Geologic Controls of Shear Strength Behavior of Mudrocks

Home , Argillite, Cohesion (geology), Mudrock, Siltstone

GEOLOGIC CONTROLS OF SHEAR STRENGTH BEHAVIOR OF MUDROCKS

A dissertation submitted to Kent State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Ala’ M. Hajdarwish

December 2006

Dissertation written by Ala’ M. Hajdarwish B. S., Yarmouk University, 1994 M. S., Yarmouk University, 1997 M. S., The University of Akron, 2001 Ph.D., Kent State University, 2006

Approved by

, Chair, Doctoral Dissertation Committee Abdul Shakoor , Member, Doctoral Dissertation Committee Peter Dahl , Member, Doctoral Dissertation Committee Neil Wells , Member, Doctoral Dissertation Committee Mandy Munro-Stasiuk , Graduate College Representative and Moderator Richard Meindl Accepted by

, Chair, Department of Geology Donald Palmer , Dean, College of Arts and Sciences John R. D. Stalvey

ii TABLE OF CONTENTS

LIST OF FIGURES ...... vi

LIST OF TABLES...... viii

ACKNOWLEDGEMENTS...... ix

INTRODUCTION ...... 1

Geologic Classification of Mudrocks ...... 3 Related Research...... 4 Objectives ...... 7

RESEARCH METHODS ...... 8

Sampling ...... 10 Laboratory Investigations ...... 12 Natural Water Content Test ...... 13 Direct Shear Test...... 13 Grain Size Distribution Analysis ...... 13 X-ray Diffraction Analysis ...... 16 Dry Density, Specific Gravity, and Void Ratio Determinations ...... 18 Absorption Test...... 20 Adsorption Test...... 21 Atterberg Limits Test...... 22 Slake Durability Index Test ...... 22 Data Analysis...... 23 Univariate Analysis...... 23 Correlation Analysis ...... 24 Regression Analysis...... 25

RESULTS OF DIRECT SHEAR TESTING...... 26

Cohesion ...... 26 Friction Angle ...... 33

RESULTS OF LITHOLOGIC AND ENGINEERING TESTING ...... 41

iii Results of Lithologic Testing...... 41 Grain Size Distribution ...... 41 X-ray Diffraction Analysis Results...... 43 Results of Engineering Testing...... 53 Natural Water Content ...... 53 Dry Density, Specific Gravity, and Void Ratio ...... 53 Absorption...... 55 Adsorption...... 56 Atterberg Limits...... 57 Slake Durability ...... 58

DATA ANALYSIS OF All MUDROCKS...... 61 Analysis of Mudrock Data...... 61 Univariate Analysis...... 61 Correlation Analysis ...... 62 Multivariate Regression analysis ...... 66 Multivariate Regression Analysis for Cohesion ...... 66 Multivariate Regression Analysis for Friction Angle...... 73

DISCUSSION...... 80 Limitations ...... 86

SUMMARY AND CONCLUSIONS ...... 87

REFERENCES ...... 90

APPENDICES

APPENDIX A: SITE LOCATION AND DESCRIPTION OF SAMPLES ...... 95

APPENDIX B: DIRECT SHEAR TEST DATA...... 104

APPENDIX C: GRAIN SIZE DISTRIBUTION RESULTS...... 132

APPENDIX D: X-RAY DIFFRACTION ANALYSIS RESULTS...... 160

APPENDIX E: WATER CONTENT DATA ...... 166

APPENDIX F: DRY DENSITY, SPECIFIC GRAVITY, VOID RATIO DATA ...... 170 APPENDIX G: ABSORPTION DATA...... 177

APPENDIX H: ADSORPTION DATA ...... 181

iv APPENDIX I: ATTERBERG LIMITS RESULTS ...... 185

APPENDIX J: SLAKE DURABILITY TEST RESULTS...... 189

APPENDIX K: UNIVARIATE DATA ANALYSIS RESULTS...... 193

APPENDIX L: BIVARIATE PLOTS ...... 199

v LIST OF FIGURES

Figure Page

1 Sample location map...... 12

2 Cross-sectional view of mudrock sample in the shear box...... 14

3 Stress-strain plots for a mudrock sample under three different values of normal loads ...... 15

4 Shear stress vs normal load plot used to obtain c and φ values ...... 15

5 Distribution of cohesion values for all mudrocks...... 28

6 Distribution of cohesion values for claystones ...... 29

7 Distribution of cohesion values for mudstones...... 30

8 Distribution of cohesion values for siltstones...... 31

9 Distribution of cohesion values for shales...... 32

10 Distribution of friction angle values for all mudrocks...... 35

11 Distribution of friction angle values for claystones...... 36

12 Distribution of friction angle values for mudstones ...... 37

13 Distribution of friction angle values for siltstones...... 38

14 Distribution of friction angle values for shales...... 39

15 X-ray diffractogram for claystone sample (S-10): (a) non-treated, (b) glycolated (c) heated at 350 ° C, (d) heated at 550 ° C...... 45

16 X-ray diffractogram for mudstone sample (S-1): (a) non-treated, (b) glycolated(c) heated at 350 ° C, (d) heated at 550 ° C...... 47

17 X-ray diffractogram for siltstone sample (S-2): (a) non-treated, (b) glycolated(c) heated at 350 ° C, (d) heated at 550 ° C...... 49

vi Figure Page

18 X-ray diffractogram of shale sample (S-32); (a) non-treated, (b) glycolated(c) heated at 350 ° C, (d) heated at 550 ° C...... 51

19a Plot of regression model number and corresponding adjusted R 2 values with respect to cohesion. Refer to Table 37 for explanations of each model .... 68

19b Plot of number of variables in each model and corresponding adjusted R 2 values with respect to cohesion. Refer to Table 37 for identification of variables ...... 68

20 Measured vs. predicted square root of cohesion values for all mudrocks based on multivariate regression equation 11 (model # 7) ...... 71

21 Residuals for square root cohesion values of shale on the basis of model # 7...... 72

22a Plot of regression model number and corresponding adjusted R 2 values with respect to friction angle. Refer to Table 39 for explanations of each model ...... 75

22b Plot of number of variables in each model and corresponding adjusted R2 values with respect to friction angle. Refer to Table 39 for identification of variables...... 75

23 Measured vs. predicted friction angle values for all mudrocks based on regression equation from model number 9 ...... 77

24 Residuals for friction angle values of all mudrocks on the basis of model # 9...... 78

25 Measured vs. predicted cohesion values for the tested samples (TS-1, TS-2, TS-3, and TS-4) ...... 84

26 Measured vs. predicted cohesion values for the tested samples (TS-1, TS-2, TS-3, and TS-4) ...... 85

vii LIST OF TABLES

Table Page

1 Geologic classification of mudrocks (modified after Potter et al., 1980, by Dick, 1992) ...... 5

2 Summary of cohesion values for all mudrocks and lithologic subgroups ...... 27

3 Summary of cohesion values for all mudrocks and lithologic subgroups ...... 34

4 Summary of grain size distribution results ...... 42

5 Summary of quantitative x-ray diffraction analysis results ...... 44

6 Summary of natural water content results ...... 53

7 Summary of dry density, specific gravity, and void ratio tests results ...... 54

8 Summary of absorption test results...... 56

9 Summary of adsorption test results...... 57

10 Summary of Atterberg Limits tests results ...... 59

11 Summary of Slake Durability Index results...... 60

12 Correlation matrix for all mudrocks as a single group ...... 63

13 Models produced by multivariate regression analysis to predict square root of cohesion (in psf) for the mudrocks group...... 67

14 Results of multivariate regression analysis to predict square root of cohesion of the mudrocks group on the basis of model # 7...... 70

15 Models produced by multivariate regression analysis to predict friction angle (in degrees) for the mudrocks group ...... 74

16 Results of multivariate regression analysis to predict friction angle of all mudrocks on the basis of model #9...... 76

17 Summary and comparison of predicted and measured cohesion and friction angle values for the different groups of mudrocks ...... 82

viii ACKNOWLEDGEMENTS

First, I would like to thank my supervisor Prof. Abdul Shakoor for his guidance, encouragement and assistance throughout the period of this research project. I also would like to thank Dr. Peter Dahl for his assistance in helping me working with SPSS, especially at the early stages of the project, and for his kind words of encouragement during the final challenges of this research. I would like to give many thanks to Dr. Neil

Wells, Dr. Mandy Munro-Stasiuk, and Dr. Richard Meindl for their distinctive critiques while editing this dissertation. My thanks to Mr. Bob Beal for his devoted help with the

XRD procedures and all the amusing stories told while working long hours in the x-ray lab.

I am most grateful to my best friend, who helped me collect the samples, helped me with laboratory work, and provided me with the best confidence, trust and peace to complete the work over the years. I am grateful to my life companion, in this life and the hereafter, my dear wife Eman AbdulAllah (Karen Traugh). I hope I will be able to pay her my devotion and patience for the rest of my life.

Last but not least, I would like to thank my parents for their love, support, encouragement, prayers, and understanding without which I would not have managed to complete this dissertation.

Finally, I dedicate this work to my daughter Nadia, the best thing that ever happened to me, and to Palestine, the land of prophets, and to the day it will be free again.

ix CHAPTER 1

INTRODUCTION

The purpose of the this research is to investigate the geological and engineering properties of mudrocks, including shear strength parameters (c and φ), and to develop statistical relationships (models) that could be used to predict shear strength parameters from lithologic characteristics and engineering properties. The term mudrock refers to the fine-grained, siliciclastic sedimentary rocks (claystones, mudstones, siltstones, and shales) in which more than 50% of the particles are smaller than 0.06 mm in size (Blatt et al., 1980; Grainger, 1984; and Dick and Shakoor, 1992). Mudrocks are the most abundant of all lithologies, constituting some 45% to 55% of sedimentary rock sequences; thus they are often encountered in all types of geotechnical engineering projects. However, because mudrocks are easily weathered, they are frequently poorly exposed. In addition, as a result of their very small grain size, their study often requires detailed and vigilant laboratory analyses.

The index and the engineering properties of mudrocks are very important in engineering construction as foundations on these materials require special care and procedures to ensure that the final structure built on, or within, them will perform satisfactorily. In particular, the swelling, slaking, compressive strength, and shear strength properties of such weak rocks are of paramount importance in foundation design.

Engineers consider mudrocks as problematic rocks because of their low durability, low

1 2

compressive and shear strength, and high swelling potential when exposed to moisture.

Swelling of mudrocks is documented to have caused substantial damage to underground structures (Lee and Klym, 1978; Olivier, 1979; Chugh et al., 1981; Wittke, 1981; Hansan,

1982; and Madsen and Muller-Vonmoos, 1985), building foundations (Ola, 1982; Berube et al., 1986; Goodman, 1992; Bell, 1994), dam foundations and construction (Zeng, 1981;

Ramachandran et al., 1982), tunnels (Madsen and Muller-Vonmoos, 1985), slopes

(Flemming et al., 1970), and highway embankments (Strohm et al., 1978). As in the case with expansive soils, the swelling property of mudrocks is dictated by the nature of the clay minerals present. Furthermore, the low durability of certain mudrocks, coupled with their physical breakdown, is responsible for countless slope instability problems (Regues et al. 1995), coal mine roof falls, and shale embankment failures (Strohm, 1980; Dick and

Shakoor, 1992; and Dounias et al., 2002). Slaking of exposed foundation excavations made into weak claystones and shales has been a problem at numerous construction sites for dams and navigation locks in the upper Ohio Valley region (U.S. Army Corps of

Engineers, 1988).

Design and analysis of engineering structures, such as dams, highway embankments, foundations, slopes, and underground excavations require a knowledge of shear strength parameters (cohesion “c” and friction angle “ φ”). However, a major problem at any given site containing any type of mudrock is obtaining undisturbed samples for determination of shear strength parameters. This problem arises because of the weak lithologic nature of mudrocks and their reaction to changes in fluid properties, drilling pressures, and time (Fam et al., 2003). Therefore, shear strength values for most 3

engineering projects involving mudrocks are either scarce or assumed. One way to overcome this problem is to develop a methodology that can be used to predict the shear strength parameters of mudrocks from their geologic characteristics, which can be measured on disturbed and smaller samples. Such a methodology requires a thorough understanding of the effect of geologic makeup of mudrocks on their shear strength.

Geologic Classification of mudrocks

Mudrocks are defined as weak rocks in which more than 50 percent of the constituent particles are smaller than 0.062 millimeters (Ingram, 1953; Dunbar and

Rogers, 1957; Blatt et al., 1980; and Lundegard and Samuels, 1980). Such a boundary includes a wide variety of lithologies. In view of that, several geologic classification systems have been developed for mudrocks. These include the classification of Folk

(1974), Lewan (1978), Lundegard and Samuels (1980), Potter et al. (1980), and Blatt

(1982).

A modified form of Potter et al.’s classification (1980), shown in Table 1, was selected to take into account the lithological diversity of mudrocks. This classification is based on three fundamental properties that include: texture (percent clay-size particles in the mudrock sample), laminations (presence or absence), and degree of metamorphism.

Siltstones, mudstones, and claystones are distinguished by the percentage of clay-size (<

0.004 mm) particles when not laminated. The term “shale” replaces “stone” for siltstones, mudstones, and claystones when the mudrock is laminated. Argillites are mudrocks that have been hardened by the influence of metamorphism but that show little or no development of slaty cleavage (Blatt et al., 1980). 4

Additional modifications were introduced by Dick (1992) to the original classification by Potter et al. (1980) to reflect the engineering applications and to present terms that are more frequently used in engineering geology practice (Table 1). Bedded siltstone was replaced by siltstone and laminated siltstone was replaced by siltshale.

Furthermore, the textural division between mudstone and claystone was placed at 50 percent to reflect a marked change in the durability behavior of mudrocks at this content

(Dick 1992).

Related Research

Mudrocks are problematic rocks, difficult to sample and test. No detailed study has been conducted previously to predict the shear strength parameters of mudrocks from their lithologic characteristics and index properties. However, similar research has been conducted to correlate geologic properties of mudrocks with other engineering properties in order to develop classification schemes that can be used to predict these engineering properties for a wide variety of mudrocks. Dick et al. (1994) investigated the effect of lithology on slake durability of many samples of mudrocks. Their objective was to develop a comprehensive durability classification system that uses one or more lithologic characteristics to predict the slake durability index for a wide range of mudrocks. Their work consisted of collecting a large number of mudrock samples, determining their lithologic and engineering properties as well as their slake durability indices, and statistically analyzing the relations between slake durability index and the other properties. They found that a relationship or a prediction model could not be established when correlating the properties of all mudrocks as a one group. Several strong 5

Table 1. Geologic classification of mudrocks (modified after Potter et al., 1980, by Dick, 1992).

PERCENT CLAY-SIZED PARTICLES

0 – 32 % 33 – 49 % 50 – 100 %

NONLAMINATED SILTSTONE MUDSTONE CLAYSTONE

LAMINATED SILTSHALE MUDSHALE CLAYSHALE

METAMORPHOSED ARGILLITE

correlations were observed, however, when the mudrocks were divided into subgroups.

The findings of Dick et al. (1994) study showed a strong relationship (r = -0.98) between percent expandable clays and slake durability index for claystones, between micro- fracture frequency index and slake durability index for mudstones (r = -0.94), and between void ratio and slake durability index for shales (r = -0.98). These results underscore the importance of distinguishing between mudrock lithologies in the durability investigations.

Sarman et al. (1994) correlated lithologic and engineering properties of forty-two mudrock samples from across the United States with their swelling properties. The purpose of their study was to identify those engineering properties which could be used to predict the volumetric increase for all types of mudrock (i.e., a development of a swelling potential classification). The samples were tested for volumetric increase in the laboratory that was then correlated with the corresponding values of all other properties, using bivariate and multiple regression analyses. The results of the statistical analysis indicated that swelling of mudrocks was not only influenced by expansive clay minerals but also by the texture. The findings also indicated that a single property could not explain and account for the total amount of swelling in all types of mudrock, and that different combinations of lithologic and engineering properties were needed to predict the volumetric increase for the different subgroups of mudrocks (i.e. claystones, mudstones, siltstones, and shales).

Olgaard et al. (1997) studied the influence of swelling clays on the deformation of mudrocks. They collected nine mudrock samples and determined their engineering 7

and lithologic characteristics such as adsorption, clay content (x-ray diffraction), specific surface area, and cation exchange capacity. The lithologic characteristics were then correlated with the strength and deformation properties (friction angle, dilation angle, and volume change). The results from their research indicated that friction angle of the mudrocks studied was inversely proportional to the swelling clay content. Other properties such as strain rate showed no influence on the strength or deformation style of mudrocks over a wide range of conditions. Considering the strong correlations produced,

Olgaard et al. (1997) concluded that these relations might provide means of predicting the mechanical properties of mudrocks such as friction angle, Young’s moduli, and dilation angle.

Objective

The objective of this research is to investigate the geologic characteristics and engineering properties of a wide range of mudrock samples, collected from different locations in the United States, and to determine the characteristics/properties that have the most effect on predicting the shear strength parameters (cohesion and friction angle) of mudrocks.

CHAPTER 2

RESEARCH METHODS

The concept of this research is based on the premise that the shear strength parameters of cohesion and friction angle (c and φ) of mudrocks are controlled by their lithologic and engineering characteristics. Whereas previous research on other properties of mudrocks, such as durability, swelling, and compressive strength, indicates that such an assertion is true, the relationships between lithologic characteristics, engineering properties, and shear strength parameters have not yet been investigated in any detail.

Once the equations to predict cohesion and friction angle of a mudrock are developed, the shear strength of that mudrock can be estimated under different normal loads.

In this study, prediction equations for cohesion and friction angle were developed on the basis of lithologic characteristics and engineering property data. The different mudrock samples used in the analysis were treated as one group and carefully selected number of variables (geologic characteristics and engineering properties) were used to develop prediction models using multivariate regression analysis. Either the original value of a given variable or one of its transformation values (either logarithmic or square root) were used, based on the strength of bivariate correlations. The selected models were used to explain the relationships between each variable and the shear strength parameters (cohesion and friction angle).

8 9

The following steps were used in the research:

1.) Collect mudrock samples from different locations in the United States to cover their

lithologic range.

2.) Classify the collected samples according to Potter et al. (1980) classification into one

of the four types of mudrocks: claystones, mudstones, siltstones, and shales.

3.) Determine the lithological characteristics of these mudrock samples such as mineral

composition (clay content and clay type).

4.) Determine the index engineering properties such as density, void ratio, slake

durability, Atterberg limits, absorption, and adsorption.

5.) Determine the shear strength parameters (cohesion and friction angle) of all collected

mudrock samples.

6.) Determine the relationships between the shear strength parameter, lithological

characteristics, and engineering properties using bivariate and multivariate analyses.

7.) Determine the best empirical equation/model, produced by regression analysis, to

predict cohesion and friction angle.

8.) Determine if one unique empirical equation can be used as a model to predict

cohesion or friction angle for all types of mudrock.

9.) Test the error of equations/models developed by calculating the strength parameters of

additional four mudrock samples (not involved in development of equations) and

compare the results with their measured values.

Sampling

Forty-five mudrock samples were collected from highway cuts, dam sites, and natural outcrop exposures from various parts of the United States of America. These samples were selected on the basis of published lithologic descriptions and observations of durability behavior made during exploratory sampling trips. Figure 1 shows the locations of the collected samples from eleven states. The samples include 10 claystones,

10 mudstones, 12 siltstones, and 13 shales. The shales consist of 8 siltshales, 4 mudshales, and 1 clayshale. The sample number, description, lithology, geologic name, geologic age, and site description of each mudrock sample are provided in Appendix A.

In order to minimize the effect of weathering on shear strength of mudrock samples, maximum care was taken to assure that the collected samples were as fresh as possible. In a few locations, fresh mudrock samples were collected from active highway and dam excavations. However, in most locations, fresh samples were manually excavated using a shovel, sledgehammer, rock pick, crow bar, and chisels. The weathered zone that had to be removed varied in depth from 0.3 m to 1.3 m. Fresh rock was distinguished from the weathered rock by the relative absence of oxidation residue.

Ten to twenty individual chunks of rock, totaling approximately 50 - 60 pounds (23 - 27 kg), were collected from each sample site. The chunks that were used in the direct shear test had to be 4 - 6 in (10 - 15 cm) thick and 3 - 5 in (8 - 13 cm) in width. At each site the samples were first wrapped individually in plastic wrap, then sealed in heavy gauge one- gallon “zip-lock” style plastic storage bags. The bagged samples were then placed in 5-

Figure 1: Sample location map. 11

gallon snap-lid plastic buckets. This procedure preserved the natural water content of the samples and provided protection against breakage and slaking during transportation.

Laboratory Investigations

Samples collected form the field were cut to appropriate sizes specified by the

American Society for Testing and Material (ASTM, 1996) for different tests. The tests were conducted on bulk samples or pulverized samples as required by the test procedure.

Some samples required as many as 62 freeze-thaw cycles to obtain the proper particle size. The shear strength parameters were determined by performing the direct shear test on samples having thicknesses of 4-6 in (10-15 cm) and widths of at least 3-5 in (8-13 cm). The desired dimensions for these samples were obtained by dry cutting the samples using handsaw. The lithologic characteristics were analyzed using a variety of geologic analyses and engineering tests. The engineering tests provide important lithologic information and corroborative support to the geologic analyses.

Mudrock lithology is characterized by texture (particle size, shape, and arrangement), mineral composition, structural features, and degree of induration. Dry density, void ratio, absorption, and specific gravity were determined to serve as indicators of the relative proportion of solids and voids. Particle size was determined for each sample using grain size distribution and hydrometer analysis. Clay mineralogy was determined using x-ray diffraction, and the results were compared to estimates made from Atterberg limits and adsorption. Slake durability index was determined to reflect the effect of wetting and drying on mudrocks under study.

Natural Water Content Test

Water content is the ratio of the weight of water to the weight of solids in a given rock mass. The test was preformed according to ASTM method D2216 (ASTM, 1996) and the water content was computed as:

Wet Wt . − Dry Wt . Natural Water Content (Percentage ) = × 100 Dry Wt .

Direct Shear Test

Direct shear test is the main test of this research. Each sample was tested under three different values of normal stress and failed by applying a shearing stress as specified by ASTM method D3080 (Figures 2 and 3). The maximum shear stress values were then plotted against the corresponding normal stress values (Figure 4). The results from this test were defined as the shear strength parameters of cohesion, c, and friction angle, φ. These parameters were correlated with different engineering and geological properties determined from the other tests.

Grain Size Distribution Analysis

Grain size distribution analysis was preformed to determine the amount of clay- size particles (<0.004 mm) and amount of clay minerals (<0.002 mm), as a percentage of the whole rock, for use in the geologic classification and quantitative analysis of clay mineralogy. Samples for grain size distribution analysis were disaggregated by alternating cycles of wetting-freezing-thawing- and drying. This procedure was repeated until no further disaggregation was observed. Poorly indurated mudrocks disaggregated 14

Normal Load

Shear Stress

Shear Zone

Sample Cement

Figure 2: Cross-sectional view of mudrock sample in the shear box.

Normal Stress = σσσ1 Normal Stress = σσσ2

2 1

Stress Stress

Strain Strain

Normal Stress 3 = σσσ3

Stress

Strain

Figure 3: Stress-strain plots for a mudrock sample under three different values of normal stress.

τττ

), MPa ), τ τ τ τ

Shear Stress ( Shear Stress

c σ σσ σ1 σ2 σ3

Normal Stress ( σσσ), MPa

Figure 4: Shear stress vs normal stress plot used to obtain c and φ values. 16

after 3 to 5 cycles. Well-indurated mudrocks required more than 60 cycles for a full disaggregation. The disaggregated mudrock samples were then sieved through a nest of #

10 (2.00 mm), # 40 (0.425 mm), # 100 (0.15 mm), and # 200 (0.075 mm) meshed sieves.

The portions retained on sieves #10 and # 40 were examined with a binocular microscope using 10 –1000 times magnification to monitor the completeness of the disaggregation process. This procedure was repeated for each sample until a satisfactory level of disaggregation was reached. After complete disaggregation and sieve analysis of the samples, it was observed that most of the grains passed sieve # 100. The dry weight of the portions retained on each sieve was measured and recorded.

The portion of mudrock sample passing #200 sieve (0.075 mm) was used for hydrometer analysis (ASTM D422). Hydrometer measurements were made at approximate time intervals of 0, 2, 5, 10, 15, 30, 60, 240, 720, and 1440 minutes, from which the percentage (by weight) of the particles ranging between 0.075 mm and 0.001 mm diameter was calculated. Grain size distribution plots for the size range 0.15 mm to

0.001 mm diameter were constructed from the data. The percentages of particles finer than 0.004 mm (clay-size particles) and 0.002 mm (clay minerals) were determined directly from the plots.

X-ray Diffraction Analysis

X-ray diffraction analysis is the standard method for identifying clay mineralogy.

The analysis provides semi-quantitative determinations of the various mineral constituents. The analysis was performed using a two-theta Rigaku Geigerflex X-ray diffractometer. All analyses were conducted using a copper K-alpha source, equipped 17

with a monochrome filter. The diffractometer was operated at 35 kV and 40 mA, with a scanning rate of 10 degrees per minute. Initial scans covered from 2 degrees to 60 degrees two-theta.

Oriented ceramic-tile type mounts of each sample were prepared using the 2- micron (0.002 mm) and smaller size particles. These particles were harvested using the technique by Moore and Reynolds (1989). This technique required mixing 10 to 20 grams of mudrock sample that passed sieve # 200 with 2 % sodiumhexametaphosphate and distilled water. The mixture then was centrifuged at 600 rpm and at 2000 rpm for 6 minutes and 22 minutes, respectively. The mix was then discarded and the 2-micron clay size particles remaining at the bottom were used. The 2-micron size was selected because it is the optimum size for separating the clay minerals from the non-clay mineral components (Grim, 1969). The mounts were prepared by placing clay and distilled water slurry on oven-dried pre-cut tiles with an eyedropper. The mounts were air dried for at least twelve hours prior to scanning and analysis.

X-ray scans were performed for a series of four treatments of the same ceramic tile mount of each sample: pretreatment (or smearing), glycolation with ethylene glycol vapor for no less than one hour at 60 ° C, heating for one hour at 350 ° C, and heating for two hours at 550 ° C. This arrangement of x-ray scanning enabled the identification of clay mineral species according to characteristic basal diffraction peak positions, peak areas and relative intensities. The scans also provided the basis for estimating the quantity of each clay mineral species, according to a method developed by Schultz

(1964). 18

According to Dick (1992), Schultz’s (1964) method of quantifying clay mineralogy is based on extensive x-ray and chemical analyses of mudrocks of the Pierre shale and stratigraphically equivalent rocks. It has also been applied to Devonian age mudrocks of the Appalachian Basin (Hosterman and Whitelow, 1983). Schultz’s method was selected over other available methods (Chung, 1974; Brindley, 1980; and Srodon,

1980 and 1984) because it is simpler to perform, reasonably accurate (5-10 percent error), and repeatable. In addition to the fact that many of the mudrocks used in this research have clay mineral compositions similar to those studied by Schultz (1964, 1965, and

1978), Schultz et al. (1980), and Hosterman and Whitlow (1983).

In Schultz’s method the weight percentages of kaolinite, illite, chlorite, montmorillonite, and mixed-layer clays are determined using mathematical relationships between the 7Å (kaolinite) peak intensity and area, the glycolated 10 Å (illite) peak area, the 350 ° C 10 Å peak intensity and area, the 550 ° C 14Å (chlorite) peak intensity, and the glycolated 17 Å (montmorillonite) peak intensity.

Dry Density, Specific Gravity, and Void Ratio Determinations

Dry density and void ratio are indicators of consolidation and induration. Dry density is defined as the mass per unit volume of dry rock, whereas void ratio is the ratio of the volume of voids to the volume of solids. Specific Gravity represents the ratio of the weight of a substance in air to the weight of the same volume of water at 4 °C.

Specific gravity, together with water content and bulk density, is an essential property in determination of mudrock phase relationships. The major mineral constituents of mudrocks are clays, quartz, feldspar, calcite, and dolomite (Pettijohn, 1975). Since these 19

minerals have similar specific gravities, void ratio and dry density can be valid indicators of the degree of induration and compaction (Hudec, 1981).

There is no standard laboratory test for the determination of dry density of irregularly shaped mudrock samples. In order to measure the dry density, a modified form of the ASTM C97 (ASTM, 1987 ) standard test method for bulk specific gravity of dimension stone was used. According to ASTM method C97, oven-dried rock samples must be submerged in water. Upon submergence, however, many mudrocks slake due to interaction between water and clay minerals. In order to avoid the slaking problem, oven-dried mudrock samples weighing between 25 and 200 grams were coated with a protective clear aerosol acrylic enamel sealant. The dry weights of the samples were measured before and after the application of the sealant. The submerged weights of the samples were also measured and recorded. The dry density was then calculated using the principle of Archimedes by dividing the dry weight by the difference between the dry weight and the submerged weight. No correction was applied to account for the sealant weight, which in all cases was less than 0.1 percent of the sample weight. The surface dried weight was measured for all samples after submergence to check for water absorption. Samples that showed a weight gain greater than 0.1 percent were rejected.

An average dry density was calculated from measurements made on at least four samples of each mudrock (Dick, 1992).

The specific gravity of solids was determined according to ASTM method C97

(ASTM, 1987 ), using three to four samples of each mudrock. ASTM method D 854

(ASTM, 1996) was also used a few times on disaggregated samples because of high 20

slaking. The results were compared to those from ASTM method C97 for the same mudrock sample to be sure of accuracy and reproducibility. Void ratio was calculated from the measured values of dry density and specific gravity of solids.

Absorption Test

Deterioration and decrease in strength of mudrocks due to wetting and drying is influenced by their ability to absorb water. Absorbed water is the water that, during submergence, fills the void spaces present in mudrocks. However, because of the fact that most mudrocks contain clay minerals that can adsorb water (surface attracted and interlayer water) during submergence, absorption measurements usually include a certain amount of adsorbed water. Absorption was determined using slightly modified form of

ASTM method C 97 (ASTM, 1987 ). The test requires submerging dried mudrock samples in water with each sample weighing at least 20-30 grams. To reduce the slaking of the tested samples, the absorption test was initiated at the natural water content of the samples (Dick, 1992). After 48 hours, the samples were removed from the water, surface dried, and weighed. The saturated samples were then oven dried at 105 ° C for 24 hours and then weighed and the percent absorption was calculated as follows:

saturated Wt . − dry Wt . Absorption ( percent ) = ×100 dry Wt .

The test was repeated for at least three samples of each mudrock from which an average value of percent absorption was calculated. Regardless of the modifications to the absorption test procedure, certain mudrocks slaked to a mud-like consistency. The absorption procedure for these samples was further modified by wrapping the sample in a 21

filter paper when submerged in water. In this case 5 to 6 samples for each mudrock were used to insure of consistency of the absorption results.

Adsorption Test

Water adsorption is an important property of mudrocks because it is sensitive to the relative quantity of clay minerals present in the mudrocks as well as the relative proportion of expandable clay minerals (Dick, 1992). Given that mudrocks are classified according to the quantity of clay content, adsorption might be a lithologic indicator that may correlate with the shear strength parameters of these mudrocks. Adsorption might be a better indicator of shear strength of mudrocks with higher percentage of clay content than that of those with lower percentage of clay content. Water adsorption was measured using a humidity and temperature-controlled chamber. Three fragments of each mudrock

(each fragment weighing between 20-30 grams) were oven dried, weighed, and placed in small open-top aluminum containers. The samples were placed in the humidity chamber at a relative humidity of 95 percent and a temperature of 20 ° C. Over a period of 96 hours, the moistened samples were weighed every 24 hours until a steady weight was reached and the percentage adsorbed water content was calculated as follows:

Moist Wt . − Dry Wt . Adsorption ( percent ) = ×100 Dry Wt .

An average adsorption value was calculated from the three tests for each mudrock. In cases where the adsorption values of the three tests were inconsistent, additional three samples were tested for adsorption.

Atterberg Limits Test

Atterberg liquid and plastic limits, determined on powdered mudrock samples, are useful in that they provide information about plasticity characteristics and clay mineral composition. Atterberg limits can be used as an approximate indicator of the types of clay mineral present in a mudrock sample (Casagrande, 1948). Because Atterberg limits are simple to determine and are commonly used by engineers, they may provide a practical alternative to the comparatively sophisticated x-ray diffraction method of clay minerals identification (Dick, 1992). The mudrocks were prepared for Atterberg limits testing by disaggregating approximately 500 grams of each mudrock employing the same wetting, freezing, thawing and drying procedure as used for the grain size analysis. The disaggregated samples were then passed through sieve # 40 and #100 to insure complete disintegration. The test was preformed on the sample that passed sieve #100. The liquid limit and plastic limit were determined according to ASTM procedures D423 and D424, respectively (ASTM, 1996). The plasticity index was computed as the numerical difference between the liquid limit and the plastic limit.

Slake Durability Index Test

Slake durability test, as described by Franklin and Chandra (1972), is the most commonly conducted test for determining durability of weak rocks. The test was preformed using ASTM method D 4644 (ASTM, 1996). As soon after collection as possible, 10 pieces of each mudrock, weighing 40 to 60 grams, were oven dried for 24 hours at 105 ° C and then subjected to two cycles of wetting and drying. The samples were weighed after each drying cycle (24 hours) and the two-cycle slake durability index 23

(Id 2) was calculated. The test was repeated three times for each mudrock sample to obtain average Id 2 values.

Data Analysis

In order to establish quantitative relationships between lithologic characteristics, engineering properties, and shear strength parameters of mudrocks, the following statistical analyses were performed:

1. Univariate analysis

2. Correlation analysis

3. Regression analysis (bivariate and multivariate)

In the above-listed statistical analyses, all mudrocks were first treated as a single group, and then as subgroups of claystones, mudstones, siltstones, and shales. However, dividing mudrocks into subgroups did not provide meaningful results because of the small sample size population and, therefore, only the analyses for all mudrocks treated as a single group were reported here. The statistical analyses were run using averages calculated for each subset of three replicates (i.e., the three repeat tests for each property for each mudrock sample). The analyses were performed using an interactive statgraphics personal computer program (SPSS 12.0 for Windows; SPSS, 2003).

Univariate Analysis

Regression analysis requires that the data be normally distributed. Thus, prior to regression analysis, the distributional characteristics of different variables were analyzed.

The distribution of different variables used in regression analysis was described using 24

univariate statistical parameters such as mean, standard deviation, standard error, minimum and maximum values (range), standardized skewness, and standardized kurtosis. The degree to which the variables approximated a normal distribution was measured using standardized skewness and standardized kurtosis statistics. Normally distributed data will have standardized skewness and standardized kurtosis values between +2 and –2 (Culek, 1985).

Non-normal distributions can often be converted to normal distributions by applying mathematical transformations. Highly skewed distributions can be made approximately normal by using a logarithmic or square root transformation whereas variables that follow Poisson distribution can be transformed using a square root function

(Davis, 1986). These transformations were applied to the data and added as a new separate set of data to achieve the best results from bivariate and multivariate regression analyses.

Correlation Analysis

Correlation analysis is usually useful in detecting covariance amongst variable pairs within a data set and, therefore, aids in the selection of input variables for regression analyses. Correlation analysis was performed on all mudrocks (claystones, mudstones, siltstones, and shales) combined treated as one group. Results of the analysis were produced in the form of a correlation matrix of all possible linear combinations of variables. The extent to which a pair of variables showed a relationship was expressed by

Pearson’s correlation coefficient (r). The null hypothesis was that where r = 0 no 25

correlation exists, and where r ≠ 0 a correlation does exists. The two-tailed t-test

(significance level = 0.01) was used to test the significance of the correlations.

Regression Analysis

Regression analysis was the principal statistical analysis used in this research. It was performed on all mudrocks (treated as one group) to identify geologic characteristics and engineering properties that, through the appropriate equations, provided the best correlation with the cohesion and friction angle values of the mudrocks studied.

Bivariate regression uses one independent variable, whereas multivariate regression uses combinations of independent variables. Selection of the final regression model (bivariate or multivariate) was based on the significance of the regression equation, and analysis of the residuals. The final regression equations/models for cohesion and for friction angle were selected based on engineering and statistical reasons.

CHAPTER 3

RESULTS OF DIRECT SHEAR TESTING

Direct shear testing was performed to determine the strength parameters of cohesion and friction angle. The results of direct shear test for individual samples are presented in Appendix B and discussed in the following sections.

Cohesion

The cohesion values of the mudrock samples in this study represent a wide range from a minimum of 5096 psf (0.24 MPa) to a maximum of 163860 psf (7.85 MPa) as can be seen from the data provided in Table 2 . The cohesion values for the various mudrock groups are also summarized in Table 2, and the distribution of these values is presented graphically in Figure 5 . Comparing the standard deviation for different groups (Table 2), it is noticed that the shale group shows the maximum variability in cohesion values. This is not unexpected as this group includes the siltshale, mudshale, and clayshale samples.

Separation of mudrocks into claystone, mudstone, siltstone, and shale subgroups produces clustered populations with narrower ranges (Figures 6, 7, 8, and 9).

Claystones and mudstones exhibit relatively smaller ranges of cohesion values.

The cohesion values for claystones range from 7072 psf (0.34 MPa) to 65992 psf (3.16

MPa) with a mean of 30335 psf (1.45 MPa) whereas those for mudstones range

Table 2: Summary of cohesion values for all mudrocks and lithologic subgroups.

Standard Lithologic Minimum Maximum Mean N Variance (psf) Deviation Group (psf) (psf) (psf) (psf) All 45 5,096 163,860 52,141.0 1,588,555,489 39,857 Mudrocks Claystones 10 7,072 65,992 30,335 372,221,323 19,293

Mudstones 10 13,860 78,261 47,310 531,804,880 23,061

Siltstones 12 10,750 132,303 67413 1,456,309,927 38,162 Shales 13 5,096 163,860 58,534 2,913,776,286 53,980

Note: 1 psf = 4.79 x 10 -5 Mpa.

180000 claystone 160000 mudstone siltstone 140000 shale 120000 100000 80000 60000 Cohesion(psf) 40000 20000 0 1 5 9 13 17 21 25 29 33 37 41 45 Sample Number

Figure 5: Distribution of cohesion values for all mudrocks.

70000

60000

50000

40000

30000

Cohesion (psf) Cohesion 20000

10000

0 10 14 17 24 29 33 34 35 36 37 Sample Number

Figure 6: Distribution of cohesion values for claystones.

90000 80000 70000 60000 50000 40000 30000 Cohesion (psf) Cohesion 20000 10000 0 1 3 9 13 18 20 28 30 38 39 Sample Number

Figure 7: Distribution of cohesion values for mudstones.

140000

120000

100000

80000

60000

Cohesion (psf) Cohesion 40000

20000

0 2 5 8 11 12 16 19 21 23 25 26 27 Sample Number

Figure 8: Distribution of cohesion values for siltstones.

180000 160000 140000 120000 100000 80000 60000 Cohesion (psf) Cohesion 40000 20000 0 4 6 7 15 22 31 32 40 41 42 43 44 45 Sample Number

Figure 9: Distribution of cohesion values for shales.

from 13860 psf (0.66 MPa) to 78261 psf (3.75 MPa) with a mean of 47310 psf (2.27

MPa) (Table 2, Figures 6 and 7). On the other hand, siltstones and shales exhibit a broader range of cohesion values. The cohesion values for siltstone range from 10750psf

(0.51 MPa) to 132303 psf (6.33 MPa) with a mean value of 67413 psf (3.23 MPa) and those for shales range from 5096 psf (0.24 MPa) to 163860 psf (7.85 MPa), with a mean value of 58534 psf (2.80 MPa) (Table 2, Figures 8 and 9).

Friction Angle

Friction angle is the second important component required to calculate shear strength of mudrocks. The friction angle values for various mudrock groups are summarized in Table 3 and the distribution of these values is presented graphically in

Figure 10 . As with cohesion, the values of friction angle for all mudrocks represent a broad range, from a minimum of 10.1 ° to a maximum of 34.8 °. Separation of the mudrocks into claystone, mudstone, siltstone, and shale subgroups produces clustered populations with smaller ranges of friction angle compared to the entire group (Figures

10 through 14 ).

Claystones and mudstones represent the lower end of the spectrum of mudrock friction angles. Claystones friction angle values vary from 10.9 ° to 30.9 ° with a mean value of 22.4 °, whereas mudstones show almost similar range of variation from 13.2 ° to

29.6 ° with a mean value of 19.1 ° (Table 3, Figures 11 and 12). Siltstones and shales, on the other hand, represent the higher end of the spectrum of mudrocks, with the friction angle values for siltstone varying from 22.0 ° to 35.8 °, with a mean value of 32.4 °, and 34

Table 3: Summary of friction angle values for all mudrocks and lithologic subgroups.

Standard Lithologic Minimum Maximum Mean Variance N Deviation Group (degrees) (degrees) (degrees) (degrees) (degrees) All 45 10.9 35.8 24.9 60.1 7.8 Mudrock Claystone 10 10.9 30.9 22.4 59.2 7.7

Mudstone 10 13.2 29.6 19.1 33.3 5.8

Siltstone 12 22.0 35.8 32.4 15.3 3.9

Shale 13 13.8 34.3 24.4 41.4 6.4

40 claystone mudstone 35 siltstone shale 30

10 Friction Angle (degrees)

0 1 5 9 13 17 21 25 29 33 37 41 45 Sample Number

Figure 10: Distribution of friction angle values for all mudrocks.

Friction Angle (degrees) Angle Friction 5

0 10 14 17 24 29 33 34 35 36 37 Sample Number

Figure 11: Distribution of friction angle values for claystones.

Friction Angle (degrees) 5

0 1 3 9 13 18 20 28 30 38 39 Sample Number

Figure 12: Distribution of friction angle values for mudstones.

10 Friction Angle (degrees) 5

0 2 5 8 11 12 16 19 21 23 25 26 27 Sample Number

Figure 13: Distribution of friction angle values for siltstones.

10 Friction Angle (degrees) 5

0 4 6 7 15 22 31 32 40 41 42 43 44 45 Sample Number

Figure 14: Distribution of friction angle values for shales.

those for shales showing a wider variation from 13.8 ° to 34.3 ° with a mean value of 24.4 °

(Table 3, Figures 13 and 14). This wider range of friction angle in shales is explained by the fact that siltshales, mudshales, and clayshales were all treated as a single group under the term “shales”. This was done because of the small number of clayshale, mudshale, and siltshale samples. Also, the failure plane in all shale samples, during the direct shear testing, developed along their natural laminations. Thus, the pre-existing planes of weakness tend to control shear strength parameters for shales. CHAPTER 4

RESULTS OF LITHOLOGIC AND ENGINEERING TESTING

Results of Lithologic Testing

Grain Size Distribution

Grain size distribution results showing the weight percentages of particles finer than 2 microns (< 0.002 mm) and finer than 4 microns (0.004 mm) are given in Table 4 .

The variation in the amount of 4-micron particles for each mudrock subgroup is defined by the constraint of the geologic classification (Table 1). The mean value of the amount of 4-micron size particles for the four subgroups is 58 % for claystones, 38 % for mudstones, 31.9 % for shales, and 24.7 % for siltstones. The percentages of 4-micron size particles for shales ranges between 19 % and 64 %, reflecting the textural variation between siltshales, mudshales, and clayshales.

Clay minerals are generally defined as those having particle diameter of 2 microns or less. The 2-micron size particle percentages are used to calculate the percentages for each clay mineral type in each mudrock during the XRD analysis. Comparing ranges and means of the 2-micron particles for the four subgroups in Table 4, claystones have the greatest amount of clay minerals with a mean of 45.7 %. Mudstones and shales have intermediate amounts of clay minerals, with mean values of 29.4 and 23.1 %, respectively. Siltstones are found to contain the least amount of clay minerals, with a

41 42

Table 4: Summary of grain size distribution results.

Particle Minimum Maximum Mean Standard Variance Size N Amount Amount Amount Deviation (%) (mm) (%) (%) (%) (%) All Mudrocks < 0.002 45 12 77 28.2 163.7 12.8 < 0.004 45 18 82 37.1 213.4 14.6 Claystones < 0.002 10 38 77 45.7 157.9 12.6 < 0.004 10 50 82 58.0 119.0 10.9 Mudstones < 0.002 10 24 39 29.4 16.8 4.1 < 0.004 10 33 45 38.0 17.0 4.1 Siltstones < 0.002 12 12 18 18.0 13.5 3.7 < 0.004 12 13 31 24.7 12.9 3.6 Shales < 0.002 13 16 46 23.1 63.2 8.0 < 0.004 13 19 64 31.9 117.5 10.8

mean value of 18.0 %. Complete range of particle size distribution for the mudrock samples are shown in the grain size distribution curves in Appendix C .

X-ray Diffraction Analysis Results

The results from the x-ray diffraction analysis, displayed as the amount of clay minerals and expressed as weight % of the whole mudrock, are given in Table 5 . The clay minerals typically occur in assemblages consisting of varying amounts of illite, kaolinite, chlorite, and mixed-layer illite-smectite groups. Overall, kaolinite is the most common clay mineral in the samples tested, as it dominates the clay fraction of all mudrocks except shales. Illite and mixed-layer clays are present in roughly equal amounts in claystones and mudstones, but in siltstones and shales the amounts of illite are relatively higher than those of mixed-layer clays. In general, chlorite is the minor constituent of most of the mudrocks. The montmorillonite group is not as common as the other clay mineral groups in the samples, but it is found in smaller percentages in some of the mudrock samples. Montmorillonite is usually most common in claystones, but it is also found in a few samples of siltstones, mudstones, and shales. Appendix D includes the amounts of various clay minerals for each sample tested as well as the x-ray diffraction peak positions, peak intensities, and peak areas used in the mathematical calculations of the quantities of clay minerals. Typical clay mineral assemblages for claystones, mudstones, siltstones, and shales are presented in the form of annotated x-ray diffraction patterns in Figures 15 through 18 .

Table 5: Summary of quantitative x-ray diffraction analysis results.

Minimum Maximum Mean Standard Variance Mineral Amount Amount Amount Deviation (%) (%) (%) (%) (%) Mudrocks (N= 45)

Chlorite 0.00 2.65 0.52 0.43 0.66 Illite 0.00 21.03 8.46 26.34 5.13 Kaolinite 1.06 53.05 12.23 108.24 10.40 Mixed -layer 0.00 32.33 6.14 52.11 7.22 Montmorillonite 0.00 14.64 0.81 7.35 2.71 Claystones (N = 10) Chlorite 0.00 2.65 1.01 0.99 1.00 Illite 2.20 21.03 8.62 34.91 5.91 Kaolinite 5.49 53.05 24.48 145.94 12.08 Mixed -layer 0.00 32.33 9.7 9 125.05 11.18 Montmorillonite 0.00 14.64 1.78 19.51 4.42 Mudstone (N= 10) Chlorite 0.00 1.44 0.38 0.30 0.55 Illite 0.00 17.02 9.32 27.90 5.28 Kaolinite 1.06 27.26 9.53 77.60 8.81 Mixed -layer 0.10 19.8 10.11 33.83 5.82 Montmorillonite 0.00 0.55 0.06 0.03 0.17 Siltstone (N= 12) Chlorite 0.00 0.60 0.19 0.05 0.22 Illite 0.00 12.67 5.89 18.83 4.34 Kaolinite 1.09 23.02 8.32 41.78 6.46 Mixed -layer 0.00 5.45 2.28 3.39 1.84 Montmorillonite 0.00 9.67 1.32 9.51 3.08 Shale (N= 13) Chlorite 0.00 1.40 0.5 4 0.17 0.42 Illite 2.45 18.1 10.06 18.12 4.26 Kaolinite 3.30 18.1 8.48 19.51 4.42 Mixed -layer 0.00 14.28 3.83 16.80 4.10 Montmorillonite 0.00 2.00 0.18 0.39 0.62

Results of Engineering Testing

Natural Water Content

The results of the natural water content tests are summarized in Table 6 . A listing of the test results for the individual samples is provided in Appendix E . The natural water content for the mudrocks ranges from 0.5 % to 22.9 %. The amount of water retained in these rocks depends on the degree of absorption and adsorption. Natural water content is also controlled by the season the sample was collected.

Table 6: Summary of natural water content test results.

Standard Lithologic Minimum Maximum Mean Variance N Deviation Group (%) (%) (%) (%) (%) All Mudrocks 45 0.5 22.9 4.5 24.6 5.0 Claystones 10 1.1 21.3 7.6 42.6 6.5 Mudstones 10 1.1 9.5 5.1 5.1 2.3 Siltstones 12 0.5 6.1 1.7 1.2 1.1 Shales 13 0.5 22.9 4.3 34.1 5.8

Dry Density, Specific Gravity, and Void Ratio

The results of dry density, specific gravity, and void ratio tests are summarized in

Table 7 . The test results for individual samples are provided in Appendix F . In general, the mudrocks tested have a mean dry density value of 150.3 lb/ft 3 (2.41 Mg/m 3), a mean specific gravity value of 2.69, and a mean void ratio value of 0.12. Overall, the claystones tend to have the lowest mean value for dry density of 145.9 lb/ft 3 (2.34 54

Table 7: Summary of dry density, specific gravity, and void ratio test results.

Engineering Standard Minimum Maximum Mean Variance Properties Deviation

Mudrocks (N = 45) Dry Density 119.2 181.7 150.3 138.6 11.8 Specific 2.47 2.97 2.69 0.008 0.091 Void Ratio 0.01 0.38 0.12 0.006 0.077 Claystones (N = 10) Dry Density 126.7 169.8 145.9 160.7 12.7 Specific 2.47 2.85 2.66 0.013 0.116 Void Ratio 0.01 0.36 0.15 0.008 0.087 Mudstones (N = 10) Dry Density 127.4 164.8 147.7 83.7 9.1 Specific 2.47 2.81 2.67 0.007 0.081 Void Ratio 0.01 0.35 0.13 0.006 0. 075 Siltstones (N = 12)

Dry Density 138.0 168.6 151.8 60.7 7.8 Specific 2.56 2.77 2.69 0.004 0.067 Void Ratio 0.01 0.21 0.11 0.002 0.047 Shales (N = 13) Dry Density 119.2 181.7 154.4 206.5 14.4 Specific 2.61 2.97 2.74 0.007 0.081 Void Ratio 0.01 0.38 0.12 0.008 0.090

Note: Dry Density unit is in lb/ft 3, (1 lb/ft 3 = 0.016 Mg/m 3)

Mg/m 3), whereas the mudstones, siltstones, and shales tend to have slightly higher mean dry density values of 147.7 lb/ft 3 (2.37 Mg/m 3), 151.8 lb/ft 3 (2.43 Mg/m 3), and 154.4 lb/ft 3 (2.47 Mg/m 3), respectively. Claystones, mudstones, and siltstones show similar mean values of specific gravity of 2.66, 2.67, and 2.69, respectively, whereas shales show a higher mean value of 2.74. Void ratio is a reflection of the degree of consolidation of mudrocks. In general, the higher the void ratio value, the poorer the degree of consolidation of mudrocks. Claystones and mudstones have similar range of void ratio values (0.01 – 0.36) and they show the highest mean values of void ratio of 0.15 and

0.13, respectively. Shales tend to have an intermediate value of mean void ratio of 0.12 and a range between 0.01 and 0.38. Siltstone samples show relatively the highest degree of consolidation reflected by a data range between 0.01 and 0.21 with a mean value of

0.11.

Absorption

The results of absorption test are summarized in Table 8 . Results for individual samples are provided in Appendix G . The mean absorption value for claystones is 37.1

%. This very high absorption value reflects the generally poor degree of consolidation of the claystones as well as the abundance of expandable clay minerals (mixed layer illite- smectite and montmorillonite) in eight of the ten claystone samples. Expandable clay minerals adsorb large amounts of water during absorption testing. This adsorbed water is naturally included with, and inseparable from, the absorbed water. The extent to which expandable clay minerals influence claystone absorption is indicated by the large range

(5.5 % to 83.7 %) of absorption values (Table 8). 56

Table 8: Summary of absorption test results.

Standard Lithologic Minimum Maximum Mean Variance N Deviation Group (%) (%) (%) (%) (%) Mudrocks 45 0.8 83.7 17.9 432.9 20.8 Claystones 10 5.5 83.7 37.1 644.7 25.4 Mudstones 10 5.8 82.1 25.5 497.5 22.3 Siltstones 12 1.4 14.8 5.2 12.3 3.5 Shales 13 0.8 25.6 9.0 76.7 8.8

The mean value of absorption for mudstones is 25.5 %, which is less than that for claystones. This value is intermediate between shales and claystones, indicating that mudstones have a higher degree of consolidation than claystones and a lower degree of consolidation than the shales. This is also in accordance with the void ratio results. All ten mudstone samples tested contained some amounts of expandable clay minerals but in smaller percentages than those in claystone samples. Siltstones and shales have mean absorption values of 5.2 % and 9.0 %, respectively. Eleven of the twelve siltstone samples, and eleven of the thirteen shale samples, contained smaller percentages of expandable clay minerals. The mean absorption value of 5.2 % for siltstones indicates the higher degree of consolidation for siltstones among the four types of mudrocks. This is also in accord with the void ratio mean value for siltstones.

Adsorption

The results of the adsorption tests are summarized in Table 9 . Results for the individual samples are provided in Appendix H . The adsorption values of mudrocks are a reflection of the amount of clay size particles (< 0.004 mm) and the amount of clay minerals present in these samples. Adsorption is also sensitive to the presence of 57

Table 9: Summary of adsorption test results.

Standard Lithologic Minimum Maximum Mean Variance N Deviation Group (%) (%) (%) (%) (%) Mudrocks 45 0.2 11.7 3.3 6.5 2.6 Claystones 10 1.5 11.7 5.4 11.5 3.4 Mudstones 10 1.5 7.4 3.9 3.4 1.8 Siltstones 12 1.1 3.2 1.8 0.3 0.6 Shales 13 0.2 10.0 2.6 5.1 2.3

expandable clay minerals. The mean adsorption value for claystones is 5.4 %, which is the highest value among the four mudrock types. This value reflects the claystones’ characteristically high percentage of clay size particles (Table 4) and their comparatively high proportion of expandable clay minerals (Table 5). The mean adsorption for mudstones and shales is 3.9 % and 2.6 %, respectively. The higher mean value for mudstones is explained by the higher percentages of expandable clay minerals. The siltstones, which contain the least amount of clay size particle (Table 4), have a proportionately lower mean adsorption value of 1.8 % and a smaller range of adsorption values.

Atterberg Limits

The mudrock samples tested for this research reveal a wide range of liquid limit, plastic limit, and plasticity index values (Table 10). A listing of the liquid limit, plastic limit, and plasticity index test results for the individual mudrocks is provided in

Appendix I . Generally, the range of Atterberg limits values for each lithology reflects the range of clay-sized particles (< 0.004 mm). These values are also influenced by the relative amount of expandable clay minerals present in these mudrocks. Given that most 58

of the mudrocks tested for this research contain some percentage of expandable clay minerals, there is considerable overlap of the ranges of liquid limit, plastic limit, and plasticity index between the mudrock subgroups.

Claystones have the highest mean liquid limit value of 42.5. This can be explained by the highest percentage of clay-sized particles for claystones. Shales have a mean liquid limit value of 28.9 followed by 27.1 and 24.4 for mudstones and siltstones, respectively. The plastic limit mean values for the mudrock subgroups show a similar trend like that for liquid limit. The claystones show the highest mean value of 24.2, followed by 21.6, 18.9, and 17.8 for shales, mudstones, and siltstones, respectively. The plasticity index is the difference between the liquid limit and the plastic limit. It indicates the range of water contents over which the mudrock material behaves as a plastic material. The mean values of plasticity index for claystones, mudstones, siltstones, and shales are 18.3, 8.3, 6.8, and 7.4, respectively.

Slake Durability

The mudrocks tested for slake durability index represent the full range of durability behavior. The second-cycle slake durability index (Id 2) ranges from a minimum of 1.0 % to a maximum of 99.1 %. The results of the slake durability tests are summarized in Table 11 . Results for the individual samples are provided in Appendix J .

The claystones, mudstones, and shales show relatively broad ranges of Id 2 values.

Claystones are the least durable mudrocks, having Id 2 values ranging between 1.2 % and

95.5 %, with the lowest mean value of 41.1 %. Mudstones exhibit a higher degree of

Table 10: Summary of Atterberg limits test results.

Atterberg Standard Minimum Maximum Mean Variance Limits Deviation

All Mudrocks (N = 45) L.L 17.4 75.0 30.3 135.9 11.7 P.L 14.0 30.2 20.5 18.1 4.3 P.I 0.5 45.2 9.8 86.2 9.3 Claystones (N = 10) L.L 27.1 75.0 42.5 284.3 16.9 P.L 18.2 30.2 24.2 12.3 3.5 P.I 2.3 45.2 18.3 244.9 15.6 Mudstones (N = 10) L.L 19.5 33.0 27.1 15.7 4.0 P.L 14.2 24.6 18.9 7.9 2.8 P.I 4.6 12.1 8.3 4.0 2.0 Siltstones (N = 12) L.L 17.4 39.6 24.4 29.0 5.4 P.L 14.0 26.5 17.8 10.7 3.3 P.I 2.1 13.7 6.7 6.4 2.5 Shales (N = 13) L.L 20.5 52.5 28.9 63.9 8.0 P.L 14.3 30.0 21.6 17.7 4.2 P.I 0.5 23.8 7.4 34.0 5.8

L.L: Liquid Limit; P.L: Plastic Limit; P.I: Plasticity Index

Table 11: Summary of slake durability test results.

Standard Lithologic Minimum Maximum Mean Variance N Deviation Group (%) (%) (%) (%) (%) All Mudrocks 45 1.0 99.1 71.4 1201.0 34.7 Claystones 10 1.2 95.5 41.1 1447.2 38.0 Mudstones 10 1.0 95.8 53.7 1296.7 36.0 Siltstones 12 74.5 99.1 94.0 43.9 6.6 Shales 13 29.9 99.0 87.4 383.7 5.8

durability having Id 2 values ranging from 1.0 % to 95.8 % with a higher mean value of

53.7 %. The shales also exhibit a broad range of durability, having Id 2 values ranging from 29.9 % to 99.0 % (Table 10). Comparing the shales to the claystones and mudstones, the shales are quite durable, having a mean Id 2 value of 87.4 %. The siltstones have a narrower range of Id 2 values towards the higher percentages. The siltstones tend to have the highest durability with a mean Id 2 value of 94.0 % and a range between 74.5 % and 99.1 %.

CHAPTER 5

DATA ANALYSIS FOR ALL MUDROCKS

A variety of statistical tests and analyses were performed on the data to evaluate the variance within each data set and to identify the variables or combinations of variables that correlate best with each of the shear strength parameters (cohesion and friction angle). This chapter is organized to discuss cohesion and friction angle in mudrocks group with respect to different geologic and engineering properties. Univariate and bivariate (correlation) analyses are performed first, followed by regression analysis of selected variables (ones which did not exhibit collinearity between them) to predict cohesion and friction angle.

Univariate Analysis

The results from the univariate analysis that describe the distributional characteristics of mudrocks are tabulated in Appendix K. In general, about half of the variables (percent clay <0.004 mm, percent illite, percent non-expandable clay, dry density, specific gravity, void ratio, percent absorption, percent adsorption, plastic limit, and slake durability index) in the mudrock group approximate normal distribution (their standardized skewness ‘Ss’ and standardized kurtosis ‘Ks’ fall within the range of +2 to –

2). The variables that did not meet the Ss and Ks criteria for normal distribution are percent clay <0.002 mm, percent chlorite, percent kaolinite, percent mixed-layer clay,

61 62

percent montmorillonite, percent expandable clays, percent expandable to non- expandable clays, natural water content, liquid limit, and plasticity index. Mathematical transformation (logarithmic and square root) of most of these mudrock variables produced normal distributions. Although the statistical analyses consider the data that are normally distributed, the non-normal data were also considered and used in the selection of the best independent variables for the regression analyses to predict the dependant variables (cohesion and friction angle).

Correlation Analysis

Correlation analysis was performed on the normally distributed and non-normally distributed mudrock data as well as on their logarithmic and squared root values. The analysis was performed on the variables with respect to cohesion and friction angle values as well as their logarithmic and squared root values. The matrix of linear correlation coefficients for the mudrock group data is presented in Table 12 . For each variable pair, the correlation coefficient (r) and the corresponding two-tailed t-test level of significance are reported. Many of the variable pairs show statistically significant correlations at the 0.01 level. Very few show statistically significant correlations at the

0.05 level. In general, all variables in the correlation matrix of mudrocks indicate very weak degree of covariance (r values between 0.050 and 0.620) with respect to cohesion and friction angle. Cohesion values show the strongest correlation with slake durability and absorption, whereas friction angle values show the strongest correlations with percent mixed layer clay, percent expandable clay, expandable to non-expandable clay ratio,

Table 12: Correlation matrix for all mudrocks as a single group.

Cohesion Friction Log c √ c Log φ √ φ (c) Angle ( φ) Lithology -.113 -.228 -.175 -.319 -.271 -.295 .193 .008 .042 .000 .001 .001 Lamination .103 -.057 .027 -.043 -.007 -.025 .236 .509 .758 .619 .936 .773 % Clay <0.002 mm -.346 -.267 -.321 -.314 -.309 -.311 .000 .002 .000 .000 .000 .000 Log % Clay <0.002 mm -.360 -.240 -.316 -.397 -.381 -.389 .000 .005 .000 .000 .000 .000 √% Clay 0.002 mm -.355 -.253 -.320 -.360 -.350 -.355 .000 .003 .000 .000 .000 .000 % Clay <0.004 mm -.308 -.235 -.285 -.299 -.293 -.296 .000 .006 .001 .000 .001 .000 Log % Clay <0.004 mm -.286 -.192 -.253 -.340 -.327 -.333 .001 .025 .003 .000 .000 .000 √% Clay <0.004 mm -.299 -.214 -.271 -.323 -.313 -.318 .000 .013 .001 .000 .000 .000 % Chlorite -.072 -.032 -.051 -.042 -.034 -.038 .405 .717 .557 .625 .695 .662 √% Chlorite .007 .034 .023 -.037 -.027 -.032 .934 .696 .787 .672 .756 .714 % Kaolinite -.263 -.204 -.238 .072 .086 .081 .002 .018 .006 .406 .319 .353 √% Kaolinite -.277 -.205 -.245 .062 .078 .071 .001 .017 .004 .477 .368 .412 % Illite -.076 .002 -.039 -.010 .028 .009 .382 .981 .655 .911 .744 .919 √% Illite -.098 -.048 -.077 -.078 -.045 -.062 .259 .579 .377 .366 .608 .474 % Mixed Layer Clay -.230 -.212 -.238 -.581 -.613 -.598 .007 .014 .005 .000 .000 .000 √% Mixed Layer Clay -.229 -.196 -.229 -.597 -.620 -.610 .008 .022 .007 .000 .000 .000 % Montmorillonite .149 .091 .119 -.183 -.204 -.193 .084 .293 .170 .034 .018 .025 √% Montmorillonite .215 .137 .176 -.221 -.248 -.234 .012 .112 .041 .010 .004 .006 % Expandable Clay -.145 -.147 -.161 -.539 -.572 -.556 .094 .088 .063 .000 .000 .000 √% Expandable Clay -.114 -.111 -.127 -.567 -.591 -.580 .187 .199 .143 .000 .000 .000 % Non- Expandable Clay -.300 -.201 -.256 .063 .097 .081 .000 .019 .003 .465 .265 .350 √% Non- Expandable Clay -.319 -.201 -.266 .053 .085 .070 .000 .019 .002 .545 .326 .421

Table 12 (Continued)

Cohesion Friction Log c √ c Log φ √ φ (c) Angle ( φ) Expandable/ Non- .085 .029 .053 -.348 -.364 -.357 Expandable Clay .327 .741 .543 .000 .000 .000 √% Expandable/ Non- .072 .024 .041 -.450 -.470 -.461 Expandable Clay .408 .785 .636 .000 .000 .000 Water Content % -.300 -.217 -.274 -.324 -.327 -.326 .000 .011 .001 .000 .000 .000 Log %Water Content -.381 -.268 -.343 -.496 -.496 -.496 .000 .002 .000 .000 .000 .000 √% Water Content -.350 -.252 -.318 -.424 -.428 -.426 .000 .003 .000 .000 .000 .000 Dry Density .095 -.065 .027 .303 .344 .324 .271 .454 .752 .000 .000 .000 Log Dry Density .105 -.052 .039 .308 .348 .329 .224 .552 .654 .000 .000 .000 √ Dry Density .101 -.058 .033 .306 .346 .326 .246 .502 .702 .000 .000 .000 Specific Gravity .042 -.105 -.017 .233 .260 .247 .629 .227 .841 .007 .002 .004 Log Specific Gravity .049 -.095 -.009 .237 .264 .251 .569 .272 .919 .006 .002 .003 √ Specific Gravity .046 -.100 -.013 .235 .262 .249 .598 .249 .880 .006 .002 .004 Void Ratio -.101 .009 -.053 -.245 -.279 -.262 .242 .913 .541 .004 .001 .002 Log Void Ratio -.066 .035 -.022 -.191 -.226 -.208 .449 .685 .804 .027 .008 .015 √ Void Ratio -.087 .024 -.038 -.227 -.263 -.246 .315 .779 .659 .008 .002 .004 % Absorption -.395 -.336 -.387 -.490 -.512 -.501 .000 .000 .000 .000 .000 .000 Log Absorption -.474 -.329 -.423 -.512 -.509 -.511 .000 .000 .000 .000 .000 .000 √% Absorption -.426 -.328 -.400 -.506 -.517 -.512 .000 .000 .000 .000 .000 .000 % Adsorption -.357 -.301 -.349 -.451 -.477 -.464 .000 .000 .000 .000 .000 .000 Log % Adsorption -.406 -.298 -.371 -.510 -.519 -.515 .000 .000 .000 .000 .000 .000 √% Adsorption -.380 -.299 -.360 -.492 -.511 -.502 .000 .000 .000 .000 .000 .000 Liquid Limit -.315 -.290 -.319 -.330 -.346 -.338 .000 .001 .000 .000 .000 .000 Log Liquid Limit -.336 -.307 -.338 -.343 -.351 -.347 .000 .000 .000 .000 .000 .000 65

Table 12 (Continued)

Cohesion Friction Log c √ c Log φ √ φ (c) Angle ( φ) √ Liquid Limit -.327 -.300 -.330 -.337 -.349 -.343 .000 .000 .000 .000 .000 .000 Plastic Limit -.275 -.290 -.296 -.259 -.258 -.259 .001 .001 .000 .002 .003 .002 Log Plastic Limit -.265 -.287 -.289 -.259 -.257 -.258 .002 .001 .001 .002 .003 .003 √ Plastic Limit -.271 -.289 -.293 -.260 -.258 -.259 .001 .001 .001 .002 .003 .002 Plasticity Index -.269 -.231 -.265 -.295 -.316 -.306 .002 .007 .002 .001 .000 .000 Log Plasticity Index -.298 -.187 -.255 -.264 -.269 -.267 .000 .030 .003 .002 .002 .002 √ Plasticity Index -.288 -.217 -.267 -.294 -.308 -.301 .001 .011 .002 .001 .000 .000 Durability Index .451 .364 .433 .545 .553 .549 .000 .000 .000 .000 .000 .000 Log Durability .399 .357 .402 .580 .616 .599 Index .000 .000 .000 .000 .000 .000 √ Durability Index .433 .366 .425 .568 .588 .578 .000 .000 .000 .000 .000 .000 Cohesion 1 .906 .978 .330 .302 .316 . .000 .000 .000 .000 .000 Log Cohesion .906 1 .973 .309 .284 .297 .000 . .000 .000 .001 .000 √ Cohesion .978 .973 1 .337 .310 .324 .000 .000 . .000 .000 .000 Friction Angle .330 .309 .337 1 .990 .998 .000 .000 .000 . .000 .000 Log Friction Angle .302 .284 .310 .990 1 .998 .000 .001 .000 .000 . .000 √ Friction Angle .316 .297 .324 .998 .998 1 .000 .000 .000 .000 .000 .

natural water content, absorption, adsorption, and slake durability index. The lower values of these correlations can be attributed to the lithologic diversity of mudrocks.

Multivariate Regression Analysis

Multivariate analyses to predict cohesion and friction angle were performed on only a few selected variables. Bivariate analysis on friction angle and its transformation values as well as cohesion and its transformation values was performed to chose the most appropriate independent variables to be used in the multivariate analysis. The selection of these variables was based on the strength of their linear relations with cohesion and friction angle in bivariate analysis. Based on the results of normality analysis, friction angle and square root of cohesion were selected as the dependent variables. The individual linear relations of each variable with respect to square root of cohesion and friction angle are presented in Appendix L.

Multivariate Regression Analysis for Cohesion

A multivariate regression analysis was performed, using the backward variable method, with the square root of cohesion as the dependant variable. Eleven independent variables were used in this analysis based on the results of bivariate analysis from

Appendix L. Eleven separate models were produced by multivariate regression analysis.

Table 13 provides the details of each model in terms of the variables used, adjusted R 2, model’s estimated error, and the number of tests required to obtain the values of each variable. Figures 19a and 19b show plots of model number and the number of variables in each model versus the corresponding adjusted R 2 values, respectively. Model number 67

Table 13 : Models produced by multivariate regression analysis to predict square root of cohesion (in psf) for the mudrocks group.

No. ofTests No. variables Adjusted Model # No. of Model Needed R

2 Estimated

Variables Error ( ±)

1 0.314 11 Sqr Rt Slake Durability Index, Void Ratio, % 72.3 7 Absorption +% Adsorption, Sqr Rt Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, % Clay <.004 mm, Dry Density pcf, Sqr Rt Non- expandable Clay, Sqr Rt Absorption, Sqr Rt Plasticity Index 2 0.330 10 Sqr Rt Slake Durability Index, Void Ratio, % 71.5 7 Absorption +% Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, % Clay <.004 mm, Dry Density pcf, Sqr Rt Non-expandable Clay, Sqr Rt Absorption, Sqr Rt Plasticity Index 3 0.337 9 Sqr Rt Slake Durability Index, Void Ratio, % 71.1 6 Absorption +% Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, % Clay <.004 mm, Dry Density pcf, Sqr Rt Non-expandable Clay, Sqr Rt Absorption 4 0.347 8 Sqr Rt Slake Durability Index, Void Ratio, % 70.6 6 Absorption +% Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, % Clay <.004 mm, Dry Density pcf, Sqr Rt Absorption 5 0.349 7 Sqr Rt Slake Durability Index, Void Ratio, % 70.5 5 Absorption +% Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, Dry Density pcf, Sqr Rt Absorption 6 0.326 6 Sqr Rt Slake Durability Index, % Absorption +% 71.7 5 Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, Dry Density pcf, Sqr Rt Absorption 7 0.278 5 Sqr Rt Slake Durability Index, % Absorption +% 74.2 4 Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, Sqr Rt Absorption 8 0.191 4 Sqr Rt Slake Durability Index, Log% Absorption +% 78.6 4 Adsorption, Sqr Rt Expandable clays, Sqr Rt Absorption 9 0.199 3 Sqr Rt Slake Durability Index, Sqr Rt Expandable 78.2 3 clays, Sqr Rt Absorption 10 0.216 2 Sqr Rt Slake Durability Index, Sqr Rt Expandable 77.4 2 clays 11 0.197 1 Sqr Rt Slake Durability Index 78.3 1

0.4 0.35 0.3 2 0.25

0.2 0.15 AdjustedR 0.1 0.05

0 0 1 2 3 4 5 6 7 8 9101112 Model Number

Figure 19a: Plot of regression model number and corresponding adjusted R 2 values with respect to cohesion. Refer to Table 13 for explanations of each model.

0.40 0.35 0.30

2 0.25 0.20 0.15

AdjustedR 0.10

0.05 0.00 12 11 10 9 8 7 6 5 4 3 2 1 0 Number of Variables

Figure 19b: Plot of number of variables in each model and corresponding adjusted R 2 values with respect to cohesion. Refer to Table 13 for identification of variables. 69

7 was selected to predict the square root of cohesion for all mudrocks. This selection was based on a significant drop in correlation coefficient values (R 2 and adjusted R 2) after model 7 as well as a comparison of the collinearity statistics between different models, showing a decrease in collinearity after model number 7. Table 14 shows the regression analysis results from model number 7. This model has an adjusted R 2 of 0.278 and an estimated error of 5500 psf (0.26 MPa). The equation to predict the square root of cohesion of all mudrock types from model number 7 is as follows:

√Cohesion = 28.69 ( √%Expandable Clay) + 193.62 ( √%Absorption) – 10.40 (%Absorption + %Adsorption) – 406.43 (Log % Absorption + %Adsorption) – 24.61 ( √1- Slake Durability Index) + 218.73 Equation 1

Equation 1 can be used to predict the square root of cohesion of all mudrocks provided that the data for the five independent variables are available. These data can be obtained by performing four different tests that include slake durability, x-ray diffraction, absorption, and adsorption. Plots of predicted versus measured square root of cohesion for all mudrocks, and the associated residuals, are shown in Figures 20 and 21 , respectively. The data are given different symbols to indicate the four types of mudrock tested and to show their degree of scatter. The data points plotted in Figure 20 do not fall close to the 1:1 line. The residuals in Figure 21 show that, over the entire range of square root of cohesion values, the maximum difference between the measured and the predicted values is about 160 √psf. The relatively small values of adjusted R2 and the larger values of residuals are due to lithologic diversity of mudrocks compared to the number of samples tested. 70

Table 14 : Results of multivariate regression analysis to predict square root of cohesion of the mudrocks group on the basis of model # 7.

Model Summary

Adjusted R Std. Error of the Model R R Square Square Estimate 7 .600 .360 .278 74.24

ANOVA

Sum of Model Squares df Mean Square F Sig. 7 Regression 120844.98 5 24168.997 4.385 .003(a) 3 Residual 214962.58 39 5511.861 1 Total 335807.56 44 4

Coefficients

Unstandardized Standardized Coefficients Coefficients

Model B Std. Error Beta t Sig. 7 (Constant) 218.725 51.054 4.284 .000 Sqr RT Exp. 28.691 10.888 .507 2.635 .012 Sqr Rt perct 193.619 75.716 4.779 2.557 .015 Absorp Ab+Ad -10.396 4.322 -2.718 -2.406 .021 LOG Ab+Ad -406.430 167.322 -2.064 -2.429 .020 Sqr Rt 1-Id -24.605 9.328 -.885 -2.638 .012

400

350

300

250

200

150 Shale 100 Mudstone Claystone 50 Siltstone

Predicted psf) Square Cohesion Root (Square Root 0 0 50 100 150 200 250 300 350 400 Measured Square Root Cohesion (Squre Root psf)

Figure 20: Measured vs. predicted square root of cohesion values for all mudrocks based on multivariate regression Equation 1 (model # 7).

200.0 Shale Mudstone Claystone Siltstone 150.0 100.0

50.0

0.0 Residuals -50.0

-100.0

-150.0 0 100 200 300 400 500 Square Root Cohesion (Square Root psf)

Figure 21: Residuals for cohesion values of all mudrocks on the basis of model # 7.

Multivariate Regression Analysis for Friction Angle

A multivariate regression analysis was performed, using the backward variable method, with the friction angle as the dependant variable. Eleven independent variables were used in this analysis based on the results of bivariate analysis provided in Appendix

L. Eleven separate models were produced by this regression analysis. Table 15 provides the details of each model in terms of the variables used, adjusted R 2, model estimated error, and the number of tests required to obtain the values of variables. Figures 22a and

22b show the plots of model number and the number of the variables in each model versus the corresponding adjusted R 2 values, respectively. Model number 9 was selected to predict the friction angle for all mudrocks. Table 16 shows the regression analysis results from model number 9. This model has an adjusted R 2 of 0.370 and an estimated error of 6.2 degrees. The equation to predict the friction angle of all mudrocks from model number 9 is as follows:

Friction Angle = 33.6 - 2.55 ( √%Expandable Clays) – 6.84 (Log %Absorption + %Adsorption) + 1.54 ( √Plasticity Index) Equation 12

Equation 12 contains three independent variables that can be determined using four different tests. These tests include x-ray diffraction, absorption, adsorption, and

Atterberg limits. Figure 23 shows a plot of friction angle values predicted from equation

12 against the measured values. It is noticed, as in the case of cohesion values, that the data points are scattered away from the 1:1 line. A plot of the residuals in Figure 24 shows that the maximum difference between the predicted and the measured values over the entire range of friction angle is about 15 degrees. 74

Table 15 : Models produced by multivariate regression analysis to predict friction angle (in degrees) for the mudrocks group.

Adjusted R No. of Testsof No. Model # variables No. of Model Needed Variables Estimated Error ( ±) 2

1 0.272 11 Sqr Rt Slake Durability Index, Void Ratio, % 6.7 7 Absorption +% Adsorption, Sqr Rt Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, % Clay <.004 mm, Dry Density pcf, Sqr Rt Non-expandable Clay, Sqr Rt Absorption, Sqr Rt Plasticity Index 2 0.291 10 Sqr Rt Slake Durability Index, Void Ratio, % 6.6 7 Absorption +% Adsorption, Sqr Rt Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, % Clay <.004 mm, Sqr Rt Non-expandable Clay, Sqr Rt Absorption, Sqr Rt Plasticity Index 3 0.307 9 Sqr Rt Slake Durability Index, Void Ratio, % 6.5 6 Absorption +% Adsorption, Sqr Rt Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, Sqr Rt Non-expandable Clay, Sqr Rt Absorption, Sqr Rt Plasticity Index 4 0.324 8 Sqr Rt Slake Durability Index, Void Ratio, % 6.4 6 Absorption +% Adsorption, Sqr Rt Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, Sqr Rt Absorption, Sqr Rt Plasticity Index 5 0.334 7 Sqr Rt Slake Durability Index, % Absorption +% 6.4 5 Adsorption, Sqr Rt Adsorption, Log% Absorption +% Adsorption, Sqr Rt Expandable clays, Sqr Rt Absorption, Sqr Rt Plasticity Index 6 0.346 6 % Absorption +% Adsorption, Sqr Rt Adsorption, 6.3 4 Log% Absorption +% Adsorption, Sqr Rt Expandable clays, Sqr Rt Absorption, Sqr Rt Plasticity Index 7 0.343 5 % Absorption +% Adsorption, Sqr Rt Adsorption, 6.3 4 Log% Absorption +% Adsorption, Sqr Rt Expandable clays, Sqr Rt Plasticity Index 8 0.358 4 Sqr Rt Adsorption, Log% Absorption +% Adsorption, 6.3 4 Sqr Rt Expandable clays, Sqr Rt Plasticity Index 9 0.370 3 Log% Absorption +% Adsorption, Sqr Rt 6.2 4 Expandable clays, Sqr Rt Plasticity Index 10 0.353 2 Log% Absorption +% Adsorption, Sqr Rt 6.3 2 Expandable clays 11 0.306 1 Sqr Rt Expandable clays 6.5 1

0.40

0.35 0.30 2 0.25

0.20

0.15 AdjustedR 0.10

0.05 0.00 0 1 2 3 4 5 6 7 8 9101112 Model Number

Figure22a: Plot of regression model number and corresponding adjusted R 2 values with respect to friction angle. Refer to Table 15 for explanations of each model.

0.40 0.35 0.30

2 0.25

0.20

0.15

AdjustedR 0.10 0.05

0.00 12 11 10 9 8 7 6 5 4 3 2 1 0

Number of Variables

Figure 22b: Plot of number of variables in each model and corresponding adjusted R 2 values with respect to friction angle. Refer to Table 15 for identification of variables. 76

Table 16: Results of multivariate regression analysis to predict friction angle of all mudrocks on the basis of model #9.

Model Summary

Adjusted R Std. Error of Model R R Square Square the Estimate 9 .643 .413 .370 6.2

ANOVA

Sum of Model Squares df Mean Square F Sig. 9 Regression 1108.358 3 369.453 9.616 .000 Residual 1575.274 41 38.421 Total 2683.633 44

Coefficients

Unstandardized Standardized Coefficients Coefficients

Model B Std. Error Beta t Sig. 9 (Constant) 33.561 2.695 12.455 .000 Sqr RT Exp. -2.550 .821 -.504 -3.105 .003 LOG Ab+Ad -6.843 2.782 -.389 -2.460 .018 Sqr Rt P.I 1.544 1.050 .247 1.470 .149

Shale 10 Mudstone Predicted Predicted Friction Angle (degrees) 5 Claystone Siltstone

0 0 5 10 15 20 25 30 35 40 Measured Friction Angle (degrees)

Figure 23: Measured vs. predicted friction angle values for all mudrocks based on regression equation from model number 9.

20.0 Shale Mudstone Claystone Siltstone 15.0

10.0

5.0

0.0 Residuals -5.0

-10.0

-15.0 0 10 20 30 40 Friction Angle (degrees)

Figure 24: Residuals for friction angle values of all mudrocks on the basis of model # 9.

In the regression analyses described above, the number of variables needed for prediction of cohesion and friction angle was reduced to make the prediction model more meaningful and robust. Because of the small sample population, compared to the number of variables involved in prediction equations 1 and 2, the mudrocks were not divided into subgroups for further analyses. The physical role of the independent variables in equations 1 and 2 in explaining the variations of cohesion and friction angle is discussed in the following chapter.

CHAPTER 6

DISCUSSION

The principle objective of this research was to investigate and quantify the relationships between shear strength parameters (cohesion and friction angle) and lithologic characteristics and engineering properties of mudrocks. Since most engineering properties of mudrocks are a reflection of their lithologic characteristics

(Dick and Shakoor, 1992), the objective of the research was also to see how the shear strength parameters of mudrocks are controlled by their lithologic characteristics. A practical outcome of the research is the development of empirical equations that can be used to predict cohesion and friction angle for a wide variety of mudrocks without performing the direct shear test. Each equation by itself reflects the various geologic and engineering variables that control cohesion and friction angle. The data required for the application of these equations can be obtained by performing a series of lithologic and engineering tests. Such equations would be useful for projects where undisturbed samples of mudrocks are difficult to obtain, where equipment for direct shear test is not available, or where financial constraints would not permit the use of direct shear test.

Selected geologic characteristics and engineering property data for all mudrocks, treated as one group, were analyzed statistically to develop equations 1 and 2 (page 71 and 75) to predict cohesion and friction angle, respectively. The main purpose of statistical analysis was to use as small a number of independent variables as possible in

80 81

each equation inorder to be able to explain the contributions of each variable with respect to variation of cohesion and friction angle.

Equation 1 was developed to predict square root of cohesion from five independent variables. It has an adjusted R 2 of 0.278 and an estimated error of prediction of 5500 psf (0.26 MPa). The five independent variables represent four main lithologic and engineering properties that include clay mineralogy, absorption, adsorption, and slake durability. It can be seen from Equation 1 (page 71) that as percent expandable clays increases the cohesion values of mudrocks increase. The opposite is true for adsorption and slake durability; as they decrease, the cohesion values of mudrocks increase. However, the role of absorption in Equation 1 is less apparent as it appears both as positive and negative quantities. Percent expandable clays in mudrocks can have a direct influence on absorption and adsorption, as well as on slake durability. The higher the percentage of expandable clays in a mudrock sample, the more water it can absorb and adsorb (Dick, 1992). The high amount of absorption and adsorption also would increase the potential for swelling of clay minerals and compression of air in the pores, thereby reducing durability. Given such relationships, it can be stated that the percent expandable clays are likely to affect the cohesion values of mudrocks the most. This observation is supported by the previous research by (Olgaard, 1997). The predicted values for the four additional test samples (TS-1 to TS-4) are presented in Table 17 . The predicted cohesion values were calculated to be 65663 psf (3.14 MPa), 50067 psf (2.40

MPa), 103744 psf (4.97 MPa), and 5586 psf (0.27 MPa) for claystone, mudstone, siltstone, and shale, respectively. The measured values for these four types of mudrocks 82

Table 17: Summary and comparison of predicted and measured cohesion and friction angle values for the different groups of mudrocks.

Claystone Mudstone Siltstone Shale Measured “c” (psf) 74,131 31,375 10,670 166,478 Measured “ φ” (º) 27 18.5 32.4 23.5

All Mudrocks Equation 1 Equation 1 Equation 1 Equation 1 Predicted “c” (psf) 65663 50067 103744 55860 Difference (psf) 8468 18692 93074 110618 All Mudrocks Equation 2 Equation 2 Equation 2 Equation 2 Predicted “ φ” (º) 27.2 28.3 21.6 28.9 Difference (º) 0.2 9.8 10.8 5.4

1 psf = 4.788 x 10 -5 MPa Equation 1 and 2 used for prediction of cohesion and friction angle of all mudrocks.

are 74131 psf (3.5 MPa), 31375 psf (1.5 MPa), 10670 psf (0.5 MPa), 166478 psf (8.0

MPa), respectively. The differences between the predicted and measured values for the tested samples are plotted in Figure 25 . The difference is considered acceptable if it was within 25 percent of the minimum cohesion value used in the data for analysis. The minimum cohesion value used in the analysis was 5095 psf. These differences are all higher than the acceptable value.

Equation 2 (page 75) was developed to predict friction angle for all mudrocks as one group using three independent variables. The equation has an adjusted R 2 of 0.370 and estimated error of prediction of 6.2 degrees. The three variables represent three lithologic characteristics and one engineering property, including clay mineralogy, absorption, adsorption, and Atterburg Limits. It can be seen from Equation 2 that as percent expandable clays, absorption, and adsorption decrease, the friction angle increases; and as plasticity index increases, the friction angle increases. As stated above for cohesion, the percent expandable clays in mudrock are most likely to influence absorption, adsorption, and Atterberg limits. Based on these relations, the percent expandable clays is a property that is most likely to influence friction angle values as well. The predicted values form Equation 2 for the test samples (TS-1 to TS-4) are presented in Table 17. These values were calculated to be 27.2˚, 28.3˚, 21.6˚, and 28.9˚

(degrees) for claystone, mudstone, siltstone, and shale, respectively. The measured values for these four types of mudrocks are 27.0 °, 18.5 °, 32.4 °, and 23.5 °, respectively.

The differences between the predicted and measured values of friction angle for the tested samples are plotted in Figure 26 . The difference is considered acceptable if it was 84

200000 Claystone Mudstone Siltstone Shale

150000

100000

50000 Predicted Cohesion (psf) Cohesion Predicted

0 0 50000 100000 150000 200000 Measured Cohesion (psf)

Figure 25: Measured vs. predicted cohesion values for the test samples (TS-1, TS-2, TS- 3, and TS-4)

Claystone 10 mudstone Siltstone

Predicted Friction Angle (degrees) Angle Friction Predicted Shale

0 0 10 20 30 40 Measured Friction Angle (degrees)

Figure 26: Measured vs. predicted friction angle values for the test samples (TS-1, TS-2, TS-3, and TS-4)

within 25 percent of the minimum friction angle value used in the data for analysis. The minimum friction angle value used in the analysis was 2.5 degrees. The difference between the predicted and measured value for claystone is acceptable, where as the differences for the other subgroups are not acceptable.

Limitations

The initial purpose of this research was to find a few variables for each equation that could be obtained by one or two engineering tests to save time and money. This was achieved by the two equations developed in the study which require few independent variables and, thus, less amount of engineering and lithologic testing. These equations lead themselves to scientific and meaningful interpretations. The limitations observed in this analysis are the lower correlation factors between the dependant and independent variables, as well as the higher estimated errors of prediction. This can be attributed to the small number of mudrock samples used for statistical analysis, which is considered to be another limitation of the research.

It is recommended that future research on cohesion and friction angle of mudrocks should concentrate on individual subgroups, collecting and testing as many samples as possible (>30-40 for each group) to develop the regression models.

CHAPTER 7

SUMMARY AND CONCLUSIONS

Forty five mudrock samples from across the United States have been studied with the objective of establishing quantitative relationships between shear strength parameters (cohesion and friction angle) and their most influential lithologic characteristics and/or engineering properties using multivariate regression analyses. The results from the univariate, bivariate, and multivariate regression analyses show that shear strength parameters, geologic characteristics, and engineering properties of mudrocks, considered as one group, are highly variable and that no single geologic or engineering property solely controls these parameters. Although no single geologic characteristic or engineering property correlates strongly with cohesion or friction angle for any of the subgroups, a combination of these variables does appear to control the shear strength parameters.

Correlation analysis of independent variables showed that many of them were inter-related (i.e. provide the same information). Therefore, the number of variables used in the analysis was reduced by using bivariate plots and by selecting only those variables that can physically explain the variations of shear strength parameters among mudrocks.

Multivariate regression analysis was performed on each shear strength parameter to determine the geologic factors that control the strength parameter. The results show that cohesion is controlled by clay mineralogy, absorption, adsorption, and slake durability

87 88

index, whereas friction angle is controlled by clay mineralogy, absorption, adsorption, and Atterburgh limits.

The relationships between the shear strength parameters, lithologic characteristics, and engineering properties of mudrocks can be expressed by regression equations.

Knowing the type of mudrock and having determined the appropriate lithologic characteristics and engineering properties, these equations can be used to predict cohesion and friction angle for a wide range of mudrocks. This would be useful in case of engineering projects where obtaining large-size intact samples of mudrock for laboratory testing is difficult and/or the equipment for shear testing of rocks is not available.

This study has identified the geologic characteristics and engineering properties that control the shear strength parameters of mudrocks. Recognizing the extreme lithologic variation of mudrocks, it is expected that future research on shear strength parameters of mudrocks will result in refinements to the results of this study. This research has demonstrated that the shear strength parameters are related to certain lithologic characteristics and engineering properties. However, this research has also shown that there is no simple substitute for doing the direct shear test, that is, cohesion or friction angle can not be estimated using the equations developed without relatively large estimated errors.

In summary, as a result of this research, a limited battery of regressors has emerged which (1) supplies some predictive power for both cohesion and friction angle,

(2) confirms the redundancy of several expensive measures, and (3) outlines future 89

sampling procedures in the search for better prediction of these two critical characteristics. New studies with more samples and fewer measures may very well reduce standard errors, increase the proportion of variance explained, and of course improve prediction. However, given this comprehensive survey of engineering properties, it may be concluded that the proportion of unexplained variations in either cohesion or friction angle, or both, is in fact large and irreducible with current methodology.

REFERENCES

American Society of Testing Materials, 1987, Annual Book of ASTM standards, soil and rock, building stones: v. 4.08, section 4, 1189 p.

American Society for Testing and Material, 1996, Annual Book of ASTM standards, soil and rock, construction: v. 8, section 4, West Conshohocken, PA, 950 p.

Bell, F., 1994, A survey of the geotechnical properties of some mudrocks of Lower Triassic age in the Scunthorpe area, Humberside, United Kingdom: Bulletin- International Association of Engineering Geology, v. 50, p. 9-16.

Berube, M.A., Locat, J., Gelinas, P., and Chagnon, J.Y., 1986, Black shale heaving at Saint-foy, Quebec: Can. Journal of Earth science, v. 23, p. 1774-1781.

Blatt, H., Middleton, G.V., and Murray, R.C., 1980, Origin of sedimentary rocks. Prentice Hall, Inc., Englewood Cliffs, N.J., 782 p.

Blatt, H., 1982, Sedimentary petrology: W. H. Freeman and Company, New York, 564 p.

Brindley, G., and Brown, G., 1980, Crystal structures of clay minerals and their x-ray identification: Mineralogical Society Monograph No. 5, Mineralogical Society, London, U.K., 495 p.

Casagrande, A., 1948, Classification and identification of soils: American Society of Civil Engineers Transaction, v. 113, p. 901-930.

Chung, F., 1974, Quantitative interpretation of x-ray diffraction patterns of mixtures I, Matrix flushing method for quantitative multi-component analysis: Journal of Applied Crystallography, v. 7, p. 519-525.

Chugh, Y.P., Okunola, A., and Hall, M., 1981, Moisture absorption and swelling behavior of the Dykersuburg shale, Transactions of the Society of Mining Engineers, v. 268, p. 1808-1812.

Culek, T., 1985, A multiple linear regression model of gravity survey over a buried valley, Brimfield Township, Portage County, Ohio: unpublished Master of Science Thesis, Department of Geology, Kent State University, Kent, Ohio, 119 p.

90 91

Davis, J., 1986, Statistics and data analysis in geology, second edition: John Wiley and Sons, New York, U.S.A., 646 p.

Dick, J., 1992, Relationships between durability and lithologic characteristics of mudrocks: Ph.D. Dissertation, Kent State University, Kent, Ohio, 243 p.

Dick, J., and Shakoor, A., 1992, Lithologic controls of mudrock durability: Quarterly Journal of Engineering Geology, v. 25, p. 31-46.

Dick, J., Shakoor, A., and Wells, N., 1994, A geological approach toward developing a mudrock-durability classification system: Canadian Geotechnical Journal, v. 31 (1), p. 17-27.

Dounias, G., Vaughan, P., and Cavounidis, S., 2002, Making an impermeable clay core from a flysch mudrock: Geotechnical and Geological Engineering, v. 20, p. 17-40.

Dunbar, C., and Rodgers, J., 1957, Principles of stratigraphy: John Wiley and Sons, Inc., New York, 365 p.

Fam, M., and Dusseault, M., and Fooks, J., 2003, Drilling in mudrocks: Rock behavior issues: Journal of Petroleum Science and Engineering, v. 38, p. 155-166.

Flemming, R.W., Spender, G.S., and Bank, D.C., 1970, Empirical behavior of clay shale slopes. U.S. Army Corps of Eng. Nuclear Cratering Group (NCG) Tech. Report, No. 15(1), 93 p.

Folk, R., 1974, Petrology of sedimentary rocks: Hemphill publishing company, Austin, Texas, 170 p.

Franklin, J.A., and Chandra, A., 1972, The slake durability test: International Journal of Rock Mechanics and Mining Sciences, v. 9 325-341.

Goodman, R.E., 1992, Engineering geology, Rock in engineering construction: John Wiley and sons, Inc., New York, 412 p.

Grainger, P., 1984, The classification of mudrocks for engineering purposes: Quaternary Journal and Engineering Geology, v. 17(4), p. 381-387.

Grim, R., 1969, Clay mineralogy: McGraw-Hill Book Company, 596 p.

Hansan, S.E., 1982, Engineering geology of underground space development in Kansas City, USA, in Proceedings of the Fourth International congress of the International Association of Engineering Geology, New Delhi, India, p. 247-257.

Hosterman, J., and Whitlow, S., 1983, Clay mineralogy of Devonian shales in the Appalachian Basin: U.S. Geological Survey Professional Paper, 1298, 31 p.

Hudec, P., 1981, Statistical analysis of shale durability factors: Transportation Research Record, No. 873, p. 28-35.

Ingram, R., 1953, Fissility of mudrocks: Geological Society of America Bulletin, v. 65, p. 869-878.

Lee , C.F., and Klyn, T.W., 1978, Determination of rock squeeze potential for underground power projects: Engineering Geology, v. 12(1), p. 181-192.

Lewan, M., 1978, Laboratory classification of fine-grained sedimentary rocks: Geology, v. 8, p. 745-748.

Lundegard, P., and Samuels, N., 1980, Field Classification of fine-grained sedimentary rocks: Journal of Sedimentary Petrology, v. 50(3), p. 781-786.

Madsen, F.T., and Muller-vonmoos, M., 1985, Swelling pressure calculated from mineralogical properties of a Jurassic opalinum shale, Switzerland: Clays and Clay Minerals, v. 33(6), p. 501-509.

Moore, D., and Reynolds, R., 1989, X-ray diffraction and the identification and analysis of clay minerals, 1 st Edition, 450 p.

Ola, S.A., 1982, Geotechnical properties of an Attapulgite clay shale in Northwestern Nigeria: Engineering Geology, v. 19(1), p. 1-13.

Olgaard, D., Urai, J., Dell’angelo, L., Nuesch, R., and Ingram, G., 1997, The influence of swelling clays on the deformation of mudrocks: International Journal of Rock Mechanics, v. 34, no. 3, p. 364.

Olivier, H.J., 1979, A new engineering-geological rock durability classification: Engineering Geology, v. 14, p. 255-279.

Pettijohn, F., 1975, Sedimentary rocks: Harper and Row, 3 rd Edition, 628 p.

Potter, P.E., Maynard, J.B., and Pryor, W.A., 1980, Sedimentology of shale. Springer- Verlag, New York, 306 p.

Ramachandran, B., Majumdar, N., Bandose, R.B., and Rawat, J.S., 1981, Influence of weak pyritiferous shale on the design of Dudhganga dam, India. Proceedings International Symposium Weak Rock, Tokyo, Japan, v. 3, p. 1472-1475.

Regues, D., Pardini, G., and Gallart, F., 1995, Regolith behavior and physical weathering of clayey mudrock as dependent on seasonal weather conditions in a badland area at Vallcebre, Eastern Pyrenees, Elsevier Science, v. 25, p. 199-212.

Sarman, R., Shakoor, A., and Palmer, D., 1994, A multiple regression approach to predict swelling in mudrocks: Bulletin of the Association of Engineering Geology, v. 31 (1), p. 107-121.

Schultz, L., 1964, Quantitative interpretation of mineralogical composition from x-ray and chemical data for the Pierre Shale: United States Geological Survey Professional Paper 391-C, p. C1-C28.

Schultz, L., 1965, Mineralogy and stratigraphy of the lower part of the Pierre Shale, South Dakota and Nebraska: United States Geological Survey Professional Paper 392-B, p. B1-B19.

Schultz, L., 1978, Mixed-layer clay in the Pierre Shale, Northern Great Plains Region: United States Geological Survey Professional Paper 1064-A, p. A1-A28.

Schultz, L., Tourtelot, H., Gill, J., and Boernger, J., 1980, Composition and properties of the Pierre Shale and equivalent rocks, northern Great Plains Region: United States Geological Survey Professional Paper, 1064 B, 114 p.

SPSS, 2003, Statistical software program for Windows 12.0: SPSS, Inc., Chicago, Illinois.

Sroden, J., 1980, Precise identification of identification of illite/smectite interstratifications by x-ray powder diffraction: Clays and Clay Minerals, v. 28, no. 6, p. 401-411.

Sroden, J., 1984, X-ray powder diffraction identification of illitic materials: Clays and Clay Minerals, v. 32, no. 5, p. 337-349.

Strohm, W.B., Bragg, G.H., and Ziegler, T.W., 1978, Design and construction of compacted shale embankments: Federal Highway Administration, U.S. Dept. Transportation, Report No. M 0543, 142 p.

Strohm, W.E., 1980, Design and construction of shale embankments: summery, U.S. Department of Transportation Report Number FHWA-TS-89-219.

U.S. Army Corps of Engineers, 1988, Point Marion Lock, Monongahela River, Features design memorandum, no. 2, Geology and Foundations, Pittsburgh District, 326 p.

Wittke, W., 1981, Fundamentals for the design and construction of tunnels in swelling rocks: Proceedings of the 23 rd symposium on Rock Mechanics, Berkeley, California, p. 710-729.

Zeng, Z.,1981, An engineering geological study of argillaceous soft rocks at the Gezhouna project on the Yangtze River: Proceedings International Symposium Weak Rock, Tokyo, Japan, v. 2, p. 1127-1133.

APPENDIX A

SITE LOCATION AND DESCRIPTION OF SAMPLES

95 96

Sample No. 1 Monongahela Group, Pennsylvanian Location: About 10 m high, east facing slope along I-77, about 3 miles south of Rockport exit, West Virginia Description: Reddish and grayish brown mudstone, interbedded with fine-grained sandstone

Sample No. 2 Conemangh Formation, Pennsylvanian Location: About 15 m high, west facing slope along I-77 N, 2 miles north of Dexter City exit, Ohio. Description: Reddish gray siltstone, interbedded with sandstone, highly weathered mudstone, and micaceous shale.

Sample No. 3 Dunkard Formation, Permian Location: About 25 m high, east facing slope along SR-7S, about 1 mile off Loganport exit, (mm=14), Ohio Description: Dark and purplish gray mudstone, collected from the upper part of alternating sequence of shale, siltstone, sandstone, and mudstone.

Sample No. 4 Conemaugh Formation, Pennsylvania Location: About 10 m high, east facing slope along SR-75, about 15 miles south of sample No. 3 location, (mm=30), Ohio. Description: Light gray silty shale with yellowish brown surface stain due to weathering, breaks easily along lamination. The slope consists of alternating layers of sandstone, shale, siltstone and thin layers of claystone.

Sample No. 5 Allegheny Group, Pennsylvanian Location: About 30 m high, east facing slope alongI-79S, approximately 1 mile north of Carnegie exit, Pennsylvania. Description: Light to dark gray and brown siltstone interbedded with alternating layers of shale, sanstone, and siltstone. Undercutting due to weathering of shale layer exists along this slope.

Sample No. 6 Glenshaw Formation, Pennsylvania Location: about 10 m high, south of Mount Morris exit, Pennsylvania. Description: Dark brownish gray silty shale with siltstone nodules and concretions, and heavily iron-stained weathered joint surfaces. The shale is overlain by a massive 3-4 m thick layer of sandstone. The shale is highly weathered and undercutting is along the slope. 97

Sample No. 7 Washington Formation, Permian Location: about 15 m high, west facing slope along I-79N, on the ramp of Bridgville exit, Pennsylvania. Description: Light brownish gray siltyshale overlain by thin layer of limestone. The shale breaks along conchoidal fractures.

Sample No. 8 Pottsville Group, Pennsylvanian Location: Highway construction ramp, Cranberry exit along I-76E and SR-19. Description: Light gray thinly bedded siltstone.

Sample No. 9 Conemaugh Formation, Pennsylvanian Location: about 5 m high, west facing slope along a road off I-77S between Ripley and Fairplain exits. Description: Brownish red mudstone with gray slickensided surfaces, breaks into irregular chunks, this layer is underlain by a layer of claystone.

Sample No. 10 Conemaugh Formation, Pennsylvanian Location: about 5 m high, west facing slope along a road off I-77S between Ripley and Fairplain exits. Description: gray claystone, breaks along weakly developed parallel joint surfaces due to weathering and forms slabs.

Sample No. 11 Conemaugh Formation, Pennsylvanian Location: About 7 m high, east facing slope along I-77S at the ramp of Eden Fork exit, West Virginia. Description: Light to dark gray micaceous siltstone,interbedded with layer of sandstone and thin layers of claystone. Weathered zones are fissile and breaks into slab- like pieces.

Sample No. 12 Monongahela, Pennsylvanian Location: About 7 m high south facing slope along SR22E, about 13 miles west of SR-7, Ohio. Description: Light gray siltstone interbedded with layers of sandstone, sitltstone, and shale.

Sample No. 13 Dunkard, Permian 98

Location: About 8 m high, east facing slope along SR-7S, 3 miles south of New Matamoras exit (SR-260), Ohio. Description: Light greenish gray mudstone interbedded with shale, sandstone, and thin layers of limestone., mudstone, and shale layers from undercutting due to differential weathering.

Sample No. 14 Mowery Shale, Cretaceous Location: About 35 m high, east-facing slope along the Missouri River off I-90W, about 1 mile north of Oacoma, South Dakota. Description: Dark gray hard claystone with 5-10 cm bands of light gray soft clay and iron stains.

Sample No. 15 Monongahela Formation, Pennsylvanian Location: About 15 m high east facing slope along SR-7S, 1 mile North of Belpre exit south of Marietta, Ohio. Description: Greenish gray siltyshale interbedded with layers of siltstone and shale.

Sample No. 16 Lewis Shale Formation, Late Cretaceous Location: About 15 m high gentle, south facing slope along SR-16W, about 4 miles east of New Castle, Wyoming. Description: Light gray weathered and fissile siltstone alternating with layers of shale and sandstone.

Sample No. 17 Lewis Shale Formation, Late Cretaceous Location: About 20 m high, east facing slope along SR-85N, (mile marker=239), Wyoming. Description: Dark gray hard and highly jointed claystone containing fossils.

Sample No. 18 Green River Formation, Eocene Location: About 20 m high, south facing slope along I-80W (mile marker =282), Wyoming. Description: Dark gray to brown, very weathered mudstone, interbedded with layers of sandstone and shale.

Sample No. 19 Green River Formation, Eocene Location: About 40 m high, south facing slope along I-80W (mile marker =216), Wyoming 99

Description: Light gray, very hard and highly jointed, siltstone interbedded with layers of sandstone and thinner layers of shale.

Sample No. 20 Red Pine Shale of Utah, Proterozoic Location: About 15 m high, east facing slope along SR-191S, about 1 mile east of Flaming Gorge Dam, Utah. Description: Dark red jointed and slightly weathered mudstone with small lenses of sandstone. This layer alternates with sandstone layers.

Sample No. 21 Green River Formation, Eocene Location: About 15 m high, east facing slope along SR 191S, about 0.5 miles south of Duchense, Utah. Description: Light gray, jointed siltstone underlain by sandstone and a thin layer of coal and overlain by sandstone and shale.

Sample No. 22 Straight Cliffs Formation, Cretaceous Location: About 12 m high east-facing slope along SR-10, 8 miles south of Price town, Utah. Description: Dark gray, weathered and highly fractured mudshale overlain by sandstone.

Sample No. 23 Chinle Formation, Triassic Location: About 15 m high south facing slope along I-70W, 1 mile east of exit 147 (Lake Powell), Utah. Description: Dark greenish gray fractured massive and hard siltstone.

Sample No. 24 Fruitland Formation, Upper Cretaceous Location: About 10 m high west facing slopealong SR-139N, 27 miles north of Loma Carfield, Colorado. Description: Gray, massive claystone overlain by 20 cm seam, shale, and sandstone layer.

Sample No. 25 South Park Formation, Paleocene Location: About 25 m high east facing slope along SR-139S, 15 miles north of Loma, Carfield, Colorado. Description: Red to greenish red, massive and fractured siltstone underlain and overlain by sandstone.

100

Sample No. 26 Mancos Shale, Cretaceous Location: About 12 m high north facing slope along I-70E (mile marker =50), Colorado. Description: Light gray fractured and weathered siltstone overlain and underlain by sandstone layers.

Sample No. 27 Wasatch Formation, Eocene Location: About 15 m high north facing slope along I-70 E (mile marker =156), Colorado. Description: Dark gray jointed siltstone underlain by sandstone and shale and overlain also by shale and sandstone.

Sample No. 28 Dakota Group, Lower Cretaceous Location: About 12 m high east facing slope along SR-159S about 700 m south of I-70, Kansas. Description: Light gray massive mudstone overlain by siltstone and massive red and gray claystone.

Sample No. 29 Dakota Group, Lower Cretaceous Location: About 12 m high east facing slope along SR-159S about 700 m south of I-70, Kansas. Description: Red and gray massive claystone, overlies a thin layer of siltstone and mudstone.

Sample No. 30 Chase Group, Permian Location: About 10 m high north facing slope along I-70 E, about 2 miles west of exit 307, Manhattan, Kansas. Description: Light gray massive and hard mudstone overlain by alternating layers of limestone and mudstone.

Sample No. 31 Chanute Formation, Middle Pennsylvanian Location: About 20 m high north facing slope along I-435S at Holiday Drive exit, Kansas. Description: Dark gray massive mudshale overlain by layers of limestone interbedded with thin layer of mudrock.

Sample No. 32 Tradewater Formation, Middle Pennsylvanian 101

Location: About 12 m high east facing slope along SR William H. Natcher Parkway at (mm=52), Kentucky. Description: Gray to light gray, massive mudshale overlain and underlain by ~ 1 m thick layers of limestone.

Sample No. 33 Conemaugh Formation, Pennsylvanian Location: Dam site at Point Marion, about 90 miles upstream along the Monongahela River from Pittsburgh, Pennsylvania. “Samples Donated by the Army Corp of Engineers, Pittsburgh Office”. Description: Light gray claystone interbedded with layers of siltstones, shales, clays, and Bakerstown coal at the bottom.

Sample No. 34 Glennshaw Formation, Pennsylvania Location: Dam site at Point Marion, about 90 miles upstream along the Monongahela River from Pittsburgh, Pennsylvania. “Samples Donated by the Army Corp of Engineers, Pittsburgh Office”. Description: Light gray claystone interbedded with layers of siltstones, shales, clays, and Bakerstown coal at the top.

Sample No. 35 Conemaugh Formation, Pennsylvanian Location: Dam site at Point Marion, about 90 miles upstream along the Monongahela River from Pittsburgh, Pennsylvania. “Samples Donated by the Army Corp of Engineers, Pittsburgh Office”. Description: Light gray claystone interbedded with layers of siltstones, shales, clays, and Bakerstown coal at the bottom.

Sample No. 36 Glennshaw Formation, Pennsylvania Location: Dam site at Point Marion, about 90 miles upstream along the Monongahela River from Pittsburgh, Pennsylvania. “Samples Donated by the Army Corp of Engineers, Pittsburgh Office”. Description: Light gray claystone interbedded with layers of siltstones, shales, clays, and Bakerstown coal at the top.

Sample No. 37 Pierre Shale, Cretaceous Location: About 15 m high west facing slope along Rooney Road, adjacent to I-70, Colorado. Description: Black and dark gray, massive claystone.

Sample No. 38 102

Lewis Formation, Upper Cretaceous Location: About 10 m high east facing slope along S-295, about 1 mile north of dam at Joe’s Valley Reservoir, Utah. Description: Dark gray, massive mudstone. Undercutting at the base of the slope occurs due to weathering of this layer.

Sample No. 39 Mancos Shale, Upper Cretaceous Location: About 12 m high east facing slope along SR-325, about 1 mile east of reservoir dam, Colorado. Description: Dark gray, massive, fossiliferous mudstone.

Sample No. 40 Pierre Shale, Upper Cretaceous Location: About 55 m high, north facing slope behind South Dakota School of Mines, Rapid City, South Dakota. Description: Dark gray clayeyshale with thin yellowish beige pockets of bentonite; breaks along conchoidal fractures.

Sample No. 41 Rome Formation, Cambrian Location: About 20 m high south facing slope behind the drag racing field (Bristol Motor Speedway) off SR-381N, Tennessee. Description: Light to dark gray hard siltyshale with some bands of iron oxide stains.

Sample No. 42 Milboro Shale, Devonian Location: About 10 m high west facing slope along SR-11 N, about 2 miles from Radford, Virginia. Description: Dark gray, highly fissile, siltyshale with pyrite and iron oxide bands.

Sample No. 43 Brallier Formation, Devonian Location: About 30 m high north facing slope along SR-100W, about 1 mile from SR- 822 intersection, Virginia. Description: Light brown gray silty shale, contains some small fossils. Thin coal seams exist at the bottom of the slope below the shale.

Sample No. 44 Allegheny Formation, Pennsylvanian Location: About 25 m high west facing slope along I-77N, about 1 mile north of Camp Creek exit, West Virginia. Description: Dark gray fractured and weathered siltyshale with iron stains.

103

Sample No. 45 Catskill Formation, Devonian Location: Austin dam site off SR-872, Potter County, Pennsylvania. Description: Yellowish beige shale, interbedded with grayish-red sandstone, siltstone, and shale.

Sample No. TS-1 Kope Formation, Upper Ordovician Location: About 30 m high, north facing slope along I-74, about 0.5 miles east of I-75 junction, Cincinnati, Ohio. Description: Dark gray claystone with sparse lenses of limestone. Underlain by thin highly weathered layer of mudstone.

Sample No. TS-2 Kope Formation, Upper Ordovician Location: About 12 m high north facing slope along I-74, about 0.25 miles east of I-75 junction, Cincinnati, Ohio. Description: Light gray fossiliferous mudstone with sparse lenses of limestone. Layers of thinner claystone overlay this layer.

Sample No. TS-3 Conemaugh Group, Pennsylvanian Location: About 10 m high strip mine highwall off Curry Hollow Road south of Pittsburgh, Pennsylvania. Description: Light gray, calcareous, pyretic siltstone overlying limestone layer and sandstone bed.

Sample No. TS-4 Olentangy Shale, Upper Devonian Location: About 12 m high east facing slope along I-270S, about 3 miles west of I-71, Columbus, Ohio. Description: Dark gray to light black, siltyshale interbedded with greenish gray mudshale.

APPENDIX B

DIRECT SHEAR TEST DATA

104 105

Table B-1: Summary of shear strength parameters for the tested samples.

Sample # Cohesion Cohesion Friction Angle "psi" " psf " degrees S-1 96.25 13859 13.2 S-2 480.93 69254 34.4 S-3 210.96 30378 23.6 S-4 59.76 8605 14.6 S-5 74.65 10749 22.0 S-6 35.39 5096 27.1 S-7 194.78 28048 23.5 S-8 490.94 70695 33.5 S-9 132.69 19107 14.5 S-10 289.61 41704 20.9 S-11 87.32 12574 31.8 S-12 408.46 58818 35.6 S-13 221.62 31913 25.8 S-14 218.70 31493 20.6 S-15 372.46 53634 27.0 S-16 406.92 58596 31.5 S-17 111.08 15996 10.9 S-18 461.76 66493 29.6 S-19 207.57 29890 34.3 S-20 306.96 44202 20.5 S-21 918.77 132303 31.9 S-22 945.50 136152 14.6 S-23 806.77 116175 27.6 S-24 129.60 18662 12.7 S-25 697.34 100417 35.8 S-26 334.43 48158 35.2 S-27 703.64 101324 35.2 S-28 467.50 67320 13.4 S-29 63.39 9128 30.9 S-30 543.48 78261 14.4 S-31 338.19 48699 28.3

106

Table B-1 (Continued)

Sample # Cohesion Cohesion Friction Angle "psi" " psf " degrees S-32 105.06 15129 20.9 S-33 264.22 38048 26.6 S-34 451.33 64992 28.4 S-35 399.50 57528 29.8 S-36 49.11 7072 30.4 S-37 130.05 18727 12.6 S-38 301.47 43412 21.7 S-39 542.75 78156 13.9 S-40 313.82 45190 29.1 S-41 594.72 85640 29.5 S-42 170.14 24500 13.8 S-43 974.31 140301 34.3 S-44 1137.90 163858 30.2 S-45 42.27 6087 23.9 TS-1 514.80 74131 27.0 TS-2 217.90 31375 18.5 TS-3 74.11 10670 32.4 TS-4 1156.10 166478 23.5

1 psf = 4.788 x 10 -5 MPa

107

160 y = 0.2336x + 96.246 140 120 100 80 y = 0.2024x + 39.547 60 40

ShearStress (psi) 20 0 0 50 100 150 200 250 Normal Stress (psi)

Figure B-1: Plot of the shear behavior for sample S-1.

900 y = 0.6841x + 480.93 800 700 600 500 400 300 y = 0.5353x + 40.525 200 Shear Stress (psi) Stress Shear 100 0 0 100 200 300 400 500 600 Normal Stress (psi)

Figure B-2: Plot of the shear behavior for sample S-2.

108

400 y = 0.4373x + 210.96

300

200 y = 0.2719x + 103.35 100 Shear Stress (psi)

0 0 50 100 150 200 250 300 350 Normal Stress (psi)

Figure B-3: Plot of the shear behavior for sample S-3.

140 120 y = 0.2595x + 59.759 100 y = 0.2097x + 36.552 80 60 40

Shear Stress (psi) Stress Shear 20 0 0 50 100 150 200 250 Normal Stress (psi)

Figure B-4: Plot of the shear behavior for sample S-4.

109

200 y = 0.404x + 74.645

150

y = 0.3303x + 45.322 100

50 Shear Stress Shear (psi)

0 0 50 100 150 200 250 300 Normal Stress (psi)

Figure B-5: Plot of the shear behavior for sample S-5.

280 240 y = 0.5122x + 35.387 200 160 y = 0.3908x + 27.502 120 80

Shear Stress (psi) Stress Shear 40 0 0 50 100 150 200 250 300 350 400 Normal Stress (psi)

Figure B-6: Plot of the shear behavior for sample S-6.

110

400 350 y = 0.4354x + 194.78 300 250 200 y = 0.3047x + 105.12 150 100

ShearStress (psi) 50 0 0 100 200 300 400 500 Normal Stress (psi)

Figure B-7: Plot of the shear behavior for sample S-7.

900 800 y = 0.6629x + 490.94 700 600 500 400 y = 0.5147x + 242.68 300 200 Shear Stress (psi) Stress Shear 100 0 0 100 200 300 400 500 600 Normal Stress (psi)

Figure B-8: Plot of the shear behavior for sample S-8.

111

250

200

y = 0.2593x + 132.69 150

100 y = 0.1904x + 53.535

Shear Stress Shear (psi) Stress 50

0 0 50 100 150 200 250 Normal Stress (psi)

Figure B-9: Plot of the shear behavior for sample S-9.

500 450 y = 0.3811x + 289.61 400 350 300 250 200 y = 0.2449x + 46.918 150

Shear Stress (psi) Stress Shear 100 50 0 0 100 200 300 400 500 Normal Stress (psi)

Figure B-10: Plot of the shear behavior for sample S-10.

112

500 450 400 y = 0.6204x + 87.319 350 300 250 y = 0.4634x + 17.263 200 150

Shear Stress (psi) Stress Shear 100 50 0 0 100 200 300 400 500 600 700 Normal Stress (psi)

Figure B-11: Plot of the shear behavior for sample S-11.

1200

1000 y = 0.7167x + 408.46 800

600

400 y = 0.4538x + 143.57

Shear Stress (psi) Stress Shear 200

0 0 200 400 600 800 1000 Normal Stress (psi)

Figure B-12: Plot of the shear behavior for sample S-12.

113

450 400 350 y = 0.4843x + 221.62 300 250

200 y = 0.2578x + 135.19 150 100 Shear Stress (psi) Stress Shear 50 0 0 50 100 150 200 250 300 350 400 Normal Stress (psi)

Figure B-13: Plot of the shear behavior for sample S-13.

400 350 y = 0.3763x + 218.7 300 250 200 150 y = 0.309x + 58.787 100 Shear Stress (psi) Stress Shear 50 0 0 50 100 150 200 250 300 350 400 Normal Stress (psi)

Figure B-14: Plot of the shear behavior for sample S-14.

114

700 y = 0.5099x + 372.46 600 500 400 300 y = 0.3569x + 161.34 200

Shear Stress Shear (psi) 100 0 0 100 200 300 400 500 Normal Stress (psi)

Figure B-15: Plot of the shear behavior for sample S-15.

900 y = 0.6132x + 406.92 800 700 600

500 y = 0.5327x + 213.03 400 300 200 Shear Stress (psi) Stress Shear 100 0 0 100 200 300 400 500 600 700 800 Normal Stress (psi)

Figure B-16: Plot of the shear behavior for sample S-16.

115

350 300 y = 0.1929x + 111.08 250 200 150 100 y = 0.1262x + 25.44

Shear Stress (psi) Stress Shear 50 0 0 200 400 600 800 1000 Normal Stress (psi)

Figure B-17: Plot of the shear behavior for sample S-17.

900 800 700 y = 0.5674x + 461.76 600 500 400 300 y = 0.433x + 76.764 200 Shear Stress (psi) Stress Shear 100 0 0 100 200 300 400 500 600 Normal Stress (psi)

Figure B-18: Plot of the shear behavior for sample S-18.

116

1200

1000 y = 0.6811x + 207.57 800

600

400 y = 0.3432x + 96.281

Shear Stress (psi) Stress Shear 200

0 0 200 400 600 800 1000 1200 Normal Stress (psi)

Figure B-19: Plot of the shear behavior for sample S-19.

600

500 y = 0.373x + 306.96 400

300

200 y = 0.3133x + 140.35

Shear Stress (psi) Stress Shear 100

0 0 100 200 300 400 500 600 Normal Stress (psi)

Figure B-20: Plot of the shear behavior for sample S-20.

117

1800 1600 y = 0.6229x + 918.77 1400 1200 1000 800 y = 0.5545x + 233.03 600 400 Shear Stress Shear (psi) 200 0 0 200 400 600 800 1000 1200 1400 Normal Stress (psi)

Figure B-21: Plot of the shear behavior for sample S-21.

1400 1200 1000 y = 0.261x + 945.5 800 600 y = 0.1835x + 470.66 400

Shear Stress (psi) Stress Shear 200 0 0 200 400 600 800 1000 Normal Stress (psi)

Figure B-22: Plot of the shear behavior for sample S-22.

118

1400 y = 0.5227x + 806.77 1200 1000 800 600 y = 0.361x + 384.38 400

Shear Stress (psi) Stress Shear 200 0 0 200 400 600 800 1000 Normal Stress (psi)

Figure B-23: Plot of the shear behavior for sample S-23.

250 y = 0.2248x + 129.6 200

150

100 y = 0.1804x + 45.621

Shear Stress (psi) (psi) Stress Shear 50

0 0 100 200 300 400 500 Normal Stress (psi)

Figure B-24: Plot of the shear behavior for sample S-24.

119

1400 1200 1000 y = 0.7216x + 697.34 800 600 y = 0.5891x + 163.12 400

Shear Stress (psi) Stress Shear 200 0 0 200 400 600 800 1000 Normal Stress (psi)

Figure B-25: Plot of the shear behavior for sample S-25.

1200

1000 y = 0.7045x + 334.43 800

600 y = 0.5457x + 134.26 400

Shear Stress (psi) Stress Shear 200

0 0 200 400 600 800 1000 Normal Stress (psi)

Figure B-26: Plot of the shear behavior for sample S-26.

120

2000 1800 y = 0.7064x + 703.64 1600 1400 1200 1000 800 y = 0.534x + 134.22 600

Shear Stress (psi) Stress Shear 400 200 0 0 200 400 600 800 1000 1200 1400 1600 Normal Stress (psi)

Figure B-27: Plot of the shear behavior for sample S-27.

600

500 y = 0.2374x + 467.5 400

300 y = 0.1636x + 121.23 200

Shear Stress (psi) Stress Shear 100

0 0 50 100 150 200 250 300 Normal Stress (psi)

Figure B-28: Plot of the shear behavior for sample S-28.

121

250

200 y = 0.5977x + 63.39 150

100 y = 0.4274x + 14.409

Shear Stress (psi) Stress Shear 50

0 0 50 100 150 200 250 Normal Stress (psi)

Figure B-29: Plot of the shear behavior for sample S-29.

800 y = 0.257x + 543.48 700 600 500 400 300 y = 0.2221x + 248.43 200 Shear Stress Shear (psi) 100 0 0 100 200 300 400 500 600 700 800 Normal Stress (psi)

Figure B-30: Plot of the shear behavior for sample S-30.

122

700 600 500 y = 0.5377x + 338.19 400 300 y = 0.348x + 151.83 200

Shear Stress (psi) Stress Shear 100 0 0 100 200 300 400 500 600 Normal Stress (psi)

Figure B-31: Plot of the shear behavior for sample S-31.

300 y = 0.382x + 105.06 250

200

150 y = 0.278x + 38.766 100

Shear Stress (psi) Stress Shear 50

0 0 100 200 300 400 500 normal Stress (psi)

Figure B-32: Plot of the shear behavior for sample S-32.

123

500 450 400 y = 0.5x + 264.22 350 300 y = 0.3x + 198.51 250 200 150

Shear Stress (psi) Stress Shear 100 50 0 0 100 200 300 400 500 Normal Stress (psi)

Figure B-33: Plot of the shear behavior for sample S-33.

800 700 600 y = 0.5399x + 451.33 500 400 300 y = 0.4632x + 147.33 200 Shear Stress (psi) Stress Shear 100 0 0 100 200 300 400 500 Normal Stress (psi)

Figure B-34: Plot of the shear behavior for sample S-34.

124

700 y = 0.5725x + 399.5 600 500 400 y = 0.5074x + 319.88 300 200

Shear Stress (psi) Stress Shear 100 0 0 50 100 150 200 250 300 350 400 Normal Stress (psi)

Figure B-35: Plot of the shear behavior for sample S-35.

250

y = 0.5864x + 49.108 200

150 y = 0.5017x + 21.559

100

Shear Stress (psi) Stress Shear 50

0 0 50 100 150 200 250 300 350 Normal Stress (psi)

Figure B-36: Plot of the shear behavior for sample S-36.

125

250 y = 0.2227x + 130.05 200

150

100 y = 0.1798x + 45.738

Shear Stress (psi) Stress Shear 50

0 0 100 200 300 400 500 Normal Stress (psi)

Figure B-37: Plot of the shear behavior for sample S-37.

600

500 y = 0.3983x + 301.47 400

300 y = 0.3362x + 135.59 200

Shear Stress (psi) Stress Shear 100

0 0 100 200 300 400 500 600 Normal Stress (psi)

Figure B-38: Plot of the shear behavior for sample S-38.

126

800 y = 0.2475x + 542.75 700 600 500 400 300 y = 0.2067x + 252.66 200 Shear Stress (psi) Stress Shear 100 0 0 100 200 300 400 500 600 700 800 Normal Stress (psi)

Figure B-39: Plot of the shear behavior for sample S-39.

700 y = 0.5555x + 313.82 600

500

400

300 y = 0.4078x + 138.42 200 ShearStress (psi) 100

0 0 100 200 300 400 500 600 Normal Stress (psi)

Figure B-40: Plot of the shear behavior for sample S-40.

127

1200 y = 0.5649x + 594.72 1000 800 600

400 y = 0.4058x + 256.93

Shear Stress (psi) Stress Shear 200 0 0 100 200 300 400 500 600 700 800 Normal Stress (psi)

Figure B-41: Plot of the shear behavior for sample S-41.

350 y = 0.2455x + 170.14 300 250 200 y = 0.1872x + 133.56 150 100

Shear Stress Shear (psi) 50 0 0 100 200 300 400 500 600 700 Normal Stress (psi)

Figure B-42: Plot of the shear behavior for sample S-42.

128

2500 y = 0.681x + 974.31 2000

1500

1000 y = 0.5521x + 311.37 500 Shear Stress (psi) Stress Shear

0 0 500 1000 1500 2000 Normal Stress (psi)

Figure B-43: Plot of the shear behavior for sample S-43.

1800 1600 y = 0.5813x + 1137.9 1400 1200 1000 800 600 y = 0.4648x + 445.82 400 Shear Stress Shear (psi) 200 0 0 100 200 300 400 500 600 700 800 Normal Stress (psi)

Figure B-44: Plot of the shear behavior for sample S-44.

129

160 y = 0.4435x + 42.27 140 120 100 80 y = 0.2476x + 37.506 60 40 Shear Stress (psi) Stress Shear 20 0 0 50 100 150 200 250 300 Normal Stress (psi)

Figure B-45: Plot of the shear behavior for sample S-45.

800 y = 0.5089x + 514.8 700 600 500 400 y = 0.3688x + 367.65 300 200 Shear Stress (psi) Stress Shear 100 0 0 50 100 150 200 250 300 350 400 Normal Stress (psi)

Figure B-46: Plot of the shear behavior for sample TS-1.

130

400 y = 0.3346x + 217.88 350 300 250 200 y = 0.2028x + 140.96 150 100 Shear Stress (psi) Stress Shear 50 0 0 100 200 300 400 500 Normal Stress (psi)

Figure B-47: Plot of the shear behavior for sample TS-2.

300 y = 0.634x + 74.13 250

200

150

100 y = 0.2958x + 39.758 Shear Stress (psi) Stress Shear 50

0 0 50 100 150 200 250 300 350 Normal Stress (psi)

Figure B-48: Plot of the shear behavior for sample TS-3.

131

1800 y = 0.4347x + 1156.1 1600 1400 1200 1000 800 600 y = 0.359x + 481.27 400 Shear Stress (psi) Stress Shear 200 0 0 200 400 600 800 1000 Normal Stress (psi)

Figure B-48: Plot of the shear behavior for sample TS-4.

APPENDIX C

GRAIN SIZE ANALYSIS RESULTS

132 133

Table C: Percentage clay (< 0.002 mm) and clay-size (< 0.004 mm) particles for the collected mudrock samples.

% Clay % Clay Sample Number Type <0.002 mm <0.004 mm 1 Mudstone 24 35 2 Siltstone 17 22 3 Mudstone 27 35 4 Silty Shale 16 19 5 Siltstone 21 27 6 Silty Shale 19 27 7 Silty Shale 22 29 8 Siltstone 24 31 9 Mudstone 29 42 10 Claystone 41 53 11 Siltstone 17 22 12 Siltstone 21 27 13 Mudstone 28 36 14 Claystone 38 52 15 Silty Shale 21 31 16 Siltstone 24 28 17 Claystone 41 53 18 Mudstone 25 33 19 Siltstone 18 22 20 Mudstone 29 33 21 Siltstone 16 26 22 Mud Shale 25 33 23 Siltstone 14 18 24 Claystone 45 57 25 Siltstone 17 28 26 Siltstone 15 23 27 Siltstone 12 22 28 Mudstone 39 43 29 Claystone 77 82 30 Mudstone 32 39

134

Table C (Continued)

% Clay % Clay Sample Number Type <0.002 mm <0.004 mm 31 Mud Shale 31 41 32 Mud Shale 28 36 33 Claystone 38 51 34 Claystone 38 50 35 Claystone 39 53 36 Claystone 39 53 37 Claystone 61 76 38 Mudstone 32 45 39 Mudstone 29 39 40 Clayey Shale 46 64 41 Silty Shale 18 24 42 Silty Shale 19 24 43 Silty Shale 19 31 44 Silty Shale 19 29 45 Silty Shale 17 27 TS-1 Claystone 36 51 TS-2 Mudstone 32 48 TS-3 Siltstone 18 31 TS-4 Silty Shale 24 29

135

100 90

80 70 60

Percent Finer by Weight Weight by Finer Percent 30

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-1: Grain size distribution curve for sample S-1.

100 90

80 70 60

50 40 30

Percent Finerby Weight 20 10 0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-2: Grain size distribution curve for sample S-2. 136

100

90 80 70 60

50 40

30 Percent FinerWeight by 20

10 0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-3: Grain size distribution curve for sample S-3.

100 90

80 70 60

50 40 30

Percent Finer by Weight 20 10

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-4: Grain size distribution curve for sample S-4. 137

100

70 60

Percent Finer by Weight by Finer Percent 30 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-5: Grain size distribution curve for sample S-5.

100

90 80 70

60 50

40 30 by Weight Finer Percent 20 10 0

0.001 0.01 0.1 1 Grain Size (mm)

Figure C-6: Grain size distribution curve for sample S-6. 138

100

90 80 70 60

50 40 30

Percent Finer by Weight 20

10 0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-7: Grain size distribution curve for sample S-7.

100

90 80

70 60

50 40 30 PercentFinerby Weight 20 10 0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-8: Grain size distribution curve for sample S-8. 139

100

90 80

70 60

50 40 30

Percent Finer by Weight 20

10 0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-9: Grain size distribution curve for sample S-9.

100

Percent Finer byWeight Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-10: Grain size distribution curve for sample S-10. 140

100

90 80

70 60

50 40

30 Percent Finer by Weight Finer Percent 20 10 0

0.001 0.01 0.1 1 Grain Size (mm)

Figure C-11: Grain size distribution curve for sample S-11.

100 90 80 70

60 50 40 30 Weight by Finer Percent 20 10 0 0.001 0.01 0.1 1 Grain Size (mm) Figure C-12: Grain size distribution curve for sample S-12. 141

100

80 70

Weight by Finer Percent 30 20

0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-13: Grain size distribution curve for sample S-13.

100 90 80 70

60 50 40 30

Percent Finer by Weight 20 10

0 0.001 0.01 0.1 1 Grain Size (mm) Figure C-14: Grain size distribution curve for sample S-14. 142

100

90 80

70 60

50 40 30

Weight by Finer Percent 20 10

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-15: Grain size distribution curve for sample S-15.

100

Weight by Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-16: Grain size distribution curve for sample S-16. 143

100

90 80 70

60 50 40

30 Percent Finer by Weight by Finer Percent 20 10

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-17: Grain size distribution curve for sample S-17.

100

Percent Finer by Weight 20

0.001 0.01 0.1 1 Grain Size (mm)

Figure C-18: Grain size distribution curve for sample S-18. 144

100

Percent Finer by Weight by Finer Percent 20

0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-19: Grain size distribution curve for sample S-19.

100

Weight by Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-20: Grain size distribution curve for sample S-20. 145

100

Weight by Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-21: Grain size distribution curve for sample S-21.

100

Weight by Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-22: Grain size distribution curve for sample S-22. 146

100

Percent Finer by Weight by Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-23: Grain size distribution curve for sample S-23.

100

Percent Finer by Weight 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-24: Grain size distribution curve for sample S-24. 147

100

Weight by Finer Percent 20

0 0.00 0.01 0.10 1.00 Grain Size (mm)

Figure C-25: Grain size distribution curve for sample S-25.

100 90 80 70

60 50 40 30

Weight by Finer Percent 20 10 0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-26: Grain size distribution curve for sample S-26. 148

100

90 80

70 60

50 40 30

Weight by Finer Percent 20 10 0 0.001 0.01 0.1 1 Grain Size (mm) Figure C-27: Grain size distribution curve for sample S-27.

100

Percent Finerby Weight 20

0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-28: Grain size distribution curve for sample S-28. 149

100

90 80 70

50 40 30 Weight by Finer Percent 20 10 0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-29: Grain size distribution curve for sample S-29.

100

90 80 70

50 40 30 Weight by Finer Percent 20 10 0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-30: Grain size distribution curve for sample S-30. 150

100

Weight by Finer Percent 20

0 0.001 0.010 0.100 1.000

Grain Size (mm) Figure C-31: Grain size distribution curve for sample S-31.

100

Weight by Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-32: Grain size distribution curve for sample S-32. 151

100

Percent Finer by Weight by Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm) Figure C-33: Grain size distribution curve for sample S-33.

100 90 80 70

60 50 40 30 Weight by Finer Percent 20 10

0 0.001 0.01 0.1 1 Grain Size (mm) Figure C-34: Grain size distribution curve for sample S-34. 152

100 90

80 70 60

50 40 30 Percent Finer by Weight by Finer Percent 20

10 0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-35: Grain size distribution curve for sample S-35.

100 90 80 70

60 50 40 30 by Weight Finer Percent 20 10 0 0.001 0.01 0.1 1 Grain Size (mm) Figure C-36: Grain size distribution curve for sample S-36. 153

100 90 80 70

60 50

40 30 Weight by Finer Percent 20 10 0

0.001 0.01 0.1 1 Grain Size (mm)

Figure C-37: Grain size distribution curve for sample S-37.

100 90

80 70 60

50 40 30

Percent Finerby Weight 20 10

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-38: Grain size distribution curve for sample S-38. 154

100 90

80 70 60

50 40 30 Percent Finer by Weight 20

10 0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-39: Grain size distribution curve for sample S-39.

100 90 80 70

60 50

40 30 Weight by Finer Percent 20 10 0

0.001 0.01 0.1 1 Grain Size (mm)

Figure C-40: Grain size distribution curve for sample S-40. 155

100

90 80

70 60

50 40 30

Percent Finerby Weight 20

10 0 0.001 0.01 0.1 1

Grain Size (mm) Figure C-41: Grain size distribution curve for sample S-41.

100 90 80 70

60 50

40 30

P % remaining in suspension in remaining % P 20 10

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-42: Grain size distribution curve for sample S-42. 156

100

90 80

70 60

50 40 30

Premaining % in suspension 20 10 0 0.001 0.010 0.100 1.000 Grain Size (mm) Figure C-43: Grain size distribution curve for sample S-43.

100

90 80 70

60 50

40 30 20 Premaining % in suspension 10 0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-44: Grain size distribution curve for sample S-44. 157

100

Weight by Finer Percent 20

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-45: Grain size distribution curve for sample S-45.

100 90 80 70

60 50

40 30 Weight by Finer Percent 20 10

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-46: Grain size distribution curve for sample TS-1. 158

100 90

80 70 60

50 40 30

Weight by Finer Percent 20

10 0 0.001 0.01 0.1 1 Grain Size (mm) Figure C-47: Grain size distribution curve for sample TS-2.

100

90 80

70 60

50 40 30

Weight by Finer Percent 20 10 0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-48: Grain size distribution curve for sample TS-3. 159

100 90

80 70

60 50

40 30 Percent Finer by Weight by Finer Percent 20 10

0 0.001 0.01 0.1 1 Grain Size (mm)

Figure C-49: Grain size distribution curve for sample TS-4.

APPENDIX D

X-RAY DIFFRACTION ANALYSIS RESULTS

160 161

Table D-1: Quantitative clay mineral fraction results for the tested samples (Calculated from the X-ray Diffraction intensities).

Weight % Clay Minerals Clay Fraction 0.002 mm Sample No. (X100) % Chlorite Kaolinite Illite Mixed Mont. S-1 0.0 4.4 13.1 82.5 0.0 0.24 S-2 1.6 62.7 29.7 6.0 0.0 0.17 S-3 0.0 34.7 38.2 27.1 0.0 0.27 S-4 3.7 45.9 20.6 29.8 0.0 0.16 S-5 1.7 43.4 36.1 18.8 0.0 0.21 S-6 1.3 50.4 42.7 5.6 0.0 0.19 S-7 1.8 40.3 53.2 4.7 0.0 0.22 S-8 2.5 38.9 35.9 22.7 0.0 0.24 S-9 4.5 34.7 33.0 27.8 0.0 0.29 S-10 2.5 39.8 51.3 6.4 0.0 0.41 S-11 1.9 94.3 3.8 0.0 0.0 0.17 S-12 0.8 57.1 31.4 10.7 0.0 0.21 S-13 0.0 3.9 50.7 45.4 0.0 0.28 S-14 0.0 80.9 5.8 13.3 0.0 0.38 S-15 5.8 63.0 31.2 0.0 0.0 0.21 S-16 0.0 95.9 0.0 4.1 0.0 0.24 S-17 0.0 47.7 11.1 39.0 2.2 0.41 S-18 0.0 97.4 0.0 0.3 2.2 0.25 S-19 0.0 11.6 63.1 25.2 0.0 0.18 S-20 2.2 25.7 58.7 13.3 0.0 0.29 S-21 0.0 11.3 49.3 0.7 38.7 0.16 S-22 2.2 11.1 20.4 57.1 9.2 0.25 S-23 0.0 7.8 8.8 14.3 69.1 0.14 S-24 0.0 40.8 8.8 45.4 5.0 0.45 S-25 3.1 22.4 74.5 0.0 0.0 0.17 S-26 0.0 14.7 60.2 25.1 0.0 0.15 S-27 0.0 72.8 0.0 27.2 0.0 0.12 S-28 3.7 69.9 8.8 17.7 0.0 0.39 Mixed.: Mixed-layer clay Mont.: Montmorillonite

162

Table D-1 (continued)

Weight % Clay Minerals Clay Fraction 0.002 mm Sample No. (X100) % Chlorite Kaolinite Illite Mixed. Mont. S-29 0.0 68.9 4.5 26.5 0.0 0.77 S-30 1.3 13.8 43.6 41.3 0.0 0.32 S-31 3.1 39.1 39.4 18.4 0.0 0.31 S-32 0.0 42.3 33.8 23.9 0.0 0.28 S-33 2.6 79.7 17.7 0.0 0.0 0.38 S-34 3.2 73.6 23.2 0.0 0.0 0.38 S-35 6.8 58.1 33.5 1.6 0.0 0.39 S-36 6.3 52.2 40.3 1.2 0.0 0.39 S-37 3.0 9.0 11.0 53.0 24.0 0.61 S-38 0.0 12.0 34.0 54.0 0.0 0.32 S-39 0.0 22.0 37.0 41.0 0.0 0.29 S-40 3.1 39.1 39.4 18.4 0.0 0.46 S-41 1.9 31.5 56.9 9.7 0.0 0.18 S-42 1.7 12.9 81.9 3.5 0.0 0.19 S-43 3.1 22.4 74.5 0.0 0.0 0.19 S-44 1.9 45.9 27.8 24.4 0.0 0.19 S-45 0.0 31.2 64.4 4.4 0.0 0.17 Mixed.: Mixed-layer clay Mont.: Montmorillonite

163

Table D-2: Quantitative clay mineral results with respect to the whole rock for the tested samples.

Weight % Clay Minerals Whole Rock Sample No. Exp. Chlorite Kaolinite Illite Mixed. Mont. Non-Exp. S-1 0.0 1.1 3.1 19.8 0.0 19.8 4.2 S-2 0.3 10.7 5.0 1.0 0.0 1.0 16.0 S-3 0.0 9.4 10.3 7.3 0.0 7.3 19.7 S-4 0.6 7.3 3.3 4.8 0.0 4.8 11.2 S-5 0.4 9.1 7.6 3.9 0.0 3.9 17.1 S-6 0.2 9.6 8.1 1.1 0.0 1.1 17.9 S-7 0.4 8.9 11.7 1.0 0.0 1.0 21.0 S-8 0.6 9.3 8.6 5.4 0.0 5.4 18.6 S-9 1.3 10.1 9.6 8.1 0.0 8.1 20.9 S-10 1.0 16.3 21.0 2.6 0.0 2.6 38.4 S-11 0.3 16.0 0.6 0.0 0.0 0.0 17.0 S-12 0.2 12.0 6.6 2.2 0.0 2.2 18.8 S-13 0.0 1.1 14.2 12.7 0.0 12.7 15.3 S-14 0.0 30.7 2.2 5.1 0.0 5.1 32.9 S-15 1.2 13.2 6.6 0.0 0.0 0.0 21.0 S-16 0.0 23.0 0.0 1.0 0.0 1.0 23.0 S-17 0.0 19.6 4.6 16.0 0.9 16.9 24.1 S-18 0.0 24.4 0.0 0.1 0.6 0.6 24.4 S-19 0.0 2.1 11.4 4.5 0.0 4.5 13.4 S-20 0.6 7.5 17.0 3.9 0.0 3.9 25.1 S-21 0.0 1.8 7.9 0.1 6.2 6.3 9.7 S-22 0.6 2.8 5.1 14.3 2.3 16.6 8.4 S-23 0.0 1.1 1.2 2.0 9.7 11.7 2.3 S-24 0.0 18.4 4.0 20.4 2.3 22.7 22.3 S-25 0.5 3.8 12.7 0.0 0.0 0.0 17.0 S-26 0.0 2.2 9.0 3.8 0.0 3.8 11.2 S-27 0.0 8.7 0.0 3.3 0.0 3.3 8.7 S-28 1.4 27.3 3.4 6.9 0.0 6.9 32.1 Mixed.: Mixed-layer clay Mont.: Montmorillonite Exp.: Total expandable clay minerals Non-Exp.: Total non-expandable minerals

164

Table D-2 (continued)

Weight % Clay Minerals Whole Rock

Exp. Sample No. Chlorite Kaolinite Illite Mixed Mont. Non-Exp. S-29 0.0 53.1 3.5 20.4 0.0 20.4 56.5 S-30 0.4 4.4 14.0 13.2 0.0 13.2 18.8 S-31 1.0 12.1 12.2 5.7 0.0 5.7 25.3 S-32 0.0 11.8 9.5 6.7 0.0 6.7 21.3 S-33 1.0 30.3 6.7 0.0 0.0 0.0 38.0 S-34 1.2 28.0 8.8 0.0 0.0 0.0 38.0 S-35 2.7 22.7 13.1 0.6 0.0 0.6 38.4 S-36 2.5 20.4 15.7 0.5 0.0 0.5 38.5 S-37 1.8 5.5 6.7 32.3 14.6 47.0 14.0 S-38 0.0 3.8 10.9 17.3 0.0 17.3 14.7 S-39 0.0 6.4 10.7 11.9 0.0 11.9 17.1 S-40 1.4 18.0 18.1 8.5 0.0 8.5 37.5 S-41 0.3 5.7 10.2 1.7 0.0 1.7 16.3 S-42 0.3 2.5 15.6 0.7 0.0 0.7 18.3 S-43 0.6 4.3 14.2 0.0 0.0 0.0 19.0 S-44 0.4 8.7 5.3 4.6 0.0 4.6 14.4 S-45 0.0 5.3 10.9 0.7 0.0 0.7 16.3 Mixed.: Mixed-layer clay Mont.: Montmorillonite Exp.: Total expandable clay minerals Non-Exp.: Total non-expandable minerals

165

Table D-3: Quantitative clay mineral fraction results for the verification tested samples (Calculated from the X-ray Diffraction intensities).

Weight % Clay Minerals Clay Fraction 0.002 mm Sample No. Chlorite Kaolinite Illite Mixed Mont. (X100) % TS-1 11 22 61 6 0 0.36 TS-2 11 21 54 14 0 0.32 TS-3 6 11 29 60 0 0.18 TS-4 3 7 76 14 0 0.24 Mixed.: Mixed-layer clay Mont.: Montmorillonite Exp.: Total expandable clay minerals Non-Exp.: Total non-expandable minerals

Table D-4: Quantitative clay mineral results with respect to the whole rock for the verification tested samples.

Weight % Clay Minerals Sample No. Whole Rock Chlorite Kaolinite Illite Mixed Mont. Exp. Non-Exp. TS-1 4.0 7.9 22.0 2.2 0.0 2.2 33.8 TS-2 3.5 6.7 17.3 4.5 0.0 4.5 27.5 TS-3 1.1 2.0 5.2 10.8 0.0 10.8 8.3 TS-4 0.7 1.7 18.2 3.4 0.0 3.4 20.6 Mixed.: Mixed-layer clay Mont.: Montmorillonite Exp.: Total expandable clay minerals Non-Exp.: Total non-expandable minerals

APPENDIX E

WATER CONTENT

166 167

Table E-1: Water Content for the tested samples.

Water Content (%) Sample No. Test 1 Test 2 Test 3 Average S-1 7.63 9.19 7.81 8.21 S-2 1.9 1.1 1.41 1.47 S-3 2.94 2.08 2.01 2.34 S-4 1.33 3.44 2.61 2.46 S-5 0.5 2.24 1.24 1.33 S-6 2.05 0.49 1.07 1.20 S-7 0.88 3.16 2.08 2.04 S-8 1.2 3.89 2.36 2.48 S-9 6.7 7.23 5.96 6.63 S-10 3.78 3.92 4.23 3.98 S-11 1.41 1.04 1.24 1.23 S-12 0.52 1.91 1.16 1.20 S-13 3.54 4.86 4.21 4.20 S-14 21.25 18.12 19.25 19.54 S-15 1.8 2.69 2.05 2.18 S-16 0.52 1.31 1.21 1.01 S-17 13.61 15.53 14.98 14.7 S-18 3.36 6.18 4.12 4.55 S-19 2.51 6.12 3.78 4.14 S-20 1.06 3.02 2.78 2.29 S-21 0.79 2.01 1.23 1.34 S-22 2.16 3.34 2.95 2.82 S-23 1.52 2.28 1.71 1.84 S-24 9.3 11.8 11.53 10.87 S-25 0.64 2.72 2.08 1.81 S-26 2.8 1.38 1.56 1.91 S-27 0.75 1.17 0.99 0.97 S-28 5.05 9.52 7.53 7.37 S-29 13.36 15.19 14.97 14.51 S-30 1.47 5.75 3.65 3.62

168

Table E-1 (Continued)

Water Content (%) Sample No. Test 1 Test 2 Test 3 Average S-31 6 8.73 8.09 7.61 S-32 4.43 8.87 7.81 7.04 S-33 1.16 1.52 1.09 1.26 S-34 1.45 1.57 1.48 1.50 S-35 1.71 1.82 1.65 1.73 S-36 2.79 2.61 2.65 2.68 S-37 4.94 4.99 4.93 4.95 S-38 5.35 5.34 5.28 5.32 S-39 6.90 6.93 6.85 6.89 S-40 22.90 22.69 22.8 22.80 S-41 0.86 1.75 1.15 1.25 S-42 3.68 1.87 2.34 2.63 S-43 0.58 0.88 1.08 0.85 S-44 0.91 0.85 1.19 0.98 S-45 2.29 2.39 2.40 2.36

169

Table E-2: Water content results for the verification test samples.

Water Content (%)

Sample No. Test 1 Test 2 Test 3 Average TS-1 2.65 2.59 2.55 2.60 TS-2 4.51 4.23 3.98 4.24 TS-3 1.53 1.61 1.57 1.57 TS-4 1.92 1.85 2.1 1.96

APPENDIX F

DRY DENSITY, SPECIFIC GRAVITY, VOID RATIO

170 171

Table F-1: Dry density test results for the tested samples.

Dry Density (lb/ft 3) Sample No. Test 1 Test 2 Test 3 Test 4 Average

S-1 157.3 151.1 142.3 147.3 149.5 S-2 167.3 155.4 154.8 159.8 159.3 S-3 159.8 154.2 147.3 152.3 153.4 S-4 176.0 179.8 154.8 167.9 169.6 S-5 153.6 151.7 149.2 152.9 151.9 S-6 175.4 181.7 177.3 177.9 178.1 S-7 151.1 171.7 140.5 152.9 154.0 S-8 152.3 164.2 153.6 157.3 156.9 S-9 143.0 146.1 143.0 144.2 144.1 S-10 166.1 147.3 159.2 155.4 157.0 S-11 160.4 161.7 159.2 159.2 160.1 S-12 173.5 151.1 156.1 160.4 160.3 S-13 156.7 153.6 161.7 156.7 157.2 S-14 142.3 138.0 139.2 139.8 139.8 S-15 159.8 169.2 173.5 167.9 167.6 S-16 135.5 142.3 142.3 138.0 139.5 S-17 131.1 130.5 139.2 134.2 133.8 S-18 143.0 140.5 141.1 141.7 141.6 S-19 144.8 149.2 154.2 149.8 149.5 S-20 167.9 160.4 164.8 164.2 164.3 S-21 162.3 149.2 168.6 157.9 159.5 S-22 154.2 151.7 153.6 153.6 153.3 S-23 151.7 152.9 154.2 154.2 153.3 S-24 126.7 135.5 131.7 131.1 131.3 S-25 142.3 143.0 141.1 143.0 142.3

172

Table F-1 (continued)

Dry Density (lb/ft 3) Sample No. Test 1 Test 2 Test 3 Test 4 Average

S-26 144.2 144.2 148.6 144.8 145.5 S-27 148.0 149.8 148.6 147.3 148.4 S-28 133.6 127.4 139.8 134.2 133.8 S-29 139.8 137.3 139.8 139.8 139.2 S-30 134.2 146.1 142.3 141.7 141.1 S-31 137.3 134.2 136.7 134.8 135.8 S-32 152.3 151.7 146.1 149.2 149.8 S-33 158.6 169.2 151.7 160.4 160.0 S-34 149.8 152.9 157.9 152.9 153.4 S-35 157.9 154.8 153.6 156.1 155.6 S-36 160.4 157.3 169.8 177.9 166.4 S-37 126.7 128.6 130.5 128.0 128.4 S-38 146.7 147.3 145.5 146.7 146.5 S-39 143.6 146.7 147.3 144.2 145.5 S-40 129.2 123.6 119.2 122.4 123.6 S-41 157.9 157.3 160.4 159.2 158.7 S-42 148.6 143.0 141.1 145.5 144.5 S-43 166.1 167.3 150.5 159.8 160.9 S-44 161.1 161.1 155.4 160.4 159.5 S-45 159.8 154.8 157.9 156.7 157.3

173

Table F-2: Dry density test results for verification tested samples.

Dry Density (lb/ft 3) Sample No. Test 1 Test 2 Test 3 Test 4 Average

TS-1 155.45 154.2 154.82 154.81 154.82 TS-2 156.8 156.51 155.9 154.99 156.05 TS-3 162.31 159.82 158.57 159.95 160.16 TS-4 150.45 150.45 149.83 149.88 150.15

174

Table F-3: Specific gravity and void ratio results for the tested samples.

Specific Gravity

Sample No. Test 1 Test 2 Test 3 Average Void Ratio S-1 2.71 2.75 2.47 2.64 0.102 S-2 2.75 2.77 2.75 2.76 0.081 S-3 2.74 2.77 2.80 2.77 0.127 S-4 2.79 2.78 2.76 2.78 0.023 S-5 2.76 2.74 2.75 2.75 0.130 S-6 2.94 2.95 2.97 2.95 0.034 S-7 2.77 2.78 2.81 2.79 0.130 S-8 2.74 2.74 2.76 2.74 0.090 S-9 2.62 2.56 2.54 2.57 0.113 S-10 2.63 2.64 2.59 2.62 0.041 S-11 2.76 2.73 2.74 2.74 0.068 S-12 2.73 2.71 2.74 2.73 0.063 S-13 2.64 2.72 2.68 2.68 0.064 S-14 2.48 2.48 2.50 2.49 0.111 S-15 2.78 2.74 2.75 2.76 0.027 S-16 2.56 2.58 2.57 2.57 0.149 S-17 2.53 2.50 2.49 2.51 0.171 S-18 2.55 2.56 2.60 2.57 0.133 S-19 2.68 2.66 2.63 2.66 0.110 S-20 2.67 2.66 2.73 2.69 0.021 S-21 2.71 2.72 2.73 2.72 0.064 S-22 2.67 2.69 2.71 2.69 0.095 S-23 2.68 2.67 2.68 2.68 0.091 S-24 2.76 2.77 2.75 2.76 0.312 S-25 2.76 2.75 2.74 2.75 0.206 S-26 2.59 2.62 2.58 2.6 0.115 S-27 2.62 2.61 2.61 2.61 0.097 S-28 2.81 2.76 2.62 2.73 0.274 S-29 2.72 2.69 2.70 2.7 0.210 S-30 2.69 2.70 2.68 2.69 0.190

175

Table F-3 (continue)

Specific Gravity

Sample No. Test 1 Test 2 Test 3 Average Void Ratio S-31 2.61 2.69 2.63 2.64 0.213 S-32 2.65 2.66 2.66 2.65 0.104 S-33 2.73 2.75 2.70 2.73 0.065 S-34 2.79 2.85 2.72 2.79 0.135 S-35 2.73 2.71 2.77 2.74 0.099 S-36 2.73 2.82 2.79 2.78 0.043 S-37 2.58 2.58 2.47 2.54 0.234 S-38 2.69 2.68 2.65 2.67 0.137 S-39 2.64 2.59 2.71 2.64 0.133 S-40 2.67 2.66 2.63 2.65 0.338 S-41 2.81 2.80 2.81 2.81 0.105 S-42 2.72 2.71 2.70 2.71 0.170 S-43 2.75 2.73 2.76 2.75 0.066 S-44 2.73 2.72 2.75 2.73 0.068 S-45 2.71 2.72 2.71 2.71 0.075

176

Table F-4: Specific gravity and void ratio results for proof tested samples.

Specific Gravity

Sample No. Test 1 Test 2 Test 3 Average Void Ratio TS-1 2.77 2.78 2.78 2.78 0.119 TS-2 2.58 2.57 2.61 2.59 0.032 TS-3 2.75 2.74 2.75 2.75 0.070 TS-4 2.57 2.59 2.61 2.59 0.070

APPENDIX G

ABSORPTION TEST RESULTS

177 178

Table G-1: Absorption test results for the tested samples.

Absorption (%) Sample No. Test 1 Test 2 Test 3 Average

S-1 62.44 82.10 49.14 64.60 S-2 8.47 6.82 7.72 7.70 S-3 6.35 7.76 8.25 7.50 S-4 5.42 5.82 4.53 5.30 S-5 4.07 5.42 3.58 4.40 S-6 3.54 4.10 3.67 3.80 S-7 3.04 4.41 4.74 4.10 S-8 3.87 4.09 4.57 4.20 S-9 60.61 63.01 67.58 63.70 S-10 45.36 49.28 37.29 44.00 S-11 3.17 3.33 2.69 3.10 S-12 2.97 4.66 3.69 3.80 S-13 40.04 34.14 35.95 36.70 S-14 37.29 53.25 46.83 45.80 S-15 4.36 3.58 4.55 4.20 S-16 7.42 5.61 5.76 6.30 S-17 79.40 75.97 83.65 79.70 S-18 11.33 9.16 9.46 10.00 S-19 9.33 8.40 8.70 8.80 S-20 12.71 8.83 10.81 10.80 S-21 1.77 2.23 1.39 1.80 S-22 14.74 15.16 13.89 14.60 S-23 3.70 4.18 3.92 3.90 S-24 66.02 66.67 66.16 66.30 S-25 14.80 14.34 13.93 14.40 S-26 3.05 3.47 3.29 3.30 S-27 1.98 1.87 1.85 1.90 S-28 27.32 26.50 27.13 27.00 S-29 61.79 62.24 62.45 62.20 S-30 6.78 5.85 6.49 6.40

179

Table G-1 (continued)

Absorption (%) Sample No. Test 1 Test 2 Test 3 Average

S-31 21.83 22.07 22.22 22.00 S-32 25.60 24.32 23.47 24.50 S-33 14.17 13.26 14.74 14.10 S-34 5.73 6.27 5.45 5.82 S-35 19.72 22.11 19.17 20.30 S-36 11.02 10.28 9.18 10.20 S-37 22.20 22.30 22.30 22.30 S-38 20.30 21.00 21.10 20.80 S-39 7.60 7.70 7.50 7.60 S-40 25.40 23.90 24.50 24.60 S-41 3.13 3.02 3.33 3.20 S-42 4.22 3.99 4.30 4.20 S-43 1.06 0.77 0.97 0.93 S-44 1.90 1.84 1.89 1.90 S-45 4.24 4.00 4.36 4.20

180

Table G-2: Absorption test results for the verification test samples.

Absorption (%) Sample No. Test 1 Test 2 Test 3 Average

TS-1 10.41 10.72 10.70 10.61 TS-2 5.60 5.41 5.72 5.58 TS-3 9.08 8.94 8.83 8.95 TS-4 3.78 3.64 3.59 3.67

APPENDIX H

ADSORPTION TEST RESULTS

181 182

Table H-1: Adsorption test results for the tested samples

Adsorption (%) Sample No. Test 1 Test 2 Test 3 Average

S-1 7.04 6.74 6.76 6.85 S-2 2.00 1.95 1.76 1.90 S-3 3.19 2.36 3.57 3.04 S-4 2.31 2.03 1.90 2.08 S-5 1.22 1.20 1.34 1.25 S-6 1.73 1.81 1.64 1.73 S-7 1.35 1.26 1.15 1.25 S-8 1.50 1.30 1.53 1.44 S-9 7.34 7.39 7.47 7.39 S-10 3.08 3.14 5.50 3.91 S-11 1.60 2.12 1.47 1.73 S-12 1.45 1.30 1.37 1.37 S-13 3.43 3.33 3.57 3.45 S-14 5.67 4.94 4.98 5.20 S-15 2.02 2.09 2.27 2.13 S-16 1.42 1.57 1.61 1.53 S-17 9.97 9.47 8.54 9.33 S-18 2.28 2.64 2.46 2.46 S-19 2.67 2.63 2.60 2.64 S-20 1.49 1.95 1.70 1.71 S-21 1.47 1.55 1.38 1.46 S-22 3.31 3.21 3.35 3.29 S-23 3.24 2.93 2.66 2.94 S-24 5.51 6.22 5.05 5.59 S-25 2.23 2.39 2.43 2.35 S-26 2.43 1.80 2.24 2.16 S-27 1.16 1.20 1.14 1.17 S-28 3.00 3.20 5.12 3.77 S-29 9.59 9.63 10.82 10.01 S-30 2.23 2.59 2.27 2.36

183

Table H-1 (continued)

Adsorption (%) Sample No. Test 1 Test 2 Test 3 Average

S-31 3.81 3.98 3.96 3.91 S-32 3.42 3.52 3.61 3.52 S-33 2.35 2.81 2.38 2.52 S-34 1.87 1.51 1.54 1.64 S-35 2.53 2.96 2.94 2.81 S-36 2.16 2.36 1.86 2.13 S-37 11.72 10.13 10.59 10.81 S-38 3.63 3.25 3.73 3.54 S-39 4.16 3.95 4.53 4.21 S-40 9.65 9.96 9.10 9.57 S-41 1.21 1.34 1.35 1.30 S-42 1.44 2.13 1.54 1.70 S-43 0.43 0.53 0.19 0.38 S-44 1.43 1.49 1.39 1.44 S-45 1.49 1.52 1.46 1.49

184

Table H-2: Adsorption test results for the verification tested samples.

Adsorption (%) Sample No. Test 1 Test 2 Test 3 Average

TS-1 3.63 3.64 3.53 3.60 TS-2 3.76 3.58 3.62 3.65 TS-3 2.67 2.58 2.78 2.68 TS-4 2.31 2.42 2.25 2.33

APPENDIX I

ATTERBERG LIMITS TEST RESULTS

185 186

Table I-1: Atterberg Limits results for the tested samples.

Sample No. Liquid Limit Plastic Limit Plasticity Index

S-1 33.0 23.8 9.2 S-2 22.3 17.2 5.1 S-3 26.7 19.8 6.9 S-4 26.6 24.8 1.8 S-5 25.4 18.9 6.5 S-6 22.1 14.6 7.5 S-7 30.1 21.2 8.9 S-8 23.4 18.8 4.6 S-9 31.1 22.3 8.9 S-10 28.1 20.4 7.7 S-11 21.8 15.4 6.4 S-12 21.9 14.6 7.2 S-13 28.2 19.8 8.4 S-14 48.4 28.9 19.5 S-15 24.3 16.0 8.2 S-16 17.4 14.7 2.8 S-17 37.9 25.6 12.3 S-18 28.0 19.4 8.6 S-19 20.8 15.7 5.1 S-20 21.5 14.8 6.7 S-21 21.0 14.6 6.4 S-22 30.8 18.4 12.4 S-23 26.0 18.0 8.0 S-24 75.0 30.0 45.0 S-25 39.6 26.2 13.4 S-26 27.6 19.3 8.3 S-27 26.1 20.1 6.0 S-28 19.5 14.6 4.9 S-29 55.1 21.3 33.8 S-30 26.1 19.0 7.1

187

Table I-1 (continued)

Sample No. Liquid Limit Plastic Limit Plasticity Index

S-31 27.7 19.2 8.5 S-32 34.0 27.6 6.4 S-33 32.7 23.4 9.4 S-34 28.3 24.6 3.7 S-35 27.1 22.8 4.3 S-36 27.3 24.0 3.2 S-37 65.0 23.0 42.0 S-38 30.0 18.0 12.0 S-39 27.0 17.0 10.0 S-40 52.5 29.1 23.4 S-41 27.8 23.3 4.5 S-42 24.3 20.6 3.7 S-43 22.7 21.3 1.4 S-44 20.5 18.8 1.6 S-45 32.8 24.5 8.3

188

Table I-2: Atterberg Limits results for the verification tested samples.

Sample No. Liquid Limit Plastic Limit Plasticity Index

TS-1 34.1 23.2 10.9 TS-2 30.0 13.0 17.0 TS-3 33.0 26.9 6.1 TS-4 33.1 22.0 11.1

APPENDIX J

SLAKE DURABILITY TEST RESULTS

189 190

Table J-1: Slake durability test results for the tested samples.

Slake Durability Index 2 (%) Sample No. Test 1 Test 2 Test 3 Average

S-1 1.03 1.67 1.30 1.3 S-2 94.01 88.42 90.16 90.9 S-3 95.75 94.39 95.41 95.2 S-4 91.95 94.22 92.80 93.0 S-5 98.79 94.76 96.52 96.7 S-6 95.50 96.31 95.84 95.9 S-7 94.51 95.10 94.87 94.8 S-8 95.03 95.03 95.05 95.0 S-9 2.94 3.69 1.98 2.9 S-10 8.27 8.96 9.24 8.8 S-11 95.70 96.96 96.13 96.3 S-12 95.26 95.77 95.51 95.5 S-13 18.49 22.17 20.19 20.3 S-14 40.91 32.06 34.82 35.9 S-15 97.68 97.14 97.39 97.4 S-16 86.74 74.51 79.93 80.4 S-17 2.39 1.22 1.45 1.7 S-18 91.55 91.06 91.29 91.3 S-19 76.06 87.54 81.54 81.7 S-20 50.04 41.13 47.57 46.3 S-21 97.86 97.50 97.61 97.7 S-22 96.57 96.74 96.71 96.7 S-23 98.18 98.13 98.17 98.2 S-24 1.78 1.54 1.59 1.6 S-25 98.91 99.04 98.95 99.0

191

Table J (continued)

Slake Durability Index (Id 2 ) (%) Sample No. Test 1 Test 2 Test 3 Average

S-26 97.95 98.54 98.45 98.3 S-27 99.12 98.08 98.56 98.6 S-28 53.10 35.80 39.89 42.9 S-29 33.31 11.78 17.59 20.9 S-30 92.98 89.67 90.12 90.9 S-31 79.38 80.39 78.98 79.6 S-32 33.84 29.91 31.29 31.7 S-33 88.28 87.56 88.53 88.1 S-34 95.16 94.68 95.46 95.1 S-35 77.95 78.23 77.68 78.0 S-36 76.46 80.41 77.36 78.1 S-37 3.20 2.95 2.92 3.0 S-38 56.22 56.32 55.45 56.0 S-39 90.77 89.03 90.31 90.0 S-40 60.45 58.06 58.61 59.0 S-41 98.19 97.72 97.87 97.9 S-42 98.31 97.63 97.72 97.9 S-43 99.01 98.87 98.90 98.9 S-44 98.52 98.73 98.61 98.6 S-45 96.3 97.3 89.6 94.4

192

Table J-2: Slake durability test results for the verification samples.

Slake Durability Index (Id 2 ) (%) Sample No. Test 1 Test 2 Test 3 Average

TS-1 43.21 57.01 50.12 50.11 TS-2 78.11 70.23 74.56 74.30 TS-3 53.12 42.96 48.92 48.33 TS-4 99.01 99.01 99.05 99.02

APPENDIX K

UNIVARIATE DATA ANALYSIS RESULTS

193 194

Table K-1: Univariate summary statistics of variables for all mudrocks.

Statistical Parameters Variables Standard Minimum Maximum Mean Variance Kurtosis Skewness Deviation < 0.002 mm 12 77 28.2 163.7 12.8 3.5 1.6 < 0.004 mm 18 82 37.1 213.4 14.6 1.1 1.2 Chlorite % 0 2.6 0.5 0.4 0.7 2.2 1.6 Kaolinite % 1.1 53.1 12.2 108.2 10.4 3.5 1.6 Illite % 0 21 8.5 26.3 5.1 -0.5 2.5 Mixed % 0 32.3 6.1 52.1 7.2 2.5 1.6 Mon. % 0 14.6 0.8 7.3 2.7 15.9 4 Exp. % 0 47 6.9 75.7 8.7 8.2 2.5 Non Exp. % 2.3 56.5 21.2 112 10.6 1.4 1 Exp./Non Exp. 0 5 0.6 1.2 1.1 8.9 3 W% 0.5 22.9 4.5 24.6 5 4.3 2.1 Dry D. (lb/ft 3) 119.2 181.7 150.3 138.6 11.8 -0.1 -0.1 Sp. Gr. 2.5 3 2.7 0.008 0.1 0.7 -0.2 e 0.01 0.4 0.1 0.006 0.08 1.3 1 AB % 0.8 83.7 17.9 432.9 20.8 1.7 1.6 AD % 0.2 11.7 3.3 6.5 2.6 2 1.7 L.L 17.4 75 30.3 135.9 11.7 4.9 2.2 P.L 14 30.2 20.5 18.1 4.3 -0.4 0.5 P.I 0.5 45.2 9.8 86.2 9.3 6.4 2.6 Id 1 99.1 71.4 1201 34.7 -0.5 -1.1 Cohesion (lb/ft 2) 5095.7 163857.6 52141 1.59E+09 39857 0.4 1 Friction Angle 10.9 35.8 24.9 60.1 7.8 -1.2 -0.3

195

Table K-2: Univariate summary statistics of variables for claystones.

Statistical Parameters Variables Standard Minimum Maximum Mean Variance Kurtosis Skewness Deviation < 0.002 mm 38 77 45.7 157.9 12.6 1.9 1.8 < 0.004 mm 50 82 58 119 10.9 0.7 1.5 Chlorite % 0 2.7 1 1 1 -1.2 0.4 Kaolinite % 5.5 53.1 24.5 146 12.1 1.5 1 Illite % 2.2 21 8.6 35 5.9 -0.2 1 Mixed % 0 32.3 9.8 125 11.2 -0.7 0.8 Mon. % 0 14.6 1.8 19.5 4.4 4.4 2.7 Exp. % 0 47 11.6 219 14.8 14.8 1.4 Non Exp. % 14 56.5 34.1 127.4 11.3 11.3 0.1 Exp./Non Exp. 0 3.3 0.6 1 1 1 2..3 W% 1.1 21.3 7.6 42.6 6.5 6.5 0.7 Dry D. (lb/ft 3) 126.7 169.8 145.9 160.7 12.7 12.7 0.1 Sp. Gr. 2.5 2.8 2.7 0.1 0.1 0.1 -0.4 e 0.01 0.4 0.1 0.008 0.1 0.1 0.6 AB % 5.5 83.7 37.1 644.7 25.4 25.4 0.4 AD % 1.5 11.7 5.4 11.5 3.4 3.4 0.6 L.L 27.1 75 42.5 284.3 16.9 16.9 0.8 P.L 18.2 30.2 24.2 12.3 3.5 3.5 0.3 P.I 2.3 45.2 18.3 244.9 15.6 15.6 0.7 Id (%) 1.2 95.5 41.1 1447.2 38 -1.8 0.3 Cohesion (lb/ft 2) 7071.6 64991.5 30335 3.72E+08 19293 -1 0.5 Friction Angle 10.9 30.9 22.4 59.2 7.7 -1.5 -0.4

196

Table K-3: Univariate summary statistics of variables for mudstones.

Statistical Parameters Variables Standard Minimum Maximum Mean Variance Kurtosis Skewness Deviation < 0.002 mm 24 39 29.4 16.8 4.1 1.1 1.1 < 0.004 mm 33 45 38 17 4.1 -1.2 0.4 Chlorite % 0 1.4 0.4 0.3 0.5 -0.3 1.1 Kaolinite % 1.1 27.3 9.5 77.6 8.8 -0.03 1.2 Illite % 0 17 9.3 27.9 5.3 -0.9 -0.4 Mixed % 0.1 19.8 10.1 33.8 5.8 -0.7 0.01 Mon. % 0 0.6 0.1 0.03 0.2 6.3 2.8 Exp. % 0.6 19.8 10.1 32.7 5.7 -0.8 0.07 Non Exp. % 4 32 19.2 51.4 7.1 0.6 -0.3 Exp./Non Exp. 0.03 4.7 0.9 1.8 1.3 5.2 2.5 W% 1 9.5 5.1 5.1 2.3 -0.8 0.01 Dry D. (lb/ft 3) 127.4 164.8 147.7 83.7 9.1 -0.2 0.1 Sp. Gr. 2.5 2.8 2.7 0.007 0.1 -0.1 -0.4 e 0.01 0.35 0.1 0.006 0.1 2.2 1.2 AB % 5.8 82.1 25.5 497.5 22.3 0.2 1.1 AD % 1.5 7.4 3.9 3.4 1.8 -0.4 0.9 L.L 19.5 33 27.1 15.7 4 -0.3 -0.6 P.L 14.2 24.6 18.9 7.9 2.8 -0.4 0.1 P.I 4.6 12.1 8.3 4 2 -0.4 0.2 Id 1 95.8 53.7 1296.7 36 -1.5 -0.2 Cohesion (lb/ft 2) 13859.4 78261.1 47310 5.32E+08 23060.9 -1.5 0.1 Friction Angle 13.1 29.6 19.1 33.3 5.8 -1.2 0.5

197

Table K-4: Univariate summary statistics of variables for siltstones.

Statistical Parameters Variables Standard Minimum Maximum Mean Variance Kurtosis Skewness Deviation < 0.002 mm 12 24 18 13.5 3.7 -0.8 0.3 < 0.004 mm 18 31 24.7 12.9 3.6 -0.8 -0.04 Chlorite % 0 0.6 0.2 0.05 0.2 -1 0.7 Kaolinite % 1.1 23 8.3 41.8 6.5 0.1 0.8 Illite % 0 12.7 5.9 18.8 4.3 -1.3 -0.1 Mixed % 0 5.4 2.3 3.4 1.8 -1.3 0.2 Mon. % 0 9.7 1.3 9.5 3.1 2.9 2.1 Exp. % 0 11.7 3.6 10.1 3.2 1.4 1.2 Non Exp. % 2.3 23 14.4 29.5 5.4 0.1 -0.7 Exp./Non Exp. 0 5 0.6 1.8 1.4 8 3 W% 0.5 6.1 1.7 1.2 1.1 6.1 2.1 Dry D. (lb/ft 3) 138 168 151.8 60.7 7.8 -0.4 0.3 Sp. Gr. 2.6 2.8 2.7 0.004 0.1 -1 -0.7 e 0.01 0.2 0.1 0.002 0.04 0.2 0.2 AB % 1.4 14.8 5.3 12.3 3.5 1.8 1.5 AD % 1.1 3.2 1.8 0.3 0.6 -0.6 0.7 L.L 17.4 39.6 24.4 28.9 5.4 3.4 1.8 P.L 14 26.5 17.8 10.7 3.3 1.7 1.3 P.I 2.1 13.7 6.7 6.4 2.5 2.5 1.3 Id 74.5 99.1 94 43.9 6.6 2.4 -1.8 Cohesion (lb/ft 2) 10748.9 132302.9 67413 1.46E+09 38161.6 -1 0.1 Friction Angle 22 35.8 32.4 15.3 3.9 2.2 -1.7

198

Table K-5: Univariate summary statistics of variables for shales.

Statistical Parameters Variables Standard Minimum Maximum Mean Variance Kurtosis Skewness Deviation < 0.002 mm 16 46 23.1 63.2 8 3.4 1.9 < 0.004 mm 19 64 31.9 117.5 10.8 4.1 2 Chlorite % 0 1.4 0.5 0.1 0.4 -0.2 0.8 Kaolinite % 2.5 18.1 8.5 19.5 4.4 -0.3 0.5 Illite % 3.3 18.1 10.1 18.1 4.3 -0.8 0.2 Mixed % 0 14.3 3.8 16.8 4.1 1.1 1.3 Mon. % 0 2 0.2 0.4 0.6 9.4 3.3 Exp. % 0 16.6 4 21 4.6 2.3 1.6 Non Exp. % 8.4 37.5 19.1 47.8 6.9 2.2 1.2 Exp./Non Exp. 0 2 0.3 0.3 0.5 7.7 2.9 W% 0.5 22.9 4.3 34.1 5.8 6.1 2.6 Dry D. (lb/ft 3) 119.2 181.7 154.4 206.5 14.4 0.1 -0.5 Sp. Gr. 2.6 3 2.7 0.01 0.1 1.6 1.1 e 0.01 0.4 0.1 0.01 0.1 1.3 1.3 AB % 0.8 25.6 9 76.7 8.8 -0.8 1 AD % 0.2 9.9 2.6 5.1 2.3 5.3 2.3 L.L 20.5 52.5 28.9 63.9 8 4 1.9 P.L 14.3 30 21.6 17.7 4.2 -0.6 0.4 P.I 0.5 23.8 7.4 33.9 5.8 2.5 3.3 Id 29.9 99 87.4 383.7 19.6 1.5 -2.1 Cohesion (lb/ft 2) 5095.7 163857.6 53979 2.91E+09 53979.4 -0.7 0.9 Friction Angle 13.8 34.3 24.4 41.4 6.4 -0.9 -0.5

APPENDIX L

BIVARIATE PLOTS

199 200

400

300

200 Cohesion Rt Sqr

100

10 20 30 40 50 60 70 80 percent Clay <.002

Figure L-1: Bivariate plot of cohesion versus percent clay <0.002.

400

300

200 Cohesion Rt Sqr

100

1.0 1.2 1.4 1.6 1.8 2.0 LOG percent Clay <.002

Figure L-2: Bivariate plot of cohesion versus log percent clay <0.002.

201

400

300

200 Rt Cohesion Sqr

100

3 4 5 6 7 8 9 Sqr Rt percent Clay <.002

Figure L-3: Bivariate plot of cohesion versus square root percent clay <0.002.

400

300

200 Rt Cohesion Sqr

100

20 40 60 80 percent Clay <.004 Figure L-4: Bivariate plot of cohesion versus percent clay <0.004. 202

400

300

200 Rt Cohesion Sqr

100

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 LOG percent Clay <.004

Figure L-5: Bivariate plot of cohesion versus log percent clay <0.004.

400

300

200

Rt Cohesion Sqr

100

4 5 6 7 8 9 10 Sqr Rt percent Clay <.004

Figure L-6: Bivariate plot of cohesion versus square root of percent clay <0.004. 203

400

300

200 Cohesion Sqr Rt

100

0 0.5 1 1.5 2 2.5 3 percent Chlorite

Figure L-7: Bivariate plot of cohesion versus percent chlorite.

400

300

200 SqrRt Cohesion

100

0 0.5 1 1.5 2 Sqr Rt percent Chlorite Figure L-8: Bivariate plot of cohesion versus square root of chlorite. 204

400

300

200

SqrRt Cohesion

100

0 10 20 30 40 50 60 percent Kaolinite

Figure L-9: Bivariate plot of cohesion versus percent kaolonite.

400

300

200 SqrRt Cohesion

100

1 2 3 4 5 6 7 8 Sqr Rt Kaolinite Figure L-10: Bivariate plot of cohesion versus square root kaolinite. 205

400

300

200 Cohesion Rt Sqr

100

0 5 10 15 20 25 percent Illite

Figure L-11: Bivariate plot of cohesion versus percent illite.

400

300

200 Cohesion Rt Sqr

100

0 1 2 3 4 5 Sqr Rt Illite

Figure L-12: Bivariate plot of cohesion versus square root illite. 206

400

300

200 RtCohesion Sqr

100

0 10 20 30 40 percent Mixed

Figure L-13: Bivariate plot of cohesion versus percent mixed layer clays.

400

300

200 Cohesion Rt Sqr

100

0 1 2 3 4 5 6 Sqr Rt Mixed

Figure L-14: Bivariate plot of cohesion versus square root percent mixed layer clays.

207

400

300

200 Cohesion Rt Sqr

100

0 3 6 9 12 15 percent Mont.

Figure L-15: Bivariate plot of cohesion versus percent montmorillonite.

400

300

200 Sqr Cohesion Sqr Rt

100

0 1 2 3 4 Sqr Rt Mont.

Figure L-16: Bivariate plot of cohesion versus square root montmorillonite. 208

400

300

200 Sqr Rt Cohesion Rt Sqr

100

0 10 20 30 40 50 percent Exp.

Figure L-17: Bivariate plot of cohesion versus percent expandable clays.

400

300

200 Cohesion Rt Sqr

100

0 1 2 3 4 5 6 7 Sqr RT Exp.

Figure L-18: Bivariate plot of cohesion versus square root percent expandable clays. 209

400

300

200 Sqr RtCohesion Sqr

100

0 10 20 30 40 50 60 percent Non-Exp.

Figure L-19: Bivariate plot of cohesion versus percent non-expandable clays.

400

300

200 Cohesion Rt Sqr

100

1 2 3 4 5 6 7 8 Sqr Rt Non-Exp.

Figure L-20: Bivariate plot of cohesion versus square root non-expandable clays.

210

400

300

200 Sqr Rt Cohesion Rt Sqr

100

0 1 2 3 4 5 6 Exp / Non-Exp Figure L-21: Bivariate plot of cohesion versus expandable to non-expandable clays ratio.

400

300

200 Cohesion Sqr Rt

100

0 0 1 2 2 2 Sqr Rt Exp/Non-Exp

Figure L-22: Bivariate plot of cohesion versus square root expandable to nonexpendable. 211

400

300

200 Cohesion Rt Sqr

100

0 5 10 15 20 25 percent Water Content

Figure L-23: Bivariate plot of cohesion versus water content.

400

300

200 Cohesion Rt Sqr

100

0.0 0.5 1.0 LOG percent Water Content

Figure L-24: Bivariate plot of cohesion versus log water content. 212

400

300

200 Sqr Rt Cohesion Rt Sqr

100

1 2 3 4 5 Sqr Rt percent Water Content

Figure L-25: Bivariate plot of cohesion versus square root water content.

400

300

200 Cohesion Rt Sqr

100

120 130 140 150 160 170 180 Dry Density pcf Figure L-26: Bivariate plot of cohesion versus dry density. 213

400

300

200 RtSqr Cohesion

100

2.08 2.10 2.12 2.14 2.16 2.18 2.20 2.22 2.24 2.26 LOG Dry Density

Figure L-27: Bivariate plot of cohesion versus log dry densiy.

400

300

200 Sqr Rt Cohesion Rt Sqr

100

11.0 11.5 12.0 12.5 13.0 13.5 Sqr Rt Dry Density

Figure L-28: Bivariate plot of cohesion versus square root of dry density. 214

400

300

200 Cohesion Rt Sqr

100

2.4 2.5 2.6 2.7 2.8 2.9 3.0 Sp. Gr

Figure L-29: Bivariate plot of cohesion versus specific gravity.

400

300

200 Cohesion Rt Sqr

100

0.40 0.42 0.44 0.46 LOG Sp.Gr Figure L-30: Bivariate plot of cohesion versus log specific gravity. 215

400

300

200

Cohesion SqrRt

100

1.575 1.600 1.625 1.650 1.675 1.700 1.725 Sqr Rt Sp. Gr

Figure L-31: Bivariate plot of cohesion versus square root specific gravity.

400

300

200 Cohesion Rt Sqr

100

0.0 0.1 0.2 0.3 Void Ratio Figure L-32: Bivariate plot of cohesion versus void ratio. 216

400

300

200 Sqr Rt Cohesion Rt Sqr

100

-1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 LOG Void Ratio Figure L-33: Bivariate plot of cohesion versus log void ratio.

400

300

200 Sqr Rt Cohesion Rt Sqr

100

0.1 0.2 0.3 0.4 0.5 0.6 Sqr Rt Void Ratio

Figure L-34: Bivariate plot of cohesion versus square root void ratio. 217

400

300

200 Cohesion Rt Sqr

100

0 20 40 60 80 percent Absorption

Figure L-35: Bivariate plot of cohesion versus absorption.

400

300

200 Cohesion SqrRt

100

-0.5 0.0 0.5 1.0 1.5 2.0 LOG percent Absorption

Figure L-36: Bivariate plot of cohesion versus log absorption. 218

400

300

200 Cohesion Rt Sqr

100

0 2 4 6 8 Sqr Rt percent Absorption

Figure L-37: Bivariate plot of cohesion versus square root absorption.

400

300

200 RtCohesion Sqr

100

0 2 4 6 8 10 12 percent Adsorption

Figure L-38: Bivariate plot of cohesion versus adsorption. 219

400

300

200

Cohesion SqrRt

100

-0.5 0.0 0.5 1.0 LOG percent Adsorption

Figure L-39: Bivariate plot of cohesion versus log adsorption.

400

300

200 Sqr Rt Cohesion Rt Sqr

100

0.5 1.0 1.5 2.0 2.5 3.0 3.5 Sqr Rt percent Adsorption

Figure L-40: Bivariate plot of cohesion versus square root adsorption. 220

400

300

200 Cohesion Rt Sqr

100

0 20 40 60 80 100 Percent Absorption+Adsorption

Figure L-41: Bivariate plot of cohesion versus absorption and adsorption.

400

300

200 Sqr Rt Cohesion Rt Sqr

100

0.0 0.5 1.0 1.5 2.0 LOG Percent Absorption+Adsorption

Figure L-42: Bivariate plot of cohesion versus log absorption and adsorption. 221

400

300

200 Sqr Rt Cohesion Rt Sqr

100

0 2 4 6 8 10 Sqr Rt Percent Absorption+Adsorption

Figure L-43: Bivariate plot of cohesion versus square root absorption and adsorption

400

300

200 RtCohesion Sqr

100

10 20 30 40 50 60 70 80 Liquid Limit

Figure L-44: Bivariate plot of cohesion versus liquid limit. 222

400

300

200 Rt Cohesion Sqr

100

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 LOG Liquid Limit

Figure L-45: Bivariate plot of cohesion versus log liquid limit.

400

300

200 RtCohesion Sqr

100

4 5 6 7 8 9 Sqr Rt Liquid Limit

Figure L-46: Bivariate plot of cohesion versus square root liquid limit. 223

400

300

200

SqrRt Cohesion

100

15 20 25 30 Plastic Limit

Figure L-47: Bivariate plot of cohesion versus plastic limit.

400

300

200 SqrRt Cohesion

100

1.2 1.3 1.4 1.5 LOG Plastic Limit

Figure L-48: Bivariate plot of cohesion versus log plastic limits. 224

400

300

200 Cohesion RtSqr

100

3.5 4.0 4.5 5.0 5.5 Sqr Rt Plastic Limit

Figure L-49: Bivariate plot of cohesion versus square root plastic limit.

400

300

200 Cohesion Rt Sqr

100

0 10 20 30 40 50 Plasticity Index Figure L-50: Bivariate plot of cohesion versus plasticity Index. 225

400

300

200 Cohesion Sqr Rt

100

-1 0 1 2 LOG Plasticity Index

Figure L-51: Bivariate plot of cohesion versus log plasticity index.

400

300

200

RtCohesion Sqr

100

0 1 2 3 4 5 6 7 Sqr Rt Plasticity Index

Figure L-52: Bivariate plot of cohesion versus square root plasticity index. 226

400

300

200 Sqr Rt Cohesion Rt Sqr

100

0 20 40 60 80 100 Slake Durability

Figure L-53: Bivariate plot of cohesion versus slake durability.

400

300

200 SqrRtCohesion

100

0.0 0.5 1.0 1.5 2.0 Log Slake Durability

Figure L-54: Bivariate plot of cohesion versus log slake durability. 227

400

300

200 Cohesion Rt Sqr

100

0 2 4 6 8 10 Sqr Rt Slake Durability

Figure L-55: Bivariate plot of cohesion versus square root slake durability.

400

300

200 Cohesion Rt Sqr

100

0 20 40 60 80 100 1- Slake Durability

Figure L-56: Bivariate plot of cohesion versus 1 – slake durability. 228

400

300

200 Cohesion Rt Sqr

100

0 2 4 6 8 10 Sqr Rt 1- Slake Durability

Figure L-57: Bivariate plot of cohesion versus square root 1 – slake durability.

Friction angle 20

10 20 30 40 50 60 70 80 percent Clay <.002

Figure L-58: Bivariate plot of friction angle versus percent clay <0.002 229

Friction angle 20

1.0 1.2 1.4 1.6 1.8 2.0 LOG percent Clay <.002

Figure L-59: Bivariate plot of friction angle versus log percent clay <0.002

Friction Friction angle

3 4 5 6 7 8 9 Sqr Rt percent Clay <.002

Figure L-60: Bivariate plot of friction angle versus square root percent clay <0.002 230

Friction angle

20 40 60 80 percent Clay <.004

Figure L-61: Bivariate plot of friction angle versus percent clay <0.004

Frictionangle

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 LOG percent Clay <.004

Figure L-62: Bivariate plot of friction angle versus log percent clay <0.002. 231

angle Friction 20

4 5 6 7 8 9 10 Sqr Rt percent Clay <.004

Figure L-63: Bivariate plot of friction angle versus square root percent clay <0.004

Friction angle 20

0 0.5 1 1.5 2 2.5 3 percent Chlorite

Figure L-64: Bivariate plot of friction angle versus percent chlorite. 232

angle Friction 20

0 0.5 1 1.5 2 Sqr Rt Chlorite

Figure L-65: Bivariate plot of friction angle versus square root chlorite.

Frictionangle 20

0 10 20 30 40 50 60 percent Kaolinite Figure L-66: Bivariate plot of friction angle versus percent kaolinite. 233

angle Friction 20

1 2 3 4 5 6 7 8 Sqr Rt Kaolinite

Figure L-67: Bivariate plot of friction angle versus square root kaolinite.

angle Friction 20

0 5 10 15 20 25 percent Illite

Figure L-68: Bivariate plot of friction angle versus percent illite. 234

angle Friction 20

0 1 2 3 4 5 Sqr Rt Illite

Figure L-69: Bivariate plot of friction angle versus square root illite clay.

Friction angle Friction

0 10 20 30 40 percent Mixed Figure L-70: Bivariate plot of friction angle versus mixed layers clays. 235

angle Friction 20

0 1 2 3 4 5 6 Sqr Rt Mixed

Figure L-71: Bivariate plot of friction angle versus square root mixed layers clays.

angle Friction 20

0 3 6 9 12 15 percent Mont. Figure L-72: Bivariate plot of friction angle versus montimorllinite. 236

Frictionangle 20

0 1 2 3 4 Sqr Rt Mont.

Figure L-73: Bivariate plot of friction angle versus square root montimorllinite.

angle Friction 20

0 10 20 30 40 50 percent Exp. Figure L-74: Bivariate plot of friction angle versus expandable clays. 237

angle Friction 20

0 1 2 3 4 5 6 7 Sqr RT Exp.

Figure L-75: Bivariate plot of friction angle versus square root expandables.

angle Friction 20

0 10 20 30 40 50 60 percent Non-Exp. Figure L-76: Bivariate plot of friction angle versus percent non-expandable clays. 238

Friction angle 20

1 2 3 4 5 6 7 8 Sqr Rt Non-Exp.

Figure L-77: Bivariate plot of friction angle versus non-expandable clays.

Friction angle Friction

0 1 2 3 4 5 6 Exp / Non-Exp Figure L-78: Bivariate plot of friction angle versus expandable to non-expandable clays. 239

angle Friction 20

0.0 0.5 1.0 1.5 2.0 2.5 Sqr Rt Exp/Non-Exp

Figure L-79: Bivariate plot of friction angle versus square root expandable to non- expandable clays.

Friction angle Friction

0 5 10 15 20 25 Percent Water Content Figure L-80: Bivariate plot of friction angle versus water content. 240

angle Friction 20

0.0 0.5 1.0 LOG Percent Water Content

Figure L-81: Bivariate plot of friction angle versus log water content.

Friction angle Friction

1 2 3 4 5 Sqr Rt Percent Water Content Figure L-82: Bivariate plot of friction angle versus square root water content. 241

angle Friction 20

120 130 140 150 160 170 180 Dry Density pcf

Figure L-83: Bivariate plot of friction angle versus dry density.

Friction angle Friction

2.08 2.10 2.12 2.14 2.16 2.18 2.20 2.22 2.24 2.26 LOG Dry Density Figure L-84: Bivariate plot of friction angle versus log dry density. 242

Friction angle Friction

10 11 12 12 12 13 14 Sqr Rt Dry Density

Figure L-85: Bivariate plot of friction angle versus square root dry density.

Frictionangle 20

2.4 2.5 2.6 2.7 2.8 2.9 3.0 Sp. Gr Figure L-86: Bivariate plot of friction angle versus specific gravity. 243

angle Friction 20

0.40 0.42 0.44 0.46 LOG Sp.Gr

Figure L-87: Bivariate plot of friction angle versus log specific gravity.

Frictionangle 20

1.575 1.600 1.625 1.650 1.675 1.700 1.725 Sqr Rt Sp. Gr Figure L-88: Bivariate plot of friction angle versus square root specific gravity. 244

Friction angle 20

0.0 0.1 0.2 0.3 Void Ratio

Figure L-89: Bivariate plot of friction angle versus void ratio.

Friction angle 20

-1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 LOG Void Ratio Figure L-90: Bivariate plot of friction angle versus log void ratio. 245

Frictionangle 20

0 0 0 0 0 1 Sqr Rt Void Ratio

Figure L-91: Bivariate plot of friction angle versus square root void ratio.

angle Friction 20

0 20 40 60 80 percent Absorption

Figure L-92: Bivariate plot of friction angle versus percent absorption. 246

Frictionangle 20

-0.5 0.0 0.5 1.0 1.5 2.0 LOG percent Absorption

Figure L-93: Bivariate plot of friction angle versus log absorption.

angle Friction 20

0 2 4 6 8 Sqr Rt percent Absorption

Figure L-94: Bivariate plot of friction angle versus square root absorption. 247

angle Friction 20

0 2 4 6 8 10 12 percent Adsorption

Figure L-95: Bivariate plot of friction angle versus percent adsorption.

angle Friction 20

-0.5 0.0 0.5 1.0 LOG percent Adsorption Figure L-96: Bivariate plot of friction angle versus log adsorption. 248

25 angle Friction 20

0.5 1.0 1.5 2.0 2.5 3.0 3.5 Sqr Rt percent Adsorption

Figure L-97: Bivariate plot of friction angle versus square root absorption.

Friction angle 20

0 20 40 60 80 100 Absorption + Adsorption Figure L-98: Bivariate plot of friction angle versus absorption and adsorption. 249

Frictionangle 20

0.0 0.5 1.0 1.5 2.0 LOG Absorption + Adsorption Figure L-99: Bivariate plot of friction angle versus log absorption and adsorption.

Frictionangle 20

0 2 4 6 8 10 Sqr Rt Absorption + Adsorption Figure L-100: Bivariate plot of friction angle versus Square root absorption and adsorption. 250

25 angle Friction 20

10 20 30 40 50 60 70 80 Liquid Limit

Figure L-101: Bivariate plot of friction angle versus liquid limit.

Frictionangle 20

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 LOG Liquid Limit Figure L-102: Bivariate plot of friction angle versus log liquid limit. 251

Frictionangle 20

4 5 6 7 8 9 Sqr Rt Liquid Limit

Figure L-103: Bivariate plot of friction angle versus square root liquid limit.

angle Friction 20

15 20 25 30 Plastic Limit Figure L-104: Bivariate plot of friction angle versus plastic limit. 252

Frictionangle 20

1.2 1.3 1.4 1.5 LOG Plastic Limit

Figure L-105: Bivariate plot of friction angle versus log plastic limit

angle Friction 20

3.5 4.0 4.5 5.0 5.5 Sqr Rt Plastic Limit Figure L-106: Bivariate plot of friction angle versus square root plastic limit. 253

angle Friction

0 10 20 30 40 50 Plasticity Index

Figure L-107: Bivariate plot of friction angle versus plasticity index.

angle Friction 20

-1 0 1 2 LOG Plasticity Index Figure L-108: Bivariate plot of friction angle versus log plasticity index. 254

angle Friction 20

0 1 2 3 4 5 6 7 Sqr Rt Plasticity Index

Figure L-109: Bivariate plot of friction angle versus square root Plasticity index.

angle Friction 20

0 20 40 60 80 100 Slake Durability Figure L-110: Bivariate plot of friction angle versus slake durability. 255

angle Friction 20

0.0 0.5 1.0 1.5 2.0 Log Slake Durability

Figure L-111: Bivariate plot of friction angle versus log slake durability.

Frictionangle 20

0 2 4 6 8 10 Sqr Rt Slake Durability Figure L-112: Bivariate plot of friction angle versus square root slake durability. 256

Frictionangle 20

10 0 20 40 60 80 100 1- Slake Durability Figure L-113: Bivariate plot of friction angle versus 1- slake durability.

Frictionangle 20

0 2 4 6 8 10 Sqr Rt 1-Slake Durability Figure L-114: Bivariate plot of friction angle versus square root 1- slake durability.