress σ v based on mid-layer location and ground water table Sand and Gravel Clay Compute friction angle: Determine relative density Dr based φ’ on Kulhawy (1989 and 1991) ’ = min(17 + 0.5N, 43) deg φ Define a valueφ’ for pile-soil Compute effective friction angle friction: Use δ = φ’ φ’ based on Schmertmann (1975 and 1978) Estimate overconsolidationφ’ ratio: 18 Assume pile-soil friction δ as a = ’ ; ’ function of φ’: Use δ = φ’ 𝑁𝑁 𝑣𝑣 𝑂𝑂𝑂𝑂𝑂𝑂 �σ 𝑣𝑣 σ 𝑖𝑖𝑖𝑖 𝑘𝑘𝑘𝑘𝑘𝑘 Comupute k0 using Jaky Find earth pressure coefficient at rest estimate for knc : k0 according to Robertson and = φ’( ) . Campanella (1983) with the constraint: . = (1 sin ’)( 0 5) 𝑘𝑘0 𝑘𝑘𝑛𝑛𝑛𝑛 𝑂𝑂𝑂𝑂𝑂𝑂 (1 sin ’) (1 + sin ’) 0 5 < k < − φ 𝑂𝑂𝑂𝑂𝑂𝑂 (1 + sin ’) (1 sin ’) − φ 0 φ φ − φ

Calculate unit shaft’ resistance: σ v , = k tan ’

𝑞𝑞𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 0 δ σ 𝑣𝑣 Use a reasonable value by Use a reasonable value by limiting unit shaft’ resistance: ’ σ v limiting unit shaftσ v resistance:

= min( , , 250 ) = min( , , 75 )

𝑞𝑞𝑠𝑠 𝑞𝑞𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑘𝑘𝑘𝑘𝑘𝑘 𝑞𝑞𝑠𝑠 𝑞𝑞𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑘𝑘𝑘𝑘𝑘𝑘 Figure 2.10. Unit shaft resistance methodology determination based on the SA method for sand, gravel, and clay

Establish soil profile based on SPT N-value result and soil type classification

Sand and Gravel Clay Silt

Estimate unit toe bearing Estimate unit toe bearing Use toe capacity coefficient resistance: resistance: d based on Fellenius (1996): , = 200 , = 54 = ( 28)/0.3 + 20 𝑞𝑞𝑡𝑡𝑡𝑡𝑡𝑡Units𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 in kPa 𝑁𝑁 𝑡𝑡𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ′ 𝑞𝑞 Units in kPa 𝑁𝑁 𝑁𝑁𝑡𝑡 With𝜑𝜑 20− 40

≤ 𝑁𝑁𝑡𝑡 ≤

Estimate unit toe bearing Limit qtoe by using: Limit qtoe by using: resistance, Nt: = min( , 12000 ) = min( , 3240 ) , , = min( ’ , 6000 𝑞𝑞𝑡𝑡𝑡𝑡𝑡𝑡 𝑞𝑞𝑡𝑡𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑘𝑘𝑘𝑘𝑘𝑘 𝑞𝑞𝑡𝑡𝑡𝑡𝑡𝑡 𝑞𝑞𝑡𝑡𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑘𝑘𝑘𝑘𝑘𝑘 𝑞𝑞𝑡𝑡𝑡𝑡𝑡𝑡 𝑁𝑁𝑡𝑡σ 𝑣𝑣 𝑘𝑘𝑘𝑘𝑘𝑘

Figure 2.11. Unit toe resistance determination for the SA method

2.6 LRFD Reliability Theory

Reliability theory is a scientific approach using probability and statistic tools to quantify chances of failure for a given structural element. Opposite to a global factor of safety where all sources of uncertainty are lumped in a unified number. This last approach is obviously qualitative.

The objective of reliability theory is to assure that the applied loads to a given structural element are less than the available resistance. For that, the following inequality must be verified:

γϕ≤ ∑ iQR ni n

where, is a load factor associated with a specific type of load , is larger than or equal to

𝑖𝑖 𝑛𝑛𝑛𝑛 𝑖𝑖 unity with𝛾𝛾 higher values attributed to loads with larger sources of𝑄𝑄 uncertainty.𝛾𝛾 is the resistance

factor, and is the nominal resistance (also known as ultimate resistance 𝜑𝜑or capacity). The

𝑛𝑛 resistance factor𝑅𝑅 is always smaller or equal to unity.

Figure 2.12. General concepts of load and resistance distribution in reliability theory.

In this theory, loads and resistance are assumed to be random variables. Those random

variables are defined using𝑄𝑄 a specific type𝑅𝑅 of frequency distribution (e.g., Normal, lognormal,

Weibull) and statistical parameters that characterizes that type of distribution (e.g., mean and

standard deviation in the case of a normal distribution). As shown in Figure 2.12 and Figure 2.13,

load and resistance distributions are illustrated. The overlap between the two curves represents the

probability of failure. When plotting R - Q, the probability of failure is represented in the

𝑓𝑓 reliability analysis by the reliability index β. The reliability index β 𝑝𝑝represents the distance

measured in standard deviations between the mean safety margin and the failure limit. The larger

the value of β the farther is the mean from failure limit suggesting a lower probability of failure.

Figure 2.13. Probability of failure and reliability index

The combination of load and resistance factors controls the probability of failure. By considering a target reliability (value of β), an acceptably small probability of failure is can be assured (Allen et al. 2005).

Estimation of reliable resistance factors must be based on a robust analysis. Paikowsky (2004),

Allen et al. (2005), Barker et al. (1991) suggested the following approach to develop resistance factors in geotechnical practice. This general approach is very intuitive and coincides with structural practice with the exception of additional sources of uncertainty that are inherent to geotechnical practice. Within this general approach, four main steps are necessary:

1- Gather sufficient data relevant to the type of considered structural element load and resistance variables. This step is needed to statistically characterize the key load and resistance random variables, such as the mean, COV and distribution function. Collected data quantity and quality must be assessed, notified and incorporated in subsequent treatments.

2- Assess design model error by estimating the reliability inherent in current design methods.

3-Select a target reliability based on the margin of safety implied in current designs, considering the need for consistency with the reliability used in the development of the rest of the AASHTO

LRFD specifications, and considering levels of reliability for geotechnical design as reported in the literature

4- Determine load and resistance factors consistent with the selected target reliability.

2.6.1 First Order Second Moment (FOSM)

This approach is a simplified way to model variability in some output y (load or resistance)

related to some inputs x1 , x2 …. xn through a model equation g :

y= gx(123 , x , x ,....., xn )

µ= ( µµµ , , ,...... , µ ) g can be approximated at the mean vector xx123 x xn by a Taylor series:

1n∂∂gg ()µµ 1nn 2 () gx()()= gµ +∑ ()xii −+µ∑∑ ()()xiijj−µµ x − + 12i=1∂xi ij=11 = ∂∂xxij

1nnn ∂3 g()µ ∑∑∑ (xxi−µµ i )( j − jk )( x −+ µ k ) ...... 6 i=111 jk = = ∂∂xxi jk ∂ x

For an estimate at the first order of accuracy, g reduces to:

1n ∂g ()µ y==+− gx() g (µµ )∑ (xii ) (2.39) 1 i=1 ∂xi

The mean value of g is given by:

+∞ µ = = gXEgx[ ()] ∫ gxf () () xdx (2.40) −∞

Inserting the first-order Taylor series from Equation (2.39) into Equation (2.40) leads to:

+∞ n ∂g()µ µµ≈+ − µ g∫ g( )∑ (xi iX ) f () x dx −∞ i=1 ∂xi

+∞ +∞ n ∂g()µ µµ≈ +−µ g ∫∫g( ) fX () x dx ∑ (xi iX ) f () x dx −∞ −∞ i=1 ∂xi

∂g()µ Since g()µ and are constants, they can be moved outside the integral: ∂xi

+∞ n ∂g()µ +∞ µµ≈ +−µ g g( )∫∫ fX () x dx ∑ (xi iX ) f () x dx (2.41) −∞ i=1 ∂xi −∞

+∞ = Or, by definition: ∫ fX () x dx 1 −∞

+∞ −=µ Also ∫ (xi iX ) f () x dx 0 −∞

Finally Equation (2.41) becomes: µµg = g()

This means that the mean of the objective function g is simply its value at the mean vector

µ . This way, the mean of the output function y requires only (1) mean of the input values x1 ,

x2 …. xn (2) A model equation g relating inputs to the output function.

The variance of g is defined by the following equation:

2 σµ2 = − ggE( gx() )

Using the formula for the variance, this equation can be written as:

2 22 σµgg=Egx( ()) −

+∞ σµ22= − 2 g∫ g(x) f Xg ( x ) dx (2.42) −∞

Inserting Equation (2.39) by replacing g by its first-order Taylor approximate at the mean vector into Equation (2.42) gives:

2 +∞ n ∂g()µ σµ22≈+ − µ − µ g∫ g( )∑ (xii ) f X () x dx g −∞ i=1 ∂xi

2 2 +∞ nn∂∂gg()µµ() σ22≈ µµ + −+ µ − µ− µ2 g∫ g() 2() g ∑∑ (xii ) (xii ) f X () x dx g = ∂∂xx= −∞ ii11ii

2 +∞ +∞ nn∂∂gg()µµ+∞ () σµ22≈ + µ −+ µ −µ − µ2 g∫∫g( ) fX () x dx 2( g )∑∑ (xiiX ) f () x dx ∫(xii ) f X () x dx g −∞ −∞ ii=11∂∂xxii−∞ =

By moving constants out of the integrals, and using the following equality, this can be proven easily recursively:

2 n∂g()µ nn∂∂gg()µµ () ∑ ()xii−=µ∑∑ ()()xxiijj−µµ − i=1∂xi ij=11 = ∂∂xxij

The variance can be expressed as:

+∞ n ∂g()µ +∞ σµ22≈ + µ −+ µ g g( )∫∫ fX () x dx 2( g )∑ (xi iX ) f () x dx −∞ i=1 ∂xi −∞

+∞ nn∂∂gg()µµ () +(x−−µµ )( x ) f ( x ) dx − µ2 ∫ ∑∑ ∂∂ i ij jX g −∞ ij=11 = xxij

Simplified, this equation can be written as:

nn∂∂gg()µµ ()+∞ σµ22≈+ −−µ µ − µ2 g g() ∑∑ ∫ (xi i )( x j jX ) f ( x ) dx g (2.43) ij=11 = ∂∂xxij−∞

Since g()µµ= g this expression can be further simplified to:

nn∂∂gg()µµ ()+∞ σ2 ≈ −−µµ g ∑∑ ∫ (xi i )( x j jX ) f ( x ) dx ij=11 = ∂∂xxij−∞

Or, by definition of covariance:

+∞ =−−µµ cov(xi , x j )∫ ( x i i )( x j jX ) f ( x ) dx (2.44) −∞

Inserting Equation (2.43) into Equation (2.44) gives:

nn 2 ∂∂gg()µµ () σ g≈ ∑∑ cov(xxij , ) ij=11 = ∂∂xxij

The indices i and j are interchangeable, expanding the equation by separating squares and simple multiplication make the calculation easier:

2 n ∂gnn ∂∂ gg()µµ () σσ22≈+2 cov(xx , ) g∑ xi  ∑∑ ij i=11∂xi i= ji ≠ ∂∂ xxij

Many of the AASHTO specifications (including AASHTO 2002 and AASHTO 2005) were based on the FOSM method. By assuming lognormal distribution for resistance, the resistance factor is given by (Barker et al. 1991):

1+ COV 2 λγ Q R()∑ iiQ 2 1+ COVR φ = (2.45) 22 Q expβ ln( 1++COVRQ)( 1 COV ) 

where λR = bias in resistance, β = target reliability index, and COVQ = coefficient of variation

σ Q of load, it is equal to the ratio of standard deviation in load to the mean of the load COVQ = µQ

COVR = coefficient of variation of the resistance.

If only dead and live loads are taken into consideration, Equation (2.45) can be rewritten as:

1++COV22 COV γ DDQ QQDL λγRL()+ 2 Q1LR+ COV φ = (2.46) λ QDQ 2 22 D +λβexp ln 1 +COV 1 ++ COV COV QL( R)( QQDL) QL 

Where γ D , γ L = dead and live load factors. They are used to represent uncertainty in these type

γ =1.25 COV =10% γ =1.75 of loads. Typical values are: D associated with QD and L associated

COV = 20% Q Q = λ , λ = with QL , D , L dead and live loads, and QD QL dead and live load bias factors

2.6.2 Statistics Necessary for Reliability Calibrations

To model the observed distribution of a random variable X for reliability purposes, a

mathematically defined distributed function is necessary. The purpose of this distribution function

is to represent conveniently the studied random variable. Numerous type of functions are available

to fit the observed distribution of resistance bias. The distribution function can be either a

probability density function (PDF) or cumulative distribution function (CDF). The most common

types of distribution functions and presented briefly here are normal and lognormal distribution.

The PDF for a normal distribution is:

2 (x−µ) − 1 2σ 2 fxX ()= e (2.47) σπ2

where µ the sample is mean, also called expectation, and σ is the sample standard deviation

The PDF for a lognormal distribution is:

1ln(x)−µ − ln 1 2σ ln fxX ()= e (2.48) σπln 2 x

where µln the sample is mean and σ ln is the standard deviation for ln(QQmp / ) values. The

parameters µln and σ ln are sufficient to fully characterize a lognormal distribution. They are characteristics and completely define the shape of the PDF. Sample and standard deviation are proxies for accuracy and variably, respectively. An accurate method on average would result in a bias close to unity. A bias larger than one means the predictive method overestimate actual

resistance, whereas a value smaller than one underestimate actual capacity on average. The

following section will explain those two concepts in more detail.

Bias and variability:

As mentioned earlier, bias is a measure of tendency of a sample to over or under estimate

resistance. It measures the systematic error between the average ratio of predicted capacity to

measured capacity (/)QQmp. A method that provides a value close to one is supposedly more

accurate on average. Bias is typically quantified with sample mean. On the other hand, variability

in (/)QQmp is quantified by sample standard deviation or coefficient of variation. Variability is

an important statistic parameter as it describes how trustworthy a method is.

Depending on the assumed distribution for (/)QQmp, a corresponding mean and standard

deviation can be determined. A normal distribution means that values of (/)QQmp are normally

distributed. Therefore, the mean and standard deviation for (/)QQmp is computed using the following equations, respectively:

1 n Q µ = ∑ m (2.49) nQi=1 p

1 n Q σµ2 = m − (2.50) − ∑ nQ1 i=1 p

where n is the sample size corresponding to the number of observations used. A mean value equal

to one represent that on average, the predictive method is perfectly accurate and predicted capacity

is equal to measured capacity. A bias value smaller than one, µ <1, means that the model, or the predictive method, under predicts the axial capacity, whereas a value larger than one means that the model over predicts the measured axial capacity. Typically, a specific method with a mean bias larger than one is conservative on average, if it is smaller the unity then it is considered non conservative on average. The variability or uncertainty in a model is quantified by the standard deviation,σ , capturing the scatter in the model. The larger the value of standard deviation, the greater the variation or dispersion of data. A low standard deviation indicates that the values

majority of (/)QQmp values are closer to the mean bias. Another measurement for variability is the coefficient of the variation (COV) in bias. It is defined as the ratio of standard deviation to the bias mean:

σ COV = (2.51) µ

COV is typically reported in percent. This measurement serve to compare scatter or uncertainty in model. A model with a larger COV compared to a second one, means the first model is poorer.

This can be seen as a proxy for the quality of a model compared to mean bias that reflects its accuracy on average. A model with a small COV is evidently preferable over a model with a relatively larger one, but this is a simplified comparison that is subjective and omits other important considerations such as the method soundness, simplicity and cost. Equations (2.49) to (51) are a means of providing quantitative descriptors of accuracy and variability. It should be noted that

COV and standard deviation are interchangeable and only one of them presented along with mean bias is sufficient, as the other statistic can be inferred easily, because the three statistics are related through Equation (2.51). In this section and later, the combination of mean bias and COV will be

the preferred one. A clear advantage of COV is its representability not only of uncertainty but also the relative standard deviation, it is a standardized measure of variability or dispersion.

If a lognormal is assumed to be a better fit to capture (/)QQmpvalues, the following calculations are used to determine mean bias and standard deviation instead. Lognormal statistics will be noted with an ln subscript referring to natural logarithm. A lognormal distribution means

that the values of ln(QQmp / ) are normally distributed. Thusly, mean bias and standard deviation

are defined in the same way as for a normal distribution with the exception of using ln(QQmp / )

instead of (/)QQmp. Accordingly the means bias µln and standard deviation for ln(QQmp / ) values are defined as:

1 n Q µ = m (2.52) ln ∑ln  nQi=1 p

2 1 n Q σµ2 = ln m − (2.53) ln − ∑ ln nQ1 i=1 p

2 2 (n - 1) is used instead of n when determining variances σ andσ ln of (/)QQmp values to ensure that the sample variance is unbiased. This is a crucial statistical requirement that means that the average of the sample variances is equal to the population variance. This is wanted as it means that sample variance is an actual representation of the population variance. It should be noted that sample variance is typically noted s2 in statistics and σ 2 denote the population sample. In this research σ 2 refers to sample bias, otherwise it should be understood from the context. It can be

proved arithmetically that the sum of sample variances using a subset of size (n-1) is equal to the

population variance.

2.7 Development of Recommended Resistance Factors for Driven Piles

Owing to the multitude of methods available for calibration, newness of reliability treatments

to geotechnical practice, and specificities of inherent uncertainty in geotechnical engineering, a

consistent, unified and automatic method for calibration of resistance factors is not available till

now. However, major progress was made in recent decades (Barker 1991, Paikowsky 2004, Allen

et al. 2005) to shorten the gap between structural and geotechnical design in aim to (1) be consistent

with AASHTO LRFD structural codes (2) Use more robust reliability approaches for

determination of resistance factors.

Driven piles as a major element of deep foundations have been studied by many researchers with regards to their reliability. Allen (2005) summarized some of this findings (see Table 2.1) for different conditions, including bearing, uplift and group uplift resistance, and using different methods, including static and dynamic testing, dynamic formulas and wave equation analysis.

(After Allen Allen (2005)) (After

. Calibration results for different strength limits of driven piles using different methods of calibration of methods different using piles driven of limits strength different for results Calibration . 1 . 2 Table Table

2.8 Summary

Driven Piles are the most common system of deep foundations and estimation of their axial capacity is an important task. One of the main methods used to predict capacity of piles is based on WEAP approach and named bearing graph analysis. This literature review provides the basics of this method as well as examples of its application.

Recently, AASHTO and FHWA recommend the usage of resistance factors to incorporate uncertainty in a quantified manner. Although many researchers (Paikowsky et al. 2004) calibrated resistance factors for WEAP, limitations were encountered either because of the lack of a specific region or because of the small size of the used database. This work aims to overcome those limitation by studying setup and calibrating resistance factors using a large database specific to one geological reason, the Puget Sound Lowlands. Chapter 4 will propose new β-coefficient models based on dynamic testing of driven piles and Chapter 5 will provide models for predicting time-dependent gain in capacity. Finally, Chapter 6, will use the same database to calibrate resistance factors for two static analyses and two WEAP based methods, providing therefore a framework for local application.

Chapter 3 Research Objectives and Program

3.1 Research Objectives

This research aims to accomplish two tasks related to driven piles design. New static models

based on the effective stress method and specific for the Puget Sound Lowlands geology were

developed, both at EOD and BOR, thus accounting for changes in resistance with time (Setup or

Relaxation). Studies for calibration of resistance factors specific to the Puget Sound Lowlands

were made for different predictive methods of axial capacity, including the FHWA (2006) static

analysis method based on SPT measurements, wave equation analysis based approach (WEAP),

as well as assessment of the new developed β-coefficident accuraly in predicting shaft resistance,

all with reference to signal matching based on observed sresses waves during pile driving

(CAPWAP technique).

3.2 Research Program

The research methodology implemented to achieve the aims of this research can be divided into two major subtopics:

A. Development of new β-coefficient models and assessment of setup include the following

components:

1) Filter developed driven piles data for piles where both End of Driving (EOD) and

Beginning of Restrike (BOR) records are available.

2) Filter again the filtered data based on depth of penetration and select piles where the depth

of penetration remains approximately the same at both conditions. A toe displacement cut

off difference of 0.1 between EOD and BOR conditions was used for the final selection.

This ensures a fair comparison in induced resistance at EOD and BOR, avoiding thus

overlap and non-total correspondence between soil segments during CAPWAP analysis as

well as insuring total coincidence between soil profile at EOD and BOR.

3) Establish representative soil profile for each pile by (1) gathering all available in situ data

from geotechnical reports, (2) develop representative generalized soil profile, (3) consider

specific geology for uncertain strata and finally infer soil profile coinciding with desired

pile location.

4) Develop a suite of continuous functions to capture β-coefficient variation by fitting USCS

soil type and soil density/consistency as a function of depth using least squares method and

forcing bias to be equal to one to ensure usability for LRFD calibrations (Chapter 4).

5) Inform about shaft distribution at EOD and Beginning or restrike and necessity of layering

to make an informed decision about setup potential and magnitude (Chapter 5).

6) Develop equations accounting for soil type and depth for prediction of setup based on new

β-coefficient models (Chapter 5).

B. Development of Calibrated Resistance Factors for Axial Capacity Using different

Predictive Methods include the following components:

1) Use of the aforementioned data to assessment of axial capacity of different predictive

methods WEAP through the bearing graph option in GRLWEAP, FHWA 2006 static

analysis method, implemented in GRLWEAP as the SA method, and the new developed

β-coefficient models (Chapter 6).

2) Develop resistance factors using Monte Carlo simulation in compliance with AASHTO

2014 load statistics at End of Driving (EOD) and Beginning of restrike (BOR) (Chapter

6).

4 Chapter 4 Development of New Shaft Resistance Models for Piles Driven in the Puget Sound Lowlands

4.1 Introduction

The design of the axial capacity of driven piles during the planning stages of a project is

typically based on a static analysis approach. The goals of this approach are to predict the

components of capacity, consisting of the shaft and toe bearing resistances, and to assess project

concept feasibility. In most cases, this analysis is based on empirically-developed methods, such

as the total stress method, also known as the α method (Tomlinson 1987), effective stress method

known as the β method (Esrig and Kirby 1979; Fellenius 1991) or a hybrid of both methods, the

λ method (Vijayvergiya and Focht, 1972). Many other methods, such as those based on in-situ test

results exist and rely on correlations of blow counts from SPT, and cone tip and sleeve friction resistance from CPT, to shaft and toe pile resistances (Schmertmann 1987; Meyerhof 1976;

Nottingham and Schmertmann 1975; Nordlund 1963; Brown 2001; Eslami and Fellenius, 1997;

Laboratoire des Ponts et Chaussees 1983; DeRuiter and Beringen 1979). Although these methods were generally developed using data from specific geological regions, they are often recommended in national design manuals (e.g., FHWA (Hannigan et al. 2006).

The study described in this chapter aims to develop new effective stress-based models for piles driven in the Puget Sound Lowlands. The models are developed for End-of-Driving (EOD) and

Beginning-of-Restrike (BOR) driving conditions. Instead of using β-coefficients based on total

capacity back-calculated from non-instrumented static pile testing, the shaft resistance distribution, soil type, and density or consistency are considered in the development of the new models. Finally, 48

considerations of the sample sizes, accuracy and uncertainty of the new developed models are evaluated as required for reliability theory-based LRFD implementation (Allen 2005; Bathurst et al. 2011).

4.2 Selection of the Reference Capacity: CAse Pile Wave Analysis Program (CAPWAP) Technique

Any consideration of the accuracy and uncertainty of a given design methodology requires the selection of the interpreted failure capacity (Stuedlein et al. 2015). In this study, the results of dynamic loading tests (DLTs) assessed with the stress wave analyses are used to develop the static failure capacity that will serve as the reference capacity for the development of accuracy statistics.

The CAPWAP technique is a post-processing signal matching method based on results gathered through the Pile Driving Analyzer (PDA; Rausche et al. 1972). The instrumentation consists of two accelerometers and two strain gages mounted in diametrically opposed pairs near the pile head. The signal matching procedure, described in detail by Rausche et al. (2010), uses the force time history computed from the measured dynamic strain as a reference, from which iterative trials of computed force time history with varying assumed static and dynamic soil resistance parameters are evaluated against. This iterative approach uses the product of the velocity time history (deduced from the acceleration measurements) and the pile impedance as an independent forcing function from which the error in signal matching iteration may be minimized. The computed force time history curve requires the selection of appropriate shaft and toe quake (i.e., the displacement corresponding to the transition from the assumed elastic and plastic displacement response), the shaft and toe damping (correlated to the dynamic component of resistance); and the static load transfer distribution along the pile.

Using measurements of the strain (and computed force) and acceleration time history at the pile head from a single blow during dynamic testing, the CAPWAP user iteratively changes the

quake and damping parameters used in the soil model to obtain the best match of a complimentary

wave. Since this procedure requires user input; they are affected by engineering judgment and

experience. Of the parameters the user may alter (i.e., soil quake, damping, shaft resistance

distribution) the most critical factor affecting the interpreted failure capacity is the shaft resistance

distribution (Hannigan et al. 2006). CAPWAP models a driven pile as a series of masses connected

by springs which in turn are connected to the surrounding soil by springs (static resistance) and

dashpots (dynamic resistance) based on the modified Smith soil model (Smith 1960). Individual

spring-mass pairs are then used to predict soil resistance distribution. CAPWAP discretizes the

pile into n equal segments and the user may assign a fraction of the total shaft resistance, Rs, to

each segment to produce a signal (i.e., stress wave) that matches the measured signal. The β-

coefficient may then be determined by comparing the unit shaft resistance, rs, to the estimated

effective stress, σ’v, at the center of each pile segment:

r β = s (4.1) ' σ v

Most of the soil segments used in this study are 2 m (6.5ft) long and the corresponding shaft

resistance percentage is estimated by a specialist based on the soil profile, the observed driving

resistance (bpf / blows per 0.3 m) during pile driving, and their considerable experience in the

geologic region.

4.3 Database of CAPWAP Dynamic Analysis Records

CAPWAP signal matching was performed by independent, specialized professional engineers with experience in dynamic testing in the Puget Sound Lowlands. For this study all dynamic tests were performed by either GRL, Inc. (42 %) or RMDT, Inc. (58 %). Because the CAPWAP technique necessitates assumptions as to the shaft resistance distribution and other soil model parameters, sound experience and judgment are of critical importance; data generated by these specialists allow for a reduced, but unquantifiable magnitude of interpretational error.

Reddy and Stuedlein (2013) collected a database of more than 237 dynamic pile tests. Of these piles, CAPWAP was performed on a subset of over 180 piles. For the purpose of study, a more refined screening was done to filter piles that meet the following conditions:

• Both EOD and BOR CAPWAP records are available;

• Depth of penetration remains approximately the same at both conditions. The reason for

that is to avoid overlap between assumed soil segments at EOD and BOR and to maintain

consistency for purposes of shaft resistance model development.

• Enough soil information was available to establish a soil profile for the pile of interest.

Representative soil profiles were obtained using borings with split-spoon sampling, cone penetration test data, and/or generalized soil profiles established by the original design team.

Whenever a test pile was located within 9 m (30 ft) of an exploration, the soil profile from the exploration was assumed to represent the conditions at that pile. If a generalized soil profile for the project of interest was made, the pile of interest was located and the corresponding soil layering at that location on the cross-section assumed. Filtering of the larger database resulted in 85 driven

piles with all necessary information including CAPWAP records at EOD and BOR, pile geometry

and soil profile information.

4.4 Typical Subsurface Conditions of Puget Sound Lowlands

This study was limited to the Puget Sound Lowland area in the State of Washington in the

USA. This region has been subjected to several consecutive glaciations, with at least six documented glaciations occurring during the Pleistocene (Eastbrook 1994). Typical Puget Sound

Lowland geology consists of near-surface fill soils underlain by alluvial and estuarine deposits, which in turn are underlain by very dense, glacially over-ridden soils (Borden and Troost 2001).

The majority of driven piles considered in this study were founded in glacial soils and therefore

had high driving resistance (> 80 bpf) at the end of driving and during restrike (Reddy and

Stuedlein 2013).

Table 4.1 presents an example of the soil profile information for one of the piles in the dataset.

The information includes SPT blow counts, USCS classifications, and geologic units. Table 4.2

summarizes the geologic units typically encountered in the Puget Sound Lowlands and cited in

Table 4.1.

4.5 Methodology for the Development of the New β-Models

The research methodology implemented to achieve the aim of this research by development of

new β-coefficient models include the following components:

1) Filter the data for piles where both End of Driving (EOD) and Beginning of Restrike (BOR)

records are available. The data is filtered again based on the depth of penetration and piles

where the depth of penetration remains approximately the same at both conditions driving

conditions, EOD and BOR, are selected. A toe displacement cut off difference of 2.5 mm

(0.1 in) between EOD and BOR conditions was used for the final selection. This ensures a

fair comparison in induced resistance at EOD and BOR, avoiding thus overlap between

soil segments during CAPWAP analysis as well as insuring coincidence of the soil profiles

at EOD and BOR;

Table 4.1. Example of a soil profile of one of the piles in the database.

Soil Top Bottom Thickness Navg USCS Geology Unit Effective Relative density or Layer Depth Depth (ft) (*) weight Stress consistency Nbr. (ft) (ft) (pcf) (psf)

1 0 10 10 13 SP- Hf 120 1200 Medium SM dense

2 10 22.5 12.5 11 SP Hh 115 2638 Medium dense

3 22.5 37.5 15 4 ML He 110 4288 Very loose

4 37.5 46 8.5 2 OH He 105 5180 Very loose

5 46 57.5 11.5 0 ML He 105 6388 Very loose

6 57.5 60 2.5 39 SM Hrw 125 6700 Dense

7 60 66 6 40 SM Qpgm 125 7450 Dense

(*) Navg corresponds to the averaged SPT N-value over the considered thickness.

Table 4.2. Geologic units and their abbreviation as encountered in the database of soil profiles. Geologic Geologic Unit Geologic Geologic Unit abbreviation abbreviation

CL/SC/SM Low Plasticity inorganic Clay / Clayey QPLS Landslide Deposits Sands / Silty Sands HA Alluvium QPNA Nonglacial Ash HAF Alluvium - fine QPNF Fluvial Deposits HAM Alluvium - medium Qpnf or Qvd Qpnf or Qvd HB Beach Deposits QPNL Lacustrine Deposits HC Colluvium QPNP Organic Peat Deposits HE Estuarine Deposits QPNS Paleosols HF Fill QPOW Outwash HL Lake Deposits QSIS Lacustrine Deposits HLS Landslide Debris QVA Advance Outwash HM Mudflat Deposits QVAT Ablation Till HP Peat QVAT/QVRO Ablation Till / Recessional Outwash HRW Holocene Reworked Sediments QVD Till-Like Deposits MW Slickensided Discontinuity Zone QVGL Glaciolacustrine Deposits QPGD Till-like Deposits (Diamict) QVGM Glaciomarine Drift QPGL Lacustrine Deposits QVIC Ice-Contact Deposits Qpgl and Hf Qpgl and Hf QVRI Ice-Contact Deposits QPGM Glaciomarine Drift QVRL Recessional Lacustrine Deposits QPGO Outwash QVRO Recessional Outwash QPGT Advance Outwash QVT Vashon Lodgement Till QPLS Landslide Deposits RUBBLE Deformed Zone QPGO Outwash SHEAR Sheared Discontinuity Zone QPGT Advance Outwash SLICK-1 Slickensided Discontinuity Zone TSI Siltstone

2) Establish representative soil profile for each pile by (1) gathering all available in situ data

from geotechnical reports, (2) develop representative generalized soil profile, (3) consider

specific geology for uncertain strata and finally infer soil profile coinciding with desired

pile location; and (4) Correlate soil profile, including soil type based on Unified Soil

Classification System (USCS; ASTM 1985) and soil density or consistency to the unit shaft

resistance determined for the EOD and BOR conditions;

3) Compute the effective stress at the middle of each CAPWAP soil-pile segment;

4) Compute the normalized unit shaft resistances using the effective stress at the

corresponding depth (i.e., the β-coefficient);

5) Separate or “bin” the computed β-coefficient values by USCS classification and the

corresponding relative density or consistency, depending on the magnitude of fines

content; and,

6) Develop a suite of continuous β-coefficient models by ordinary least squares fitting.

The soil segmentation in the CAPWAP records does not coincide with the corresponding soil stratigraphy. Often a CAPWAP segment will overlap two consecutive soil layers. One solution is to assign the CAPWAP segment to the thicker of the two corresponding soil layers. Another solution is to average the parameter of interest (e.g., unit weight) with respect to depth. The former solution is conservative but simplistic, whereas the latter is more realistic but time consuming. The loosest soil will likely return the highest setup ratio, so the most likely attribution for “setup” would be for the loosest and softest soil. However, the potential for error is the largest with the

“simplistic” approach. Therefore, a weighted average of relevant soil parameters weighted by the thickness of the layer portion corresponding to the “setup” observation was used. For example, if setup quantity observed spans 0.6 m (2 ft) of soft soil, and 1.4 m (4.5 ft) of dense soil, the unit weight is computed as follows:

γavg =0.6mm ⋅+ γγss 1.4 ⋅ds (4.2)

where γavg = averaged unit weight, γss = unit weight of soft soil, and γds = unit weight of dense soil.

The soil unit weights were estimated using recommendations from Peck et al. (1974). Table 4.3

present correlations between SPT N-values, relative density, and moist unit weights for granular soils. Table 4.4 shows the range in unit weights estimated for cohesive soils.

Table 4.3. Correlation between SPT N-value, relative density and unit weight for granular soils (after Peck et al. 1974).

SPT N-value Relative density Moist unit weight Moist unit weight (pcf) (kN/m3) 0 to 4 Very loose 14.9 to 16.5 95 to 105 4 to 10 Loose 16.5 to 17.3 105 to 110 10 to 30 Medium dense 17.3 to 18.9 110 to 120 30 to 50 Dense 18.9 to 20.5 120 to 130 50+ Very dense 20.5 to 22.0 130 to 140

Table 4.4. Correlation between SPT N-value, relative density and unit weight for cohesive soils (after Peck et al. 1974).

SPT N-value Relative density Moist unit weight Moist unit weight (pcf) (kN/m3) 0 to 2 Very soft 90 to 95 14.2 to 14.9 2 to 4 Soft 95 to 105 14.9 to 16.5 4 to 8 Medium Stiff 105 to 115 16.5 to 18.0 8 to 15 Stiff 115 to 125 18.0 to 19.7 15 to 30 Very Stiff 125 to 135 19.7 to 21.3 30+ Hard 135 to 140 21.3 to 22.0

4.6 Estimation of Axial Capacity Using the β-coefficient and Toe Bearing Capacity Coefficient

4.6.1 Estimation of β-coefficient in the literature

By definition, the β-coefficient is equal to the unit shaft resistance normalized by the effective stress at a given depth (Equation 4.1). Displacement at the soil-pile interface along with the normal effective stress and strength of the interface dictate the mobilized resistance. This dependency is accounted for through soil-pile friction angle denoted δ’. The theoretical expression for β is

therefore:

βδ=K ⋅ tan( ') (4.3)

where K is the actual lateral earth pressure coefficient. This lateral pressure coefficient is noted K

not to be confused with the at rest earth pressure coefficient K0. For this reason K is a function not

only of K0 but also pile type, installation method and soil density.

For normally consolidated granular soils K0 can be estimated using (Jaky 1943):

K0 =1 − sin(φ ') (4.4)

where ϕ’ is the friction angle of the soil.

For overconsolidated sands, the following equation was inferred using well known cases

(Kulhawy and Mayne 1990):

OCR 3 OCR =−φ +− K0 (1 sin( ')) (1− sin(φ ')) 1 (4.5) OCRMax 4 OCRMax

where ϕ’ = soil effective friction angle, OCR = overconsolidation ratio.

If we assume that K is related to K0 through a coefficient D: K = DK0, where D is an empirical

factor that accounts for type of pile installation and soil density. D can vary generally between 1

and 1.8. Lower values are given to jetted and non-displacement piles. For those piles, loose soils

would result in a smaller value of D compared to denser soils. On the other hand, displacement

(driven) piles result in lager values of D, if the sand is denser this value is even larger.

The soil-pile friction angle is a function of the soil friction angle and the pile surface type. In

general its value may range in the interval 0.5φδ '≤≤ 1.0 φ '.

Accounting for the dependence of β-coefficient on the aforementioned parameters, a general

expression can be proposed:

β=D ⋅−(1 sin( φφ ')) ⋅ tan(C ⋅ ') (4.6)

where C = Ratio of δ’ and ϕ’. By assuming a value for C and D, β-coefficient can be computed

as a function of friction angle. Figure 4.1 shows an example of such a calculation. By varying

friction angle, Fellenius (1991) established a relationship for β-coefficient based on soil type (clay,

silt, sand, and gravel). By classifying a soil into one of the four major soil types and estimating its

effective friction angle ϕ’, an estimate of β-coefficient is feasible by using one of the four linear

relationships shown in Figure 4.1. This method suffer from two evident limitations: (1) the back-

calculated values used to support the relationships with relevant statistics to assess the accuracy

and uncertainty are not presented, and (2) the effect of stress-dilatancy, which is commonly

correlated to depth (i.e, a proxy for confining or mean effective stress) are not accounted for. This

study attempts to overcome the aforementioned limitations and develop depth- or stress-dependent estimates of the β-coefficient based on extensive field data.

Figure 4.1. Chart for Estimating β-coefficient versus Soil Type ϕ’ (after Fellenius 1991)

Table 4.5. Approximate ranges of β-coefficients based on case histories compiled by Fellenius (2008)

Soil Type Friction Angle, φ’ β-Coefficient Clay 25-30 0.15-0.35 Silt 28-34 0.25-0.50 Sand 32-40 0.30-0.90 Gravel 35-45 0.35-0.80

Other authors proposed β-coefficients as a function of depth for sandy gravel and gravelly sand

(e.g., Meyerhof 1976, O’Neill and Reese 1999, Rollins et al. 2005, Stuedlein et al. 2012) or plasticity index (Clausen et al. 2005). The unit shaft resistance corresponds to the ultimate resistance of the pile (Fellenius 2014). Typically, just 2 to 5 mm of relative soil-pile movement is sufficient to mobilize the ultimate shaft resistance along the pile (Rausche et al. 1972, Hannigan

1990, Fellenius 2014).

4.6.2 Estimation of Toe Bearing Capacity Coefficient

In a similar fashion, unit toe resistance may be correlated to a toe bearing capacity coefficient,

Nt through the following relationship:

' qNt= tv.σ (4.7)

where qt = unit toe resistance, Nt = toe bearing capacity coefficient, and σ’v = effective normal stress. Figure 4.2 shows an example for estimating Nt based on Fellenius (1991) database.

Figure 4.2. Chart for estimating Nt Coefficients versus Soil Type ϕ' Angle (after Fellenius, 1991)

4.7 New developed Models for β-Coefficient Specific to the Puget Sound Lowlands

Typically-accepted β-coefficient models vary as a function of depth for deep foundations, such as driven piles (Meyerhof 1976) and drilled shafts (O’Neill and Reese 1999). However, the statistical treatment of the proposed models is rarely presented along with appropriate soil descriptions, such as the USCS classification, or the density/consistency of the soils considered.

Owing to the transition of design from a deterministic framework to a reliability based design approach, quantification of accuracy and uncertainty are required to develop appropriate resistance factors. In this study, a general mathematical form based on visual quality of fit was adopted to capture the variation of β-coefficient as a function of depth based on the USCS classification and

the soil density/consistency. Each specific model is presented independently (see Figures 4.3 to

4.18) in the following sub-sections. All the proposed models follow the same general functional

form used by Miyata and Bathurst (2012) to model the results of MSE reinforcement pullout tests:

ββ01− ββ()z = + 1 (4.8) exp(β2 ⋅ z)

where z is the depth blow the ground surface, and β0, β1 and β2 are fitting parameters. This

expression seems to capture the variation of β-coefficient as a function of depth. Because the

continuous exponential function is differentiable and strictly positive the proposed expression for

β-coefficient can be easily used in further mathematical treatments. Some of the characteristics

and advantages are the following:

• The function is smoothly continuous with depth z;

• β0 : captures the initial value of β-coefficient. It corresponds to β-coefficient at the ground

surface. Although it is expected that β0 should be largest near the ground surface due to

the effects of stress-dilatancy, it can often take very low or high values owing to the data

available which drives the magnitude of β0 from statistical regression;

• β1 : captures the asymptotic value of β-coefficient. At large depths where z tends infinity,

β-coefficient tend toward β1 as expected from stress-dilatancy; and,

• β2 : captures the slope of curvature from the initial value of β-coefficient (equal to β0) to

the asymptotic value of β-coefficient (equal to β1). The larger the value of β2 , the steeper

the curvature.

To determine the most appropriate β-coefficient model parameters, a fitting procedure is necessary. In this study, the model is fitted to the data for all of the USCS and relative density/consistency classes considered. To determine the three parameters β0, β1 and β2 several

options are possible. It is possible to minimize the coefficient of determination (also known as R2) by varying those coefficients (β0, β1 and β2) without any constraints. This method assures a

minimum R2, but the model might under- or over-estimate the measured β-coefficient values to

produce a consistent bias.

In this investigation, the parameters were determined by constraining the mean bias, defined

as the back-calculated β-coefficient over the predicted β-coefficient, to as close to one as possible.

This condition ensures that the model can be used in reliability theory or the framework of load

and resistance factor design (LRFD). It is always desirable to have a low value of coefficient of

variation (COV) as this ensures that the model has a small variation and thus the predicted value

can be used with more confidence. The assessment of low variation is subjective and depends on the phenomena studied (Miyata and Bathurst 2012).

4.7.1 β-Coefficient Models Based on USCS Classification

The compilation of unit shaft resistances from the CAPWAP segments produced 1,216 data pairs. Significant effort was made to partition the data into groups according to USCS classification while respecting two requirements:

• Each group must have a significant number of data points so any subsequent treatment does

not suffer from sampling size issues. Some studies have shown that an appropriate sample

size for reliability-based, foundation engineering design models are those that are larger

than about 40 (Stuedlein and Reddy 2014);

• A given group must have some corresponding physical compatibility (i.e., sandy soils

should not be combined with clayey soils).

Eight groups were selected to meet the requirements discussed above as summarized in Table

4.6. The USCS classifications can be divided into four major groups: gravel, sand, and inorganic and organic, fine-grained soils including plastic silts and clays. It should be noted that one of the groups considered, SM/ML, does not correspond to any specific group with USCS categorization, but was adopted in local practice by some firms in the Pacific Northwest.

It is reasonable practice not to account for the upper 2 diameters of the pile when estimating axial capacity (O’Neill and Reese 1999). In this study, the β-coefficient data points within the upper 4 m were not used when fitting the model.

Table 4.6. Number of soil segments per chosen USCS group

USCS group(s) Number of Soil segments CH ; CL ; CL-ML 168 GP ; GW ; GM ; 82 GW-GM ; GP-GM ML 152 OH ; OL ; PT 26 SM ; SC 213 SM / ML 113 SW-SM ; SP-SM 220 SW ; SP 242 Total 1216

4.7.1.1 Model No 1: CH, CL, and CL-ML

This family of models applies to clayey soils including CH, CL and CL-ML groups based on

USCS method of classification. Figure 4.3 (a) shows the 168 data corresponding to clayey soils at

EOD as well as the suggested model based on (1) best fit using the least squares procedure and (2) forcing the mean bias to be independent of the predicted or nominal β-coefficient (3) ignoring the

back-calculated β-coefficients within the upper 4 m when fitting the proposed equation. Figure 4.3

(b) shows the computed sample biases. The variability in the model is quantified by coefficient of

variation (COV), defined as the standard deviation of the sample biases normalized by the mean

bias. At EOD, the fitted model has a COV of 100% and a mean bias of one as shown by the trend

line in Figure 4.3 (b).

For both conditions, EOD and BOR, the trend in bias has a small slope meaning that the

proposed model does not depend on the magnitude of the nominal β-coefficients. This requirement

ensures compatibility with LRFD framework where non dependency between nominal resistance

and sample bias must be verified. Figure 4.4 (a) shows the back-calculated values of β-coefficient

versus depth below the ground surface at BOR for clayey soils. The COV in back-calculated data

at BOR for the clayey group is 83%, smaller than the COV at EOD by 17%. Figure 4.4 (b) shows

the variation in sample bias with β-coefficient at BOR.

β-Coefficient a) 0.0 0.5 1.0 1.5 2.0 2.5 0

USCS groups: CH, CL, CL-ML 20

z(m) Summary Statistics: 30 n = 168, R2 = 0.21 λ = 1.00, COV = 100% Depth, 40

50 EOD, z ≤ 4 m EOD, z > 4 m EOD fit 60 8 b) Calculated Bias trend 6 λ λ = -0.47β + 1.06 4 R² = 0.0013

Bias, 2

0 0.0 0.2 0.4 0.6 0.8 β-Coefficient

β-Coefficient a) 0.0 0.5 1.0 1.5 2.0 2.5 0

20 USCS groups: CH, CL, CL-ML z(m) 30

Depth, Summary Statistics: 40 n = 168, R2 = 0.23 λ = 1.00, COV = 83%

50 BOR, z ≤ 4 m BOR, z > 4 m BOR fit 60

b) 8 Calculated Bias trend 6

λ λ = -0.14β + 1.04 , , 4 R² = 0.0005

Bias 2

0 0.0 0.2 0.4 0.6 0.8 1.0 β-Coefficient

4.7.1.2 Model No 2: GP, GW, GM, GW-GM, and GP-GM

In this subset, the database was filtered for all gravelly soils, including those falling under the

USCS groups of GP; GW; GM; GW-GM; GP-GM. A major reason for using this family of soils

under one group is to ensure the requirement of sample size representability by having a relatively

high number of segments. This group included 82 segments of unit shaft resistance to a depth over

80 meters, making it the deepest sample size of those considered in this study. As expected, the β-

coefficient values are larger at EOD and BOR on average when compared to other USCS groups

because of their higher permeability, and the ability to densify these materials as a result of pile

driving. Figure 4.5 and Figure 4.6 present the back-calculated values of β-coefficient versus depth

and model bias at EOD and BOR, respectively. It should be noted that only few CAPWAP

segments were available for the depths of 20 and 50 meters. Also, at larger depths, some measured

β-coefficients are very small (close to zero). As shown in the Figures 4-5 (b) and 4-6 (b), each of the proposed models are unbiased with respect to magnitude of β-coefficient.

β-Coefficient a) 0.0 1.0 2.0 3.0 4.0 0

30 USCS groups: GP, GW, GM, (m) 40 GW-GM, GP-GM

50 Summary Statistics: 2 Depth,z n = 82, R = 0.11 60 λ = 1.00, COV = 180%

80 EOD, z ≤ 4 m EOD, z > 4 m EOD fit 90

8 b) Calculated Bias trend 6

λ , 4 λ = 0.04β + 1.00 R² = 1E-05

Bias 2

0 0.0 0.5 1.0 1.5 β-Coefficient

β-Coefficient a) 0.0 1.0 2.0 3.0 4.0 5.0 0

30 USCS groups: GP, GW, GM, 40 z(m) GW-GM, GP-GM

50 Summary Statistics: 2 Depth, n = 82, R = 0.14 60 λ = 1.00, COV = 124%

80 EOD, z ≤ 4 m EOD, z > 4 m BOR fit 90

8 b) Calculated Bias trend 6

, , λ = -0.02β + 1.00 4 R² = 2E-05 Bias 2

0 0.0 0.5 1.0 1.5 β-Coefficient

4.7.1.3 Model No 3: ML

Figure 4.7 (a) shows the back-calculated values of β-coefficient versus depth at EOD for the

152 CAPWAP segments in soils that falls under the ML group based on the USCS classification.

The solid curve represents the fitted model for data using the same three parameter exponential

function (Equation (4.8)). Figure 4.8 (a) shows the calculated β-coefficient values as a function of depth as well as the proposed model to predict β-coefficient at BOR. For this group, the best fit resulted in a β-coefficient at the ground surface β0 = 1.07 at EOD, whereas at

BOR, β0 = 1.66. Although it might be expected to have a larger value of β-coefficient at EOD

compared to BOR at shallow depths because of heave due to dilation, the observed values can be

justified by the fact that data in the upper 4 m were ignored when fitting Equation (4.8). The

asymptotic value of β-coefficient at EOD occurring at approximately 15 m at EOD is equal to

0.07, whereas the asymptotic value for β-coefficient at BOR is 0.19 starting around 20 m. A practical implication of this observation is that shaft resistance at least doubled in silty soils.

Figure 4.7 (b) and Figure 4.8 (b) show the computed sample biases at EOD, and BOR, respectively. As for models No. 1 and model No. 2, the mean bias is equal to one suggesting that the proposed models are accurate on average.

β-Coefficient a) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0

20 USCS group: ML z(m) 30

Summary Statistics: Depth, n = 152, R2 = 0.13 40 λ = 1.00, COV = 109%

50 EOD, z ≤ 4 m EOD, z > 4 m EOD fit 60

b) 8 Calculated 6 Bias trend

λ , , 4 λ = -0.13β + 1.01 R² = 0.0001 Bias 2

0 0.0 0.2 0.4 0.6 0.8 1.0 β-Coefficient

β-Coefficient a) 0.0 1.0 2.0 3.0 4.0 5.0 0

20 USCS group: ML z(m) 30

Summary Statistics: Depth, 2 40 n = 152, R = 0.12 λ = 1.00, COV = 101%

50 BOR, z ≤ 4 m BOR, z > 4 m BOR fit 60

8 b) Calculated 6 Bias trend

λ , , 4 λ = -0.034β + 1.01 R² = 5E-05 Bias 2

0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 β-Coefficient

4.7.1.4 Model No 4: OH, OL, and PT

This model is specific to organic soils including USCS groups OH, OL and PT. This group of

soils consisted of 26 data points making it the smallest sample in this USCS based categorization

used in this study. The back-calculated values of β-coefficient are derived from relatively shallow

depths as compared to other soils. This is expected as most of the organic soils are typically found

near ground surface. Similar to the ML group at EOD, β-coefficient models for organic soils group

has β0 = 0.11 and β0 = 0.29 at EOD and BOR, respectively. Again those values can be attributed to the range of values of back-calculated β-coefficient and/or the fitting process. Figure 4.9 (a) and

Figure 4.10 (a) show the back-calculated values of β-coefficient at both EOD and BOR as well as the proposed models. Surprisingly, β-coefficient values at BOR for the organic soils group is larger than that for clays and silts. Figure 4.9 (b) and Figure 4.10 (b) present the sample biases, back- calculated, at EOD and BOR, respectively.

β-Coefficient a) 0.0 0.5 1.0 1.5 2.0 2.5 0

10 USCS group: OH, OL, PT z(m) 15 Summary Statistics: n = 26, R2 = 0.77 Depth, λ = 1.00, COV = 81% 20

25 EOD, z ≤ 4 m EOD, z > 4 m EOD fit 30

b) 8 Calculated 6

λ , , 4 Bias 2

0 0.0 0.2 0.4 0.6 0.8 β-Coefficient

β-Coefficient a) 0.0 0.5 1.0 1.5 2.0 2.5 0

USCS group: z(m) OH, OL, PT 15

Depth, Summary Statistics: 20 n = 26, R2 = 0.83 λ = 1.00, COV = 72%

25 BOR, z ≤ 4 m BOR, z > 4 m BOR fit 30

b) 8 Calculated 6 λ , 4 Bias 2

0 0.0 0.2 0.4 0.6 0.8 β-Coefficient

Figure 4.10. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for organic USCS soils (OH, OL, and PT) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient.

4.7.1.5 Model No 5: SM and SC

This subset of soils include silty sand (SM) and clayey sand (SC). It is based on 213 data points

back-calculated from CAPWAP records normalized by estimated effective stress at the same

depth. Figure 4.11 (a) and Figure 4.12 (a) show the back-calculated values of β-coefficient as a

function of pile length in meters, at EOD and BOR, respectively. It extends to approximately 50

meters (164 ft) below ground surface. This fitted β-coefficient model for EOD resulted in a mean bias of one and a COV of 161%. The high value of COV can be attributed mainly to the large scatter in the CAPWAP-based unit shaft resistances for depths less than 20 m. It should be noted that this model present the most gradual transition from the initial value β0 = 0.42 to the

asymptotic value β1 = 0.04. This is quantified by the small β2 = 0.07, which captures the lack

curvature of the proposed model. Sample biases are compared to the predicted β-coefficient for

SM and SC at EOD are presented in Figure 4.11 (b). The mean bias is equal to one ensuring that

the model is accurate on average. At BOR, the fitted model also exhibits low curvature with

β2 = 0.04, which is the smallest for all models at BOR. The best fit resulted in a COV of 113%

and an R2 value of 0.06, suggesting relatively large uncertainty in the back-calculated data of β-

coefficient for SM and SC soils.

β-Coefficient a) 0.0 1.0 2.0 3.0 4.0 0

20 USCS group: z(m) SM, SC

Depth, 30 Summary Statistics: n = 213, R2 = 0.05 λ = 1.00, COV = 161%

40 EOD, z ≤ 4 m EOD, z > 4 m EOD fit 50

b) 8 Calculated 6 Bias trend

λ , , 4 λ = -0.28β + 1.04 R² = 0.0002 Bias 2

0 0.0 0.2 0.4 0.6 0.8 β-Coefficient

Figure 4.11. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for sandy USCS soils (SM and SC) at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient.

β-Coefficient a) 0.0 1.0 2.0 3.0 4.0 5.0 0

z(m) USCS group: SM, SC

Depth, 30 Summary Statistics: n = 213, R2 = 0.06 λ = 1.00, COV = 113% 40 BOR, z ≤ 4 m BOR, z > 4 m BOR fit 50

8 b) Calculated Bias trend 6 λ λ = 0.22β + 0.90 , 4 R² = 0.0009 Bias 2

0 0.0 0.2 0.4 0.6 0.8 1.0 β-Coefficient

Figure 4.12. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for sandy USCS soils (SM and SC) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient.

4.7.1.6 Model No 6: SM/ML

This group is unique as it does not correspond directly to any of the existing USCS groups. It

was noted that many sublayers contain silty sand (ML) intermixed with sandy silt (SM) without a clear or definitive indication that the soil layer should be ascribed to one group or the other. For this reason, a new category was created under the group name SM/ML referring to those silty sandy intermixed soils. It was observed that USCS suffers from a considerable limitation as it does not explicitly differentiate between plastic silt and non-plastic silt but include both of them under the group name ML.

The filtration of back-calculated values of β-coefficient points corresponding to SM/ML soils

resulted in 113 data points. Figure 4.13 (a) and Figure 4.14 (a) show the back-calculated values of

β-coefficient as well as the proposed models at EOD and BOR, respectively. All data values of β-

coefficient at EOD are less than 0.4 even at shallow depths. This is opposite to other soil groups

where at shallow depths β-coefficient are high in general with some of them exceeding a value of

one. For this reason, the best fit using the proposed exponential function resulted in approximately

a constant function. Figure 4.13 (b) and Figure 4.14 (b) show sample biases values for SM/ML

group at EOD and BOR respectively.

β-Coefficient a) 0.0 0.5 1.0 1.5 2.0 0

20 USCS group: SM / ML z(m)

30 Summary Statistics: Depth, n = 113, R2 = 0.04 λ = 1.00, COV = 75%

EOD, z ≤ 4 m EOD, z > 4 m EOD fit 50

8 b) Calculated Bias trend 6

λ , , 4 λ = 0.073β + 0.9934 R² = 3E-06 Bias 2

0 0.0 0.2 0.4 0.6 0.8 β-Coefficient

β-Coefficient a) 0.0 0.5 1.0 1.5 2.0 2.5 0

USCS group: 20 SM / ML z(m)

Summary Statistics: Depth, 30 n = 113, R2 = 0.17 λ = 1.00, COV = 65%

BOR, z ≤ 4 m BOR, z > 4 m BOR fit 50

8 b) Calculated Bias trend 6

λ , , 4 λ = 0.1902β + 0.9532 R² = 0.0001 Bias 2

0 0.0 0.2 0.4 0.6 0.8 β-Coefficient

4.7.1.7 Model No 7: SW and SP

Sand is by far the most common major soil type in the database collected in this study from

Puget Sound Lowlands followed by Silty soils intermixed with sand. The filtered group herein

corresponds to relatively clean sand with less than 5% of other soil types as observed in the samples

obtained from in-situ investigations. The family of soils filtered in this group include USCS groups

SW and SP. The group contains 242 data points distributed from the ground surface to a depth of

46 m. Although, as with all soil groups in this study, significant scatter is observed, it can be

inferred that the proposed model capture well the trend in β-coefficient as a function of depth at

both EOD and BOR. Figure 4.15 (a) and Figure 4.16 (a) present the data points of back-calculated

β-coefficient values at EOD and BOR respectively. Equation (4.8) is fitted to the data at both driving conditions and presented by the continuous thick black curve. A COV of 97% and 96%

was obtained with a mean bias of one at EOD and BOR, respectively. At BOR, this group has the

largest asymptotic (or minimum) β-coefficient with a value of 0.39. At EOD, β-coefficient at larger depths is also the largest with a value of 0.16.

4.7.1.8 Model No 8: SW-SM and SP-SM

This group is the last in the USCS categorization used in this study to capture the variation of

β-coefficient as function of depth. This group includes both SW-SM and SP-SM soils. Figure 4.17

and Figure 4.18 present β-coefficient data points, proposed models and model bias at EOD and

BOR, respectively. The model at BOR is less variable compared to EOD with a COV = 82% at

BOR and a COV = 111% at EOD.

a) β-Coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

20 USCS group: SW, SP z(m)

30 Summary Statistics: Depth, n = 242, R2 = 0.12 λ = 1.00, COV = 97%

EOD, z ≤ 4 m EOD, z > 4 m EOD fit 50

b) 8 Calculated 6 Bias trend

, λ β 4 = 0.01 + 1.00 R² = 5E-07 Bias 2

0 0.0 0.2 0.4 0.6 0.8 1.0 β-Coefficient

a) β-Coefficient 0.0 1.0 2.0 3.0 4.0 5.0 0

USCS group: 20 SW, SP z(m)

Summary Statistics: n = 242, R2 = 0.22 Depth, 30 λ = 1.00, COV = 96%

40 BOR, z ≤ 4 m BOR, z > 4 m BOR fit 50

b) 8 Calculated 6 Bias trend

λ λ = -0.01β + 1.00 , , 4 R² = 4E-06 Bias 2

0 0.0 0.3 0.6 0.9 1.2 1.5 β-Coefficient

Figure 4.16. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for clean sandy USCS soils (SW and SP) at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient.

β-Coefficient a) 0.0 1.0 2.0 3.0 4.0 0

20 USCS group: SW-SM, SP-SM z(m) 30

Depth, Summary Statistics: n = 220, R2 = 0.09 40 λ = 1.00, COV = 111%

50 EOD, z ≤ 4 m EOD, z > 4 m EOD fit 60

b) 8 Calculated 6 Bias trend

, , λ = -0.01β + 1.00 4 R² = 1E-06 Bias 2

0 0.0 0.2 0.4 0.6 0.8 β-Coefficient

a) β-Coefficient 0.0 1.0 2.0 3.0 4.0 0

20 USCS group: SW-SM, SP-SM z(m) 30 Summary Statistics: n = 220, R2 = 0.38

Depth, λ = 1.00, COV = 82% 40

50 EOD, z ≤ 4 m EOD, z > 4 m BOR fit 60

b) 8 Calculated 6 Bias trend

λ λ = 1.00

, , 4 R² = 1E-07

Bias 2

0 0.0 0.5 1.0 1.5 β-Coefficient

4.7.2 Observations

Based on USCS rules, 8 groups were created and 16 β-coefficient models were proposed, 2

models per soil group, one corresponding to EOD driving condition and one corresponding to BOR

driving condition. All of the proposed models correspond to a general three parameter exponential

function. This function seemed to capture the general trend of the back-calculated β-coefficient

data in addition to providing certain mathematical advantages. Table 4.7 shows values of fitted parameters,β0, β1 and β2 corresponding to each USCS group.

A great advantage of this study is the use of a considerable number of β-coefficient data points

therefore providing realistic bounds on observed shaft resistance and a representative statistical

sample.

Table 4.7. Fitting parameters for proposed β-coefficient models per USCS group

EOD BOR Model Group β0 β1 β2 β0 β1 β2 No. 1 CH, CL, and CL-ML 0.45 0.04 0.08 0.83 0.10 0.07 No. 2 GP, GW, GM, GW-GM, and GP-GM 1.15 0.11 0.15 1.52 0.22 0.11 No. 3 ML 1.07 0.07 0.22 1.66 0.19 0.14 No. 4 OH, OL, and PT 0.11 0.11 1.04 0.29 0.29 2.17 No. 5 SM and SC 0.42 0.04 0.07 0.82 0.00 0.04 No. 6 SM/ML 0.23 0.08 0.17 0.34 0.00 0.02 No. 7 SW and SP 0.70 0.16 0.33 3.11 0.39 0.43 No .8 SW-SM and SP-SM 0.46 0.11 0.12 1.06 0.06 0.05

Except for the organic soils group Model No. 4 (OH, OL, PT) with 26 data points, all other soil groups has over 80 data points. The overall impression is that considerable scatter exist in back-calculated β-coefficient values, determined using CAPWAP records from experienced

practitioners and soil profile determined using state of the practice procedures. This scatter is a

good indicator of the magnitude of the quality of correlation between (1) subsurface investigation

(2) CAPWAP shaft distribution (3) physical representability of shaft resistance magnitude by

USCS classification without direct consideration of particle shape or the spatial variability, and (4)

inclusion of both steel and concrete piles in the data without separate consideration for the pile

material. For all of USCS subgroups, the COV at BOR is lower than that at EOD. It should be

noted that although the value of β-coefficient at the ground surface, β0 , is expected to be higher

at EOD due to the heave that occurs after the pile toe passes the near surface, unconfined soil,

some models (i.e., CH, CL, CL-ML) exhibit a larger β0 at BOR. This is a result not only of the

available data but also the fitting procedure and therefore the limitation of the model in capturing

all expected soil mechanics should be acknowledged and addressed when the proposed models are

used.

4.7.3 β-coefficient Based on Density or Consistency

The same data was also classified in function of density/consistency of soils and resulted in 8

groups: Cohesive soils categorized into 4 groups based on their consistency: soft, medium stiff,

stiff and very stiff, and hard soils. All cohesive soils subgroups presented a large sample size except hard soils with only 17 data points. Granular soils were also divided into four groups: very loose and loose, medium dense, dense, and very dense. Table 4.8 presents the number of pile segments

per group based on soil density/consistency. One major observation is that the medium dense group

of soils has 439 data points and present a greater scatter than that of other densities. This can be

justified by the fact that the SPT range is the greatest for the medium dense class of soils (10 to 30

blow counts). It is also noticed that the scatter for granular soils (sandy silty soils) is clearly greater

than those for cohesive soils. Table 4.9 summarizes the fitting parameters for the proposed model

for each soil group based on density/consistency classification. It should be noted that for medium

stiff, stiff and very stiff, a constant model was used because opting for the three parameter function

was not justified. However, the proposed three parameter function reduces to a constant equal to

β0 when β1 and β2 are assumed null and therefore the constant models can be included in the suite

of fitted models (see table 4.9). For hard soils, no fit is proposed because this group presented very few data points. Also, it should be noted that the fitting procedure based on density or consistency groups excluded the upper 4 meters (See Appendix A). This suite of β−coefficient models based

on density/consistency can be used in parallel with those based on USCS classification.

Table 4.8. Number of soil segments per density (consistency) group

Relative density/ Nbr. of soil Consistency segments V. loose ; Loose 156 M. dense 439 Dense 135 V. dense 140 V. soft ; Soft 200 M. stiff 51 Stiff ; V. stiff 78 Hard 17 Total 1216

Table 4.9. Fitting parameters for proposed β−coefficient models per density group

EOD BOR

Density β0 β1 β2 COV λ β0 β1 β2 COV λ Very loose and loose 0.16 0.01 0.02 139 0.01 0.54 0.07 0.03 85 0.05

M. dense 1.64 0.12 0.38 128 0.11 1.11 0.22 0.10 101 0.10

Dense 1.25 0.10 0.31 93 0.20 3.85 0.31 0.39 87 0.18

V. dense 1.58 0.01 0.06 155 0.15 2.38 0.20 0.07 103 0.26

Soft 0.40 0.01 0.08 107 0.19 0.90 0.05 0.07 83 0.23

Medium stiff 0.10 0.00 0.00 84 0.00 0.21 0.00 0.00 105 0.00 Stiff and very stiff 0.13 0.00 0.00 84 0.00 1.82 0.14 0.10 76 0.00

4.8 Summary

This chapter discusses the development of a new framework for axial static capacity analysis

of driven piles. A new effective stress suite of models (β-coefficient) specific to the Puget Sound

Lowlands was developed based on USCS classification as well as density/consistency of soils. The

method uses the shaft distribution back-calculated from CAPWAP analysis at both driving

conditions, EOD and BOR, and matches unit shaft resistance for each soil layer to the

corresponding soil type with consideration of its depth. Based on USCS rules, eight groups of soil

were defined with two models for β-coefficient, one for EOD and the other for BOR. All models followed a general mathematical form corresponding to a three parameter exponential function.

The fitting parameters were fitted to the back-calculated data using the least squares approach with

a constraint as to ensure a mean bias of unity for all models to ensure LRFD based design

implementation.

Now that a new suite of models has been developed for the effective stress method (β-

coefficients) specific to the Puget Sound Lowland, its usage to predict shaft resistance is feasible.

Also implementation of this method in LRFD approach by producing representative resistance

factors is possible. In Chapter 6, an evaluation of how accurate the new suite of models is made

by comparing predicted total shaft resistance determined from the new models to CAPWAP total

shaft resistance at both driving conditions, EOD and BOR. This comparison is made for different

predictive methods, including Wave Equation Analysis Program (WEAP) and a common FHWA

(2006) recommended static analysis method.

Chapter 5 Assessment of Time-Dependent Capacity Gain for Piles Driven in the Puget Sound Lowlands

5.1 Background

The time-dependent increase in pile capacity, also known as “setup”, was first mentioned in the engineering literature in 1900 by Wendel (Long et al. 1999). Setup is mainly attributed to dissipation of excess pore water pressure surrounding the pile, especially in the nearby zone extending from the pile axial center to few pile diameters and can contribute significantly to long- term ultimate capacity (Svinkin et al. 1999). If it was possible to incorporate the effects of setup during initial stages of design, considerable advantages could be obtained. For example, it may be possible to reduce the pile diameter or length by accounting for the gain in shaft resistance. Any one of the aforementioned possible sources of reduction in pile geometry should result in a more optimal and cost effective design. It is also possible to notice a decrease in capacity with time, this phenomenon is called relaxation and is mainly observed in dense sands and over consolidated clays (Komurka et al. 2003).

Setup is predominately associated with an increase in shaft resistance, not toe resistance

(McVay, 1999; Komurka et al. 2003). Setup occurs in all type of soils such as organic and inorganic clays, silt, sandy silt, silty sand, and fine sand, and to a lesser extent in gravelly soils.

The rate of setup, with respect to time, is a function of both soil and pile properties (Komurka et al. 2003). In cohesive soils, setup is mainly due to dissipation of pore water pressure and subsequent gain in effective stress. It was observed by Axelsson (1998) that the shear strength of the disturbed and reconsolidated soil is higher than the soil’s undisturbed initial shear strength in

normally consolidated clays. In granular soils, the majority of setup is attributed to creep-induced breakdown of driving-induced arching mechanisms, aging, and to some extent to pore water

dissipation for fine grained granular soils (Axelsson, 1998; Schmertmann, 1981: Komurka et al.

2003). This is typically accompanied with densification of the surrounding soils.

It is observed that the more permeable the soil, the faster setup develops. This observation explains the long duration that cohesive soils take to develop the majority of setup compared to granular soils. As a result, the rate of setup rate can be correlated to the grain size distribution

(Komurka 2003). The finer the soil, the greater likelihood for a larger setup to occur.

Numerous empirical relationships have been developed to predict setup (Skov and Denver

1988; Guang Yu 1988; Svinkin 1996; Svinkin and Skov 2000; Reddy and Stuedlein 2014). The accuracy and replicability of these relationships is limited, due to one or a combination of the following causes of variability:

• The limited number of variables considered in the relationship, omitting other

governing parameters for sake of simplification. Examples of such parameters include

time, pile type, soil friction.

• Use of total resistance (shaft and toe resistance) instead of separate shaft and toe

resistances. In fact, many relationships lump both shaft and toe resistance increase in

one factor while it is known that their contribution is different and setup is due mainly

to gain in shaft resistance (Skov and Denver 1988; Svinkin and Skov 2000; Komurka

et al. 2003).

• Use of confounding variables where the back-calculated parameter is a governing

variable (Komurka et al. 2003).

• The inherent variability of soil from site to site and within the same site. This source of

uncertainty makes a generalized empirical or semi-empirical formulation difficult to

formulate with good accuracy (Reddy and Stuedlein 2014).

• The complexity of the mechanisms governing setup and limited understanding of their

nature. Although the possible sources of setup behavior have been studied, a

comprehensive framework identifying the true mechanisms of setup is not available.

Such comprehensive framework may require microscale studies.

This chapter aims to accomplish two objectives. In the first step a thorough discussion of setup mechanisms and existing methods to predict it are presented. After that a set of examples will shed light on the necessity of considering shaft resistance distribution when assessing setup potential or distribution by examining setup of soil segments collected from dynamic testing using pile driving analyzer (PDA) device and interpreted using CAPWAP in order to quantify the effect of time, soil type, soil density/consistency, and effective stress. Finally a set of equations based on the results of the developed β-coefficient models in Chapter 4 are proposed and a comparison of predicted and actual setup for shaft resistance is provided for a set of piles.

5.2 Mechanisms of Setup

The mechanisms justifying setup have been studied by many researchers and investigators

(Skov et al. 1988; Schmertmann 1991; Svinkin et al. 2000; Komurka 2003). A general framework to model gain in resistance with time can be achieved by considering three phases after pile installation:

• Phase 1: Logarithmically parabolic rate of excess pore water pressure dissipation dependent

of effective stress. The rate of dissipation of excess pore water pressures during this phase

is not constant, not linear, with respect to the log of time.

• Phase 2: Logarithmically linear rate of excess pore water pressure dissipation dependent of

effective stress.

• Phase 3: Aging: This phase is independent of Effective Stress and includes other effects

occurring with time after phase 1 and phase 2 are completed. It refers to a time-dependent

change in soil properties at a constant effective stress, has a frictional and mechanical cause,

is active for both fine-and coarse grained soils, and is attributable to thixotropy , secondary

compression, particle interference, and clay dispersion (Camp et al. 1993; Long et al. 1999;

and Schmertmann 1991).

This mechanism is more pronounced in cohesive soils where logarithmically linear dissipation, corresponding to Phase 2, may continue for a long time ranging from several weeks to several months, or even years (Skov et al. 1988). These first two phases are directly related to change in stress state by increasing effective stress due to decrease in pore water pressure.

Excess pore water pressure dissipation during both Phases 1 and 2 is a function of soil engineering properties such us soil type, permeability, and sensitivity and also pile properties including material type, permeability, and section size and length (Komurka 2003)

Aging effects can increase at a rate approximately linear with the log of time but with a slower rate compared to Phase 2 (Schmertmann 1991).

Figure 5-1 shows the three phases described. This description using three different stages of setup is similar to the settlement performance of soils. Correspondingly, Phase 1 would correspond

to immediate settlement, Phase 2 to primary consolidation, and Phase 3 to secondary consolidation.

Note that physical correspondence between the two phenomena is not suggested as they are governed by different mechanisms in general.

Phase 1: Nonlinear rate of porewater pressure Phase 2: Log-linear rate of porewater dissipaton pressure dissipation Phase 3: Aging initial /Q t Q

Time (log)

Figure 5.1. Theoretical idealization scheme of setup phases (modified from Komurka 2003)

5.3 Empirical Relationships for estimate of Setup

5.3.1 Existing empirical relationships for estimate of setup

Owing to its crucial importance in driven piles design, estimate of setup can result in a more optimal design. For this reason, many researchers investigated, especially during the late eighties and nineties (Skov and Denver 1988; Svinkin et al. 1994), possible empirical or semi empirical relationships to quantify setup. While many relationships and methods were proposed, major limitations still exist keeping those equations from general acceptance or application. Herein, some of the well-known relationships in the literature used to predict setup will be presented. They are mainly empirical relationships back calculated from non-instrumented static loading tests.

By far, the most popular relationship for quantifying set up as a function of time was presented by Skov and Denver (1988). The relationship models setup as a linear function with respect to the log of time. It describes phase 2 (See Figure 5-1) where the rate of excess pore water pressure dissipation becomes constant, meaning it is linear with respect to the log of time. The predicted axial capacity at a time t in the future after pile installation is related to an initial axial capacity and an empirical constant A through the following equation:

Q t t =+⋅1A log  (5.1) Qt00

where: Qt = axial capacity at time t after driving; Q0 = axial capacity at time t0; A = a constant, depending on soil type; t0 = an empirical value measured in days.

The time t0 is a function of soil type, and pile size. Table 5.1 present values back calculated by different investigators during the nineties. While the reported values ranges from 0.01 days

(Long et al. 1999) to 2 days (Camp and Parmar 1999; Svinkin et al. 1994), a general consensus

around about 1 day can be observed as suggested by many investigators (Axelsson 1998; McVay

1999; Bullock 1999; Svinkin et al. 1994).

The constant A is a function of soil type, pile material, type, size, and capacity (Camp and

Parmar 1999, Svinkin et al. 2000) but is independent of depth, and porewater pressure dissipation

(McVay et al. 1999, Bullock 1999). Table 5.2 shows presented values by three researchers as back calculated from loading tests. The value of the empirical constant A ranges between 0.21 and 0.8.

Table 5.1. Proposed values for t0 from different authors in the literature

Author(s) t0 Camp and Parmar (1999) 2 Svinkin et al. (1994) 1 to 2 Axelsson (1998) 1 Bullock (1999) 1 McVay (1999) 1 Long et al. (1999) 0.01

Table 5.2. Proposed values for empirical constant A in the Skov and Denver (1988) equation by different authors from the literature

Author(s) A Chow (1998) 0.25 to 0.75 Axelsson (1998) 0.2 to 0.8 Bullock (1999) 0.21

It is important to note that t0 and A are not independent (Bullock 1999). Because the two

parameters are empirical parameters (fitting constants) without specific physical justification, and

the possibility that the prediction needs more or less parameters to quantify capacity in time,

accuracy of the prediction is not guaranteed especially if it falls outside the soil type, pile type and

the geology on which they were based. Svinkin and Skov (2000) stated that Equation (5.1) is

appropriate for clay and cohesive soils.

Komurka (2003) in his report to Wisconsin department of transportation noted that Equation

(5.1) was based on total resistance (sum of shaft and toe resistances). Accordingly, the majority of studies, which empirically determined recommended values of t0 and A were also based on

combined resistance data. As demonstrated earlier, the relative contributions from shaft and toe

resistance affect the back-calculated values of t0 and A. And since both variables are a function of

soil type, values of t0 and A back-calculated using combined resistance data in non-uniform soil

profiles are averaged values and more accurate predictions require determination not just of the

averaged setup, but of the setup distribution along the pile shaft. (Komurka 2003).

Komurka (2003) in his report to Wisconsin department of transportation stated an example that shows this point:

“consider two piles driven side-by-side, each of which has 50 tons of shaft resistance at the end of drive (“EOD”), and each of which experiences set-up which doubles the shaft resistance to 100 tons at the time of retesting. The first pile is driven to a hard layer, and has a toe resistance of 100 tons (at both EOD and at the time of retesting). This first pile had an EOD capacity of 150 tons, and a retested capacity 200 tons, for a set-up ratio (the ratio of a long-term capacity to the end-of-drive capacity) of 1.33. The second pile stops just short of the hard layer, and has a toe resistance of only 25 tons (at both EOD and at the time of retesting). This second pile had an EOD capacity of 75 tons, and a retested capacity of 125 tons, for a set-up ratio of 167. The same piles, driven through the same soil deposits which exhibited the same set-up in both cases, yield different set-up factors. Use of these data in other empirical predictive methods will similarly yield different back-calculated values of other parameters.”

During the same year the Skov and Denver (1988) equation was proposed, other relationships

were developed to predict pile capacity increase with time by Guang Yu (1988), Huang (1988).

The aforementioned relationships will be presented as well as other relevant equations proposed

afterwards by Svinkin (1996), and Svinkin and Skov (2000).

Guang Yu (1988) back calculated capacity after 14 days of EOD for sensitive clayey soils and

proposed the following empirically developed equation:

Q14 =(0.375 ⋅+ SQt 1) EOD (5.2)

where: St = soil sensitivity; Q14 = Pile capacity at 14 days; and QEOD = Pile capacity at End of

driving

Huang (1988) proposed a predictive function that depends on end of driving capacity and

time but requires also estimate of a maximum pile capacity:

QQt= EOD +0.236 ⋅+[ 1 log(tQ ) ⋅ (max − QEOD )] (5.3)

Where: t = time after end of driving in days; Qt = pile capacity at time t ; QEOD = Pile capacity at

EOD; and Qmax = maximum pile capacity

Svinikin (1996) proposed two limiting values for estimating axial capacity after end of driving. The two equations are as follow:

0.1 Upper bound Qt =⋅⋅1.4 QtEOD (5.4)

0.1 Lower bound Qt =1.025 ⋅⋅ QtEOD (5.5)

Svinkin and Skov (2000) suggested a relationship similar to Equation (5.1) by using t0 = 0.1

days and replacing the constant A by a new constant noted B in Equation (5.1), Equation (5.6) can

be obtained and is written as follow:

Qt() =+⋅1Bt( log( ) + 1) (5.6) QEOD

where B = a constant, depending on soil type.

5.3.2 Observations and Discussion of existing methods

Like the Skov and Denver (1988) relationship, all the other presented formulas were developed

using combined total resistance, lumping shaft and toe resistance. All other formulas use the

instantaneous capacity at End of Driving, QEOD which can be determined by dynamic monitoring

through PDA instrumentation and subsequent CAPWAP capacity estimate. On the other hand,

Skov and Denver (1988) uses axial capacity at a specific time after End of Driving, Q0.

Reddy and Stuedlein (2014) presented a study for 76 driven pile case located in the Puget

Sound Lowlands where setup is frequently observed after pile installation. All the studied piles

were dynamically monitored using PDA and where subsequent estimate of capacity was made at

both End of Driving (EOD) and beginning of Restrike (BOR). The setup time corresponding to the time between EOD and BOR was reported to range between 5.5 and 312.5 hours. The study assessed the accuracy and precision of the Skov and Denver (1988) model to predict setup between

EOD and BOR. Evaluation of the method resulted in a relatively high uncertainty quantified by a

COV of 45 to 59 percent. Specific recalibration to the local database using a hyperbolic function and least squares regression improved the precision of the Skov and Denver (1988) method by reducing COV to 29 to 32 percent. It was noted by the authors that the new modified version of

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the Skov and Denver (1988) model is purely empirical and should be used within the bounds of the dataset parameters including pile types, pile sizes and geology, and it can be trusted only under similar considerations.

5.3.3 Current practices for estimating Setup: State of the practice

Soil setup factor, is defined as the ratio of long term capacity over EOD static resistance as shown in the following equation:

Ru fsetup = (5.7) Ru− eod

Rausche, et al. (1996) studied a database of 99 test piles from 46 different sites. Averaged setup factors were based on the predominant soil type along the pile shaft. In that study, the end of driving resistance was based on Wave Equation Analysis Program (WEAP) analysis.

Subsequently, the soil setup factor was defined as the static load test failure load as inferred from the Davisson method divided by the end-of-drive wave equation capacity. Table 5.3 present the result of this study with observed ranges of setup for each soil type as well recommended values and percent cases corresponding to that soil. (Hannigan et al. 2006 or FHWA 2006 Driven Piles

Volume 1).

These setup factors values for different soil conditions are also endorsed by the FHWA Manual on the Design and Construction of Driven Pile Foundations, Reference Manual-Volume 1

(Hannigan et al 2006). Such values are meant to provide the foundation designer with specific guidelines, but, in reality, the opposite is the truth. They only generate a sense of uncertainty. For instance, setup factor for clay ranges between 1.2 and 5.5, for silt between 1.5 and 5.0, for sand- clay mixtures between 1.0 and 6.0. This considerable scatter, of about 500%, shed the light on the considerable uncertainty designers are faced with. Following the recommended soil setup factor

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values would only result in over conservative design or inaccurate considerations. More importantly, such conduct affect negatively the practice of foundation engineering by inducing non quantifiable uncertainties. A comparable situation is the factor of safety used to capture uncertainties when determining the allowable capacity of foundations. If a more descriptive name would be given to this factor, it should be factor of ignorance, because the designer is enable to quantify in a rational manner the chances of failure using such a global factor. Fortunately, the geotechnical practice is moving steadily toward the reliability based design where sources of uncertainty are quantified statistically. If this is said, is to promote efforts aiming to establish a more effective and rational framework for assessing setup.

Not only is the magnitude in capacity gain subject to a considerable scatter and debate. Also, in practice, when a restrike is decided, the waiting time before restrike is a clear issue. In fact,

Governmental and state organism suggest widely scattered waiting times. AASHTO recommends the required wait time before restrike based on one of the following: clean sands at 1 day, silty sands at 2 days, sandy silts at 3-5 days, and clays at 7 days (AASHTO 2009). Oregon Department of Transportation (ODOT) bridge foundation construction specifications typically require a one- day minimum setup period before a restrike can be performed (Smith 2009). FHWA 2006 recommends five to seven days to assess accurately setup in granular soils and at least two weeks in cohesive and fine grained soils.

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Table 5.3. Soil setup factors (After Rausche et al, 1996)

Range in soil setup Recommended soil Number of sites and factor setup factor (Percentage of Data Base) Clay 1.2 - 5.5 2.0 7 (15%) Silt - Clay 1.0 – 2.0 1.0 10 (22%) Silt 1.5 – 5.0 1.5 2 (4%) Sand - Clay 1.0 – 6.0 1.5 13 (28%) Sand - Silt 1.2 – 2.0 1.2 8 (18%) Fine Sand 1.2 – 2.0 1.2 2 (4%) Sand 0.8 – 2.0 1.0 3 (7%) Sand - Gravel 1.2 – 2.0 1.0 1 (2%)

5.4 Development of Setup Estimation Methods

This section present the magnitudes of setup observed in the Puget Sound Lowlands as a

function of soil type, density and depth. Depth represents a proxy for effective vertical or confining

stress. Three examples of the observed EOD and BOR shaft resistance distributions are chosen

from a total of 89 piles, the remainder of which are presented in Appendix B. All of these piles

were monitored using a Pile Driving Analyzer (PDA) and subsequent CAPWAP signal matching

was performed to determine the static total resistance and shaft resistance distributions at EOD and BOR. Although an overall setup was observed for all of the piles with total shaft resistance at

BOR being larger than that at EOD, the piles presented in the next sections illustrate some cases

where portions of the soil profile experienced partial liquefaction and setup or relaxation. Those

observations are essential to establish informed decisions about the variation of soil-pile resistance

with time, location and soil type. CAPWAP analysis allows determination of unit shaft resistance

distribution, enabling possible correlations between specific soil types and effects of stratigraphy

on the gain in pile capacity.

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5.4.1 Example 1: Setup in all layers

The first example consists of a solid section prestressed concrete pile. The pile is 0.6 m (24

in) in diameter closed section with an area of 0.30 m2 (477 in2), a total length of 41 m (135 ft), and

a depth of penetration of 25.3 m (83 ft). The pile was constructed to support the development of a

port structure. The driving system consisted of a single acting diesel hammer Delmag D62 with a

ram weight of 5,443 kg (12 kips). The maximum rated stroke is about 3.8 m (12.4 ft) and a

maximum energy of 200 kN-m (149 kip-ft).

The soil profile was established from a boring located approximately 3 m (10 ft) away, providing relatively good confidence of the stratigraphy. The geology of the site consists of estuarine deposits altered with some shallow seams of peat (He/Hp) at shallow depths. Underlying deposits surrounding the lower half of the pile consist of alluvium (Ha). At the pile’s location, soil conditions included very loose silt with traces of low plasticity organic soil to a depth of 3.5 m

(11.5 ft) approximately. Medium dense, dense to very dense sandy soils with cohesionless silt seams extend to a depth of 23 m (75.5 ft) approximately. Below the toe of the pile, the major soil type consisted of medium dense cohesionless silt.

The CAPWAP-based EOD unit shaft resistance distribution is presented in Figure 5-2 and indicated using a thick dashed line, and shows very low shaft resistance for the majority of shaft length. An EOD shaft resistance equal to 400 kN (90 kips) was determined, compared to the toe resistance of 580 kN (130 kips). Following the initial drive to 25.2 m, a restrike was performed after 43 hours had elapsed. Although the pile was not driven hard enough to produce geotechnical failure, sufficient displacement to fully mobilize shaft resistance was obtained, on the order of about 3 mm (0.12 in). CAPWAP analysis resulted in an ultimate resistance of 2,400 kN (540 kips), partitioned into 1,870 kN (420 kips) for shaft resistance and 530 kN (120 kips) for toe resistance.

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The gain in resistance is likely contributed by shaft resistance due to dissipation of pore water pressure and soil reconsolidation. The overall or global setup ratio is 2.45, meaning that capacity had doubled in less than two days. Since toe resistance can be considered constant due to the very small change, shaft resistance-specific setup ratio was 4.66. The resulting setup distribution is illustrated with a solid line in Figure 5-2. Setup ratio is larger than one at all depths, indicating that a gain in capacity occurred along all portions of the pile. Setup ratio varied between 1.6 and 33.4

with lowest value occurring at shallow depths in very loose fill of organic and silty soil. The largest setup was observed in the vicinity of the pile toe, in medium dense nonplastic silt.

5.4.2 Example 2: Inferred Liquefaction in Response to Driving

The next example has been selected owing to its performance during driving. TP19 is one test

pile from 24 test piles installed at a project in Seattle, Washington. This pile was a production pile

as part of a foundation for a stadium. The steel pile was a closed pipe with an outside diameter of

475 mm (18 in) and wall thickness of 12.7 mm (0.5 in). The cross sectional area was 0.018 m2

(27.5in2) and the base area was 0.16 m2 (254 in2). The pile length was 24.4 m (80 ft) and the depth of penetration was about 23.8 m (78 ft).

The geological deposits in the vicinity of pile include alluvial and estuarine strata and underlain by glaciomarine drift (Qpgm), which formed the bearing layer for the pile toe. The investigation program included CPT and SPT borings, the closest of which was located 7.6 m (25 ft) away.

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Unit Shaft Resistance (kPa) 0 40 80 120 160 200 0 OL/ML V. loose

10 SM M. dense

15 Depth (m) SP-SM Dense 20 SM/ML V. dense

33.4 ML 25 M. dense

ML M. dense 30 + 0 2 4 6 8 10 Setup Ratio EOD Resistance BOR Resistance Setup Ratio

Figure 5.2. Pile ID: RI-001&WSP6. Unit shaft resistance and Setup ratio variation as a function of depth .Example 1 illustrating setup in all soil layers

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The soil profile along the pile shaft is shown in the right column of Figure 5-3. The general

subsurface conditions includes the presence of soft and very loose to loose soils overlying the

bearing layer consisting of very dense silt intermixed with sandy soils. Except the upper 3 m (9.8

ft) where medium dense silty sand was encountered, very loose materials extends to approximately

20 m (65.6 ft) below the ground surface before reaching a bearing competent layer consisting of very dense silt intermixed with sand.

Dynamic measurements were made using the PDA during continuous driving and restrikes.

Following the completion of the test, CAPWAP analysis were performed. The reported total EOD resistance from CAPWAP analysis is 3,560 kN (800 kips) shared consisting of 445 kN (100 kips) for the shaft and 3,115 kN (700 kips) for the toe resistance. Driving resumed 168 hours after EOD completion to provide the BOR capacity. The total CAPWAP resistance for the restrike was about

4,492 kN (1010 kips), divided between 2,090 kN (470 kips) and 2,402 kN (540 kips) for shaft and toe resistances, respectively. The overall setup ratio was 1.26, however toe resistance had decreased. The observed penetration resistance at EOD and BOR is 180 bpf (bows/0.3m) and 192 bpf (bows/0.3m), respectively. This increase in penetration resistance, coupled with the fact that a heavier driving system was used for BOR, confirm the increase in resistance.

A unit shaft resistance of less than 2.6 kPa (0.054 ksf) was observed in the upper 13 m (42.7 ft) of the pile suggesting that the soil may have liquefied by losing its strength. Plunging was observed during penetration between 1.5 and 8.5 m (4.92 and 27.9 ft) of penetration coinciding with the very loose soil encountered during investigations.

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Unit Shaft Resistance (kPa) 0 30 60 90 120 150 180 0 SM M. dense

10.0 SP-SM 5 Loose 27.8

33.3 ML V. loose 10 33.4

33.4 SM 21.2 Loose Depth (m) 15

ML V. loose

20 ML/SM V. dense

ML V. dense

25 + 0 2 4 6 Setup Ratio EOD Resistance BOR Resistance Setup Ratio

Figure 5.3. Pile ID: RI-007&TP19. Unit shaft resistance and Setup ratio variation as a function of depth .Example 2 illustrating liquefaction at low depths in loose sandy silty soils

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The soils may also have liquefied between 3 and 13 m (9.8 and 42.6 ft) and experienced an

increase in shaft resistance of over 10 times the EOD shaft resistance following reconsolidation.

This 10 m thick soil layer is composed of six soil segments in the CAPWAP model, with setup

ratios ranging from 10 to 33.4. The EOD shaft resistance due to the six segments is 9.1 kN while

the BOR shaft resistance is 238.4 kN.

The average setup ratio from these six segments is: 238.4 / 9.1= 26.2 , or about twenty times

the setup ratio that the pile experienced overall. However, the contribution of this increase to the

shaft resistance increase of the pile was less than 10%. Therefore, it can be included that although

setup is very high in some layers, it does not necessarily produce an overall large increase in shaft

resistance, especially for shallow depths.

5.4.3 Example 3: Relaxation in some soil layers

The third pile will illustrate a case of partial relaxation, where although the pile experienced

an overall increase in capacity, some layers underwent relaxation. Such observation wouldn’t be

possible without a detailed resistance distribution at EOD and BOR.

The test pile was a steel material with 0.6 m (24 in) outside diameter pipe and 12.7 mm (0.5

in) thick wall. The cross sectional area was 0.023 m2 (36.9 in2) and a closed-end section with an

area of 0.29 m2 (452 in2). The total pile length was approximately 49 m (161 ft) with an embedded length of 43.3 m (142 ft) during the dynamic test.

A Delmag D 46-23 single acting diesel hammer was used to drive the pile for all aspects of

installation. The reported nominal ram weight for this model and the manufacturer’s rated

maximum energy are 44.9 kN (10.1 kips) and 145 kN-m (107 kip-ft), respectively. The driving

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system consisted of a 15.6 kN (3.5 kip) Delmag helmet and a Conbest and aluminum hammer

cushion 50 mm (2 in thick) with a cross section of 0.27 m2 (415 in2).

The geological deposits at the site, located in Tacoma, WA, include deep alluvial materials.

The soil investigation program is composed of borings and CPTs. The nearest CPT and boring were about 18.2 m (60 ft) from the location of the pile. These logs indicate loose sandy silt or soft

clay to a depth of about 15 m (49.2 ft), and very dense sand with traces of silt from 15 m (49.2 ft) to 21 m (68.9 ft). Below 21 m depth, silty sand with varying relative densities was encountered.

The time elapsed between installation and restrike was approximately 45 hours. At the end of driving the computed resistance was 3870 kN (870 kips), with 3120 kN (702 kips) shaft resistance and 750 kN (168 kips) for toe resistance. Similarly, a total resistance of 4010 kN (902 kips) was inferred from CAPWAP analysis, with 3380 kN (760 kips) of shaft resistance and 630 kN (142 kips) fortoe resistance at BOR.

The reported driving resistance (bpf / blows per 0.3 m) was 135 blows per 0.3 m (bpf) at the end of driving and 180 blows per 0.3 m (bpf) at the beginning of restrike, respectively. Thus, it is very possible that only a portion of the total resistance was mobilized, and the capacity calculated with CAPWAP is a lower bound for the true pile capacity. As a general rule of thumb, shaft resistance is fully mobilized when the pile experiences 3 to 5 mm (0.12 to 0.20 in) of continuous displacement (Fellenius 2014), while toe resistance requires significantly larger displacements.

Typically during pile driving, shaft resistance is fully-mobilized while toe resistance is only partially mobilized. Only a hammer capable of causing a larger permanent displacement can mobilize significant toe bearing resistance. In the case of this particular pile, an average set per blow at the end of driving and beginning of restrike is 1.7 mm (0.07 in) and 2.3 mm (0.09 in), respectively, which confirms that a large portion of the shaft resistance was mobilized, especially

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at the end of driving. On the other hand, these displacements are not capable of producing large toe bearing resistances.

Figure 5-4 presents the unit shaft distribution at EOD and BOR. Although the shaft resistance has increased from 3,120 kN (702 kips) to 3,380 kN (760 kips), relaxation occurred at many soil segments. As indicated by the setup ratio line, an initial value slightly less than one was observed in the upper 6 m (19.7 ft), then setup ratio increased constantly for the loose layers, between 6 and

15 m (19.7 ft and 49.2 ft). As the soil stiffness increased between 15 m (49.2 ft) and the toe of the pile, setup ratio decreased, leading to the relaxation noted below 26 m (85.3 ft).

Relaxation was encountered in some layers, mainly those expected to exhibit dilative behavior such as very dense granular soils. When relaxation occurs, the waiting time must be studied carefully and cautions must be taken to estimate the proper long term capacity. And if similar soils are encountered in the site, reduction factors must be used in order not to overestimate actual available resistance. Restrikes are thus highly recommended in dense and hard soil materials as well as loose and soft, so as to identify and quantify the potential for relaxation.

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Unit Shaft Resistance (kPa) 0 40 80 120 160 0

ML 5 V. loose ML/SM Loose 10 CL/ML V. loose 15

SM/SP-SM 20 V. dense SM/SP-SM M. dense

Depth (m) 25 ML M. dense

30 SP-SM/SM M. dense SP M. dense 35 ML/SM M. dense 40 SP/SP-SM M. dense 45 0 1 2 3 4 Setup Ratio EOD Resistance BOR Resistance Setup Ratio

Figure 5.4. Pile ID: RI-002&T1. Unit shaft resistance and Setup ratio variation as a function of depth .Example 3 illustrating relaxation in some layers

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5.5 Quantification of Setup using the Proposed β-Coefficient Models

The suite of β-coefficients models specific to the Puget Sound Lowlands and presented in

Chapter 4 was developed for both driving conditions, EOD and BOR, therefore presenting a means for estimating setup. Each model considers a specific soil type according to USCS classification rules at EOD or BOR as a function of depth. All proposed models follow the general form of a three parameters exponential function as presented in Chapter 4:

ββ01− ββ()z = + 1 (5.8) exp(β2 ⋅ z)

To differentiate between EOD and BOR conditions, appropriate subscripts specifying the driving condition have been added to the β-coefficients herein. Therefore, the β-coefficient for a specific USCS soil at EOD and depth is given by:

ββEOD,0− EOD,1 ββEOD ()z = + EOD,1 (5.9) exp(βEOD,2 ⋅ z)

Similarly, for the same USCS soil at BOR, the β-coefficient model is given by:

ββBOR,0− BOR ,1 ββBOR ()z = + BOR,1 (5.10) exp(βBOR,2 ⋅ z)

The setup ratio as defined in Equation (5.7) is the ratio of long term ultimate resistance and resistance at EOD. As described earlier, setup is mainly attributed to gain in resistance in shaft resistance, and therefore ignoring changes in the toe resistance represents a reasonable assumption. By discretizing the soil profile along the shaft into n layers of the pile as shown in

Figure 5-5 and subdividing the CAPWAP segments into the corresponding USCS groupings as described in Chapter 4, the new suite of β-coefficient models can be used to predict the setup

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Soil Layer 1

Soil Layer i

Soil Layer n

Figure 5.5. Soil layering along the shaft of a driven pile

related to shaft resistance. Total shaft resistance is the sum of individual shaft resistances contributed by the different soil layers. This can be written as follow:

n RRs= ∑ si, (5.11) i=1

th where Rs,i = Shaft resistance attributed to the i soil layer. In the effective stress analysis approach using β−coefficients, it is defined as follows

' Rsi,0=⋅βσ v ⋅⋅ pl i i (5.12)

th where σ’v0 = vertical effective stress for the i soil layer, typically determined at the middle of

th th th the i layer, pi = pile outside perimeter at i the layer, and li = length of the i layer. Using the newly developed models, Rs,I can be defined as follow:

' Rs, i ,EOD =βσEOD ⋅ v0 ⋅⋅pl i i (5.13)

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Similarly, at BOR, Rs,i can be written as follow:

' Rs, i ,BOR =βσBOR ⋅ v0 ⋅⋅pl i i (5.14)

It should be noted that in reality, changes in the effective stress occur due to dissipation of porewater pressure along with the consolidation or densification of the soil, thus resulting in an increase in magnitude where setup is observed or a decrease where relaxation was observed.

However, these effects are difficult to quantify accurately; therefore, it is assumed that the effective stress at BOR is equal to that at EOD. Therefore, from the β-coefficient back-calculated and used in Equation 5.14 is somewhat higher than in actuality, but produces an accurate shaft resistance if the pre-driving vertical effective stress is used.

Therefore, the setup at each individual layer, i for sake of generality, can be computed as follow:

Rsi, ,BOR fsetup, i = (5.15) Rsi, ,EOD

By inspecting Equations (5.13) and (5.14), Equation (5.15) can be further simplified, and the setup ratio for the ith soil is simply the ratio of β-coefficient at BOR to those at EOD:

βi, BOR fsetup, i = (5.16) βi, EOD

Or in a more detailed form:

ββBOR,0− BOR ,1 + βBOR,1 exp(βBOR,2 ⋅ z ) fsetup, i = (5.17) ββEOD,0− EOD,1 + βEOD,1 exp(βEOD,2 ⋅ z )

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Table 4.8 (see Chapter 4) present the values for coefficients, βEOD,0; βEOD,1; βEOD,2; βBOR,0;

βBOR,1; and βBOR,2 necessary for estimate of setup of individual soil layers. Based on the new β- models developed for eight USCS soil groups, and by using Equation (5.16), a new set of models for setup was produced. Figure 5.6 and 5.7 present the actual setup ratios with markers, as well as models (black curves) inferred from the proposed β-coefficient models using Equation (5.16) for the eight groups considered in Chapter 4 based on USCS classification. It should be noted again that the β-coefficient models assume that the use of the pre-driving effective stress regime is valid for both EOD and BOR shaft resistances and therefore do not account for reconsolidation. Additionally, the models implied by Equation (5.16) represent ratios of the

EOD and BOR β-coefficient models, and do not represent a direct fit to the back-calculated setup ratios shown in Figures 5.6 and 5.7, but do capture the average setup observed with depth.

The user can choose to use Equation (5.16) directly or some constant that captures the desired level of conservatism.

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a) Setup Ratio b) Setup Ratio 0.0 2.0 4.0 6.0 8.0 0.0 2.0 4.0 6.0 8.0 0 0

10 10

20 20

30 30 Depth, z (m) 40 Depth, z (m) 40

50 50

60 60 Setup Ratio Setup Ratio c) 0.0 2.0 4.0 6.0 8.0 d) 0.0 2.0 4.0 6.0 8.0 0 0

10 10

20 20

30 30 Depth, z (m) 40 Depth, z (m) 40

50 50

60 60

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a) Setup Ratio Setup Ratio b) 0.0 2.0 4.0 6.0 8.0 0.0 2.0 4.0 6.0 8.0 0 0

10 10

20 20

30 30 Depth, z (m) 40 Depth, z (m) 40

50 50

60 60 Setup Ratio Setup Ratio c) 0.0 2.0 4.0 6.0 8.0 d) 0.0 2.0 4.0 6.0 8.0 0 0

10 10

20 20

30 30 Depth, z (m) 40 Depth, z (m) 40

50 50

60 60

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Finally, by computing setup ratio for all layers, shaft resistance at BOR (or the long term condition) can be obtained by multiplying the shaft resistance at EOD for a layer, Rs,i , with its corresponding setup ratio fsetup,i (determined from Equation 5.17 and Table 5.4) and summing them over the length of the pile:

nn βi, BOR Rs=∑∑ fR setup, i ⋅= s ,, i EOD ⋅Rs,, i EOD (5.18) ii=11= βi, EOD

Rs,i,EOD is usually determined from dynamic tests with CAPWAP signal matching. It is also possible to determine long term capacity based on a static analysis approach then reduce that by a factor to account for conditions during driving. Figure 5.8 (a) shows the predicted setup in shaft resistance for 85 piles using the newly developed β-coefficient models versus calculated setup from CAPWAP estimate of setup, inferred from total shaft resistance at EOD and BOR.

Predicted setup is computed by dividing total shaft resistance predicted using β-coefficient models developed for the BOR driving condition by the total shaft resistance produced using those β-coefficient models specific to EOD (see Chapter 4). The mean bias, defined herein as the ratio of measured setup and predicted setup is equal to 0.93 and associated with a COV of

51%. It is important to note that the sample used to compare predicted and measured setup is the same one used to create β-coefficients, and therefore issues of confounding variables may exist.

Better conclusions could be drawn by assessing an independent sample. To investigate any possible bias dependency in the proposed models, Figure 5.8 (b) present the bias as a function of nominal setup. The existing slope confirms that there is bias dependency and that the model over-predict setup for low setup ratios and under-predict them for high setup ratios. This can be

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visualized by comparing the setup data points to the 1:1 line as shown in measured vs predicted space in Figure 5.8 (a).

a) 12.0 n = 85 λ = 0.93 10.0 COV = 51%

8.0

6.0

4.0 Predicted Setup

2.0

0.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Measured Setup

b) 4 Calculated λ = 0.08 setup + 0.92 Bias trend 3 R² = 0.78

, 2

Bias 1

0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Nominal Setup

Figure 5.8. (a) Predicted setup using β-coefficient models versus CAPWAP measured setup of shaft resistance (b) Bias as a function of nominal setup.

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For a specific pile experiencing setup, it is anticipated that the capacity will increase with time. Figure 5.9 shows setup ratio for each soil segments and the corresponding time. No clear trend between setup ratio and time can be inferred. This may be explained in part by the heterogeneity in soils considered and/or the fact that only one measurement after EOD was typically conducted. Table 5.4 presents time statistics per USCS soil group as considered for the

β−coefficient models. The setup time ranges between 2.5 and 312 hours with a mean ranging between 83.7 for ML soils and 174.8 for clays (CH; CL). It is believe that if the restrikes were carried out over a longer duration, a clearer trend in the setup ratio with time could be obtained.

Figure 5.10 investigates the possible relationship between setup ratio and EOD resistance for all soil segments developed in this research. It is observed that data points with the higher setup ratios exhibit a low EOD resistance whereas the highest resistances at EOD correspond to low setup ratios.

15 Setup = -0.0083t + 6.24 Setup Ratio 10

0 0 50 100 150 200 250 300 350 Time (hours)

Figure 5.9. Setup ratio as a function time for all studied soil segments

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15 Setup Ratio

0 0 1 2 3 4 5 EOD Resistance (kips)

Figure 5.10. Setup ratio versus EOD resistance for all soil segments used in this study

Table 5.4. Descriptive statistics of time (in hours) for different soil groups

Granular USCS group(s) Cohesive USCS group(s) Descriptive SW- GP ; GW ; GM ; OH ; SW ; SM ; SM / CH ; CL- Statistics SM ; GW-GM ; GP- ML OL ; SP SC ML CL ML SP-SM GM PT Min 2.5 21.0 2.5 2.8 2.5 21.0 22.5 2.5 21.0 Median 120.9 90.9 92.0 77.3 118.0 168.0 126.0 72.0 65.0 Mean 137.2 91.3 86.7 85.1 88.7 174.8 137.9 83.7 99.0 Max 312.5 168.0 287.0 168.0 146.0 287.0 312.5 237.0 287.0 Sample size 242 213 219 113 82 72 96 151 26 Standard 3.7 16.6 error 5.7 2.7 3.7 5.6 11.9 8.2 4.9 Standard deviation 89.3 39.4 54.6 39.3 50.6 101.0 80.7 59.9 84.8

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5.6 Summary

This chapter begins with an overview of setup mechanisms, state of the art relationships to

quantify it as well as a summary of available protocols implemented in design codes. Plotting unit

shaft resistance distribution at EOD and BOR for 89 piles (see Appendix B) allow for inference of

valuable insights to make a more informed decision about setup patterns. Three examples, showing

respectively, a case of setup in all soil layers, partial liquefaction, and partial relaxation are presented to demonstrate the necessity of considering stratigraphy when assessing changes in shaft resistance. Afterwards, the new models developed in Chapter 4 are used to present a new procedure for assessing setup in shaft resistance using individual soil layers classified using USCS rules. It is recognized that since a quantified implementation of time was not possible because of the limited number of testing with respect to time (mainly two tests, EOD and BOR), the formulas are limited to the range of wait time used in the data.

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6 CHAPTER 6 Development of Calibrated Resistance Factors for Static Axial Capacity of Piles Driven in the Puget Sound Lowlands

6.1 Introduction

The assessment of variability on the estimation of axial capacity is treated indirectly through

experience and judgment, and/or directly through consideration of reliability-based design. The

geotechnical engineering profession is moving toward reliability based design where sources of

uncertainty are assessed rationally and can result in harmonization with structural design codes to

achieve a uniform probability of failure (pf; for the ULS; e.g., Whitman 2000, Huffman and

Stuedlein 2014).

This chapter focuses on reliability-based design analyses using an extensive region-specific database. The specific objectives of this study are to quantify the accuracy and uncertainty in: (1)

“bearing graph”-type wave equation analysis of piles (WEAP) calculations for several shaft resistance distribution assumptions, (2) a commonly-used static analysis method, and (3) the newly developed shaft resistance models that are applicable to the Puget Sound Lowlands. Another objective is to calibrate resistance factors for piles driven in the Puget Sound Lowlands for each of the axial capacity estimation methods. First, the database used is described; then, the capacity estimation methods used in this work are identified and relevant governing factors discussed. The chapter then focuses on the quantification of method accuracy, uncertainty, and statistics appropriate for calibration of resistance factors. Thereafter, the resistance factors for common loading statistics are presented and implications for design discussed. Although this work is

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applicable to a single geologic region, the framework is broadly applied to any region where data of similar quality can be developed.

6.2 Selected Static Axial Capacity Estimation Methods

Static Analysis using Standard Penetration Test Correlations

A commonly-used static analysis (SA) method for axial capacity based on correlations of typical strength parameters to the results of the standard penetration test (SPT), NSPT, is recommended by the FHWA (Hannigan et al. 2006). This method is implemented in GRLWEAP within the Variable Resistance Distribution option with minor modifications (termed FHWA-SA herein). The FHWA-SA method can be used for plastic, fine-grained and granular soils to predict the shaft and toe resistance (Rs and Rt, respectively). The user of GRLWEAP can input either the friction angle or the relative density for granular soils. For plastic, fine-grained soils, the undrained shear strength or friction angle can be used. Alternatively, the user may enter the unit shaft and toe bearing resistances for any soil layer directly. Refer to Chapter 2, GRLWEAP (2010) and

Hannigan et al. (2006) for a summary of this design method.

Wave Equation-based Bearing Graph Static Axial Capacity

In general dynamic WEAP computations, the pile and driving system, including the hammer, helmet, and pile and hammer cushions, are modeled by a set of lumped masses connected with springs and dashpots. In GRLWEAP 2010, the default pile mass segment length is equal to one meter. Smaller lumped mass segment lengths may be specified to improve the accuracy of the solution, but usually requires a longer computational time. The stiffness of the attached springs is computed from the specified modulus of elasticity, unit weight, and cross sectional area of the pile or hammer. Hammer and pile cushions are typically used for concrete piles in practice, whereas

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only a hammer cushion is used for steel piles owing to their greater compressive and tensile resistance. In addition to geometrical and material parameters, the coefficient of restitution (COR)

can be specified to model energy losses in cushion materials. The COR is a parameter representing

the kinetic energy remaining in one object after collision with a second object. The default option

implemented in GRLWEAP was used to generate cushion thicknesses and CORs.

In order to capture the static and dynamic resistance of the soil to pile penetration, every

embedded pile lumped mass segment is connected to a soil element with springs and dashpots.

The static soil resistance is modeled by an elasto-plastic spring and the dynamic soil resistance by

a dashpot (Smith 1960). Refer to the literature review for further detail regarding the hammer-

cushion-pile-soil model in GRLWEAP 2010.GRLWEAP 2010 implements the wave equation to

simulate pile driving under different scenarios to relate the resistance to penetration (i.e., pile

capacity) to driving resistance (blow count). This kind of relationship is termed a bearing graph.

Figure 6.1 presents a flow chart of the steps necessary to produce a bearing graph. Development

of a bearing graph requires the specification of the percent toe and shaft resistance (of the total

resistance) and the assumed shaft resistance distribution. Modelers typically assume linear shaft

distributions in consideration of the typical geostatic effective stress distributions. The percentage

toe and shaft resistance is estimated using static analysis methods or varied to capture different

driving scenarios to capture the range in possible driving responses. In this study, the percentage

of shaft resistance was based on three approaches: (1) “WEAP 1”, where the percent shaft

resistance is set equal to that determined from CAPWAP signal matching, and (2) “WEAP 2”,

which uses the FHWA-SA method to infer percent shaft resistance. The former case implies

perfect knowledge of the relative contributions of toe and shaft load transfer, whereas the second

case represents the more typical, a priori, design case where the actual capacity is not known prior

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to signal matching. The bearing graph (i.e.., pile penetration blow count vs. capacity) was used to infer the capacity corresponding to the actual observed driving resistance at the EOD, and is considered equal to the predicted capacity. Refer to GRLWEAP (2010) for examples and detailed steps to generate a bearing graph.

Input Generate discrete driving Choose a range in system-pile-soil model ultimate resistance to be evaluated Hammer Model: ID, Name and Type Ram Velocity, Define the percent of Static Resistance shaft resistance and and Dynamic Resistance shaft distribution are calculated Cushion Information: Thickness, COR... Pile velocities, Stresses Residual Stress Analysis: and Energy transfer are

Yes or No calculated

Pile Information: Material, Geometry

Select the time Blow Count for each increments for numerical Resistance is determined integration Soil Parameters: Quake and Damping for Shaft and Toe Bearing Graph generated: Blow Counts Vs Static Resistances

Figure 6.1. Flow chart for the development of bearing graph in WEAP analysis

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6.3 Assessment of Static Axial Capacity Methods at EOD

In this section, only piles monitored at end of driving were studied. The database was filtered for piles driven at EOD. This resulted in 95 dynamically monitored piles at 26 different project sites in Washington State, in which piles were driven for ports, terminals, bridges, and different types of structures (e.g., stadiums, museum, parking structures). This subset is larger than that used in Chapter 4 to establish the new β-coefficient models because the requirement for having both

EOD and BOR information for a given pile is not necessary, and only EOD information is

sufficient. Typical records of pile driving included information about penetration resistance

(number of blows per foot), the observed blow rate and hammer stroke, and other remarks related to driving conditions. This information was accompanied with dynamic measurements using a

PDA. The materials comprising the piles were steel or prestressed concrete. Pile lengths ranged from approximately 22.8 to 56.38 m with an average length of about 37.7 meters. The predominant concrete pile section was a 0.6 m (24 in) octagonal section with an area of 0.31 m2 (477 in2), whereas the most common open pipe section was a 0.6 m (24 in) diameter and 12.5 mm (0.5 in)

thick wall. Sixteen different hammers were used to drive these piles, with open-ended single acting

diesel hammer Delmag D62-22 and D80-23 being the most common used. The distributions of

pile material used, pile shape types and hammer types of the 95 piles gathered for end of driving

is shown in Figure 6.2.

The axial capacity at EOD as derived from the CAPWAP signal matching analyses ranged

from 400 kN (90 kips) to 9,500 kN (2,135 kips) for 92 piles. The remaining 3 piles exhibited higher

resistances of approximately 20,000, 25,000 and 30,000 kN (4,496, 5,620 and 6744 kips) due to

their very large section: 72 steel open pipe pile with 1.5 in wall thick.

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Each pile case history is described in in Appendix C, where details such as the length, section,

depth of penetration, and pile driving system (i.e., hammer type and model, ram weight, rated

energy, manufacturer’s rated stroke) is presented. Driving resistance (bpf / blows per 0.3 m) was

collected from driving logs.

80 Hammers Shapes Materials 60 40

Frequency 20 0

Figure 6.2. Summary of pile database used in EOD WEAP analysis by material, shape and hammer type

Summary statistics such as bias and coefficient of variation will be used to quantify the

accuracy and uncertainty in each of the selected static analysis methods. Bias is a measure of the

tendency of a sample to over- or under-estimate some observed phenomenon. In this study, it is

defined as the ratio of measured capacity to predicted capacity λ = Qm/Qp .A static axial capacity

prediction method that provides an average bias close to one is relatively accurate, on average.

Bias is typically quantified with sample mean and its variability quantified by the sample standard deviation or coefficient of variation (COV). The COV in bias is defined as the ratio of standard deviation to the average bias:

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σ COV = (6.0) µ

The advantage in the use of the COV is that it represents a standardized measure of variability

or dispersion. Bias statistics µλ, σλ, and COV(λ) are essential metrics for reliability based design

approach for determining resistance factors within the LRFD framework (Allen et al. 2005).

6.4 Accuracy of and Uncertainty in Selected Static Analysis Methods at EOD

The selected static axial capacity estimation methods were investigated for accuracy by comparing each prediction or estimate of axial capacity, Qp, to that back-calculated from

CAPWAP signal matching at the EOD, Qm. By doing this for all piles at the end of driving

database, an assessment of the agreement between predicted axial capacity and dynamically

measured capacity is feasible. Two estimation methods, respectively designated WEAP 1 and

WEAP 2, are based on wave equation analysis. The basic difference between the two methods is

the shaft resistance percentage resulting from the FHWA-SA method. In WEAP 1, the shaft

resistance percentage is inferred from the CAPWAP analysis (implying an assumed “perfect”

knowledge), whereas shaft resistance percentage in WEAP 2 is based on a selected static analysis

method FHWA-SA. The conceptual differences between the case of WEAP 1 and WEAP 2 is that

the error in WEAP 1 can be assumed to be attributed to the error in the wave equation simulation

and assumed shaft resistance distribution, whereas WEAP 2 will include additional error due to

error in the static analysis computations of toe bearing and shaft resistance associated with design

methodology. The capacity predicted using the wave equation analysis is based on magnitude of

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penetration resistance. The bearing graph (i.e.., pile penetration blow count vs. capacity) is used to infer the capacity corresponding to the actual observed penetration value. This resistance is considered the predicted capacity. The third and fourth methods assessed herein, designated

FHWA-SA and PSL-SA, assess the accuracy and uncertainty in the static analysis of capacity estimated using the FHWA-SA and PSL-SA methods. In the former, the total capacity is evaluated, whereas the shaft resistance (only) is assessed in the PSL-SA method (see Chapter 4).

Accuracy and Uncertainty of Case WEAP 1 at EOD

The predicted capacity for case WEAP 1 for the 95 piles evaluated in this chapter are plotted

against that inferred from CAPWAP signal matching at EOD is shown in Figure 6.3. The abscissa

corresponds to the measured CAPWAP capacity at End of Driving while the ordinate presents the

predicted capacity at the EOD. The mean bias is equal to 0.99, indicating that this method is highly

accurate on average. The COV of 26% is relatively small compared to many geotechnical design models (Smith 2011 with a COV of 70% based on 175 piles; Paikowsky et al. (2004) with a COV

of 72% based on 99 piles), suggesting that the scatter associated wave equation analyses can be

relatively low if good a priori estimates of shaft and toe bearing resistance can be provided. By

inspection, the scatter in the data appears relatively uniform around the 1:1 line at a given

magnitude of capacity, however, the magnitude in scatter does appear to increase with increasing

capacity, indicating some degree of heteroscedasticity.

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10000 n = 95 λ = 0.99 COV = 26% 8000

6000

4000 (WEAP 1EOD) at(WEAP (kN) p 2000 Q

0 0 2000 4000 6000 8000 10000

CAPWAP at EOD, Qm (kN)

Figure 6.3. Predicted capacity of case WEAP 1 versus CAPWAP measured capacity at End of Driving (EOD) for all piles

Accuracy and Uncertainty of Case WEAP 2 at EOD

The investigation case WEAP 2 also assesses the accuracy of the wave equation analyses as

implemented in GRLWEAP software and the bearing graph analysis. Case WEAP 2 evaluates the accuracy and uncertainty in WEAP analyses when using shaft resistance percentages that are based on the static analysis method FHWA-SA, discussed earlier. The results for case WEAP 2 are shown in Figure 6.4. The resulting mean bias for this method is 0.98 and the COV is 27%, indicating that little loss in prediction accuracy or gain in prediction variability occurred due to the error in percent shaft resistance estimates. Moreover, the predicted capacity from both methods seems to be similar for each individual pile. Therefore, it can be concluded that shaft resistance percentage based on FHWA-SA is relatively accurate, or that this parameter assumption does not affect the calculation considerably. This is a desirable result as the FHWA-SA method does not

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require actual testing since it’s based solely on standard penetration test measurements, which are performed during the investigation program prior to pile installation.

10000 n = 95 λ = 0.98 COV = 27% 8000

6000

4000 (WEAP (WEAP 2 at EOD) (kN) p

Q 2000

0 0 2000 4000 6000 8000 10000

CAPWAP at EOD, Qm (kN)

Figure 6.4. Predicted capacity of case WEAP 2 versus CAPWAP measured capacity at End of Driving (EOD) for all piles

Accuracy and Uncertainty of Case FHWA-SA Compared to CAPWAP EOD Resistance

One of the two static analysis method assessed herein is FHWA-SA, described in Chapter 2.

The estimate of axial capacity was made using this method for each of the 95 piles considered in this chapter using the boring data associated with each test pile. The comparison of measured and predicted capacity for the FHWA-SA method, along with the bias statistics, are shown in Figure

6.5. The mean bias for FHWA-SA is 1.08, indicating that this static analysis method is slightly conservative on average. However, the scatter in this method is considerable. The COV in sample

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bias is 85%, indicative of significant prediction variability. Owing to its scatter, it may be

anticipated that any resistance factor calibrated within a reliability-based design (RBD) framework

will likely be quite low.

10000 n = 95 λ = 1.08 COV = 85% 8000

6000 SA) (kN) SA) -

4000 (FHWA p Q 2000

0 0 2000 4000 6000 8000 10000

CAPWAP at EOD, Qm (kN)

Figure 6.5. Predicted capacity of case FHWA-SA versus CAPWAP measured capacity at End of Driving (EOD) for all piles

Accuracy and Uncertainty of Case PSL-SA at EOD

The case PSL-SA based on the newly developed β-coefficients models for EOD conditions

based on USCS rules was used herein to evaluate the shaft resistance for 85 piles. Figure 6.6

presents the comparison of shaft resistance determined using CAPWAP technique and that based

on the static analysis method PSL-SA. The mean bias is 1.57 suggesting that the method is

conservative on average for EOD condition. It is noted that the method under-estimates pile capacities at lower magnitudes, say less than 1,500 kN, and over-estimates the capacities at the higher end. The associated scatter is represented by a COV of 53%. It should be noted that this

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method evaluates only the shaft resistance, opposed to the other methods where total capacity is

assessed.

10000 n = 85 λ = 1.57 COV = 53% 8000

6000 SA at EOD) (kN) SA - 4000 (PSL p

Q 2000

0 0 2000 4000 6000 8000 10000

CAPWAP at EOD, Qm (kN)

Figure 6.6. Predicted shaft resistance of case PSL-SA versus CAPWAP measured shaft resistance at EOD 85 piles

Comparison between the Selected Static Capacity Analysis Methods

Four different procedures were assessed in total, namely the wave equation method as

implemented in GRLWEAP, a modified version of the recommended FHWA (2006) static analysis method implemented also in GRLWEAP under SA, and PSL-SA method for estimation of shaft resistance based on the β–coefficients suite of models developed in chapter 4, were used to

estimate driving resistance at End of Driving (EOD). There is seen to be good agreement about

mean bias in WEAP1, WEAP2, and FHWA-SA, and considerable variation in the COV exhibited

by the different methods. The mean bias ranged between 0.98 and 1.57 while COV varied between

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16% and 85%. The dynamically based approaches tended to have relatively less scatter and seemed to be good estimates of measured capacity compared to the static analyses based methods. In the

next two sections, the effect of material type and shape of the pile on accuracy and dispersion will

be analyzed by filtering the analyzed data.

Also, in order for a design method to be acceptable for resistance factor calibration, there must

not exist any dependence of the prediction accuracy (i.e., the bias) on the nominal predicted

capacity. Bias dependence may be considered to exist if the p-value computed is less than 0.05

(Stuedlein et al. 2012). Comparison of the p-value from the non-parametric Spearman rank

correlation tests for dependence were conducted for the point bias-nominal capacity pairs for

WEAP 1, WEAP 2, and FHWA-SA, and produced p-values for the null hypothesis of dependence

of 0.09, 0.32, 3.87E-6, respectively. Thus it is shown that there is no bias dependency for the cases

WEAP 1 and WEAP 2, but there is a potential bias dependence for FHWA-SA case. Inspection of

the actual variation in bias with nominal capacity indicated that just two, low capacity piles

controlled the correlation test, and that the FHWA-SA method may be assumed to produce

unbiased estimates of axial capacity.

Figure 6.6 suggests that there may be some bias dependence for the PSL-SA case when using

all eight of the new β-coefficient models to predict the total shaft resistance. The Spearman rank

correlation test for bias dependence produced a p-value of 3.05E-15, confirming that bias

dependence exists. While the number has been calculated, it should not be interpreted as "correct",

rather it is an indication of the order of magnitude of the actual confidence in the statistical test.

Because the p-value is less than 0.05, the models should not be used as a “suite of models”, but

individually with individual resistance factors calibrated to the same risk level. This approach is

more appropriate as it accounts for different level of uncertainties corresponding to different soil

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types (Ching et al. 2013). From the eight β-coefficient models, seven have produced p-values

larger than 10% at EOD, and model No. 8 was the only one to produce a value less than 5% (0.1%);

therefore, this model will not be selected for resistance factor calibration.

Effect of Pile Material Type on Accuracy and Uncertainty in Static Capacity at EOD

The database of test pile was roughly split evenly between concrete and steel material types.

Owing to their difference interface (smooth – steel, concrete – rough), impedances, and axial stiffness, all characteristics that affect pile drivability and capacity, it was of interest to see if there was a dependence of accuracy on pile material type. Therefore, the 47 concrete piles and 48 steel piles are assessed separately for potential differences in accuracy in EOD capacity as compared to the combined dataset. Figure 6.7 presents the subset of concrete piles for the four cases assessed previously. The following observations specific to the concrete pile subset can be drawn:

• For all of the methods considered, except PSL-SA, the mean bias for concrete pile subset

is smaller than the corresponding mean bias for total dataset. This indicates that predicted

capacity for concrete piles is overestimated by all methods on average. The mean bias

decreased from 0.99 to 0.88, and from 0.98 to 0.86 for the wave equation-based methods,

WEAP 1 and WEAP2, respectively. The mean bias decreased by 11% from 1.08 to 0.96

for the FHWA-SA while it increased by 25% from 1.57 to 1.79 for the PSL-SA case.

• On the other hand, the Coefficient of variation (COV) was observed to increase slightly for

the concrete pile subsets evaluated herein for all methods except PSL-SA. The COV in

sample bias increased from 26% to 28%, 27% to 28%, 85% to 89% for the WEAP 1, WEAP

2, and FHWA-SA, respectively, and decreased from 53% to 45% for the PSL-SA case.

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10000 Concrete Piles n = 48 n = 48 λ = 0.86 8000 λ = 0.88 COV = 28 % COV = 28%

6000 (kN)

p 4000 Q

2000

(a) WEAP 1 (b) WEAP 2 0

10000 n = 37 n = 48 λ = 1.79 λ = 0.96 COV = 45% 8000 COV = 89%

6000 Predicted Capacity at EOD, Capacity Predicted

4000

2000

(c) FHWA-SA (d) PSL-SA 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 CAPWAP at EOD, Q (kN) m Figure 6.7. Predicted capacity for different predictive methods versus CAPWAP measured capacity at EOD for concrete piles

• For WEAP 1 and WEAP 2 cases, the capacity estimated by the various methods over–

estimated the CAPWAP capacity for most of the piles, in addition to on average. This can

be noticed by comparing the number of piles above the diagonal to the number of piles

below it. For example, approximately 80% of the pile concrete subset was over-predicted

by the WEAP-based methods.

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Similar to the previous case, it was of interest to evaluate the accuracy and uncertainty in the various axial capacity estimation methods for the steel pile subset. Figure 6.8 presents the predicted capacity versus measured capacity for steel pile subset for the various methods investigated. Some of the major observations include:

• The mean bias for all of the methods is larger than one, indicating that the axial capacity

of the steel piles in the database is under–predicted, on average. The mean bias for WEAP

1, WEAP 2, FHWA-SA, and PSL-SA is 1.09, 1.10, 1.24, and 1.39, respectively. This result

could be anticipated given the results observed for the concrete piles.

• The magnitude of scatter is smaller for the steel piles in the dataset as compared to the

concrete piles for all methods except PSL-SA. A decrease of 7% in the COV of point bias

was observed for WEAP 1 and WEAP 2, 5% for FHWA-SA, and an increase of 4% for

the PSL-SA method with all COVs compared to the COVs associated with the combined

dataset.

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10000 Steel Piles n = 47 n = 47 λ = 1.10 8000 λ = 1.09 COV = 20% COV = 19%

6000 (kN)

p 4000 Q

2000

(a) WEAP 1 (b) WEAP 2 0

10000 n = 48 n = 47 λ = 1.39 λ = 1.24 COV = 59% 8000 COV = 80%

6000 Predicted Capacity at EOD, Capacity Predicted

4000

2000

Figure 6.8. Predicted capacity for different predictive methods versus CAPWAP measured capacity at EOD for steel piles

Effect of Pile Shape and Condition on Accuracy and Uncertainty in Static Capacity at EOD:

It was of interest to investigate the effect of pile shape (e.g., pipe vs. octagonal) and soil

displacement (low – open-ended vs. high – closed ended) on the accuracy and uncertainty of the selected static axial capacity methods. The pile database assessed in this study consisted of closed

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octagonal (COPC) and open cylindrical (OCPC) prestressed concrete piles. Figure 6.9 and Figure

6.10 present the measured and predicted capacity of the axial capacity methods for COPC and

OCPC piles, respectively. Because the sample size of the OCPC piles is significantly smaller than previously assessed, at seven, the statistical significance of conclusions drawn for the OCPC case is questionable. Nevertheless, the following observations can be drawn:

• COPC exhibits larger uncertainty for all four predictive methods. COV decreases from

31% to 8%, 31% to 9%, and 96% to 44%, for WEAP 1, WAP 2, and FHWA-SA methods,

respectively, from COPC to OCPC subset of piles. Again, the smaller sample size of

OCPC is key and cannot be discarded. The 85 piles evaluated for PSL-SA case did not

include any OCPC piles, and this is the reason Figure 6.10 includes only the other three

methods.

• The mean bias is approximately the same for COPC subsets when compared to their

corresponding mean bias for concrete pile subsets.

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10000 Concrete Octagonal Closed Piles n = 41 λ = 0.86 8000 n = 41 COV = 31% λ = 0.88 COV = 31% 6000 (kN)

p 4000 Q

2000

(a) WEAP 1 (b) WEAP 2 0

10000 n = 41 n = 37 λ = 1.79 λ = 0.96 COV = 45% 8000 COV = 96%

6000 Predicted Capacity at EOD, Capacity Predicted

4000

2000

(c) FHWA-SA (d) PSL-SA 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 CAPWAP at EOD, Q (kN) m Figure 6.9. Comparison of measured and predicted capacity at End of Driving (EOD) and for closed octagonal pre-stressed concrete piles

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10000 Concrete Cylindrical Open Piles n = 7 8000 n = 7 λ = 0.86 λ = 0.89 COV = 9% COV = 8% 6000

4000 (WEAP (kN) 2 EOD) (WEAP at (WEAP (kN) 1 EOD) (WEAP at p p Q

Q 2000

0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000

Qm (CAPWAP at EOD) (kN) Qm (CAPWAP at EOD) (kN) 10000 n = 7 λ = 0.97 COV = 44% 8000

6000 SA) (kN) SA) -

4000 (FHWA p Q

2000

0 0 2000 4000 6000 8000 10000

Qm (CAPWAP at EOD) (kN)

Figure 6.10. Comparison of measured and predicted capacity at End of Driving (EOD) and for concrete cylindrical open piles

Figure 6.11 and Figure 6.12 present the variation of predicted axial capacity with that inferred from CAPWAP signal matching for steel closed-end pipe piles (SCPP) and steel open-ended pipe piles (SOPP), respectively. In general, COVs are similar between the two subsets wheras a sharp differenece in mean bias is exhibited by FHWA-SA and PSL-SA. The mean bias with FHWA-

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SA method decreased sahrply from 2.23 to 1.29 between SCPP and SOPP while it increased from

1.19 to 1.51 for PSL-SA. It should be noted that the SCPP subset sample size is 15 for WEAP 1,

WEAP 2, and FHWA-SA, whereas it is equal to 17 for PSL-SA case.

10000 Steel Closed Pipe Piles n = 15 n = 15 λ = 1.06 8000 λ = 1.07 COV = 20 % COV = 21%

6000 (kN) p

Q 4000

2000

(a) WEAP 1 (b) WEAP 2 0 10000 n = 17 n = 15 λ λ = 1.16 = 2.23 COV = 59% 8000 COV = 75 %

6000 Predicted Capacity at EOD, Capacity Predicted

4000

2000

(c) FHWA-SA (d) PSL-SA 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 CAPWAP at EOD, Q (kN) m Figure 6.11. Predicted capacity for different predictive methods versus CAPWAP measured capacity at EOD for steel closed pipe piles

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10000 Steel Open Pipe Piles n = 32 n = 32 λ = 1.12 8000 λ = 1.10 COV = 20 % COV = 19%

6000 (kN)

p 4000 Q

2000

(a) WEAP 1 (b) WEAP 2 0

10000 n = 31 n = 32 λ = 1.51 λ = 1.29 COV = 57% 8000 COV = 87 %

Predicted Capacity at EOD, Capacity Predicted 6000

4000

2000

(c) FHWA-SA (d) PSL-SA 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 CAPWAP at EOD, Q (kN) m Figure 6.12. Predicted capacity for different predictive methods versus CAPWAP measured capacity at EOD for steel open pipe piles

Effect of Driving Resistance on Accuracy and Uncertainty in Static Capacity at EOD

Driving penetration resistance rate is one of the main parameters affecting pile driving response

and the resulting resistance. Of particular interest in this work was the investigation of the potential correlation between the COV in point bias and magnitude of driving resistance. Figure 6.13, Figure

6.14, and Figure 6.15 show the variation of sample bias for the total pile dataset with the driving resistance in blow counts per foot (bpf) or blow per 0.3m, and separated in bins of 20 bpf. The

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mean and standard deviation in sample bias for each bin is represented the diamond marker and a

shaded bar, respectively. For case WEAP 1 and WEAP 2 it is observed the average bias is relatively stable and near a value of one (i.e., it is accurate on average) across the domain of driving resistance, the largest variability in predicted static axial capacity occurs at low driving resistances of less than 20 bpf. It is noted that this range in driving resistance corresponds to easy driving with high magnitudes of pile head acceleration. GRLWEAP Background report mentioned that easy driving may lead to inaccurate results. The finding of this research support this recommendation.

For the FHWA-SA, no clear trend between driving resistance and prediction bias exists, indicating that the driving resistance at EOD is not well correlated with the capacity predicting for this method. In fact, the FHWA-SA method was developed for long-term static (or begin of restrike) capacity (Hannigan et al. 2006). Since PSL-SA is used to only assess shaft resistance, the uncertainty in the magnitude of driving resistance was not studied.

2.00

1.60

1.20

0.80 Sample Bias Sample

0.40

0.00 20 40 60 80 100 120 140 160 180 200 220 240 Driving Resistance (bpf / blows per 0.3m)

Figure 6.13. Variation in prediction bias for case WEAP 1 at the end of driving condition as a function of the terminal pile set.

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2.00

1.60

1.20

0.80 Sample Bias Sample

0.40

0.00 20 40 60 80 100 120 140 160 180 200 220 240 Driving Resistance (bpf / blows per 0.3m)

Figure 6.14. Variation in prediction bias for case WEAP 2 at the end of driving condition as a function of the terminal pile set.

3.00

2.50

2.00

1.50 Sample Bias Sample 1.00

0.50

0.00 20 40 60 80 100 120 140 160 180 200 220 240 Driving Resistance (bpf / blows per 0.3m)

Figure 6.15. Variation in prediction bias for case FHWA-SA at the end of driving condition as a function of the terminal pile set.

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Figure 6.16 to Figure 6.19 show the histogram and calculated normal and lognormal distributions for WEAP 1, WEAP 2, FHWA-SA, and PSL-SA in which the sample bias is defined as the ratio of measured capacity by CAPWAP to that predicted by the selected method, both at

EOD. The normal and lognormal distributed curve fits are best fitted distributions in order to

capture the data statistically.

16 Normal Distribution 14 Lognormal Distribution n = 95 12 λ = 0.99 COV = 26% 10

Frequency 6

0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Sample Bias

Figure 6.16. Histogram and frequency distributions of sample bias based on WEAP 1 methods at End of Driving (EOD) grouped in 0.1 sized bins

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18 Normal Distribution 16 Lognormal Distribution

14 n = 95 λ = 0.98 12 COV = 27% 10

Frequency 6

0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Sample Bias

Figure 6.17. Histogram and frequency distributions of sample bias based on WEAP 2 methods at End of Driving (EOD) grouped in 0.1 sized bins

16 Normal Distribution 14 Lognormal Distribution n = 95 12 λ = 1.08 COV = 85% 10

Frequency 6

0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0 6.4 6.8 Sample Bias

Figure 6.18. Histogram and frequency distributions of sample bias based on FHWA-SA method grouped in 0.1 sized bins

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12 Normal Distribution Lognormal Distribution 10 n = 85 λ = 1.57 8 COV = 53%

6 Frequency 4

0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 Sample Bias

Figure 6.19. Histogram and frequency distributions of sample bias based on PSL-SA method grouped in 0.1 sized bins

6.5 Assessment of Static Axial Capacity Methods at BOR

Ninety four pile case histories were available for assessment of static capacity at BOR. Several of these cases were not paired with a corresponding EOD, owing to various project-related decisions. Similar to EOD, the typical record for each pile case included the driving resistance, observed hammer stroke, and general information related to the driving conditions. Figure 6.20 summarizes the pile database used at BOR hammer type, material type and pile shape. The reference capacity at BOR is the sum of shaft resistance at BOR and toe resistance at EOD. Since toe resistance is fully mobilized at EOD but only partially mobilized at BOR, using toe resistance at EOD is more representative of the actual toe resistance. Shaft resistance on the other hand at

BOR incorporates the effect of time such as dissipation of pore-water pressure and therefore is

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more representative of long term shaft resistance. This combination of toe resistance at EOD and

shaft resistance at BOR will be used as the reference capacity for total BOR capacity.

77 80 Hammers Shapes Materials 56 51 60 43 38 40

Frequency 8 20 4 2

Figure 6.20. Summary of pile database used in BOR WEAP analysis by material, shape and hammer type

Similar to EOD analysis, the selected static axial capacity estimation methods were investigated for accuracy by comparing each prediction or estimate of axial capacity, Qp, to that back-calculated from CAPWAP signal matching at the BOR, Qm. The four investigated methods,

explained earlier, are:

• WEAP 1, based on wave equation theory and uses shaft resistance percentage as reported

in CAPWAP analysis.

• WEAP 2, based on wave equation methodology as well but uses shaft resistance

percentage from SA method analysis.

• FHWA-SA based on FHWA recommendations (Hannigan et al. 2006).

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• PSL-SA based on the newly developed models for β-coefficients at BOR (see Chapter

4). This approach will be used to estimate shaft resistance only.

Restrike analysis resulted in larger scatter compared to End of driving for WEAP-based

methods. The predicted capacity using WEAP 1 method for all 94 piles plotted versus measured

axial capacity from CAPWAP at Beginning of Restrike (BOR) is shown in Figure 6.21. The mean

bias is equal to 1.04 meaning that this method underestimate capacity by 4% on average. The

COV of 34% is relatively small suggesting that WEAP 1 does not present a large scatter at

Beginning of Restrike. However, this is larger than mean bias at EOD of driving by 8%. WEAP 2 resulted in larger scatter with a COV of 42%. Figure 6.22 present measured versus predicted axial capacities at BOR for WEAP 2.

10000 n = 94 λ = 1.04 8000 COV = 34%

6000

4000 (WEAP at(WEAP 1 BOR) (kN) p Q 2000

0 0 2000 4000 6000 8000 10000

Qm (CAPWAP at BOR) (kN)

Figure 6.21. Comparison of measured and predicted capacity using WEAP 1 at BOR, assuming that BOR capacity is the sum of BOR shaft resistance and EOD toe resistance.

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10000 n = 94 λ = 1.07 8000 COV = 42%

6000

4000 (WEAP at(WEAP 2 BOR) (kN) p Q 2000

0 0 2000 4000 6000 8000 10000

Qm (CAPWAP at BOR) (kN)

Figure 6.22. Comparison of measured and predicted capacity using WEAP 2 at BOR, assuming that BOR capacity is the sum of BOR shaft resistance and EOD toe resistance.

The FHWA-SA method was used to estimate the capacity of each of the 95 piles using the boring data associated with each test pile at BOR this time. The comparison of measured and predicted capacity for the FHWA-SA method, along with the bias statistics, are shown in Figure

6.23. The mean bias for FHWA-SA is 1.41, indicating that this static analysis method is very conservative on average. However, the scatter in this method is considerable, with a COV equal to

65%, indicative of significant prediction variability. Owing to its scatter, any associated resistance factor for this case will be quite low.

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10000 n = 95 λ = 1.41 COV = 65% 8000

6000 SA atSA BOR) (kN) - 4000 (FHWA

p 2000 Q

0 0 2000 4000 6000 8000 10000

CAPWAP at BOR, Qm (kN)

Figure 6.23. Comparison of measured and predicted capacity using FHWA-SA at BOR, assuming that BOR capacity is the sum of BOR shaft resistance and EOD toe resistance.

The PSL-SA method based on β-coefficients developed in Chapter 4 was used to estimate the capacity of each of 85 piles at BOR. The comparison of measured and predicted capacity for the

PSL-SA method, along with the bias statistics, are shown in Figure 6.24. The mean bias for PSL-

SA is 1.17, indicating that this static analysis method is slightly conservative on average. The scatter associated with this method is quantified by a COV of 32%, 21% less than that at EOD.

Therefore PSL-SA method is more accurate and less certain for long term estimation of shaft resistance.

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10000 n = 85 λ = 1.17 COV = 32% 8000

6000 SA at BOR) (kN) SA - 4000 (PSL p

Q 2000

0 0 2000 4000 6000 8000 10000

CAPWAP at BOR, Qm (kN)

Figure 6.24. Comparison of measured and predicted shaft resistance using PSL-SA at BOR

Similar to EOD, there must not exist any dependence of the prediction accuracy on the nominal predicted capacity to ensure appropriate LRFD calibrations. Comparison of the p-value from

Spearman rank correlation tests for dependence were conducted for WEAP 1, WEAP 2, FHWA-

SA, and produced p-values for the null hypothesis of dependence of 0.55, 0.56, 8.44E-10, respectively. Thus it is shown that there is no bias dependency for the cases WEAP 1 and WEAP

2 at BOR, but there is a potential bias dependence for FHWA-SA case. Inspection of the actual variation in bias with nominal capacity indicated that three capacity piles controlled the correlation test, and that the FHWA-SA method may be assumed to produce unbiased estimates of axial capacity. For PSL-SA case, the non-bias dependence is verified for the suite of β-coefficient models based on USCS classification (i.e., Model No. 1 to No. 8). All eight groups exhibited p-

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values for the null hypothesis of dependence larger than 5%, ensuring therefore no bias

dependency for individual β-models at BOR.

Figure 6.25 and Figure 6.26 display bias data for steel and concrete subset piles. Opposite to what was observed at End of Driving, COV is larger for steel piles compared to concrete piles for

all methods except FHWA-SA. The PSL-SA has shown little variation in mean bias and COV

between concrete and steel piles at BOR.

10000 Concrete Piles n = 43 n = 43 λ 8000 λ = 0.92 = 0.94 COV = 44% COV = 35%

6000

(kN) 4000 p Q

2000

(a) WEAP 1 (b) WEAP 2 0 10000 n = 48 n = 37 λ = 1.29 λ = 1.14 COV = 62% 8000 COV = 32%

6000 Predicted Capacity at BOR, Capacity Predicted 4000

2000 (d) PSL-SA (c) FHWA-SA 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000

CAPWAP at BOR, Q (kN) m

Figure 6.25. Comparison of measured and predicted capacity at BOR for concrete piles. Note that PSL-SA estimate shaft resistance only.

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10000 Steel Piles n = 51 n = 51 λ 8000 λ = 1.13 = 1.18 COV = 24% COV = 43%

6000 (kN)

p 4000 Q

2000

(a) WEAP 1 (b) WEAP 2 0 10000 n = 48 n = 47 λ = 1.19 λ = 1.53 COV = 32% 8000 COV = 65%

6000 Predicted Capacity at BOR, Capacity Predicted

4000

2000 (d) PSL-SA (c) FHWA-SA 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 CAPWAP at BOR, Q (kN) m

Figure 6.26. Comparison of measured and predicted capacity at BOR for concrete piles. Note that PSL-SA estimate shaft resistance only.

Figure 6.27 to Figure 6.30 present measured versus predicted capacity of all studied methods for concrete octagonal closed piles (COCP) and concrete cylindrical open piles (OCPC), steel open pipe piles (SOPP), steel closed pipe piles (SCPP), respectively.

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10000 Concrete Octagonal Closed Piles n = 38 λ 8000 n = 38 = 0.86 λ = 0.83 COV = 21% COV = 21%

6000

(kN) 4000 p Q

2000

(a) WEAP 1 (b) WEAP 2 0

10000 n = 41 n = 37 λ = 1.26 λ = 1.14 8000 COV = 61% COV = 32%

6000 Predicted Capacity at BOR, Capacity Predicted

4000

2000

Figure 6.27. Comparison of measured and predicted capacity at BOR and for closed octagonal pre-stressed concrete piles

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10000 Concrete Octagonal Closed Piles n = 5 λ = 1.51 8000 n = 5 COV = 40% λ = 1.66 COV = 49% 6000

4000 (WEAP (kN) 1 BOR) (WEAP at (WEAP (kN) 2 BOR) (WEAP at p p Q

2000 Q

(a) WEAP 1 (b) WEAP 2 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 Q (CAPWAP at EOD) (kN) m Qm (CAPWAP at EOD) (kN)

10000

8000

6000 SA atSA BOR) (kN) - 4000

(FHWA 2000 n = 7 p λ = 1.35 Q COV = 71% (c) FHWA-SA 0 0 2000 4000 6000 8000 10000

CAPWAP at BOR, Qm (kN)

Figure 6.28. Comparison of measured and predicted capacity at BOR and for concrete cylindrical open piles

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10000 Steel Open Pipe Piles n = 35 8000 n = 35 λ = 1.24 λ = 1.17 COV = 47% COV = 24%

6000 (kN) p 4000 Q

2000

(a) WEAP 1 (b) WEAP 2 0

10000 n = 32 n = 31 λ = 1.58 λ = 1.24 COV = 30% 8000 COV = 72%

6000 Predicted Capacity at BOR, Capacity Predicted

4000

2000

Figure 6.29. Predicted capacity for different predictive methods versus CAPWAP measured capacity at BOR for steel open pipe piles

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10000 Steel Closed Pipe Piles n = 12 n = 12 8000 λ = 0.99 λ = 0.99 COV = 22% COV = 22%

6000 (kN)

p 4000 Q

2000

(a) WEAP 1 (b) WEAP 2 0

10000 n = 15 n = 17 λ = 1.49 λ = 1.10 8000 COV = 49% COV = 38%

6000 Predicted Capacity at BOR, Capacity Predicted

4000

2000

CAPWAP at BOR, Q (kN) m

Figure 6.30. Predicted capacity for different predictive methods versus CAPWAP measured capacity at BOR for steel closed pipe piles

Similar to pile penetration resistance trend at EOD, easy driving at BOR exhibit larger

uncertainty. Figure 6.31 show the blow counts per foot (bpf), presented in bins of 20 BPF, and

plotted against their respective bias for WEAP 1 and WEAP 2 at BOR. Figure 6.32 presents

variation in prediction bias for FHWA-SA as a function of the terminal set using BOR CAPWAP resistance as the reference capacity.

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2.50

2.00

1.50

Sample Bias Sample 1.00

0.50

(a) WEAP 1 0.00 2.50

2.00

1.50

1.00 Sample Bias Sample

0.50

(b) WEAP 2 0.00 40 80 120 160 200 240 280 320 360 400 440 480 520 560 Driving Resistance (bpf / blows per 0.3m)

Figure 6.31. Variation in prediction bias for case (a) WEAP 1 and (b) WEAP 2 at BOR as a function of the terminal pile set.

162

3.00

2.50

2.00

1.50

Sample Bias Sample 1.00

0.50

0.00 40 80 120 160 200 240 280 320 360 400 440 480 520 560 Driving Resistance (bpf / blows per 0.3m)

Figure 6.32. Variation in prediction bias for case FHWA-SA at BOR as a function of the terminal pile set . Figure 6.33 (a), Figure 6.33 (b), Figure 6.34, and Figure 6.35 show the histogram and calculated normal and lognormal distributions for WEAP 1, WEAP 2, FHWA-SA, and PSL-SA at

BOR. The normal and lognormal distributed curve fits are best fitted distributions in order to capture the data statistically.

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20 Normal Distribution (a) WEAP 1 18 Lognormal Distribution 16 n = 94 λ = 1.04 14 COV = 34% 12 10

Frequency 8 6 4 2 0

20 (b) WEAP 2 Normal Distribution 18 Lognormal Distribution 16 n = 94 λ = 1.07 14 COV = 42% 12 10

Frequency 8 6 4 2 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Sample Bias

Figure 6.33. Histogram and frequency distributions of sample bias grouped in 0.1 sized bins for case (a) WEAP 1 and (b) WEAP 2.

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14 Normal Distribution 12 Lognormal Distribution n = 95 10 λ = 1.41 COV = 65% 8

6 Frequency

0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0 6.4 6.8 Sample Bias

Figure 6.34. Histogram and frequency distributions of sample bias grouped in 0.1

sized bins for case FHWA-SA.

16 Normal Distribution 14 Lognormal Distribution

12 n = 85 λ = 1.17 10 COV = 32%

Frequency 6

0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 Sample Bias

Figure 6.35. Histogram and frequency distributions of sample bias grouped in 0.1

sized bins for case PSL-SA.

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6.6 LRFD RELIABILITY THEORY AND RESISTANCE ACTOR CALIBRATION IN SELECTED STATIC APACITY ETHODS

The LRFD methodology at the ULS states that the nominal loads (e.g., dead, live, extreme)

applied to a structure be factored by a load factor (γ), and compared to a nominal resistance reduced

using a resistance factor (φR). At the ULS, the basic inequality is satisfied for the target probability

of exceedance:

∑γφi, jQR ni ,, j≤ R ni, (6.1)

where γi,j = load factor, Qn,i,j = nominal load, and Rn,i = nominal resistance. In LRFD calibrations,

Qn,i,j and Rn,i are assumed to be random variables and are sampled from source distributions.

With multiple load sources, typically dead and live loads, the nominal load may be expressed as follow (Reddy and Stuedlein 2013):

QQ⋅+η Q = nDL,, nLL (6.1) nj, η +1

where η is the ratio of dead to live load. Also, a weighted load factor should be used to adjust

multiple nominal loads (Stuedlein et al. 2012). This weighted load is designated γavg and is

expressed as follow:

λDL⋅ γ DL ⋅+ ηλ LL ⋅ γ LL γ avg = (6.1) λDL⋅+ ηλ LL

where γDL, γLL, λDL and λLL equal the dead and live load factor, and bias in dead and live load,

respectively.

Figure 6.36 shows the empirical, and fitted normal and lognormal cumulative distribution

functions of the sample bias for WEAP 1, WEAP 2, and FHWA-SA methods at EOD. Fig. present

the fits for the seven unbiased β-coefficient models at EOD. Given the apparent suitability of fit

166

with summary statistics shown in Figure 6.36 and Figure 6.37, the lognormal distribution was adopted for sampling nominal resistances in the Monte Carlo simulations (MCS) used to calibrate the resistance factors forWEAP1, WEAP2, FHWA-SA and PSL-SA at EOD.

The loading statistics used herein were selected in accordance with AASHTO (2014)

specifications, with dead and live load factors equal to γDL = 1.25 and γLL = 1.75, respectively. The

loads were assumed normally distributed and associated with a mean bias in dead and live load

equal to λDL = 1.05 and λLL = 1.15, and a coefficient of variation equal to COVQ,DL = 10% and

COVQ,LL = 20%, respectively.

Similarly Figure 6.38 shows the empirical, and fitted normal and lognormal cumulative

distribution functions of the sample bias for WEAP 1, WEAP 2 and FHWA-SA methods at BOR.

Figure 6.39 shows the normal and lognormal cumulative fits for all eight unbiased β-coefficient

models at BOR used to estimate capacity for the PSL-SA case.

Monte Carlo simulation allows random sampling from source distributions to generate a

distribution from complex functions that contain multiple and potentially correlated sources of

variability. Specifically, for LRFD calibration, it allows independent sampling from the resistance

distribution and the dead and live load distributions to compute the inequality given in Equation

(6.1 for a given target probability of exceedance. By iteration, the method converges to an

appropriate resistance factor φR. The procedure is described in more detail by Allen et al. (2005).

Deterministic methods for computing resistance factors also exist. First Order Second Moment

(FOSM) method was used in many calibration, especially by DOT’s and AASHTO previous to

2007 and the work of Allen et. al (2005). As described in the literature review, it truncates Taylor

Series approximation and results in a deterministic closed form (see Chapter 2). Recently, Monte

Carlo Simulation became more desirable due to its evident statistical advantages:

167

• Monte Carlo simulation is a probabilistic approach incorporating the likelihood of each

outcome.

• Through the iteration procedure it is easy to see which inputs largely effect the resistance

factor leading to relevant conclusions.

3.0 Sample Bias Lognormal Distribution Normal Distribution 2.0

1.0

0.0

-1.0 n = 95

Z n = 95 λ = 0.99 λ = 0.98 -2.0 COV = 25.6% COV = 26.5%

(a) WEAP 1 (b) WEAP 2 -3.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 3.0

2.0 Standard Normal Variate, 1.0

0.0

-1.0 n = 95 λ = 1.08 COV = 84.7% -2.0 (c) FHWA-SA -3.0 0.0 2.0 4.0 6.0 8.0 λ Sample Bias, Figure 6.36. Cumulative distribution functions of the sample biases for the selected capacity estimation methods for EOD with summary statistics for fitted lognormal distributions.

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Sample Bias 3.0 Lognormal Distribution Normal Distribution 2.0

1.0

n = 168 0.0 λ n = 82 n = 152 = 1.00 λ = 1.00 λ COV = 100% = 1.00 COV = 180% COV = 109% -1.0

Model No. 1: Model No. 2: Z -2.0 CH, CL, and CL-ML GP, GW, GM, GW- Model No. 3: ML GM, and GP-GM -3.0 3.0

2.0

1.0

0.0 Standard Normal Variate, n = 213 n = 26 λ n = 113 λ = 1.00 = 1.00 λ = 1.00 -1.0 COV = 81% COV = 161% COV = 75%

-2.0 Model No. 4: Model No. 5: Model No. 6: OH, OL, and PT SM and SC SM / ML -3.0 0.0 2.0 4.0 6.0 0.0 2.0 4.0 6.0 0.0 2.0 4.0 6.0 3.0

2.0

1.0

0.0 n = 242 λ = 1.00 -1.0 COV = 97%

-2.0 Model No. 7: SW and SP -3.0 0.0 2.0 4.0 6.0 λ Sample Bias, Figure 6.37. Cumulative distribution functions of the sample biases for the β-coefficient models used in the PSL-SA method at EOD with summary statistics for fitted lognormal distributions.

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3.0 Sample Bias Lognormal Distribution Normal Distribution 2.0

1.0

0.0

-1.0 n = 95

Z n = 95 λ = 0.99 λ = 0.98 -2.0 COV = 25.6% COV = 26.5%

(a) WEAP 1 (b) WEAP 2 -3.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 3.0

2.0 Standard Normal Variate, 1.0

0.0

-1.0 n = 95 λ = 1.08 COV = 84.7% -2.0 (c) FHWA-SA -3.0 0.0 2.0 4.0 6.0 8.0 λ Sample Bias, Figure 6.38. Cumulative distribution functions of the sample biases for the selected capacity estimation methods for BOR with summary statistics for fitted lognormal distributions.

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Sample Bias 3.0 Lognormal Distribution Normal Distribution 2.0

1.0

0.0 n = 168 n = 82 n = 152 λ = 1.00 λ = 1.00 λ = 1.00 COV = 83% COV = 124% COV = 101% -1.0 Model No. 2: -2.0 Model No. 1: GP, GW, GM, GW- Model No. 3: ML CH, CL, and CL-ML GM, and GP-GM -3.0 3.0 Z

2.0

1.0

0.0 n = 26 n = 213 n = 113 λ = 1.00 λ = 1.00 λ = 1.00 -1.0 COV = 72% COV = 113% COV = 65%

-2.0 Model No. 4: Model No. 5:

Standard Normal Variate, Model No. 6: OH, OL, and PT SM and SC SM / ML -3.0 0.0 2.0 4.0 6.0 0.0 2.0 4.0 6.0 0.0 2.0 4.0 6.0 3.0

2.0

1.0

0.0 n = 242 λ = 1.00 n = 220 λ -1.0 COV = 96% = 1.00 COV = 82%

-2.0 Model No. 7: Model No. 8: SW and SP SW-SM and SP-SM -3.0 0.0 2.0 4.0 6.0 0.0 2.0 4.0 6.0 λ Sample Bias,

Figure 6.39. Cumulative distribution functions of the sample biases for the β-coefficient models used in the PSL-SA method at BOR with summary statistics for fitted lognormal distributions.

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Resistance factors were determined for different levels of reliability and load conditions.

Accidental loads such as wind, earthquake were neglected and only dead and live loads were

considered.

Figure 6.40 shows the resistance factors calibrated for various dead to live load ratios, η, for

WEAP 1, WEAP 2, and FHWA-SA at EOD, at β = 2.33 and 3.09. A power low captures the

variation of resistance factor as a function of η, similar to the findings of Stuedlein et al. (2012) and Reddy and Stuedlein (2013). The resistance factor calibrated for WEAP 1 and WEAP 2 equaled 0.67 and 0.65, respectively, for β = 2.33 and η = 3. These resistance factors are similar

across all η since there is very little difference in the source distributions for nominal resistance.

Because of its large COV, the FHWA-SA method resulted in a relatively low resistance factor of

0.20. The PSL-SA individual models produced resistance factors ranging between 0.04 and 0.22

for β = 2.33 and η = 3 at EOD. Figure 6.41 shows the resistance factors calibrated for the seven unbiased β-coefficient models at EOD (Model No. 1 to Model No. 7 in Chapter 4).

Similarly Figure 6.42 shows the resistance factors calibrated for various dead to live load

ratios, η, for WEAP 1, WEAP 2 and FHWA-SA at BOR, at β = 2.33 and 3.09. The resistance

factor for WEAP 1, WEAP 2 decreased from 0.67, 0.65 to 0.53 and 0.46 from EOD to BOR,

respectively, for β = 2.33 and η = 3. On the other hand, resistance factors increased for the FHWA-

SA method from 0.20 to 0.36. Again a power low captures satisfactorily the variation of resistance

factor as a function of η. Figure 6.43 shows the resistance factors calibrated for all eight unbiased

β-coefficient models at BOR as a function of η.

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Critically, the reference or measured pile capacity used in this study for EOD is derived from dynamic loading tests (DLTs) at EOD. Since EOD corresponds to short term resistance, adjustment of capacity by incorporating the conversion from DLT to static loading test (SLT) long-term capacity was not necessary. For BOR however, the resistance distributions have been adjusted per

Reddy and Stuedlein (2013).

0.75 2.33 3.09 0.70 ϕ = 0.698η-0.043 R -0.043 ϕR = 0.679η 0.65

0.60

0.55

0.50 R -0.043 φ ϕR = 0.5675η , ϕ = 0.550η-0.043 0.45 R (a) WEAP 1 (b) WEAP 2

Factor 0.40 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 0.25 ϕ = 0.207η-0.047

Resistance 0.20

0.15

0.10 ϕ = 0.118η-0.038

0.05

Figure 6.40. Variation in resistance factors as a function of dead to live load ratio for different predictive methods based on driving resistance at EOD

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0.20 0.10

-0.043 2.33 0.15 ϕR = 0.145η 3.09 ϕ = 0.047η-0.033 0.10 0.05 R

-0.047 0.05 ϕR = 0.078η ϕ = 0.021η-0.02 Model No. 1 Model No. 2 R 0.00 0.00 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 0.15 0.20 ϕ = 0.124η-0.043 R ϕ = 0.153η-0.048 0.15 R R φ 0.10 , 0.10 0.05 Factor -0.047 0.05 ϕR = 0.065η -0.036 ϕR = 0.066η Model No. 3 Model No. 4 0.00 0.00 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 0.10

Resistance 0.25 -0.047 ϕR = 0.228η 0.20 -0.054 ϕR = 0.055η 0.15 0.05 0.10 -0.045 ϕR = 0.136η 0.05 ϕ = 0.026η-0.04 Model No. 6 Model No. 5 R 0.00 0.00 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

0.15 -0.045 ϕR = 0.135η

0.10

0.05 -0.041 ϕR = 0.073η

Model No. 7 0.00 1 2 3 4 5 6 7 8 9 10 η Dead to Live Load Ratio,

Figure 6.41. Variation in resistance factors as a function of dead to live load ratio for the seven unbiased β-coefficient models at EOD

174

0.55 -0.046 ϕR = 0.548η 2.33 0.50 3.09 ϕ = 0.477η-0.044 0.45 R

0.40

0.35 ϕ = 0.408η-0.047

R R φ , 0.30 -0.041 (a) WEAP 1 (a) WEAP 2 ϕR = 0.337η

Factor 0.25 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 0.45 Resistance 0.40 -0.043 ϕR = 0.383η 0.35

0.30

0.25

0.20 -0.040 ϕR = 0.237η (c) FHWA-SA 0.15 1 2 3 4 5 6 7 8 9 10 Dead to Live Load Ratio, η

Figure 6.42. Variation in resistance factors as a function of dead to live load ratio for different predictive methods based on driving resistance at BOR

175

0.25 0.10 -0.047 0.20 ϕR = 0.195x -0.049 ϕR = 0.094η 0.15 0.05 0.10 -0.043 -0.044 ϕR = 0.113η ϕR = 0.046η 0.05 Model No. 1 Model No. 2 0.00 0.00 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 0.20 0.30 -0.052 ϕ = 0.251η-0.048 0.15 ϕR = 0.142η 0.25 R 0.20 0.10 0.15 R φ 0.10

, 0.05 -0.044 ϕ = 0.132η-0.043 ϕR = 0.076η R Model No. 3 0.05 0.00 Model No. 4 0.00 Factor 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 0.15 0.40 0.35 ϕ = 0.105η-0.046 -0.044 R ϕR = 0.306η 0.10 0.30 Resistance 0.25 0.05 0.20 -0.046 ϕR = 0.053η 0.15 -0.044 Model No. 5 Model No. 6 ϕR = 0.196η 0.00 0.10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 0.20 0.25 -0.048 ϕR = 0.2123η -0.048 0.20 0.15 ϕR = 0.1358η 0.15 0.10 0.10 -0.045 ϕR = 0.1229η 0.05 -0.036 ϕR = 0.0727η 0.05 Model No. 7 Model No. 8 0.00 0.00 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 η Dead to Live Load Ratio, Figure 6.43. Variation in resistance factors as a function of dead to live load ratio for the eight β-coefficient models at BOR.

176

In an effort to calibrate resistance factors using WEAP analysis for the Oregon Department of

Transportation (ODOT), Smith (2011) developed the PSU Master database. This database

consisted of 175 piles from the USA and other countries. The least represented region in the

database was from the Northwest with 16 piles, and the number of piles for Oregon was 2 (Figure

6.40). The study resulted in a mean bias of 1.56 and a COV of 70% for the nominal WEAP bearing

graph-type static axial capacity at EOD, with recommended resistance factor of 0.35. Paikowsky

et al. (2004) recommended a resistance factor of 0.40 for WEAP analysis at EOD using a national

database, which was based on 99 piles associated with a mean bias of 1.66 and a COV of 72% assuming pf = 1% (β = 2.33).

Compared to the recommended φR from Paikowsky et al. (2004) and Smith (2011), φR

determined in this study increased by more than 50% for the WEAP method at EOD, a significant

gain in nominal axial resistance. Those differences may be attributed to either the limited regional

scope and/or higher quality of the database evaluated. Both Paikowsky et al. (2004) and Smith

(2011) studies were based on national or global databases with a variety of geologic regions.

Additionally, Smith (2011) reported that 28 pile cases exhibited anomalies, such as differences in

the reported and evaluated driving resistances. The scope of this study was limited to steel and

prestressed concrete piles, with the significant majority of hammers consisting of diesel hammers,

and little variation in construction practices (e.g., use of pile cushions). This regionally-limited

scope and specific ranges in pile capacities, lengths, and types may have contributed to the

improvement in bias statistics and the resulting resistance factors. This study also shows that the

WEAP-based methods are more accurate and less uncertain than FHWA-SA static analysis

method, producing a resistance factor that is more than 3 times larger at a given η and β.

177

Table 6.1 summarizes previous works regarding resistance factors calibration for the use of the

WEAP method. A thorough look in the literature for resistance factors has shown a great

divergence between values reported by different researchers and organisms. This divergence is

totally justified view the different methods, quality and quantity of data, geology representing the

different location of piles used in the analysis, type of and properties of piles and construction

practices. However, only high quality, geology specific calibration can ensure meaningful and

representative resistance factors.

Table 6.1. Resistance factors using the WEAP method at EOD from the literature

Source Location Resistance Driving Reliability Remarks factor (*) Condition Index NCHRP 507 National 0.40 EOD 2.33 99 Piles Smith (2011) Oregon 0.35 to 0.50 EOD 2.33 206 Piles Long et al. Illinois 0.74 EOD 2.33 39 Piles IDOT Iowa 0.75 EOD 2.33 32 Piles

(*) Resistance factor is specific to a chosen probability of failure, (or reliability index, β), and driving conditions, either EOD or BOR. Typically = 1.0%, = 2.33, or = 0.1%, = 3.0. 𝑃𝑃𝑓𝑓

𝑃𝑃𝑓𝑓 𝛽𝛽 𝑃𝑃𝑓𝑓 𝛽𝛽

178

179

6.7 Summary

Calibration of resistance factors specific to the Puget Sound Lowlands were conducted for

different static axial capacity methods at the end-of-driving and beginning of restrike for driven

piles based on a unique database of piles. Specifically, the FHWA-SA method (Hannigan et al.

2006) recommended static analysis method based on SPT measurements, wave equation analysis

(WEAP) using load transfer percentage from CAPWAP signal matching, as well the aforementioned static analysis method were assessed, and a new method for evaluating shaft resistance based on the newly developed β-coefficients in chapter 4, and named PSL-SA herein. The WEAP-

based methods produce generally accurate estimates of capacity and agree with one another, with

a mean bias of 0.99 and 0.98 and COV of 26% and 27% at EOD. The FHWA-SA method produce considerable variability in accuracy with a mean bias of 1.08 and COV of 85% based on EOD

CAPWAP capacity and improved to a mean bias of 1.39 and a COV of 65% when compared to

BOR CAPWAP capacity. The PSL-SA approach based on its individual β-coefficient models

produced resistance factors ranging between 0.04 and 0.22 at EOD, and between 0.09 and 0.29 at

BOR. The region-specific resistance factors determined for WEAP-based capacity estimates are greater than national database-sourced calibrations by approximately 50%. These findings indicate that limiting the database to a particular geologic region will provide improved reliability and cost- effectiveness, and will produce performance consistent with sound, experience-based engineering judgment.

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7 Chapter 7 SUMMARY AND CONCLUSIONS

7.1 Summary of Research

Reddy and Stuedlein (2013) collected information on driven piles specific to the Puget Sound

Lowlands region area in Seattle, to improve predictions for pile capacity and to develop resistance factors appropriate for LRFD- based design reflective of the state of the practice in the Puget Sound

Lowlands. Several topics relevant to the daily tasks of a deep foundation designer were investigated including calibration of resistance factors specific to the Puget Sound Lowlands, development of new effective stress models (also known as the β-method) to predict ultimate

capacity of driven piles taking into account the specific geology of the region and the local pile

driving practice, as well as evaluation of setup in a more rigorous approach by considering soil

layering instead of lumping total resistance increase in one factor.

The initial collected database consisted of over 237 dynamic loading tests of driven piles all

installed in the Puget Sound Lowlands. Pile dynamic testing was conducted in 40 different project

and construction sites throughout Puget Sound Lowlands, Seattle and Tacoma. All piles were steel

closed, open pipe, or H-steel piles, concrete octagonal fully closed piles or concrete cylindrical

open piles. For 95 piles, measurements of penetration resistance were recorded for end of driving

(EOD) and beginning of restrike (BOR) conditions. Estimate of static capacity was deduced from

CAPWAP analyses at end of driving (EOD) and beginning of restrike (BOR). This database

allowed evaluation of accuracy and variability of compressive and tensile driving stresses, and

penetration resistance, predicted using WEAP analyses. Also, assessment of default and standard

181

model parameters, as well as those estimated using the corresponding CAPWAP signal matching

analyses and their effect on design methods reliability.

7.2 Conclusions

Studies for calibration of resistance factors specific to the Puget Sound Lowlands were made for different predictive methods for capacity, including the FHWA 2006 static analysis method based on SPT measurements, wave equation analysis (WEAP) using shaft distribution from

CAPWAP records and from static analysis, and new static models based on the effective stress method developed specifically for the Puget Sound Lowland at end of driving (EOD) and

Beginning of Restrike (BOR) thus accounting for changes in resistance with time (Setup or

Relaxation). The agreement between measured and predicted capacity for WEAP methods are significantly better than observed in previous calibrations, especially nationally gathered database.

Static capacity determined using the new developed effective stress models improved considerably the prediction of shaft resistance compared to the existing FHWA 2006 recommended method.

Comparisons of predicted and measured capacity based on wave analysis and static methods have shown that dynamic based predictions are generally more accurate and reliable. The reason agreement improved can be primarily contributed to either the scope or the quality of the database.

The scope of this latter was limited to steel and prestressed concrete piles, driving system consisted mainly of Diesel hammers and a smaller percentage of external combustion hammer, pile cushions thicknesses were consistent with little variation. As the data was collected by the major professor, who served as the geotechnical engineer designer in many of the used projects, valuable insights into the quality and assessment of the soundness of the collected information were possible.

Although this last fact cannot be quantified easily, it is believed to be of primer effect in the analysis.

182

The new static models based on the effective stress method were created by using a subset

database comprised of 85 piles monitored at End of Driving (EOD) and Beginning of Restrike

(BOR) using CAPWAP procedure, all located in the Puget Sound Lowland region. This set of piles

had to conform to specific filtering criteria, including existence of all driving information, pile information, soil information, as well as avoidance of overlap between soil segments at EOD and

BOR by insuring very close depths of penetration at both EOD and BOR. Established soil profiles based on blow count from the standard penetration test (SPT) and geology were matched with their corresponding unit shaft resistance profiles from CAPWAP, which resulted in more than 1000 soil segments. Following that, 16 new models were developed to predict the coefficient beta at EOD and BOR: 8 models based on USCS classification and 8 models based on soil stiffness or consistency. Each soil model incorporate tow sub-models, representing conditions at EOD and

BOR. Each model is a three-parameter exponential function, calibrated to capture the profile of coefficient beta with depth. These models could benefit the designer by providing them with a simple, rational model that accounts for geology, setup and soil stiffness/consistency in a smooth, continuous function with depth. A parallel analysis was performed to assess the accuracy and variability of the formulated prediction models to ease implementation in load and resistance factor design (LRFD).

Development of new static models for predicting shaft resistance at EOD and BOR, as explained in the previous paragraph, as a function of soil type and depth, allows for development of more accurate methods for prediction of gain in resistance, known as setup. It is known that setup is due mainly to dissipation of pore water pressure and reconstitution of soil and is mainly attributed to shaft resistance, however, available setup predictive methods lump shaft and toe resistance and do not take account for soil layering. The proposed equations can be seen as semi-empirical tools to

183

better capture changes in resistance. It has to be admitted that setup is a very complicated problem, where not only the mechanisms are not all understood, but the high number of parameters that are involved is high and discourage any general observation. One main component is time, having one restrike for most piles made it difficult to correlate time to resistance increase in a justified, quantitative manner. For future work, driving piles at several distinct point in times after end of driving is necessary to establish, maybe, a measurable cause effect relationship between resistance variations and time. Unit shaft resistance profiles at end of driving and beginning of restrike and the corresponding setup ratio was developed for 85 piles as a function of depth, soil type, consistency or stiffness. These information is included in Appendix B and can provide rich insights into the type of distribution of setup ratio as function of depth, pile, geology and soil classes.

7.3 Recommendations for Future Work

This information, analyses, and results will help practitioners evaluate the probability of exceeding allowable stresses given selected equipment and model parameters. Because one geological region was considered, and high quality data was gathered, it was expected to produce very good estimates of driving performance with little variability. However many limitations still persist and should be further investigated:

• Separation of concrete and steel piles when predicting shaft resistance since β-coefficient

directly depend on the interface soil-pile friction.

• Dynamic testing of a considerable sample size of piles to infer an accurate medialization

of time dependent capacity gain for driven piles.

• Microscale analyses should be performed to better understand and quantify setup by

addressing phenomena like diffusion.

184

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APPENDICES

191

Appendix A β-Coefficients models Based on Consistency/Density

192

β-Coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

15 Density groups: Very loose and Loose 20

25 Summary Statistics: n = 156, R2 = 0.01 30 Depth,z (m) λ = 1.00, COV = 139%

40 EOD, z ≤ 4 m 45 EOD, z > 4 m EOD fit 50

8 Calculated 6 Bias trend y = -0.6648x + 1.1114 4 R² = 0.0135 Bias 2

0 0.0 0.2 0.4 0.6 0.8

βEOD

193

β-Coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

15 Density groups: Very loose and Loose 20

Depth,z (m) Summary Statistics: 30 n = 156, R2 = 0.05 λ = 1.00, COV = 85% 35

40 BOR, z ≤ 4 m 45 BOR, z > 4 m BOR fit 50

8 Calculated 6 Bias trend y = 0.0112x + 0.9946 R² = 3E-06 4 Bias 2

0 0.0 0.2 0.4 0.6 0.8

βBOR

Figure A-2. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for loose granular soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient

194

β-coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

15 Density group: 20 Medium dense

25 Summary Statistics: 30 n = 439, R2 = 0.11 Depth,z (m) λ = 1.00, COV = 128% 35

40 EOD, z ≤ 4 m 45 EOD, z > 4 m EOD fit 50

8 Calculated 6 Bias trend y = -0.6648x + 1.1114 4 R² = 0.0135 Bias 2

0 0.0 0.5 1.0 1.5 βEOD, M. dense

Figure A-3. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for medium dense granular soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient

195

β-coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

15 Density group: 20 Medium dense

30 Summary Statistics: Depth,z (m) n = 439, R2 = 0.10 35 λ = 1.00, COV = 101%

45 BOR, z ≤ 4 m BOR, z > 4 m BOR fit 50

8 Calculated 6 Bias trend y = -0.0015x + 1.0008 R² = 1E-07 4 Bias 2

0 0.0 0.5 1.0 1.5

βBOR, M. dense

196

β-coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

10 Density group: 15 Dense

25 Summary Statistics: n = 135, R2 = 0.20 30 λ = 1.00, COV = 93% Depth,z (m)

40 EOD, z ≤ 4 m 45 EOD, z > 4 m EOD fit 50

8 Calculated 6 Bias trend

y = -0.6648x + 1.1114 4 R² = 0.0135 Bias 2

0 0.0 0.5 1.0 1.5 βEOD, Dense

Figure A-5. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for dense granular soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient

197

β-coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

20 Density group: 25 Dense z(m) 30 Summary Statistics: 2 35 n = 135, R = 0.18 λ = 1.00, COV = 87% 40

45 BOR, z ≤ 4 m BOR, z > 4 m BOR fit 50

8 Calculated 6 Bias trend

y = -0.0085x + 1.004 4 R² = 3E-06 Bias 2

0 0.0 0.5 1.0 1.5 βBOR, Dense

Figure A-6. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for dense granular soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient

198

β-coefficient 0.0 1.0 2.0 3.0 4.0 5.0 0

20 Density group: 30 Very dense

40 Summary Statistics: 50 n = 140, R2 = 0.15 Depth,z (m) λ = 1.00, COV = 155% 60

80 EOD, z > 4 m EOD fit 90

8 Calculated 6 Bias trend y = -0.6648x + 1.1114 4 R² = 0.0135 Bias 2

0 0.0 0.5 1.0 1.5 βEOD, V.dense

199

β-coefficient 0.0 1.0 2.0 3.0 4.0 5.0 0

30 Density group: Very dense 40

Depth,z (m) Summary Statistics: n = 140, R2 = 0.26 60 λ = 1.00, COV = 103%

80 BOR, z > 4 m BOR fit 90

8 Calculated 6 Bias trend

y = 0.6016x + 0.7009 4 R² = 0.0319 Bias 2

0 0.0 0.5 1.0 1.5 2.0

βBOR, V. dense

200

β-coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

10 Consistency group: 15 Very soft and soft

20 Summary Statistics: 25 n = 200, R2 = 0.19 λ = 1.00, COV = 107% 30 Depth,z (m)

45 EOD, z ≤ 4 m EOD, z > 4 m EOD fit 50

8 Calculated 6 Bias trend

y = -0.6648x + 1.1114 4 R² = 0.0135 Bias 2

0 0.0 0.5 1.0 1.5 βEOD, Soft

201

β-coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

20 Consistency group: Very soft and soft 25

30 Depth,z (m) Summary Statistics: n = 200, R2 = 0.23 35 λ = 1.00, COV = 83% 40

45 BOR, z ≤ 4 m BOR, z > 4 m BOR fit 50

8 Calculated 6 Bias trend y = 0.029x + 0.9827 4 R² = 8E-05 Bias 2

0 0.0 0.5 1.0 1.5

βBOR, Soft

Figure A-10. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for soft plastic soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient

202

β-coefficient 0.0 0.5 1.0 1.5 2.0 0

10 Consistency group: 15 Medium stiff

25 Summary Statistics: n = 51, R2 = 0.00 Depth,z (m) 30 λ = 1.00, COV =84%

45 EOD EOD fit 50

Figure A-11. Determined β-coefficient values from CAPWAP records and effective normal stress filtered for medium stiff plastic soils at EOD

203

β-coefficient 0.0 0.5 1.0 1.5 2.0 0

10 Consistency group: 15 Medium stiff

25 Summary Statistics: n = 51, R2 = 0.00 Depth,z (m) 30 λ = 1.00, COV =84%

45 EOD EOD fit 50

Figure A-12. Determined β-coefficient values from CAPWAP records and effective normal stress filtered for medium stiff plastic soils at BOR

204

β-coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

15 Consistency group: Stiff and Very stiff 20

25 Summary Statistics: n = 78, R2 = 0.00 30 Detph,z (m) λ = 1.00, COV = 84%

45 EOD EOD fit 50

8 Calculated 6

4 Bias 2

0 0.0 0.1 0.2 0.3 0.4

βEOD, Stiff

Figure A-13. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for very stiff plastic soils at EOD: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient

205

β-coefficient 0.0 0.5 1.0 1.5 2.0 2.5 0

15 Consistency group: Stiff and Very stiff 20

30 Summary Statistics: Depth,z (m) n = 78, R2 = 0.00 λ = 1.00, COV = 76% 35

45 BOR BOR fit 50

8 Calculated 6 Bias trend y = 0.0279x + 0.987 4 R² = 6E-05 Bias 2

0 0.0 0.5 1.0 1.5

βBOR, Stiff

Figure A-14. Comparison of CAPWAP-based back-calculated β-coefficient and fitted β-coefficient model for very stiff plastic soils at BOR: (a) Comparison with depth, and (b) Comparison of sample bias with nominal β-coefficient

206

βEOD, Hard 0.0 0.5 1.0 1.5 2.0 2.5 0 Range: 0.03 to 0.57 Mean: 0.15 Median: 0.07 10 COV: 1.07

30 z(m) 40

EOD 70

Figure A-15. Determined β-coefficient values from CAPWAP records and effective normal stress filtered for hard plastic soils at EOD

207

βBOR, Hard 0.0 0.5 1.0 1.5 2.0 2.5 0 Range: 0.05 to 0.95 Mean: 0.29 10 Median: 0.28 COV: 0.83

30 z(m) 40

BOR 70

Figure A-16. Determined β-coefficient values from CAPWAP records and effective normal stress filtered for hard plastic soils at BOR

208

Appendix B Shaft Resistance Distribution for Piles Used to Develop the New Beta Models

209

Figure B-1. Pile 1: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

210

Figure B-2. Pile 2: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

211

Figure B-3. Pile 3: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

212

Figure B-4. Pile 4: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

213

Figure B-5. Pile 5: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

214

Figure B-6. Pile 6: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

215

Figure B-7. Pile 7: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

216

Figure B-8. Pile 8: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

217

Figure B-9. Pile 9: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

218

Figure B-10. Pile 10: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

219

Figure B-11. Pile 11: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

220

Figure B-12. Pile 12: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

221

Figure B-13. Pile 13: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

222

Figure B-14. Pile 14: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

223

Figure B-15. Pile 15: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

224

Figure B-16. Pile 16: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

225

Figure B-17. Pile 17: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

226

Figure B-18. Pile 18: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

227

Figure B-19. Pile 19: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

228

Figure B-20. Pile 20: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

229

Figure B-21. Pile 21: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

230

Figure B-22. Pile 22: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

231

Figure B-23. Pile 23: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

232

Figure B-24. Pile 24: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

233

Figure B-25. Pile 25: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

234

Figure B-26. Pile 26: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

235

Figure B-27. Pile 27: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

236

Figure B-28. Pile 28: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

237

Figure B-29. Pile 29: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

238

Figure B-30. Pile 30: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

239

Figure B-31. Pile 31: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

240

Figure B-32. Pile 32: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

241

Figure B-33. Pile 33: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

242

Figure B-34. Pile 34: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

243

Figure B-35. Pile 35: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

244

Figure B-36. Pile 36: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

245

Figure B-37. Pile 37: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

246

Figure B-38. Pile 38: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

247

Figure B-39. Pile 39: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

248

Figure B-40. Pile 40: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

249

Figure B-41. Pile 41: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

250

Figure B-42. Pile 42: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

251

Figure B-43. Pile 43: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

252

Figure B-44. Pile 44: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

253

Figure B-45. Pile 45: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

254

Figure B-46. Pile 46: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

255

Figure B-47. Pile 47: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

256

Figure B-48. Pile 48: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

257

Figure B-49. Pile 49: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

258

Figure B-50. Pile 50: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

259

Figure B-51. Pile 51: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

260

Figure B-52. Pile 52: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

261

Figure B-53. Pile 53: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

262

Figure B-54. Pile 54: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

263

Figure B-55. Pile 55: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

264

Figure B-56. Pile 56: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

265

Figure B-57. Pile 57: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

266

Figure B-58. Pile 58: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

267

Figure B-59. Pile 59: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

268

Figure B-60. Pile 60: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

269

Figure B-61. Pile 61: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

270

Figure B-62. Pile 62: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

271

Figure B-63. Pile 63: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

272

Figure B-64. Pile 64: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

273

Figure B-65. Pile 65: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

274

Figure B-66. Pile 66: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

275

Figure B-67. Pile 67: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

276

Figure B-68. Pile 68: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

277

Figure B-69. Pile 69: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

278

Figure B-70. Pile 70: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

279

Figure B-71. Pile 71: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

280

Figure B-72. Pile 72: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

281

Figure B-73. Pile 73: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

282

Figure B-74. Pile 74: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

283

Figure B-75. Pile 75: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

284

Figure B-76. Pile 76: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

285

Figure B-77. Pile 77: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

286

Figure B-78. Pile 78: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

287

Figure B-79. Pile 79: Unit shaft resistance versus depth and corresponding soil profile at EOD and BOR, and setup ratio.

288