UNIVERSITY OF CALGARY. Time-Independent and Time-Dependent Behavior of Clearwater Clay Shale Underneath

Transcription

1 UNIVERSITY OF CALGARY Time-Independent and Time-Dependent Behavior of Clearwater Clay Shale Underneath Large Storage Tanks Laboratory Testing and Numerical Modelling by Ramin Ghassemi A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN CIVIL ENGINEERING CALGARY, ALBERTA SEPTEMBER, 2016 Ramin Ghassemi 2016

2 Abstract The Clearwater clay shale overlays the Wabiskaw-McMurray bitumen deposit over most of the extent of Athabasca Oil Sands Area in northeastern Alberta, Canada. Both shortterm and long-term settlement need to be assessed in a standard foundation design. Accuracy of these assessments depend on the knowledge of the real soil behavior in the field. Therefore, characterizing the behavior of this shale is of prime importance from geotechnical engineering perspective. The goal of this research is to investigate timeindependent and time-dependent behavior of Clearwater clay shale in order to develop numerical tools for design, prediction, and analysis of structures over such clay shale formation. To this end, a set of laboratory testing and numerical modeling are completed. An extensive experimental study, including XRD analyses, free swell tests, oedometer tests, constant rate of strain consolidation tests, triaxial tests, and stress relaxation tests, was conducted on various facies of Clearwater Formations (Kcc-710, Kcb-700, Kcb-650, and Kca-625). The results of ten consolidated drained triaxial compression tests and two consolidated undrained triaxial tests were used to determine elastic parameters, Mohr- Coulomb shear parameters, parameters of the Chsoil model to characterize the timeindependent response of facies of the Clearwater clay shale. Stress relaxation behavior of facies of the Clearwater clay shale was experimentally examined. Scrutinizing the obtained results, an expression was suggested for stress relaxation of Clearwater clay shale based on the final relaxed normalized deviatoric stress and half relaxation time, the time elapsed for half the stress relaxation in term of stress takes place. Then, a novel application of parameters of stress relaxation test in a model to predict creep settlement was introduced. Hence, a rheological model, the Zener model, was ii

3 calibrated for facies of the Clearwater clay shale to predict the creep behavior under loading. The results were implemented in FLAC to predict Short-time and Long-time settlement of a test fill constructed on the Clearwater clay shale. The results of short-term analysis were in good agreement with the measured field data and those of the long-term analysis signified the importance of both creep and consolidation phenomena in the settlement assessment. Keywords: Clearwater clay shale, triaxial test, stress relaxation, creep, timeindependent, time-dependent, Chsoil model, Zener model, FLAC. iii

4 Acknowledgements Firstly, I would like to express my sincere gratitude to my advisor Prof. Ron Wong for his supports and for providing me with the opportunity to to pursue my Ph.D. study and related research, for his patience and persistence. The door to his office was always open whenever I ran into a trouble spot or had a question about my research. Besides my advisor, I would like to thank the rest of my thesis committee: Prof. Richard Wan, Prof. Jocelyn Grozic, Prof. Les Sudak, and Dr. Michael Hendry for their insightful comments and encouragement, but also for the hard questions which incented me to widen my research from various perspectives. My sincere thanks also go to Mr. Trempess Moore from Thurber Engineering Ltd., who provided me an opportunity to work there as an intern. I am also grateful to Mr. Iain Gidley from Thurber Engineering Ltd. for the assistance he provided during numerical simulation of this research project. I am thankful to Mr. Mirsad Berbic for his helps in the experimental study at University of Calgary. I thank my fellow colleagues Dr. Morteza Mohamadi, Mahdad Eghbalian, Dr. Mehdi Pouragha, Rajitha Eranga Wickramage, Mohammad Moravvej, Ahmad Booshehrian Pedram Kaheh, Abbas Pourdeilami, and Parham Joulani in Civil Engineering department for the stimulating discussions and for all the fun we have had in the last four years. The financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), Thurber Engineering Ltd., and the Department of Civil Engineering at University of Calgary is greatly appreciated. iv

5 Last but not the least, I would like to thank my family, my parents and my brothers for supporting me spiritually throughout my studies and my life in general. Also I thank my friends, particularly those in Calgary for all wonderful memories during the last four years. v

6 Dedication Dedicated to my father and my mother vi

7 Table of Contents Abstract... ii Acknowledgements... iv Dedication... vi Table of Contents... vii List of Tables... xii List of Figures and Illustrations...xv List of Symbols, Abbreviations and Nomenclature... xxiii Epigraph... xxviii CHAPTER 1: INTRODUCTION Significance of the Research Background Research objectives and scope Investigation of geotechnical properties of facies of Clearwater clay shale Determination of parameters of a constitutive model for geotechnical behavior of Clearwater clay shale Numerical modeling of performance of storage tanks over clay shale Organization of the thesis...5 CHAPTER 2: LITERATURE REVIEW Geology (geological history and stratigraphic framework) Geological framework of Western Canada Sedimentary Basin Geological history of Lower Cretaceous Mannville Group Clearwater Formation Athabasca Oil Sands area Fort McMurray stratigraphic framework Site characterization and subsurface conditions Clay Shale Clay shale classification Clay shale geological classification Clay shale engineering classification Clay shale characteristics Density Porosity Water content Permeability Mineralogy Microstructure Clearwater clay shale Cretaceous Clearwater Formation Studies on Clearwater clay shale Syncrude oil sands mine at north of Fort McMurray, Alberta Horizon oil sands project at north of Fort McMurray, Alberta Time-dependent behaviour of clays...34 vii

8 Creep Effects of fluctuations of temperature on time-dependant behavior Swelling of clay shale Stress relaxation Rate effects on clay shale - experimental studies Long-term strength Macrorheology (rheological models) Method of mechanical rheological models (differential approach) Maxwell material Kelvin material Zener s model Engineering theories of creep Method of integral representation (hereditary approach)...53 CHAPTER 3: EXPERIMENTAL WORK Test material Atterberg s limit and moisture content Specific gravity Organic content Dimensions and densities of the samples Swell tests Swelling anisotropy and its variation with smectite content Variation of swelling anisotropy with time (or swelling strain) Mineralogy X-ray diffraction (XRD) analysis XRD analyses results One-dimensional consolidation tests Oedometer consolidation tests Constant-rate-of-strain consolidation tests Triaxial tests detail and procedure Sample preparation Test apparatus and setup Test apparatus Sample setup Load and displacement transducers Triaxial tests detail and data reduction Results of consolidation tests Consolidated drained triaxial compression tests - Group A Test #6: consolidated drained triaxial compression test Saturation and consolidation Drained shearing Test #5: consolidated drained triaxial compression test Saturation and consolidation Drained shearing Consolidated drained triaxial compression tests - Group B Test #12: consolidated drained triaxial compression test Saturation and consolidation viii

9 Drained shearing Relaxation stages Test #1: consolidated drained triaxial compression test Saturation and consolidation Drained shearing Relaxation stages Test #2: consolidated drained triaxial compression test Saturation and consolidation Drained shearing Relaxation stages Test #3: consolidated drained triaxial compression test Saturation and consolidation Drained shearing Relaxation stages Test #4: consolidated drained triaxial compression test Saturation and consolidation Shearing stages Relaxation stages Consolidated drained triaxial compression tests - Group C Test #9: consolidated drained triaxial compression test Saturation and consolidation Shearing stages Relaxation stages Test #10: consolidated drained triaxial compression test Saturation and consolidation Shearing stages Relaxation stages Multistage consolidated drained triaxial compression test - Group D Test #11: consolidated drained triaxial compression test Consolidation Shearing stages Relaxation stages Consolidated undrained triaxial compression tests - Group E Test #7: consolidated undrained triaxial compression test Saturation and consolidation Shearing stages Test #8: consolidated undrained triaxial compression test Saturation and consolidation Shearing stages Corrections to triaxial test data Area corrections Barrelling Single-plane slip Membrane corrections Barrelling Slip plane ix

10 Side drain corrections Barrelling Slip plane Summary Analysis of triaxial test data Secant Young s modulus and Poisson s ratio Dependence of secant Young s modulus on confining pressure Estimation of Mohr-Coulomb shear parameters Correlations between results of triaxial tests and properties of samples Correlations with clay content Correlations with peak strength Analysis of results of stress relaxation tests CHAPTER 4: FLAC SIMULATION OF TEST FILL BASED ON TRIAXIAL TESTS DATA Model description Model geometry Fluid properties Boundary conditions Material properties Elastic properties Plastic properties (Mohr-Coulomb shear parameters) Undrained analyses Verification of geostatic stresses and hydrostatic pore pressure Numerical modeling cases Case 1: Poro-elastic analysis of a homogenous soil layer in undrained condition Case 2: Poro-elasto-plastic analysis of a homogenous soil layer in undrained condition Case 3: Poro-elastic analysis of a layered soil profile in undrained condition Case 4: Poro-elasto-plastic analysis of a layered soil profile in undrained condition Comparison of results of Cases 1-4 with field data and previous analyses Previous analyses by Moore (2007) and Moore et al. (2011) Comparison of models predictions with field data Numerical simulation implementing the Chsoil model (Cases 5, 6, and 7) Chsoil model description Mohr-Coulomb parameters Model specific parameters Dilation law Friction hardening Calibration of the Chsoil model parameters using the results of the triaxial tests Selected parameters Calibrated parameters Case 5: Test fill analysis using the Chsoil model x

11 4.9. Case 6: Test fill analysis using the modified Chsoil model Case 7: Test fill analysis using the improved Chsoil model Analysis of the creep effects in the field using the FLAC Selection of the creep constitutive law Maxwell viscoelastic model Burgers-creep viscoplastic model Zener s viscoplastic model Description of the deviatoric behavior of the Zener s viscoplastic model Description of the volumetric behavior of the Zener s viscoplastic model Estimation of the maximum creep time step Burgers and Zener model formulation Calibration of creep parameters of the Burgers-creep viscoplastic model using the relaxation test results Poro-elasto-visco-plastic (creep) analysis in undrained condition (Case 8) Poro-elasto-plastic analysis in drained condition (Case 9: consolidation analysis) Consolidation parameters Consolidation analysis results Poro-elasto-visco-plastic analysis in drained condition (Case 10: coupled creep-consolidation analysis) Analysis results CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS General Summary and Significance Summary and conclusions Index parameters and mineralogy Swell tests Triaxial tests (consolidation and shear) Triaxial tests (stress relaxation) Numerical analyses Recommendations for future studies BIBLIOGRAPHY xi

12 List of Tables Table 2.1. The Mannville Group sub-units in Athabasca region (Glass, 1997)...55 Table 2.2. The subdivisions of Wabiskaw Member (Haug, et al., 2014) Table 2.3. Facies classification for the Horizon oil sand project (Moore, 2007)...56 Table 2.4. Relation between investigated clay shale facies and the other stratigraphy units and formations (Moore, 2007)...57 Table 2.5. Shale geological classification (Underwood, 1967)...58 Table 2.6. Classification by British Standard Institute (1957)...59 Table 2.7. Morgenstern and Eigenbrod (1974) classification...60 Table 2.8. Porosity, depth, and densities of shales of Eau Claire Formation and Maquoketa Formation (Wisconsin Geological and Natural History Survey, 2013)...61 Table 2.9. Porosity of undisturbed shale of Oligocene and Miocene age from Eastern...61 Table Porosity and depth of shales of Cretaceous age...62 Table Swelling rate of shales and shaly limestones measured in free swell test (Lo et al., 1978)...63 Table Index parameters of Kca samples (Wedage et al., 1998)...64 Table Results of direct shear tests on Kca material (Wedage et al., 1998)...64 Table Grain size distribution, Atterberg s limits, and moisture content of the Clearwater facies at the West Tank Farm (Pinheiro et al., 2013)...65 Table Direct shear test results of the Clearwater facies at the West Tank Farm (Pinheiro et al., 2013)...66 Table Initial estimates of soil parameters for FLAC analysis (Moore, 2007)...67 Table Best fit soil properties for FLAC analysis (Moore et al., 2011)...68 Table Range of allowable temperature fluctuation for creep tests...69 Table 3.1. Results of Atterberg s limits and moisture content tests Table 3.2. Specific gravity of facies of Clearwater clay shale Table 3.3. Organic content of facies of Clearwater clay shale Table 3.4. Dimensions and densities of clay shale samples used in triaxial testing Table 3.5. Average values of density for facies of Clearwater clay shale Table 3.6. Mineralogy of Clearwater clay shale samples from XRD analyses Table 3.7. Clay mineral content of samples of clay shale facies from XRD analyses 153 Table 3.8. Clay mineral content from XRD analyses (illite and smectite separated)..154 Table 3.9. Average mineralogy of facies of clay shale from XRD analyses Table Average content of clay minerals of clay shale facies from XRD analyses (illite and smectite not separated) Table Average content of clay minerals of facies of clay shale from XRD analyses Table Estimated coefficient of consolidation and secondary compression index for each stress level in oedometer test (Kcb-700 facies) Table Estimated OCRs of clay shale layers Table Summary of one-dimensional consolidation tests on the Clearwater clay shale Table Triaxial tests matrix xii

13 Table Drainage conditions and pore pressure measurement methods in triaxial tests Table Estimated consolidation parameters from the consolidation stage of triaxial tests Table List of different stages in test #12, kcc-710 facies Table List of different stress relaxation stages in test #12, kcc-710 facies Table List of different stress relaxation stages in test #11, kcc-710 facies Table List of stages in test #1, Kca-625 facies Table List of stress relaxation stages in test #1, Kca-625 facies Table List of stages in test #2, Kca-625 facies Table Secant Young s modulus at different axial strains for different facies and confining pressures Table List of stress relaxation stages in test #2, Kca-625 facies Table Secant Young s modulus at different axial strains at the start and end of the stress relaxation stages Table List of stages in test #3, Kcb-700 facies Table Secant Young s modulus at different axial strains for tests under 100 kpa confining pressure Table List of stress relaxation stages in test #3, Kcb Table List of different stages in test #4, Kcb-650 facies Table Secant Young s modulus at different axial strains for tests under 100 kpa confining pressure Table List of different stress relaxation stages in test #4, Kcb-650 facies Table List of different stages in test #9, Kcb-700 facies Table List of different stress relaxation stages in test #9, Kcb-700 facies Table List of different stages in test #10, Kcb-650 facies Table List of stress relaxation stages in test #10, Kcb-650 facies Table List of different consolidation stages in test#11, kcc-710 facies Table List of different stages in test#11, kcc-710 facies Table List of different stress relaxation stages in test #11, kcc-710 facies Table Soil categories according to Black and Lee (1973) for the study of saturation effect Table List of different stages in test #7, Kcb Table Secant Young s modulus at different axial strains for tests under 500 kpa confining pressure Table Typical A-values at failure (Skempton, 1954) Table List of different stages in test #8, Kcb Table Secant Young s modulus at different axial strains for tests under 500 kpa confining pressure Table Measured shear band angles and calculated single-plane slip correction coefficient Table Summary of corrections to triaxial data Table Secant Young s modulus at different axial strains for different facies and confining pressures Table Average secant Young s modulus at different axial strains for different facies at confining pressures range of kpa xiii

14 Table Poisson s ratio calculated for facies of Clearwater clay shale at various axial strains Table Internal friction angle (at peak strength and post-peak) and cohesion for facies of Clearwater clay shale Table Parameters of lines fitted into results of stress relaxation tests conducted before the peak-strength (presented in Figure 3.123) Table Parameters of lines fitted into results of stress relaxation tests conducted before the peak-strength (presented in Figure 3.124) Table 4.1. Estimate of the coefficients of the earth pressure at rest of clay shale layers 296 Table 4.2. Layers properties and specifications in addition to the total stresses, effective stresses, and hydrostatic pore pressure at bottom of each layer Table 4.3. Comparison of hand-calculated values of vertical total stresses and pore pressures with those calculated by FLAC Table 4.4. Soil properties for FLAC analyses (Case 1) Table 4.5. Soil properties for FLAC analyses (Case 2) Table 4.6. Soil properties for FLAC analyses (Case 3) Table 4.7. Soil properties for FLAC analyses (Case 4) Table 4.8. Shear parameters determined from the triaxial tests Table 4.9. Shear parameters used in Chsoil model for fill test simulation after calibration Table Model predictions under 150 kpa applied load (Case 5) Table Soil properties for FLAC analysis using the Chsoil model (Case 5: original Chsoil model) Table Shear parameters used in the modified Chsoil model for fill test simulation Table Model predictions under 150 kpa applied load (Case 6) Table Soil properties for FLAC analysis using the Chsoil model (Case 6: modified Chsoil model) Table Shear parameters used in the improved Chsoil model for fill test simulation (Case 7) Table Soil properties for FLAC analysis using the Chsoil model (Case 7: improved Chsoil model) Table Different model predictions under 150 kpa applied load Table List of creep models incorporated in the FLAC and the number of input parameters for each one Table Parameters needed for Zener s viscoplastic model Table Soil properties for calibrating creep parameters using relaxation data in FLAC (Case 8) Table Estimated coefficient of consolidation and secondary compression index for each stress level in oedometer test (Kcb-700 facies) Table Hydraulic properties of different facies of Clearwater clay shale Table Soil properties for the consolidation analysis in FLAC (Case 9) Table Soil properties for the coupled creep-consolidation analysis in FLAC (Case 10) Table Different model predictions under 150 kpa applied load xiv

15 List of Figures and Illustrations Figure 2.1. Phanerozoic rocks thickness east of the Cordilleran Foreland Thrust Belt (Porte et al., 1982)...70 Figure 2.2. Shallow inland seaways in North America during the mid-cretaceous period (Cobban and McKinney, 2015)...70 Figure 2.3. The Athabasca Oil Sands area bitumen outline (Teare et al., 2014) and Fort McMurray area map (Haug et al., 2014) Figure 2.4. Fort McMurray area stratigraphic (Haug et al., 2014) Figure 2.5. Schematic representation of stratigraphic units of the interbedded soil layer at the test fill site (Moore, 2007) Figure 2.6. The effect of change in structure of shale and sand on porosity-depth relationship (Schön, 2011) Figure 2.7. Porosity-depth field data (Fowler et al., 1985) and relationship (Revil et al., 2002)...74 Figure 2.8. Variation of porosity with depths of undisturbed shale of Oligocene and Miocene age from Eastern Venezuela (Hedberg, 1936)...74 Figure 2.9. Uniaxial compressive strength versus water content for various clay shales (Hsu and Nelson, 1993)...75 Figure Permeability range of shale in comparison with other geomaterials (Schon, 2011; Hearst et al., 2000)...75 Figure Schematic change of water content with depth of burial and stages of clay shale formation (Bjerrum, 1967)...76 Figure Schematic of clay shale fabric (Wong, 1998)...76 Figure Residual strength of the Kca clay shale from direct shear test (El-Ramly et al., 2003)...77 Figure Layout of slope inclinometers and wire piezometers (Moore et al., 2006)...77 Figure Cumulative and incremental deformations perpendicular to fill face measured 10 m off the west face by SI01 (Moore et al., 2006)...78 Figure Schematic representation of the stress-strain behavior: a. isochronic stress-strain diagrams at different time periods); b. creep curve. c. stress relaxation curve (Feda, 1992) Figure Stress relaxation: (a) Stress strain diagrams of three different relaxation tests (A, B, and C) where the strain rate prior to relaxation varies and (b) the normalized deviator stress versus log time for the three relaxation tests. q is the deviator stress and q 0 is the stress at the beginning of relaxation (Augustesen, 2004) Figure Rheological model of a Zener s material: a) creep. b) relaxation. c) set of isochronic linear stress-strain curves (Feda, 1992) Figure 3.1. Water content of Clearwater clay shale samples Figure 3.2. Variation of volumetric strains with time in free swell tests (approximated with power function) Figure 3.3. Linear variation of volumetric strain with smectite content in free swell tests xv

16 Figure 3.4. Power function trends of coefficients c and d with time in free swell tests Figure 3.5. Comparison of experimental and predicted values of volumetric strain versus time in free swell tests (Kca-625 facies from borehole C) Figure 3.6. Variation of anisotropy ratio (ratio of axial strain to radial strain due to swelling) with smectite content in free swell tests Figure 3.7. Variation of anisotropy ratio (ratio of axial strain to radial strain due to swelling) with time in free swell tests Figure 3.8. Correlation between axial and radial strains in free swell tests Figure 3.9. Schematic of borehole locations in the perimeter of thickener tanks 1001 and Figure Volumetric strain versus time from oedometer test using fresh water (Kcb-700 facies) Figure Results of oedometer tests using fresh and saline water (Kcb-700 facies) Figure Coefficient of consolidation versus axial pressure in the oedometer test using fresh water (Kcb-700 facies) Figure Void ratio versus axial stress in the CRS consolidation test (Kcb-700 facies) Figure Void ratio versus axial stress in the CRS consolidation test (Kcb-650 facies) Figure Volumetric strain versus square-root of time (test #6, Kca-625 facies)..195 Figure Deviatoric stress versus axial strain (test #6, Kca-625 facies) Figure Volumetric strain versus axial strain (test #6, Kca-625 facies) Figure Secant Young s modulus versus axial strain (test #6, Kca-625 facies) Figure Secant Young s modulus versus axial strains between 0.01 % and 0.1 % (test #6, Kca-625 facies) Figure Secant Young s modulus versus axial strains greater than 0.1 % (test #6, Kca-625 facies) Figure Poisson s ratio versus axial strain (test #6, Kca-625 facies) Figure Deviatoric stress versus axial strain (test #5, Kcb-650 facies) Figure Volumetric strain versus axial strain (test #5, Kcb-650 facies) Figure Secant Young s modulus versus axial strain (test #5, Kcb-650 facies)..199 Figure Volumetric strain versus square-root of time (test #12, kcc-710 facies).200 Figure Deviatoric stress versus axial strain for different shearing and stress relaxation stages (test #12, kcc-710 facies) Figure Volumetric strain versus axial strain for different shearing and stress relaxation stages (test #12, kcc-710 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #12, kcc-710 facies) Figure Volumetric strain versus square-root of time (test #1, Kca-625 facies)..202 Figure Deviatoric stress versus axial strain for shearing and stress relaxation stages (test #1, Kca-625 facies) Figure Volumetric strain versus axial strain for shearing and stress relaxation stages (test #1, Kca-625 facies) xvi

17 Figure Deviatoric stress versus axial strain for different shearing and stress relaxation stages (test #1, Kca-625 facies) Figure Volumetric strain versus axial strain for different shearing and stress relaxation stages (test #1, Kca-625 facies) Figure Normalized deviatoric stress versus axial strain rate (test #1, Kca-625 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #1, Kca-625 facies) Figure Changes in volumetric strain versus time for different stress relaxation stages (test #1, Kca-625 facies) Figure Volumetric strain versus square-root of time (test #2, Kca-625 facies)..206 Figure Deviatoric stress versus axial strain for different shearing and stress relaxation stages (test #2, Kca-625 facies) Figure Volumetric strain versus axial strain for different shearing and stress relaxation stages (test #2, Kca-625 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #2, Kca-625 facies) Figure Deviatoric stress versus axial strain at the start and end of stress relaxation stages before the peak strength (test #2, Kca-625 facies) Figure Changes in volumetric strain versus time for different stress relaxation stages (test #2, Kca-625 facies) Figure Normalized volumetric strain versus time for different stress relaxation stages (test #2, Kca-625 facies) Figure Volumetric strain versus square-root of time (test #3, Kcb-700 facies).209 Figure Deviatoric stress versus axial strain for different shearing and stress relaxation stages (test #3, Kcb-700 facies) Figure Volumetric strain versus axial strain for different shearing and stress relaxation stages (test #3, Kcb-700 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #3, Kcb-700 facies) Figure Deviatoric stress versus axial strain at the start and end of stress relaxation stages before the peak strength (test #3, Kcb-700 facies) Figure Ratio of axial strain to deviatoric stress versus axial strain at the start and end of stress relaxation stages before the peak strength (test #3, Kcb-700 facies) Figure Changes in volumetric strain versus time for different stress relaxation stages (test #3, Kcb-700 facies) Figure Normalized volumetric strain versus time for different stress relaxation stages (test #3, Kcb-700 facies) Figure Volumetric strain versus square-root of time (test #4, Kcb-650 facies).213 Figure Deviatoric stress versus axial strain for shearing (loading, unloading, and reloading) and stress relaxation stages (test #4, Kcb-650 facies) Figure Volumetric strain versus axial strain for shearing (loading, unloading, and reloading) and stress relaxation stages (test #4, Kcb-650 facies) Figure Secant Young s modulus versus axial strain for loading, unloading, and reloading stages (test #4, Kcb-650 facies) xvii

18 Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #4, Kcb-650 facies) Figure Changes in volumetric strain versus time for different stress relaxation stages (test #4, Kcb-650 facies) Figure Normalized volumetric strain versus time for different stress relaxation stages (test #4, Kcb-650 facies) Figure Volumetric strain versus square-root of time (test #9, Kcb-700 facies).217 Figure Local axial strains versus square-root of time (test #9, Kcb-700 facies) 217 Figure Deviatoric stress versus axial strain for different strain rates and the stress relaxation stages (test #9, Kcb-700 facies) Figure Volumetric strain versus axial strain for different strain rates and stress relaxation stages (test #9, Kcb-700 facies) Figure Normalized deviatoric stress versus axial strain rate (test #9, Kcb-700 facies) Figure Normalized deviatoric stress versus logarithm of time for stress relaxation stages (test #9, Kcb-700 facies) Figure Normalized volumetric strain versus time for stress relaxation stages (test #9, Kcb-700 facies) Figure Dissipation of excess pore pressure with time during consolidation stage (test #10, Kcb-650 facies) Figure Degree of consolidation, U, versus square-root of time (test #10, Kcb- 650 facies) Figure Deviatoric stress versus axial strain for different strain rates and stress relaxation stages (test#10, Kcb-650 facies) Figure Volumetric strain versus axial strain for different strain rates and stress relaxation stages (test #10, Kcb-650 facies) Figure Deviatoric stress versus axial strain (test#10, Kcb-650 facies) Figure Volumetric strain versus axial strain (test #10, Kcb-650 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test#10, Kcb-650 facies) Figure Changes in volumetric strain versus time for different stress relaxation stages (test #10, Kcb-650 facies) Figure Normalized volumetric strain versus time for different stress relaxation stages (test #10, Kcb-650 facies) Figure Coefficient of consolidation versus confining pressure (test#11, kcc- 710 facies) Figure Coefficient of volumetric compressibility versus axial pressure from a constant rate of strain consolidation test on Kcb Figure Deviatoric stress versus axial strain for different strain rates and stress relaxation stages before peak (test#11, kcc-710 facies) Figure Volumetric strain versus external axial strain for different strain rates and stress relaxation stages before peak (test#11, kcc-710 facies) Figure Deviatoric stress versus external axial strain for different strain rates and stress relaxation stages (test#11, kcc-710 facies) Figure Volumetric strain versus external axial strain for different strain rates and stress relaxation stages (test#11, kcc-710 facies) xviii

19 Figure Volumetric strain versus time for different strain rates and stress relaxation stages (test#11, kcc-710 facies) Figure Deviatoric stress versus mean effective stress (test#11, kcc-710 facies) 228 Figure Normalized deviatoric stress versus time for different stress relaxation stages (test#11, kcc-710 facies) Figure Change in deviatoric stress versus axial strain for stress relaxation stages (test#11, kcc-710 facies) Figure Change in deviatoric stress versus confining pressure for different stress relaxation stages (test#11, kcc-710 facies) Figure B-values measured at different levels of back pressure (test #7, Kcb- 700) Figure B-values related to degree of saturation and soil stiffness (Black and Lee, 1973) Figure Volumetric strain versus square-root of time (test #7, Kcb-700) Figure Deviatoric stress versus axial strain for different strain rates (test #7, Kcb-700) Figure Excess pore pressure versus axial strain for different strain rates during shearing stages (test #7, Kcb-700) Figure A-values measured at different strain rates during shearing stages (test #7, Kcb-700) Figure Typical relationship between A-values at failure and overconsolidation ratio (Head, 1998) Figure Deviatoric stress versus mean effective stress (test #7, Kcb-700) Figure Secant Young s modulus versus axial strain (test #7, Kcb-700) Figure Secant Young s modulus versus axial strains greater than 0.1 % (test #7, Kcb-700) Figure Volumetric strain versus square-root of time (test #8, Kcb-700) Figure Deviatoric stress versus axial strain for different strain rates (test #8, Kcb-700) Figure Secant Young s modulus versus axial strain (test #8, Kcb-700) Figure Excess pore pressure versus axial strain (test #8, Kcb-700) Figure A-values measured during shearing stages (test #8, Kcb-700) Figure Deviatoric stress versus mean effective stress (test #8, Kcb-700) Figure Secant Young s moduli verses axial strain in log-log scale at confining pressure of 100 kpa Figure Secant Young s modulus versus axial strain at different confining pressure of Kca-625 facies Figure Coefficients A and B versus confining pressure from tests on Kca-625 facies Figure Stress states at the peak and post-peak deviatoric stress in q-p' plane..240 Figure Deviatoric stress, q, versus mean effective stress, p', at the end of the triaxial tests Figure Friction angle at the end of the tests versus clay contents of the samples Figure Friction angle at the end of the tests versus clay contents of the samples at different confining pressures xix

20 Figure Friction angle at the end of the tests versus smectite contents of the samples Figure Friction angle at the end of the tests versus smectite portion of clay fraction Figure Friction angle at the end of the tests versus illite contents of the samples at different confining pressures Figure Estimated depth of the samples versus clay content Figure Surface hardness versus clay content of Clearwater clay shale samples Figure Liquid limit versus clay contents for facies of Clearwater clay shale Figure Clay and smectite content of triaxial samples versus liquid limit Figure Density versus clay content of samples used in triaxial testing Figure Peak strength versus density for confining pressures of 100, 300, and 500 kpa Figure Peak strength versus density for samples of facies Kcb Figure Maximum deviatoric stress versus measured shear band angles Figure Maximum deviatoric stress versus measured shear band angles (divided in groups) Figure Approximation of actual relaxation curve with a line (Lacerda and Houston, 1973) Figure Influence of prior strain rate on the time to start of stress relaxation Figure Normalized deviatoric stress change in relaxation tests with prerelaxation axial strain rate of 5.32 %/day at axial strains before peak strength Figure Normalized deviatoric stress change in relaxation tests at axial strains after peak strength Figure Normalized deviatoric stress change in relaxation tests at axial strains after peak strength in comparison with those presented in Figure Figure 4.1. Grids of finite difference model and layered soil profile Figure 4.2. Vertical displacements contours in meter (Case 1) Figure 4.3. Horizontal displacements contours in meter (Case 1) Figure 4.4. Displacements vectors contours in meter (Case 1) Figure 4.5. Shear stresses contours in Pa (Case 1) Figure 4.6. Change in vertical stresses contours in Pa due to loading (Case 1) Figure 4.7. Excess pore pressure contours in Pa due to loading (Case 1) Figure 4.8. Change in effective vertical stresses contours in Pa due to loading (Case 1) Figure 4.9. Vertical displacements contours in meter (Case 2) Figure Horizontal displacements contours in meter (Case 2) Figure Displacements vectors contours in meter (Case 2) Figure Shear stresses contours in Pa (Case 2) Figure Change in vertical stresses contours in Pa due to loading (Case 2) Figure Excess pore pressure contours in Pa due to loading (Case 2) Figure Change in effective vertical stresses contours in Pa due to loading (Case 2) Figure Vertical displacements contours in meter (Case 3) Figure Horizontal displacements contours in meter (Case 3) xx

21 Figure Displacements vectors contours in meter (Case 3) Figure Shear stresses contours in Pa (Case 3) Figure Change in vertical stresses contours in Pa due to loading (Case 3) Figure Excess pore pressure contours in Pa due to loading (Case 3) Figure Magnitude of compressive volumetric strain versus depth at tank centerline, 10 m and 20 offset from tank centerline (Case 3) Figure Change in effective vertical stresses contours in Pa due to loading (Case 3) Figure Vertical displacements contours in meter (Case 4) Figure Horizontal displacements contours in meter (Case 4) Figure Displacements vectors contours in meter (Case 4) Figure Shear stresses contours in Pa (Case 4) Figure Change in vertical stresses contours in Pa due to loading (Case 4) Figure Excess pore pressure contours in Pa due to loading (Case 4) Figure Magnitude of compressive volumetric strain versus depth at tank centerline, 10 m and 20 offset from tank centerline (Case 4) Figure Change in effective vertical stresses contours in Pa due to loading (Case 4) 347 Figure Comparison of magnitude of compressive volumetric strain versus depth at tank centerline (Cases 3 and 4) Figure Comparison of magnitude of compressive volumetric strain versus depth at 10 m offset from tank centerline (Cases 3 and 4) Figure Measured settlement at tank center post and different model predictions (MC stands for Mohr-Coulomb model) Figure Average measured settlement at tank edge and different model predictions Figure Measured horizontal displacement at 10 meter offset from tank edge and different model predictions Figure Measured excess pore pressure in center of tank at 12 m depth and different model predictions Figure Measured and simulated stress-strain behavior of Kca-625 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated volumetric behavior of Kca-625 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated stress-strain behavior of Kcc-710 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated volumetric behavior of Kcc-710 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated stress-strain behavior of Kcb-700 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated volumetric behavior of Kcb-700 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated stress-strain behavior of Kcb-650 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated volumetric behavior of Kcb-650 facies in drained triaxial compression test at various confining pressures xxi

22 Figure Measured horizontal displacement at 10 meter offset from tank edge and different model predictions Figure Measured horizontal displacement at 10 meter offset from tank edge and different Chsoil model predictions Figure Measured settlement at the tank center post and different model predictions (MC stands for Mohr-Coulomb model) Figure Average measured settlement at the tank edge and different model predictions Figure Measured excess pore pressure in center of the tank at 12 m depth and different model predictions Figure Vertical displacements contours in meter (Case 7) Figure Horizontal displacements contours in meter (Case 7) Figure Displacements vectors contours in meter (Case 7) Figure Shear stresses contours in Pa (Case 7) Figure Change in vertical stresses contours in Pa due to loading (Case 7) Figure Excess pore pressure contours in Pa due to loading (Case 7) Figure Change in effective vertical stresses contours in Pa due to loading (Case 7) Figure Burger s viscoelastic model schematic (Itasca Consulting Group, 2011) Figure Zener s viscoelastic model schematic Figure Stress relaxations from Test#12 on Kcc-710 and the FLAC result (Zener model) Figure Stress relaxations from Test#3 on Kcb-700 and the FLAC result (Zener model) Figure Stress relaxations from Test#4 on Kcb-650 and the FLAC result (Zener model) Figure Stress relaxations from Test#1 on Kca-625l and the FLAC result (Zener model) Figure Vertical displacements contours in meter (Case 8) Figure Horizontal displacements contours in meter (Case 8) Figure Displacements vectors contours in meter (Case 8) Figure Shear stresses contours in Pa (Case 8) Figure Pore pressure contours in Pa due to loading (Case 8) Figure Vertical displacements contours in meter (Case 9) Figure Horizontal displacements contours in meter (Case 9) Figure Displacements vectors contours in meter (Case 9) Figure Shear stresses contours in Pa (Case 9) Figure Vertical displacements contours in meter (Case 10) Figure Horizontal displacements contours in meter (Case 10) Figure Displacements vectors contours in meter (Case 10) Figure Shear stresses contours in Pa (Case 10) xxii

23 List of Symbols, Abbreviations and Nomenclature CEC PVC CH CPT CRS DCM FLAC GDS LVDT OCR Pl SEM SPT WIPP XRD Cation exchange capacity Polyvinyl chloride Clay of high plasticity Cone penetration test Constant-rate-of-strain Dielectric constant measurement Fast Lagrangian Analysis of Continua GDS Instruments (A division of Global Digital Systems Ltd) Linear variable differential transformer Overconsolidation ratio Plastic Scanning electron microscopy Standard penetration test Waste Isolation Pilot Plant X-ray diffraction a Experimental coefficient A Experimental coefficient A c Initial area α At-rest rebound parameter of the soil α Biot coefficient α Ratio of the shear modulus to the Kelvin shear modulus b Experimental coefficient B Experimental coefficient c Cohesion c Cohesion intercept of the failure line in the q p plane c(t) Creep function Ch Chlorite C α Secondary compression index C c Compression index. C gw Compressibility of water-gas mixture Cu0 Undrained shear strength at natural water content c v Coefficient of consolidation d Experimental coefficient D Diameter of the sample D Dolomite Cu Strength loss after softening to equilibrium water content L Vertical movement of the upper part of the sample from the start of slip LI Change in liquidity index cr t max Maximum creep time step V Change in volume due to drainage w Change in water content after softening e Void ratio E Secant Young s modulus, Young's modulus xxiii

24 E M Maxwell elastic modulus E K Kelvin elastic modulus E D Deformation modulus in Maxwell materials E 0 Initial deformation modulus in Zener s materials E Ultimate deformation modulus in Zener s materials E ref Young s modulus number ε Strain ε Strain rate ε 0 Initial strain ε Ultimate strain ε V, ε Volumetric strain ε a Axial strain ε a Axial strain rate ε r Radial strain ε s Axial strain after start of slip ε q Shear strain rate e ij Deviatoric strain rate e ij K Contributions of Kelvin component to the deviatoric strain rate e ij H Contributions of Hookean component to the deviatoric strain rate e ij P Contributions of plastic component to the deviatoric strain rate e vol Total volumetric strain rate P e vol Plastic volumetric strain rate η Viscosity η M Maxwell viscosity η K Kelvin viscosity F Force F Change in force with time f b Correction factor for area due to barrelling f s Slip area factor φ p Internal friction angle at the peak deviatoric stress φ r Internal friction angle at post-peak φ Internal Effective stress friction angle φ d Dilation law constant φ cv Friction angle at constant volume φ m Mobilized friction angle φ f Ultimate friction angle g Gravitational acceleration g Potential function G Shear modulus, Hookean shear modulus, Current secant shear modulus G Gypsum G s Specific gravity G i Initial secant shear modulus G e Mobilized elastic shear modulus Shear modulus number G ref xxiv

25 G K γ γ p H 0 I I-S mix K K k k K K gw K g k H k H K w K 0nc K 0oc K w K t K e K ref K-f L LI LL λ λ m m v M M p M r n n n ν P P Py p P a p ref p i Shear modulus of Kelvin mechanism Unit weight of fluid Plastic shear strain Thickness of compressible layer Illite Illite and smectite mixture in inter-layer Bulk modulus Kaolinite Permeability or the mobility coefficient Elastic constant Bulk modulus, drained bulk modulus of the porous medium Bulk modulus of water-gas mixture Gas bulk modulus Hydraulic conductivity Coefficient of permeability or hydraulic conductivity Bulk modulus of water Coefficient of the earth pressure at rest of a normally-consolidated soil Coefficient of the earth pressure at rest of an overconsolidated soil Fluid bulk modulus Bulk modulus number Mobilized elastic bulk modulus Bulk modulus number K-feldspar Length of the sample Liquidity index Liquid limit Drainage boundary condition coefficient Plastic multiplayer Bulk modulus exponent Coefficient of volume compressibility Biot modulus Slope of failure line in the q p plane Slope of the post-peak strength line Porosity Slope of the constant confining pressure line in (1 q r) ε a plane Shear modulus exponent Poisson s ratio Axial force Plagioclase Pyrite Mean effective stress Atmospheric pressure Reference pressure Initial effective pressure xxv

26 PI Plastic index PL Plastic limit q Deviatoric stress, corrected deviatoric stress, deviatoric stress at any time q 0 Deviatoric stress at the start of relaxation q r Deviatoric stress at the end of the relaxation stage q Normalized deviatoric stress q 0 Normalized deviatoric stress at the start of the stress relaxation, equal to unity q r Normalized deviatoric stress at the end of the stress relaxation q Deviatoric stress rate q n Intercept of the constant confining pressure line in (1 q r) ε a plane q u Undrained shear strength Q Quartz R f Failure ratio r(t) Stress relaxation function ρ Solid bulk density (total density) ρ d Bulk density of the dry matrix ρ w Density of the fluid phase (water) S Smectite in inter-layer s Coefficient of the stress relaxation equation of Lacerda and Houston (1973) S w Degree of water saturation S ij Deviatoric stress σ Stress σ Stress rate σ Effective stress σ c Confining pressure σ t Tensile strength σ 0 Mean effective stress σ 1 Minimum principal stress σ 3 Maximum principal stress ψ Dilation angle ψ m Mobilized dilation angle ψ f Dilation angle t Time t Membrane thickness t50 Time of softening for loss of 50% of Cu0 t 100 Time representing theoretical 100 % consolidation t c Time of retardation in Kelvin s material t rs Time of retardation in Zener s materials t h Half relaxation time t r Relaxation time in Maxwell s materials t p Duration of primary consolidation Total I Illite in and out of interlayer mixture with smectite τ Current shear stress Maximum shear stress τ max xxvi

27 τ K θ u V c W N WS z ζ Ratio of Kelvin viscosity to Kelvin shear modulus Angle of the slip plan with vertical direction Velocity Volume at the start of shearing Natural water content Maximum water content due to slaking Depth Variation of fluid volume per unit volume of porous material xxvii

28 Epigraph "The outcome of any serious research can only be to make two questions grow where only one grew before." Thorstein Veblen xxviii

29 Chapter 1: Introduction In recent oil sand plant developments, large storage tanks (up to 60 m in diameter and 20 m high equal to a vertical load of 180 kpa) have been constructed near Fort McMurray, Alberta. These tanks are commonly founded over the Cretaceous Clearwater Formation, which is a very stiff to hard clay. Being referred to as clay shale, this formation might have been subjected to preshearing during glaciations and may exhibit a strain weakening behavior when loaded (Moore, et al., 2006). Excessive short- and long-term settlements of the tanks foundation could be critical for the operation and safety of the tanks. Therefore, a design tool capable of predicting the foundation settlement accurately is required. The success of such an endeavor hinges on the accurate knowledge of the geotechnical response of Cretaceous Clearwater Formation (clay shale) during loading Significance of the Research Background Due to the uncertainty associated with the behavior of the clay shale and the risk of improper tank performance, a full-scale field load test was carried out to investigate foundation performance. A 40 m square test fill with a maximum height of 9 m and two vertical faces was constructed using local sand. The foundation performance was monitored during construction of the fill using 18 vibrating wire piezometers, 8 slope inclinometers, and 21 survey monitoring points (Moore, et al., 2006). 1

30 The test fill was loaded at a rate of 10 kpa per day and was constructed in a period of 18 days (15 days of loading and three days delay during the period). The test was stopped when the fill height reached a vertical load of 150 kpa and there was a 40 mm of horizontal movement in a concentrated shear zone in the clay shale. The data from the full-scale load test were used, in an iterative process, to calibrate an explicit finite difference model in FLAC 1 to obtain reasonable parameters for a constitutive model. The model and the calibrated parameters were implemented during the detailed design stage (Moore, et al., 2011). The performed FLAC analysis is associated with the following limitations: - Dissipation of pore pressure was not allowed in the FLAC model and it was run in an undrained mode. The undrained pore pressures predicted by FLAC were matched with partially dissipated field pore pressures observed in the field. Therefore, the model prediction is only applicable where the loading rate for a structure is similar to the loading rate for the test fill (Moore, 2007). - The long-term behavior of test fill was not addressed in the performed analyses. An analyses of clay shale behavior under test fill load in long term, should account for consolidation and creep phenomena. Knowledge of the permeability of Clearwater facies is necessary for a consolidation analysis while a model capable of incorporating timedependent characteristics of clay shale is required for a creep analysis. 1 Fast Lagrangian Analysis of Continua 2

31 - The back-calculated parameters for the FLAC model are only representative of the soil and loading condition of the specific test fill study and may not be suitable to model situations with different soil and stress conditions (initial stress state, strain history, and strain path). - There is no unique set of input parameters that allow the model to match the observed behavior. Because the FLAC model requires a large number of input parameters, including constitutive ones, and more than one parameter has an influence on the predicted behavior in each case of attempting to predict pore pressure, ground deformation, or the failure onset (Moore, 2007). - The constitutive model implemented in FLAC (the quasilinear hyperbolic elastic model of Duncan and Chang (1970) in conjunction with the Mohr-Coulomb constitutive model) does not incorporate volume changes from shear dilatancy Research objectives and scope Settlement of the foundation for the large storage tank in oil sand plant should be limited to that necessary to ensure the proper operation and safety of the tank. Hence, it is critical to estimate the settlement of the foundation of the tank above clay shale accurately. Thus, the engineering properties and the geotechnical behaviour of local clay shale during loading should be known. To this end, the goal of this research is to develop numerical tools for design, prediction, and analysis of storage tank systems founded over such clay shale formation. This goal is accomplished by completing through the tasks, which comprise both laboratory testing and numerical modeling. 3

32 Investigation of geotechnical properties of facies of Clearwater clay shale At present, Clearwater shale facies have been distinguished based on a qualitative description. To develop a better quantitative description, index properties and mineralogy of different facies of Clearwater shale using X-ray diffraction analysis will be determined. The permeability of shales is usually low and difficult to measure. The permeability of each facies of this clay shale will be estimated experimentally. Clay shale formations are potentially subjected to swelling when they are exposed to fresh water. The swelling phenomenon and its probable correlation with mineralogy will also be examined. Stress-strain behaviour of clay shale will be investigated and elastic parameters will be calculated, which can be implemented in an elastic analysis of the problem Determination of parameters of a constitutive model for geotechnical behavior of Clearwater clay shale Drained and undrained triaxial compression tests will be carried out on Cretaceous Clearwater Formation core samples to quantify the mechanical and hydraulic characteristics of clay shale. Moreover, multiple stress relaxations tests will be conducted during triaxial tests at different axial strains to obtain a data set for studying the time-dependent behaviour. Results from all laboratory tests will be used to determine the parameters of various constitutive models to calibrate for Cretaceous Clearwater Formation. 4

33 Numerical modeling of performance of storage tanks over clay shale The finite difference program (FLAC) with calibrated constitutive models, the Mohr-Coulomb or Chsoil model for time-independent response and the Zener model for time-dependent behaviour, will be used to analyze the case study, a test fill constructed on layers of the Clearwater clay shale. The performed short-term and long-term analyses of the test fill can function as a numerical tool or model for future design and analysis Organization of the thesis This thesis consists of five chapters. Chapter 1 provides a brief background of the topic, motivation of the research, and objectives of the present study. In Chapter 2, geological history of Cretaceous Clearwater Formation as a unit of the Mannville Group in the Western Canada sedimentary basin in northeastern Alberta, Canada is briefly reviewed. Then, classifications, characteristics, and engineering properties of clay shales, particularly Clearwater clay shale, are presented based on the previous studies. In addition, timedependent behaviour of clays and relevant rheological models are described. In Chapter 3, the results of experimental investigations conducted on four facies of Clearwater clay shale are presented. Swelling behaviour and mineralogy of the Clearwater clay shale are explored according to the results of free swell tests and X-ray diffraction analyses, respectively. Results and details of oedometer tests, constant-rate-of-strain consolidation tests, consolidated drained triaxial compression tests, and consolidated undrained triaxial tests are presented. Moreover, Calculated secant Young s modulus and Mohr-Coulomb shear parameters, obtained 5

34 correlations between results of triaxial tests and properties of samples, analyze of stress relaxation tests are presented in this chapter. In Chapter 4, procedure and results of the FLAC simulations of the test fill based on triaxial tests data are presented. The model geometry, material properties, and applied boundary conditions are initially described. Then, the short-term (time-independent) response of clay shale beneath the test fill is studied in seven numerical cases. Moreover, results of various models, poro-elastic, poro-elasto-plastic, and Chsoil models, are compared with the field data. In the next step, the longterm (time-dependent) response of the Clearwater clay shale under test fill is explored. Implemented creep model and its calibration are explained. Then, numerical cases of an undrained creep analysis, a consolidation analysis, and a coupled creep-consolidation analysis are presented. In Chapter 5, the results of this research are summarised along with some recommendations for future studies. 6

35 Chapter 2: Literature review 2.1. Geology (geological history and stratigraphic framework) Geological framework of Western Canada Sedimentary Basin Western Canada Sedimentary Basin is a wedge of strata extending southwest from a zero edge at the Canadian Shield outcrop to a maximum thickness at the Cordilleran Foreland Thrust Belt (Figure 2.1). Two fundamentally different tectonic settings play part in the geological history of the Western Canada Sedimentary Basin. Transgressive onlap of the Precambrian crystalline basement of the North American craton and the development of epeirogenic arches and basins on the cartonic platform took place during the initial platformal phase. This phase is dominated by shallow water carbonates and evaporite sequences and coincides with the deposition of late Proterozoic to Jurassic sediments (Porte et al., 1982). Allochthonous oceanic terranes were accreted to the western margin of North America during the late Jurassic to Paleocene interval. To form the present eastern part of the Cordillera, the continental terrace wedge was compressed, detached from its basement and thrust over the flank of the craton. The tectonic loading led to the continental lithosphere isostatic flexure and initiation of the development of a foreland basin to the east. Clastic detritus, shed by the evolving Cordillera, form the sediments that filled the foreland basin (Porte et al., 1982) Geological history of Lower Cretaceous Mannville Group Mannville Group is distributed in the area between Edmonton, Athabasca, and Lloydminster in Alberta and extended southward to the international boundary, westward to the disturbed Mesozoic 7

36 belts of the foothills and, eastward into central and southwestern Saskatchewan. The southern edge of the Deep Basin area is approximately the northem limit of the Mannville Group. This group consists of interbedded nonmarine sands and shales overlain by a thin, nonmarine calcareous member which is overlain by marine shales, glauconitic sands and nonmarine salt-and-pepper sands in southern and central Alberta. The marine sequence is overlain by a paralic and nonmarine sequence having a diachronous contact with the marine sequence in east-central and northeastern Alberta (Glass, 1997). The oldest Cretaceous rocks over most of the Western Canada Sedimentary Basin are found in Mannville Group and equivalent strata. After a long period of uplift, exposure and erosion of older strata, this group represents a major episode of subsidence and sedimentation. Ranging from less than 40 m thick in some areas of the plains to more than 700 m thick in the Rocky Mountain Foothills, Mannville strata cover the entire basin. The section is erosionally truncated along its eastern and northeastern limits (Hayes et al., 1994). The earliest synorogenic clastic wedge shed from the emerging Cordillera comprises formations within the Mannville Group. The Mannville Group was deposited within a shallowwater basin which opened toward the northwest (Figure 2.2). The basin floor, the pre-mannville unconformity surface, consisted of westward-dipping strata ranging in age from Jurassic in the west to Devonian in the east. A series of northwest-southeast trending ridges and valleys was developed due to differential erosion and incised drainage. These ridges and valleys created topographic relief which influenced sedimentation and led to the subsequent entrapment of heavy oil (Porte et al., 1982). 8

37 The Mannville Group is divided into three subunits: - The lower Mannville deposited as fluvial and estuarine valley fill sediments in the incised valleys of the pre-cretaceous unconformity surface. These sedimentations were activated by a marine transgression which originated from the northwest (Williams, 1963). - The middle Mannville comprises sheet sands and shales deposited by repeated marine transgressive-regressive events. These depositions were result of the stalling of a southward transgression of the Boreal Sea and the initiation of a major regression (Jackson, 1984). - A large influx of clastic sediments overcame basin subsidence by upper Mannville time, which caused a relative lowering of sea level and the return of regressive (Jackson, 1984). The shoreline prograded from the Hoadley Barrier in central Alberta to the Clearwater shale basin in the northwest. The upper Mannville comprises nonmarine sediments in southern Alberta, nearshore marine sediments capped by nonmarine sediments in central Alberta, and marine sediment in northern Alberta. The Grand Rapid Formation and the Clearwater Formation make up the upper Mannville in northern Alberta. The Clearwater Formation consists of a thick sandstone unit between thin shale layers, which represent transgressive marine pulses. The shales are the two most continuous aquitards within the Mannville Group, despite the fact that they are generally less than 10 m thick (Hitchon et al., 1989). The Mannville Group comprises repeated alternations of marine and nonmarine deposits in general. Deep channels occur at all levels and are filled with either sand, or shale and silt, making 9

38 the Mannville sedimentation complex (Hitchon et al., 1989). The Mannville Group resides under the Colorado Group (Joli Fou Formation), separated from it with a widespread disconformity, and overlies the post-paleozoic unconformity (Glass, 1997). The sub-units of Mannville Group in Athabasca region are presented in Table Clearwater Formation The Clearwater Formation is a stratigraphic unit of early Cretaceous age (Albian) in the Western Canada sedimentary basin in northeastern Alberta, Canada. The existence of low permeability marine shales in the Clearwater Formation contributes to the trapping mechanism for underlying the Athabasca oil sands (Glass, 1997). This formation primarily consists of shales in black and greenish grey colour, with interbedded grey and green sands and siltstone, and ironstone concretions. A thin glauconitic sand called the Wabiskaw Member is at the base of the formation (Badgley, 1952). Continuous massive salt-and-pepper sands, glauconitic sands, and interbedded shales are found in the Clearwater Formation to the southeast in the Cold Lake area. So-called salt-and-pepper sands are similar in appearance and characteristics to deposits of the present-day rivers. The salt in the sands is common quartz, but the pepper sands are more distinctive dark grains and fragments of volcanic glass. This formation is present in the subsurface of northeastern and central Alberta, and is exposed on lower course of the Athabasca River and along Christina River southeast of Fort McMurray. Its thickness varies between 85 meters on the lower Athabasca River area to 6 meters in the Cold Lake area. It is recognized from northeastern Alberta to the Edmonton area in central 10

39 Alberta. The Clearwater Formation conformably overlies the McMurray Formation and is conformably overlain by, and laterally interfingers with the Grand Rapid Formation. The Bluesky Formation and the Lower Sprit River Formation in the Peace River Region are equivalent to this formation (Glass, 1997). The Wabiskaw Member, which forms the base of the Clearwater Formation, consists of one or more argillaceous, fine grained, well-sorted, glauconitic salt-and pepper sands, with interbeds of black fissile shale. This shale forms the boundary from the underlying McMurray Formation. The Wabiskaw member sands can be distinguished from the sands of underlying McMurray Formation in that fact that they contain more than 10% chert and glauconite pellets. This member forms the main reservoir and is saturated with bitumen in the western extension of the Athabasca oil sands deposit. The Wabiskaw member thickness averages approximately 10 m in the general Fort McMurray area while it is not recognized in central Alberta or in the Cold Lake area (Glass, 1997) Athabasca Oil Sands area Initial volume in place of crude bitumen for the entire Athabasca oil sands area Wabiskaw- McMurray deposit is estimated to be m 3 for mineable resources and m 3 for in-situ resources (Teare et al., 2014) Fort McMurray stratigraphic framework The stratigraphic and hydrostratigraphic succession within the area is illustrated in Figure 2.4. The Devonian carbonates, evaporites, shales, and sandstones are the lowest units in the succession and 11

40 sit unconformably above the Precambrian basement. The Devonian strata form an eastwardtapering wedge in region. The sandstone and shale succession of the Lower Cretaceous Mannville Group unconformably overlain the Devonian strata. Unconsolidated Quaternary and Holocene sediments form the uppermost units (Haug et al., 2014). The McMurray Formation is the basal unit of the Lower Cretaceous Mannville Group. It directly overlies the sub-cretaceous unconformity and comprises fluvio-estuarine clastic deposits which are commonly bitumen saturated. Stacked channels produce a variety of lithofacies, including blocky channel sands, interbedded sandstone, and shale in the form of inclined hetrolithic strata, channel abandonment mud plugs, breccia horizons, and intervals deposited on muddy flood plains and tidal flats (Haug et al., 2014). The McMurray-Wabiskaw strata has been widely investigated and mapped in this region (Hein et al., 2012). The Clearwater Formation, a succession of marine mudstone and siltstone including the Wabiskaw Member at its base, overlies the McMurray Formation. The Wabiskaw Member can be divided to different units (Table 2.2). The Clearwater Formation, comprises largely silty shale with minor component of interbedded siltstone, is a laterally continuous unit. This formation subcrops Quaternary sediments where the Grand Rapids Formation is eroded. The Clearwater Formation has been eroded in the Clearwater and Athabasca River Valleys (Haug et al., 2014). The alternating sandstone and mudstone shoreface deposits of the Grand Rapids Formation overlain the Clearwater Formation. The Grand Rapids Formation may be overlain by the Joli Fou and Viking Formations of the Colorado Group, but these units have been removed across most of Fort McMurray area by the erosion prior to deposition of Quaternary sediments (Haug et al., 2014). 12

41 The Quaternary sediments rest unconformably on Lower Cretaceous succession. The sedimentary strata overlying the post-cretaceous unconformity in the Fort McMurray area is composed of finer grained sediments deposited during advance and retreat of Quaternary ice sheets as well as a sequence of coarser fluvial sediments (Andriashek et al., 2007) Site characterization and subsurface conditions Geological cross section consists of Holocene (postglacial) and Pleistocene (glacial) deposits from Quaternary period, overlying the Lower Cretaceous Grand Rapids Formation (KcG facies), Cretaceous Clearwater Formation clay shale (Kc facies), and McMurray Formation oil sand (Km facies), which are underlain by Devonian limestone. The near surface soils at the site include peat (Ho facies 898), fluvial sand (Hf facies 896 and Pfs facies 860), glacio-lacustrine clay (PI facies 880), and clay till (Pgtc facies 830) which are shown in Figure 2.5. Discontinuous layers of indurated siltstone or sandstone are found in Clearwater Formation clay shale. The Clearwater clay shale is usually dark grey with zones of low-density clay rich strata and siltstones. The clay fraction is composed of mainly illite, with lesser amounts of kaolinite, smectite, and chlorite. The clay shale is classified as having a very high potential for expansion and swelling, based on its high liquid limit (Mimura, 1990; Holtz et al., 2010). The four facies of Clearwater clay shale (Kcc 710, Kcb 700, Kcb 650, and Kca 625) that will be investigated in this study along with the overlying and underling facies (Kcc 720 and Kcw 600, respectively) are described, according to facies classification for the Horizon oil sand project, in Table 2.3. All of these four facies of the Clearwater Formation had been deposited in an offshore 13

42 environment (Moore, 2007). A schematic representation of these four facies and other stratigraphic units at the site is shown in Figure 2.5. Additionally, the period and epoch/formation of the investigated clay shale facies along with those of the other stratigraphy units are presented in Table Clay Shale Clay shale classification Argillaceous materials such as mudstone, claystone, siltstone, and clay shale generally show a wide variation in their composition, mineralogy, and engineering properties. This group of geomaterials is fine-grained and composed predominantly of clay and silt sized materials. Most of classification used for argillaceous materials are geological and therefore, are based on properties such as quartz content, grain size, color, and the degree of compaction. The common characteristics of clay shales are as follows: - usually highly overconsolidated, - commonly small scaled fissured, - strong diagenteic bonding, - tendency to slake when rewetted after drying, - high swelling pressure in the presence of fresh water, and - significant disintegration as a result of interaction with water (William, 2005). 14

43 Clay shale geological classification The main goal of geological classification is to determine the geological history of deposits. Therefore, grain size was a major factor in early classifications and the boundary between argillaceous material and the remaining sedimentary materials was set arbitrarily (Wentworth, 1922). Mead (1936) classified shales based on their cementation into two main groups: first, compacted shales consolidated under stress by the overlying sediment without a cementing agent; second, cemented shales containing intergranular cement (calcareous, siliceous, or ferruginous) or a bonding material formed by recrystallization of clay minerals. Philbrick (1950) took the classification process one step further by designing and carrying out a simple weathering test, consisted of five cycles of drying and wetting. Based on the results, it was suggested that the shales that have reduced to grain sized particles be termed compacted shales and ones that have not affected be termed cemented shale. Ingram (1953) implemented percentage of silt and clay components to characterize all clayey materials along with their breaking characteristics. The fine scale fracturing in the surface of shale (fissility) was used to distinguish shale from stone. Based on the relative percentages of the grainsize components, it was suggested to use prefixes clay, silt, or mud and terms such as claystone, siltstone, mudstone, and clay shale was defined. Underwood (1967) introduced new terms such as soil-like shale for compacted shale and rock-like shale or bonded shale for cemented shale in a geological classification (Table 2.5), but these two categories are not clearly defined. Bjerrum (1967) classified shales and clay-shales 15

44 based on stress history as overconsolidated plastic clays with strongly and poorly developed diagenteic bonds, respectively. Folk (1968) refined the classification of Ingram (1953) by clarifying the definition of mudstone as an argillaceous materials with sub-equal amounts of clay and silt. Gamble (1971) modified the division of Ingram (1953) so that terms clay shale and silt shale changed into clayey shale and silty shale, respectively. The introduction of the term clayey shale facilitates to distinguish a clay rich shale (a fissile rock that is rich in clay content) from a clay shale in engineering usage Clay shale engineering classification Terzaghi (1936) proposed an engineering classification, in which clays were divided based on the stiffness and the presence or absence of fissures into three main groups: soft clays without fissures, stiff clay without fissures, and stiff fissured clay. British Standard Institute (1957) implemented similar terms and developed a classification based on consistency or strength (Table 2.6). Bjerrum (1967) followed a different approach and introduced three major terms, based on bond strength. He extended these three overlapping terms up to shale materials. Bejerrum s classification divided the material based on the following terms: - overconsolidated clays without bond or with weak bond, - overconsolidated clays with developed diagenetic bonds (clay shales), and - overconsolidated clays with strongly defined diagenetic bonds (shales). 16

45 These classifications have caused some confusion, especially when terms such as overconsolidated and stiff fissured clay were used to describe weakly bonded shale. This inconsistency in terminology is strongly marked for argillaceous materials, since these materials are transitional between normally consolidated clays and intact shales. Latter investigators tried to include the potential changes in material behavior with time in classification schemes. The term slaking was introduced to account for the influence of durability. Gamble (1971) carried out extensive investigation on the durability of different shales based on correlations of material properties, such as moisture content, liquid limit, and dry density. He suggested to classify these materials on the basis of the relationship between a two cycle slake durability index and their plastic index. Gamble also recognized the need to correlate laboratory results with field data. Deo (1972) introduced another classification based on the importance of shale deterioration, in which the argillaceous materials were classified on account of their susceptibility to deterioration instead of the initial state of material. Based on the measured shale durability using different tests, he subdivided shales into soil-like shale, two type of intermediate shale, and rocklike shale. Morgenstern and Eigenbrod (1974) attempted to combine earlier classification schemes, which were based on initial properties with durability based classification. They suggested two classification schemes: first, based on the rate of slaking versus the amount of slaking and second, based on the undrained shear strength, the strength loss after softening, changes of water content after softening, and the time of softening (Table 2.7). 17

46 The scheme implemented three potentially conflicting properties (undrained shear strength at natural water content, strength loss after softening to equilibrium water content, and change in water content after softening) with emphasis on the influence of softening on strength and water content to classify the argillaceous material into either soil or rock. After that, slaking characteristics are used to distinguish the clay shale. According to this two-part-classification, a shale may be classified as rock-like based on its initial strength characteristics and may also be classified soil-like according to its response to softening Clay shale characteristics The properties of shale such as density, porosity (void ratio), water content, permeability, and specific gravity are affected by multiple factors such as microstructure, mineralogy, fabric, degree of weathering, and cementation type. The content of clay substance is a key decisive factor behind shale properties, but the engineering properties of any shale with a given mineralogical composition may range between those of soil and those of a real rock Density Shale density is affected by its burial depth and amount of infillings. The increase in overburden leads to decrease of cracks and open joints and as a result an increase in density. Deen (1981) concluded that the bulk density of shales to be between 2 to 2.73 t/m 3 based on tests on different shales. This variation in density is due to the influence of existence of different minerals, different 18

47 organic content, and different porosity. Densities of shales of Eau Claire Formation and Maquoketa Formation along with their porosity and depth are presented in Table Porosity Porosity of a shale, which changes during its geological history, affects shale density, strength, and elasticity. Porosity reduces with increase in the depth of burial. For argillaceous material, permeability is usually correlated with porosity, e.g., Sclater and Christie (1980). Porosity in shale also changes with the amount and distribution of the clay minerals within the sandstone (Crain, 2000). Freeze and Cherry (1979) has reported the porosity for shale (rock) in the range of 0.0 to 0.1. Porosity of undisturbed shales of Oligocene and Miocene age from Eastern Venezuela has been reported by Hedberg (1936), which are in range of to for depths between 89 and 1882 m. These porosity values along with the corresponding depth of samples are presented in Table 2.9 and plotted in Figure 2.8, where a linearly decrease in porosity with increase in the depth is observed. Generally in sedimentary areas, porosity reduces nonlinearity with depth as a result of compaction. The mean effective stress is the controlling property for this compaction process (Schön, 2011). Many simple empirical porosity-depth relationships for different lithologies have been proposed, which fall into four groups: Exponential, Linear, Parabolic, Power law (Liu and Roaldset, 1994). For instance, Sclater and Christie (1980) studied various relationships between 19

48 porosity and depth. They suggested the following expression for the shale from the northern North Sea: n = exp( z) (2.1) where n is the porosity and z is the depth in meter. The initial porosity is specified as in the above formula because of higher porous structure of the clay component 1 (the initial porosity is assigned as 0.49 in a similar expression for sand). Moreover, the rock skeleton compressibility of the shale is m 1 in the above formula which is larger (meaning softer) than that of the similar formula for sand ( m 1 ). Schön (2011) demonstrated the effect of mechanical compaction process in shales, and in comparison with sands, on porosity-depth relationship schematically in Figure 2.6. According to this figure, the depositional porosity of shales are usually higher than those of sands. At shallow depths and during mechanical compaction, the porosity gradient with depth of shales is steeper than that for sands; while at greater depths and during chemical compaction (the quartz cementation of sands), the porosity gradient with depth will be steeper for sands than that for shale (Avseth et al., 2005). The compaction process may be due compressibility of rock skeleton under effective pressure increase due to overburden sediment. The drainage of pore fluid and grain rearrangement may be other process contributing to shale compaction (Schön, 2011). 1 Porosity values in a range of 0.40 to 0.90 are normal and have been previously noted in the case of ocean superficial sediments. For example, porosity values exceeding 0.77 has been reported for cores from the Red Sea at the depth of 1 m (Manheim et al., 1974) 20

49 Pelchau et al. (1997) reported a range of 0.50 to 0.90 for the porosity of shales based on compilation of porosity-depth curves in literature. Revil et al. (2002) assumed that decrease in porosity to be proportional to the difference between existing porosity and residual porosity, the one at the end of compaction process, and then presented the following formula for shale (Oman abyssal plain) based on field data from Fowler et al. (1985): n = exp( p ) (2.2) where p is the effective stress in Pa. The above formula implies a residual porosity of 0.07, at p, and an initial porosity of 0.56, at p = 0. Porosity and depth of shales from Wisconsin (Eau Claire Formation and Maquoketa Formation) are also presented in Table 2.8. Porosity and depth of various shales of Cretaceous age are presented in Table Water content Banks (1971) estimated the water contents of shales to be in a range of 5% to 35%. Generally the compressive strength of a sample decreases with an increase in water content (Horn and Deere, 1962). Colback and Wild (1965) reported that the compressive strength of a saturated shale was about half of that of the dry shale. Similar trends have been reported by Kjaernsli and Sande (1966) and Moon (1993). Hsu and Nelson (1993) found a strong correlation between the unconfined compressive strength and water content for clay shales of North America (Figure 2.9). Therefore, one of the experimental problems is the effect of fluctuations of water content on measured behaviour. Effect of a small change in water content on strength depends on initial value 21

50 of water content, usually more prominent in low water content range. To remove the sensitivity of soil sample to changes in water content, the sample is saturated before onset of test and kept saturated during the test; thus water content is maintained constant Permeability Permeability is a measure of the fluid flow rate through a porous material due to a pressure gradient. Permeability of argillaceous units are very low, usually between to m 2 (or hydraulic conductivity of to 10 9 m s) for porosities less than 0.4 (Neuzil, 1994). Permeability range of shale in comparison with other geomaterials is demonstrated in Figure Best and Katsube (1995) reported shale permeability, to be in a range of to m 2, decreases as a function of pressure. Shales require a long time to establish a steady-state flow. Hence, it is not generally practical to determine the permeability of such a low permeable soil using steady state methods. Thus, investigators have correlated permeability with porosity. For instance, England et al. (1987) suggested an expression to estimate permeability based on porosity (fraction) for shales and mudstones: where k is permeability, in md, and n is porosity. k = n 8 (2.3) An intrinsic permeability anisotropy may exist due to the sedimentation. A particular type of macroscopic anisotropy is observed in finely laminated sediments, which is created by an alternating change of permeability between coarse and fine layers or between shale, to 1 md, and thin sand layers, 100 to 10,000 md (Schon, 2011). Experimental data from a North Sea well 22

51 exhibited that the ratio of horizontal permeability to vertical one may vary from 0.1 to 1000 in a reservoir with porosity up to 0.30 (Bang et al., 2000) Mineralogy Shale generally contains a mixture of clay-sized particles such as quartz, feldspar, micacalcite, iron minerals, clay minerals (illite, smectite, chlorite, and kaolinite) and organic matter (Underwood, 1967). The source of formation, climate, and diagenetic history of shale have influence on the type of its clay minerals. Illite and chlorite are more common in marine shales among clay minerals, while smectite and kaolinite are more common in non-marine environment (Brown et al., 1977). High percentage of illite and smectite in a shale leads to lower shear strengths and higher swelling potential than a shale with a high percentage of kaolinite and/or only low percentage of illite,smectite, or other mixed-layer minerals (Underwood, 1967). Behaviour of shale is largely controlled by amount and type of its clay minerals. Clay content determines the specific surface area of soils and thus their plasticity is dependent to a great extent by clay content (Kirchhof, 2006). Dependence of elastic parameters on clay content had been reported in literature (Vanorio, et al., 2003). Different methods had been used to determine the amount and type of clay minerals of shale such as X-ray diffraction (XRD), scanning electron microscopy (SEM), dielectric constant measurement (DCM), and cation exchange capacity (CEC). 23

52 X-ray diffraction (XRD) analysis XRD is a semi-quantitative method for mineralogical analysis of soils. In this method, X-rays are used to probe the crystal structure of minerals. The various atoms in a mineral are ordered in a regular fashion and form layers with a definite interatomic spacing. From the difference in the paths travelled by the X-rays reflected by the various layers of the crystal, the diffraction angle is calculated based on the Bragg s Law. The intensities of the diffracted X-rays as a function of measured angle for each mineral are unique and thus the mineralogical composition of each sample can be identified (Mah, 2005). Details of principle and application of this method can be found in literature (Reynolds, 1989a; Reynolds, 1989b; Srodoi, et al., 2001; Harris and Norman, 2008; Hubert, et al., 2009) Effect of clay content and mineralogy on permeability Progressive decrease in permeability with increase in clay content has been observed by several researchers in different geomaterials, including sandstones (Thompson, 1978), shales (Xu and White, 1998), and mudstones (Dewhurst et al., 1999). Investigation of permeability of illite-rich shale, recovered from the Wilcox Formation, demonstrated that permeability in both parallel and perpendicular to bedding depends on clay content. Comparison of data and best fit relations between permeability and effective stress for low clay content samples (40%) and high clay content samples (65%) reveal a decrease in permeability of a factor of about five times (Kuwano et al., 2000; Kwon et al., 2004). 24

53 Microstructure Engineering behavior of a geomaterial is dependent on its microstructure, fabric, and mineralogical composition (Yumei et al., 1993). Mechanism of deformation have generally been inferred from macroscopic and microscopic models for clay shale (Jordan et al., 1989). Internal structural features such as micro-cracks as well as water within inter-layers of clays may control deformation and strength of shale (William, 2005). Ibanez et al. (1993) investigated the influence of micro-cracking in shale by carrying out triaxial compression test on illite rich shale at various confining pressures. Based on optical microscopy and transmission electron microscopy of sheared shales, they made the following observations: - Brittle micro-cracking and dilatant mechanisms have contributed to deformation. - Fine scale bending in individual illite and chlorite platelets has took place. - Micro-crack bands were common within the shear zones regardless of the degree of orientation relative to the laminations. Dilatant mechanisms of micro-cracking and fracture have been reported in shale studies (Bell et al., 1986; Christoffersen et al., 1990; and Mares et al., 1990). The shear on clay platelets has been assumed to take place by frictional sliding on hydrated clay surfaces in these studies. Plastic deformation is a result of either micro-cracks development or localized plastic yielding (William, 2005). Different reasons have been suggested for development of micro-cracks: - Different elastic rebound of constituent minerals of shale after overburden stress relief. 25

54 - Cooling induced thermal cracking. - Microhydraulic fracturing of overpressured pore fluid due to overburden relief. - Concentrated bottom-hole stressing (drilling induced disking, petal, and petal-centerline fractures resulted from concentrations of in-situ stress by the well-bore bottom-hole cavity). - In-situ microcracks (Vernik, 1994). - Internal structural deformation due to rearrangement of clay platelets as a result of compaction (Bennet and Hubert, 1986). Microhydraulic fracturing, which is common in shale during erosion, happens when pore pressure exceeds the normal total stress acting on the rock. Formation of microcracks is a direct result of microhydraulic fracturing (Meissner, 1978). Geological processes such as cementation have influence on microstructure of a soil. The cementation process usually follows compaction and includes precipitation of mineral material in the pore spaces or pre-existing microcracks (Bell, 1993). This cementing agent forms bonds between particles, which resist the development of cracks. Source of the cementation material may be partial intrastratal solution of grains, or may be extraneous, transported by pore fluid (William, 2005). Experiments on Pierre shale revealed that clay minerals were apparently cemented to detrital grains such as quartz and calcite (Olgaard et al., 1997). They described cementing mechanism as a wrapping process between the phyllosilicate framework and detrital grains. Cementation process in shale may happened during deposition of sediments in which ions such as K +, Na +, and Ca ++ 26

55 reacted directly with the clay minerals in depositing basin lakes. These ions occupy the open pores existed between clay mineral platelets (Bennet and Hubert, 1986). Bjerrum (1967) presented a model for formation of clay shales based on the consolidation and subsequent unloading of clay deposits (Figure 2.11). In the shallow burial state, the effective stresses overcome the osmotic stress and collapse the clay spacing to less than 2 nm. In the mechanical deformation stage, consolidation continues by rearrangement of particles and changing their shape. This stage corresponds to emergence of nonlinearity in the water content-log pressure curve. In the recrystallization stage, geothermal temperatures have reached to that lead to initiation of diagenetic alterations in the clay minerals (Hower et al., 1976). In the last two stages, the original depositional microstructure is demolished and clay particles are arranged in stacks in a preferred orientation. Increasing pressure and temperature lead to precipitation of cement. Many clay shales, such as Pierre shale and Bearpaw shale, has formed in the mechanical stage (Wroth, 1987). Some clays, such as the Bowen basin shale in Queensland, have formed in the recrystallization stage (Hower et al., 1976). Gens and Alonso (1992) and Huckel (1992) have briefly described the microstructure of highdensity clay or shale. Their description is based on previous studies on clay mineralogy, such as Collins (1984) and Stepkowska (1990). Three basic microfabric features are recognized: - Elementary particles clusters, which consist of clay particles in a parallel arrangement. Water absorbed within this parallel structure cannot flow in ambient conditions; - Particle assemblages (matrix), which form by array of elementary particle clusters. The water that fills the intramatrix pores includes free water and intercluster water. Under 27

56 normal condition, free water is capable of moving due to hydraulic gradient, while intercluster water envelopes particle clusters and is restrained from flow. - Pore spaces (Wong, 1998). Wong (2001) performed triaxial tests on samples from Labiche shale at various confining pressure. This shale has a clay content of about 18.8 %, with water content in range of 11.5 % to 12.4 % over a depth of 61m and 83 m. The plastic and liquid limits lie in the ranges of 19.2 % to 24.1 % and 44.6 % to 45.8 %, respectively. The pre-peak portion of the resulted stress-strain curve are linear and independent of the confining pressure. This type of behaviour implies that the mechanical properties of the cement bonds control the strength component and modulus in the prepeak region Clearwater clay shale Cretaceous Clearwater Formation The Clearwater Formation creates a cap for underlying oil sands, the McMurray Formation. This formation comprises primarily laterally extensive, flat lying clay shale, clay silts and fine grained sands deposited in a shallow marine environment (Kosar, 1992). The Clearwater Formation has not been divided into formal members, except for Wabiskaw Member (Kcw), which overlies the McMurray Formation. Isaac et al. (1982) and Isaac and Dusseault (1984) have divided the Clearwater Formation into several informal members based on characteristic geophysical log responses from the oldest to youngest as follows: Kca, Kcb, Kcc, Kcd, Kce, Kcf and Kcg. All members vary laterally in thickness and lithology. The Kcb and Kcd 28

57 tend to be sandy while Kca, Kcc, and Kce tend to be clayey. Members tend to alternate in glauconite content, a greenish mica group mineral, with the Kcw, Kcb, Kcd, and Kcf members being rich in this mineral. Since this formation was buried under 1000 meters of overburden before regional uplift and erosion, it is very heavily overconsolidated (Lobb, 1982). The sediments were subjected to temperatures of up to 40 C during burial (Kosar, 1992).The Clearwater Formation was deposited with a regional dip of 0.1 to 0.4 degrees towards the southwest (Parsons, 1990). Most of the clay layers in the formation are sheared and therefore at their residual strength. Different processes have been proposed as the cause of the preshearing in these layers: bedding plane slips, tectonic deformations, and shearing associated with glacial tectonics (Morgenstern, 1987). In-situ stresses are variable in the Clearwater Formation near Cold Lake, Alberta. Therefore, K 0 (the ratio of horizontal and vertical in-situ stresses) can be less than, equal to, or greater than one within an area of several square kilometers (Gronseth and Kry, 1987). No tectonism or faulting of any consequence has took place since maximum burial except for karst solution collapse within the Devonian limestones and glacial thrusting (Issac and Dusseault, 1984). No depressions in the limestone has been found (Hackbarth and Nastasa, 1979), hence the karst collapse cannot be the cause of clay layers shearing. Therefore, the glacial tectonics is the most probable cause for the sheared clay layers. The bedrock was sheared by the 2000 m thick advancing ice sheets. Ice-thrust features are widespread on the Prairies in North America (Tsui, 1987). 29

58 Studies on Clearwater clay shale Syncrude oil sands mine at north of Fort McMurray, Alberta A Syncrude oil sands mine is located 40 km north of Fort McMurray, Alberta. The dyke of the tailings basin is constructed on two Clearwater clay shale units, Kca and Kcw (El-Ramly et al., 2003). Kca is a 5 m thick dark grey slickensided clayey silt, thinly laminated with churned bedding. Kca is a weak highly plastic unit that was weakened by glaciotectonic deformation. Kcw, the layer underneath the Kca material, is an approximately 2 m thick grey-colored and fissured clay shale. The Kcw layer, a very stiff material, consists of thinly laminated dark slickensided gray clay silt. The Kcw material is underlain by the oil sand of the McMurray Formation (Alencar et al., 1994). Major horizontal movements have been observed along the Kca unit while the Kcw layer exhibited no significant movement due to dyke construction (Wedage et al., 1998). The Clearwater Formation was prone to thrusting and transportation by glacial ice based on the geological evidence. A detailed description of the geology at the tailings pond is presented in Fair and Handford (1986), which reveals existence of distinctive shear planes in the glacially disturbed clay shale raft, Kca, under the downstream slope. Results of direct shear tests conducted on 80 samples of Kca facies of the Clearwater Formation are presented in Figure The mean failure envelope, which results in a mean residual friction angle of 7.5, is also plotted in Figure 2.13 (El-Ramly et al., 2003). Due to the scatter of the data around the mean failure envelope, there is a high uncertainty in the value of the residual friction angle (in the range of with the standard deviation of 2.1 ). 30

59 Alencar et al. (1994) reported direct shear tests conducted on intact and slickensided samples of the clay shale. They reported friction angles of 23 and 7.5 for Kcw at peak and residual states, respectively (with no cohesion at peak strength). For Kca, the friction angles of 23 and 12.5 has been obtained from tests on intact and slickensided samples, respectively. The residual friction angle of Kca is reported 7.5, same as that of the Kcw, for both tests on intact and slickensided samples. Wedage et al. (1998) performed a series of direct shear tests and ring shear tests on Kca samples, obtained from 3 m depth. Kca samples were classified as high plastic clays, CH, according to the Unified Soil Classification system. They reported a clay fraction of 49% for this clay shale along with liquid limit and plasticity index of 135% and 107%, respectively (Table 2.12). In addition, results of direct shear tests on Kca sample are presented in Table They observed that the residual strength increases with the shear rate and found that rate effects depend on soil plasticity Horizon oil sands project at north of Fort McMurray, Alberta In recent oil sand plant developments, large storage tanks (up to 60 m in diameter and 20 m high equal to a vertical load of 180 kpa) have been constructed in the Horizon oil sands project site near Fort McMurray, Alberta. These tanks are commonly founded over the Cretaceous Clearwater Formation, which might have been subjected to pre-shearing during glaciations (Moore et al., 2006). Overall stability was recognized as the primary geotechnical design issue (Moore et al., 2011). 31

60 Due to the uncertainty associated with the behavior of the clay shale and the risk of improper tank performance (excessive short- and long-term settlements of the tanks foundation), a full-scale field load test was carried out to investigate foundation performance. A 40 m square test fill with a maximum height of 9 m and two vertical faces was constructed using local sand. The foundation performance was monitored using 18 vibrating wire piezometers, 8 slope inclinometers (Figure 2.14), and 21 survey monitoring points (Moore et al., 2006). The test fill was loaded at a rate of 10 kpa per day. The test was stopped when the fill height reached a vertical load of 150 kpa and there was 40 mm of horizontal movement in a concentrated shear zone in the clay shale. Zones of shear deformation was observed in the upper 1 m of the Clearwater Formation at all of the slope inclinometers. These movements were significant in the Kcc-710 with lesser amount in the underlying Kcb-700. A movement zone was also detected near the bottom of the Kca-625 facies in the slope inclinometers extended into the oil sand (SI01 and SI14). Cumulative and incremental deformations perpendicular to fill face measured 10 m off the west face by SI01 are shown in Figure An immediate pore pressure response to loading was observed in piezometers measurements. The ratio of change in the measured pore pressure to the change in total vertical stress at the tip of each piezometer was calculated, using Boussinesq s equation, for each increment of fill height. This ratio was in the range of 0.6 to 1 for the piezometers ending in Kcb-700 and less than 0.4 for those ending in Kcb-650, with the exception of VW05B (the calculated ratio varied between 0.5 and 1). Moore et al. (2006) estimated a time frame of 5 to 10 years for full dissipation of induced excess pore pressure under the fill. 32

61 The actual performance of the foundation was measured during the hydro-testing of the tanks. Three tanks in West Tank Farm and ten tanks in the East Tank Farm, in the Horizon oil sands project site, were instrumented and monitored during the hydro-testing. The tank 72-TK-1A, constructed in the West Tank Farm and located in a place where the Clearwater Formation was thick and shallow in comparison with the other tanks, was the most instrumented tank during the hydro-testing (Moore et al., 2011). Grain size distribution, Atterberg s limits, and moisture content of the Clearwater facies at the West Tank Farm are presented in Table 2.14 (Pinheiro et al., 2013). Sixty equally spaced monitoring points were located around the perimeter of the tank, which were surveyed to determine the settlement of the tank foundation. Settlements at the center of the tanks were determined by observing the displacements of the center post of the tank. The tank foundation settlements were also monitored using four settlement plates installed around the inside edge of the tank. The horizontal displacement was measured by slope inclinometers: three located at 10 m offset from the tank edge and two more at 16 m and 32m offset from tank edge. The foundation pore pressure response was monitored using vibrating piezometers installed at two depths beneath the tank center. An initial estimates of soil parameters were made from field and laboratory tests (Table 2.16): First, soil strengths were obtained from results of a multistage consolidated undrained triaxial test and direct shear tests (Table 2.15). Second, soil bulk moduli were estimated from the consolidation phase of the multistage triaxial test and seismic cone penetration (CPT) tests. Third, shear moduli of facies were obtained from seismic CPT tests. 33

62 A Mohr-Coulomb constitutive model in conjunction with a strain-softening function was incorporated in the FLAC to update the elastic parameters with changes in stress and strain. The data from the full-scale load test was used to calibrate an explicit finite difference model in FLAC to obtain a reasonable set of parameters for the mentioned constitutive model (Table 2.17). An iterative process was followed to obtain a reasonable match between FLAC and observed behaviour of the test fill foundation, including profiles of horizontal displacement and pore pressure measurements. The model and the calibrated parameters were implemented during the detailed design stage (Moore et al., 2011) Time-dependent behaviour of clays There are widespread evidence of time-dependent behavior of clay in construction fields, e.g. Crawford and Morrison (1996). Most soils exhibit time-dependent stress-strain behavior because of their viscosity (Mitchell, 1993). Clayey soils containing montmorillonite mineral depict strong time-dependent behavior such as creep and swelling, both of which have strong influence on the deformation and failure of structures (Yin and Tong, 2011). Processes related to the soil viscosity can be categorized as follows (Tong, 2011): - Creep, viscous deformation in the course of time under constant effective stress. - Swelling, the reverse behavior to creep process in a saturated soil. - Stress relaxation, decrease of stress over time in a material that is strained up to a specific value and kept constant with time. Stress relaxation is considered the opposite of creep phenomenon. 34

63 - Strain rate dependency or loading-rate effects, change in the stress-strain behavior of soil with strain or stress rate. - Long-term strength, the probable decreased strength of a soil under a constant load after a long time (for instance, undrained shear strength). Other classifications of rheological behavior of clays were introduced in literature. For instance, Augustesen et al. (2004) categorized the time-dependent behavior into the: creep, stress relaxation, rate dependency, and accumulated effects. It is necessary to adopt a constitutive model that accounts for time-dependency of the stressstrain-strength properties of soils to achieve realistic solutions for time-dependent engineering problems. The relations between stress, strain, and time are aim of the rheological investigation. Three major tasks in geomaterials rheology are: study of creep, examination of stress relaxation, and investigation of the long-term strength (Feda, 1992). The schematic stress-strain-time behavior of a geomaterials is demonstrated by curves in the Figure For a specific constant effective stress of σ (such as section 1 1 in Figure 2.16a) the strain increases with time, creep behavior, and the creep curve, shown in Figure 2.16b, can be obtained by recording the strain after time intervals of t 1, t 2, t 3,. The stress relaxation curve versus time, Figure 2.16c, can be found by following a vertical section, 2 2 in Figure 2.16a. Examination of creep and stress relaxation constitutes two main tasks of rheology. Strength of material, peak stresses, also decreases with time (Figure 2.16a) to the long-term resistance, dashed line A. The investigation of the long-term resistance of material represents the third main task of rheology. 35

64 Creep Geomaterials subjected to a constant stress deform over time. Gradual increase of strain under constant sustained effective stress over time is called creep behavior. The strength of the material structure specifies the magnitude of this time-dependent deformation. The structure strength depends upon the dimension, composition, and fabric of the structural units (grains or clusters of particles), their geometrical arrangement, the magnitude, shape, and distribution of pores, the internal stress state, and the nature of the bonds in and between the structural units (Feda, 1992). Due to temperature variations and poorly defined boundary conditions, field tests are not alone sufficient for creep investigation. On the other hand the experimental results mirror true behavior of geomaterials distorted by parasitic effects, which should be minimized and removed from row data. Parasitic are categorized into two groups: - Effects that alter the state of the sample such as temperature and water content. - Apparatus related effects such as frictional effects on the base platen of a triaxial equipment (Feda, 1992). Oedometer test may be the most common creep test, generally used to study the secondary compression (Ladd and Preston, 1965; Walker and Raymond, 1968; Mesri and Godlewski, 1977; Tavenas et al., 1978; Graham et al., 1983; Leroueil et al., 1985; Mesri and Castro, 1987; Mesri and Ajlouni, 1996; Niemunis and Krieg, 1996; Yin, 1999). Beside odometer tests, triaxial creep tests have been used in most laboratory investigation of the time effects associated with undrained shear strength of clays. Time dependence of clay response is illustrated quite well in literature, e.g. Singh and Mitchell (1968), Akai et al. (1975), Tavenas et al. (1978), and Havel (2004). Only a few tests 36

65 were carried out on direct shear apparatus to investigated creep phenomenon (Tian et al., 1994). Experimental problems associated with investigation of time-depended behavior include membrane linkage, sample end-effect, temperature fluctuation, and limited stress conditions (Jamiolkowski et al., 1985) Effects of fluctuations of temperature on time-dependant behavior Similar to the increase of the water content, the increase of temperature increases the deformability of geomaterials. The exact effect of temperature change depends on soil structures and stress levels. In general, tests on soils with weak structure and under high stress levels or in undrained conditions in which pore-pressure is susceptible to the temperature, are more sensitive to temperature fluctuation. Range of allowable temperature fluctuation for creep tests from various references is summarized in Table Swelling of clay shale Many researchers have investigated the swelling potential of clay shale (Madson and Muller- Vonmoos, 1985; Wong, 1998; Powel et al., 2013). Different methods have been used which correlate the soil indices or mineral composition with swelling potential. Swelling potential increases with the increase in the expansive mineral (such as smectite) content in soils (Nelson and Miller, 1992; Jones and Jefferson, 2012). The swelling potential of soil is dependent on its initial water content, void ratio, structure, insitu stress, and the amount of clay minerals (Bell et al., 2001). Moreover, any change in pore water 37

66 chemistry (ions presented and their concentration) that alters the double layers condition leads to a change in swell potential (Mitchell, 1993). The existence of certain minerals determines the expansive nature of soil. Smectite, nontronite, vermiculite, illite, and chlorite are expansive clay minerals (with different degrees of expansion). Nonetheless, the presence of non-swelling materials such as carbonate and quartz dilutes the effect of expansive minerals (Kemp et al., 2005). Free swell test is an appropriate index test for shales that do not slake. For clay shales, linear strains of between 0.02% and 7% are expected. The test results depend on the initial moisture content, rate of wetting, and the chemical composition of the fluid (Olivier, 1979). This index test serves as a first indication of the problem of swelling. Differences in the measured swelling strains in different directions provide an indicator of swelling anisotropy factor of soil. In this test the unrestrained deformation in three directions are recorded with time. Both horizontal and vertical swelling usually vary linearly with logarithm of time between ten and 100 days (Lo and Hefny, 2001). The slope of this linear relationship is termed as swelling rate, i.e., percent strain per logcycle of time. The measured swelling rates of some shales and shaly limestones are presented in Table Stress relaxation Stress relaxation regularly occurs in field and practice. For example, changes in horizontal stress and porewater pressure around a penetrating device immediately after termination of penetration lead to stress relaxation. Another example is the stress relaxation due to short-term change in lateral earth pressure after support system installation (Zhu, 1999). 38

67 Creep and stress relaxation, based on their definitions, are assumed to be two aspects of a unique phenomenon (Feda, 1992). Previous studies postulated the similar mechanisms occurring in creep and stress relaxation in soils, while this hypothesis has not been supported by any experimental or field study. With validity of this assumption, the deduction of the course of relaxation from that of the creep and vice versa will be possible. Both creep and relaxation are special forms of a general stress-strain-time relation for geomaterials, i.e. they both are assumed to lie on a unique stress-strain-time surface. In general, results of creep tests have been used to find a basic constitutive law for the material, whereas the stress relaxation results have been used to verify the developed creep law (Tong, 2011). Since creep is more significant in the engineering practice, the most of the investigations in literature are related to creep rather than relaxation. Creep tests, although of significantly longer duration, have been used more extensively than triaxial stress relaxation for the study of time effects on clay response. The reason for this was probably the technical difficulties associated with the running of true stress relaxation tests (Silvestri et al., 1988). Stress relaxation has been examined by relatively few researchers in the past. Stress relaxation tests have not been as common as conventional creep tests, but always were considered as an important alternative way for investigating the rheological properties of a material. Relaxation tests may be performed as easy as creep tests with the technical facilities existing today. The stress relaxation test is the only test to determine the long-term strength of the soil skeleton as it is. In a drained creep test, it is difficult to separate primary consolidation effects from those due to creep. In an undrained creep test, there is difficulty in relating the applied stress to the 39

68 nonhomogeneous strain state throughout the sample, since both the effective stresses and the soil structure are changing continuously as a result of increasing strains. Therefore, stress relaxation tests offer better insight into the mechanisms controlling the mobilization of the shear strength in clays than creep tests (Silvestri et al., 1988). Performing stress relaxation tests is another way for estimating the creep parameters (Lacerda and Houston, 1973; Ladanyi and Benyamina, 1995). Moreover, using a relaxation test is more appropriate than using a creep test to study time-dependent stress-strain behavior of soils in failure states, since the failure states last only a very short time in the creep test (Tong, 2011). In other words, the stress relaxation test has advantages of a strain-controlled test against the creep test, a stress-controlled test. Yoshikuni et al. (1995a, 1995b) performed special odometer tests with different phases of consolidation and relaxation. They conducted stress relaxation tests with a constant volume strain by not allowing any drainage and observed significant increase in the pore water pressure during relaxation. They related the magnitude of generated excess pore pressure to the duration of consolidation before onset of the stress relaxation and found that the higher the strain rate at which secondary consolidation is terminated, the higher is the generated excess pore fluid pressure. Similar results have been observed in isotropic consolidation tests followed by undrained creep tests (Holtzer et al., 1973) There is a disagreement among researchers about the existence of a final relaxed stress level: - Some researchers did not find a limiting equilibrium stress or deviator stress in undrained triaxial relaxation tests after 24 hours (Vyalov and Skibitsky, 1961 and Wu et al., 1962). 40

69 Akai et al. (1975) did not obtain a limiting value after approximately 167 hours of stress relaxation tests on two remolded saturated clays. Zhu (1999) also reported no relaxed level after about 1000 min of stress relaxation tests on samples from Hong Kong marine deposits. - While other researchers have reported a final relaxed stress level. For example, a limiting equilibrium stress level was obtained in a series of undrained triaxial relaxation test on four saturated remolded clays performed by Oda and Mitachi (1988). In addition, Silvestri et al. (1988) and Sheahan et al. (1994) reported similar results. Schematic results of three stress relaxations tests are demonstrated in Figure After an initial time period, the deviatoric stress variation against the logarithm of time is found to be linear (Lacerda and Houston, 1973). Similar pattern was reported in previous studies: Murayama and Shibata (1961), Vyalov and Skibitsky (1961), Saada (1962), Christensen and Wu (1964), Murayama et al. (1974), and Akai et al. (1975). The slope of deviatoric stress versus logarithm of time depends on the axial strain level prior to the onset of relaxation (Oda and Mitachi, 1988) and is independent of confining pressure (Lacerda and Houston, 1973). One-dimensional relaxation tests can be conducted both in creep region and in swelling region (Tong and Yin, 2011). Swelling in a saturated soil is due to time-dependent expansion of the skeleton of the saturated clay plates with negative charge due to the entrance of the absorbed water with dipole attraction to the clay surface. Therefore, swelling is opposite of creep process in a saturated soil (Mitchell, 1993). Singh and Mitchell (1968) proposed power-law dependence of the creep rate on time. By inverting Singh and Mitchell s (1968) equation for creep, Lacerda and Houston (1973) established an empirical equation for the decayed deviatoric stress: 41

70 q = 1 s log ( t ), for t > t q 0 t 0 0 (2.4) in which q 0 is the deviatoric stress at the onset of relaxation, q is the deviatoric stress at any time t, and s is an experimental coefficient. A series of stress relaxation tests on undisturbed San Francisco Bay mud, a remolded kaolinite, clean quartz sand, and compacted clay validated the above equation (Lacerda and Houston, 1973) Sheahan et al. (1994) carried out K 0 -consolidated undrained triaxial compression relaxation tests on resedimented Boston Blue clay. They found that the variation of pore pressure during the relaxation is not significant. This observation is consistent with the findings of Lacerda and Houston (1973). Moreover, they suggested that multiple relaxation tests could be conducted reliably on a single sample (Sheahan et al., 1994). Results of undrained triaxial stress relaxation tests on a remolded bentonite, performed by Hicher (1988), showed that no pore pressure is generated at the strains of 2 % and 4 %; while small excess pore pressure was observed at the test with a constant strain of 6 %. He concluded that the stress relaxation leads to pore pressure increase at large strains Rate effects on clay shale - experimental studies Strain rate studies on hard dry rocks have shown an increase in the strength of sample and a decrease in strain to failure with increase in the strain rate (Jaeger and Cook, 1976). Results of consolidated undrained triaxial on a Jurassic shale revealed an increase of up to 40 % for a 30-fold strain rate increase (Wichter, 1979). 42

71 Swan et al., (1989) had investigated strain rate effects in triaxial compression tests on saturated Kimmeridge Bay shale, a soft shale from Dorest, U.K. Their results of undrained tests showed that there is an insignificant effect of strain rate up to an axial strain rate of 0.1/min; thereafter both the peak deviatoric stress and the strain at peak deviatoric stress increase with the axial strain rate, the latter more rapidly than the former. They observed in drained/undrained tests (drainage provided and being assumed to be complete when the axial strain rate had fallen to a very low value) that the peak deviatoric stress and the strain at peak first decreased to a minimum strength with the increase in axial strain rate at a strain rate of 0.1/min, then increased with further increase in the strain rate. The rate of increase of the peak stress and the strain at peak, at higher strain rates, is lower for the drained/undrained tests than the undrained ones. Moreover, they reported a change in failure mode, from a macroscopic fault plane deformation at low rates to a disturbed shear microcracking at high rates, at this distinct critical rate (0.1/min). Cook et al. (1991) studied the effects of strain rate and confining pressure on the deformation and failure of shale by performing triaxial tests on two nonswelling shales, of Jurassic Age, from outcrops on the English coast. They concluded that shale behavior is governed by effective stress at low strain rate, while it depends on total stress at high strain rates. In addition, they found that the strength and ductility of shale with very high pore pressure increase rapidly with the strain rate. Most of their observations were explained in terms of nonuniform effective stresses within the shale. These stresses are nonuniform because the extremely low permeability of the shale restricts fluid flow, even over microscopic distances, around growing cracks. 43

72 Ibanez and Kronenberg (1993) performed strain rate stepping (progressively decreased the axial strain rate) in triaxial compression tests on an illite-rich shale. Strength decreased 11 %, 9 %, and 7 % over three times decrease in the axial strain rate for samples bedding oriented parallel, normal, and at 45 to the loading direction, respectively. Al-Bazali et al. (2008) reported the experimental results on the effect of strain rate on two types of shale. They observed decrease and increase in the deviatoric stress, respectively, for the soft Pierre I shale and the highly compacted Arco shale with increasing strain rate, which was attributed to pore pressure build-up and dilatancy hardening effects. According to dilatancy hardening mechanism, the pore volume in a sample increases by dilatant cracking. The excess volume is filled by the pore fluid flow from outside of sample at low strain rates, while this flow is restrained at high strain rates and the pore pressure drops because of low permeability of the rock. As a result, the effective stress increases inside the sample at high strain rates leading to an increase in shear resistance (Brace and Martin, 1968). Al-Bazali et al. (2008) mentioned formation of micro-cracks within Acro shale network which lead to dilatancy and thus pore pressure reduction as a reason for strength increase with strain rate. They suggested dominance of pore pressure build-up effect is the reason for the decrease of Pierre I shale strength with the strain rate. No excess pore pressure build-up was detected in their drained biaxial compressive tests when the strain rates were /s and /s for the Pierre I shale and Arco shale, respectively. 44

73 Long-term strength The long-term strength stress-strain curve represents shear stresses under which sample will not exhibit any shear displacement even after a long period of time. In other words, these stresses forms a lower bond for the long-term strength of soil. Feda (1992) conducted direct shear tests on Zbraslav sand with constant rate of displacement, paused the shearing at different shear displacement intervals and measured the stress relaxation until shear stress became constant in each stage. Two stress-strain curve can be drawn based on the initial and final stresses measured in each stage. The lower curve represents the long-term strength stress-strain curve Macrorheology (rheological models) Macrorheology is an attempt to analytically describe rheological phenomena by macromechanical approach, which is usually divided into three general categories: - The method of mechanical rheological models, also known as the differential approach. - The method of integral representation, also referred to as the hereditary approach. - Engineering theories of creep. The first method, described before (in section 2.4), predicts real behavior of material with a combination of different elementary rheological models (ideal materials). In the second method, creep is defined by a creep function and similarly the stress relaxation by a relaxation function, which are memory (hereditary) functions describing stress-history dependence of strain and straindependence of stress, respectively (Freudenthal and Geiringer, 1958). Both method are capable of 45

74 characterizing both linear and nonlinear behavior. Generally the nonlinearity is attributed to structural changes, which occur with time, time-induced strain, stress, and stress-induced strain. General theories, widely applied in the field of metals and ice, are applied for determining inelastic creep response of solids in the third approach. Engineering theories of creep do not provide unique methods for describing the creep phenomenon. They are only phenomenological laws based on experimental results. The material structure is not represented in the rheological models because the share of individual mechanisms with specific structures is specified only by the magnitude of the constitutive parameters in the global scale (Kafka, 1984). The structural parameters are derived from data of macroscopic (phenomenological) experiments, which are found by means of analysis of the creep or stress-relaxation curve for viscous materials or the stress-strain graph for elastoplastic materials. This method is based on the assumption that the characteristic features of the microstructure do not alter in the deformation process Method of mechanical rheological models (differential approach) The stress-strain-time behavior of a geomaterials has demonstrated schematically in the Figure 2.16 and discussed in section 2.4. Such a described complex can be simplified in particular cases to ideal material representing only one of the mechanically important characteristics such as, reversibility, plasticity, or time-dependency. Ideal materials are classified in thermodynamic based on their ability to adsorb the deformation work: 46

75 - Elastic materials do not absorb any work, and their structure will not sustain any permanent change, and thus exhibit reversible deformations. The most simple elastic behavior is the time-independent linear one, which is represented by a spring called Hookean element. - Viscous and plastic materials absorbs and dissipates all their deformation work, which is spend on changing their structure, and as a consequence all their deformations are irreversible. Fluids form the category of ideal viscous materials. Their strength is timedependent and are represented by a dashpot, a Newtonian element. Ideal plastic materials exhibit time-independent behavior, dissipating energy in pure shear, represented by a slider called Saint-Venant s element. Stress path independence is the common feature of all the ideal materials, the past history of straining, stressing, etc. does not have any effect on their behavior. The reason for the elastic materials (Hookean solids) is that the structure remain intact during past processes and for plastic and viscous (Saint-Venant s solids and Newtonian fluids) is that significant structural changes remove footprints of all previous processes. It is implicitly assumed in mechanical rheological models that the real behavior of geomaterials may be obtained by implementing different combination of ideal materials (Feda, 1992). Modeling of the mentioned rheological behavior of clay depends upon development of constitutive models based on laboratory tests. The time-dependent response of soil is determined implementing three standard tests: creep test, stress relaxation test, and constant rate of strain test (Augustesen et al., 2004). The simplest combination of ideal material, elastic and viscous, are the following: 47

76 - Maxwell material, viscoelastic homogeneously stressed material: ε = σ η M + σ E M (2.5) in which ε is the strain rate; σ and σ are the stress and stress rate; η M is the Maxwell viscosity; and E M is the Maxwell elastic modulus. - Kelvin material, viscoelastic homogenously strained material σ = E K ε + η K ε (2.6) in which σ is the stress; ε and ε are strain and strain rate; η K is the Kelvin viscosity; and E K is the Kelvin elastic modulus Maxwell material Maxwell s linear nonhomogeneous equation can be solved, considering initial condition of σ = σ 0 at t = 0, to derive a creep expression: or where ε = σ 0 η M t + σ 0 E M (2.7) E D = ε = σ 0 E D (2.8) η ME M E M t + η M (2.9) As indicated by equation (2.7), the isochronic stress-strain relations are linear for t = constant and the strain-time relation is linear for σ 0 = constant, only secondary creep is modelled. According to 48

77 expression (2.9), the deformation modulus, E D, decreases with time and reaches zero at infinite time leading to infinite strain, which is unrealistic. Similarly, for ε 0 = constant (or ε = 0 ), stress relaxation equation for Maxwell s material is: σ = σ 0 exp( E Mt η M ) (2.10) or σ = σ 0 exp( t t r ) (2.11) where t r = η M E is the relaxation time. Solving the above equation for t r: t t r = Ln(σ 0 σ) (2.12) σ = σ 0 e for t = t r, therefore, relaxation time is the time at which the initial stress drops to its 1/e-value Kelvin material In a Kelvin, viscoelastic homogenously strained, material: σ = E K ε + η K ε (2.13) Solving this equation: ε = σ 0 E K [1 exp( t t c )] (2.14) where, t c is the time of retardation: t c = η K E K (2.15) 49

78 Zener s model The Maxwell material exhibits an exponential, reversible, stress relaxation and a linear, non reversible, strain creep; it is also referred to as the relaxation element. The kelvin material depicts an exponential, reversible, strain creep but no stress relaxation; it is also referred to as the retardation element. Consequently, the real material, exhibiting both relaxation and creep phenomena, should be modelled by some combination of Maxwell and Kelvin materials, such as Burgers model (Maxwell in series with Kelvin) or the Zener s model (Hockean in series with Kelvin). The Zener model, also called Poynting-Thompson s model or standard rheological model, was introduced by Zener (1948) for anelastic metals. The constitutive relation of the Zener s model (Figure 2.18) is: (E M + E K )σ + η K σ = E M E K ε + E M η K ε (2.16) Solving the above equation, creep and stress relaxation relationships, respectively, are as follows: ε(t) σ = 1 E M (1 + E M E K [1 exp ( E Kt η K )]) σ(t) ε = E ME K [ E M e (E M +E K )t η K + 1] E K + E M E K (2.17) (2.18) Considering E 0 = E M, E = E ME K E K +E M, and t rs = η K E K, the Zener s material constitutive relation also can be rewritten as: E 0 σ + t rs E σ = E 0 E ε + E 0 E t rs ε (2.19) in which E 0 and E are initial and ultimate deformation moduli, respectively; while t rs is the time of retardation. 50

79 For σ = constant: σ = E ε + E t rs ε (2.20) Solving for strain: ε = σ E σ( 1 E 1 E 0 )exp( t t rs )] (2.21) Substituting σ E = ε and σ E 0 = ε 0 : ε = ε (ε ε 0 )exp( t t rs ) (2.22) where ε 0 and ε are initial and ultimate strain, respectively. The above expression is depicted in Figure 2.18a. For ε = constant, from (2.19): ε = 1 E σ + t rs E 0 σ (2.23) Solving for strain and, then, substituting E M ε 0 = σ 0 and E ε = σ : σ = σ 0 +(σ 0 σ )exp( σ 0 t ) t rs σ (2.24) which is demonstrated in Figure 2.18b. Zener s model realistically reflects both creep and relaxation. In contrast to the Maxwell s material, where the deformation modulus becomes zero when times goes toward infinity, non-zero value for the deformation modulus exist at infinite time (it is evident in diagram of isochronic stress-strain curves in Figure 2.18c). The method of the rheological models is capable of modeling different time effects, however, rheological models are only a general description of the phenomenological behavior and not a 51

80 visualization of the microstructural changes during the deformation process. However, the rheological models illustrate the constitutive relations in a graphical form and different structural information can be extracted by analyzing the viscoelastic behavior on the phenomenological level (Feda, 1992) Engineering theories of creep The geomaterials rheological behavior is governed by their natural structure and its changes during the deformation. Consequently, the parameters of the rheological constitutive relations depend on the state parameters (stress, strain, and time). The relations may express the changes of the state by stress magnitude changes and its redistribution in time, time effects (time-hardening, aging), and strain effects (strain-hardening). Since the theory does not adequately incorporate the time and strain effects, they are evaluated on the basis of experimental data. Therefore, the engineering theories of creep have been formulated, which are represented by Skrzypek (1993) as follows: 1. The total strain model ε = f(σ)g(t) (2.25) 2. The time-hardening model ε = f(σ)g(t) (2.26) 3. The strain-hardening model ε = f(σ)g(ε) (2.27) 52

81 Sobotka (1981) indicates that these theories yield mutually corresponding results if the respective functions are expressed in the form of a power-law. Moreover, the same results can be obtained from the constitutive relation of a Maxwell material with a nonlinear Newtonian element., According to Vyalov (1986), the above theories do not differ much for soils, but the theory of strain-hardening appears to be the most suitable one in practice. Vyalov s conclusion seems to be quite reasonable for all materials where none of the three state parameters (stress, strain, and time that are mutually interrelated) takes a prominent position (Feda, 1992). Based on the similarity between the creep curves of a variety of materials, two main mechanisms acting on the structural level can be distinguished: strain hardening and strain softening (recovery). The strain hardening increases the resistance to flow while the strain softening decreases the resistance. In primary creep, the first mechanism is dominant; in secondary creep there is balance of both mechanisms; and in the tertiary creep, the strain softening mechanism is prevailing (Conrad, 1961; Schoeck, 1961) Method of integral representation (hereditary approach) In this method the current strain is obtained by integration over the entire loading history, all infinitesimal stress changes until the current time. This method has been studied in literature, e.g. Meschyan (1995). The approach has developed for two cases: - Based on linear viscosity, a generalization of the method of mechanical rheological models. - Based on nonlinear material behavior, a generalization of the engineering theories of creep. 53

82 The method of integral representation is usually considered too complex to implement in soil mechanic (Liingaard, 2004). For instance, 28 tests are required to describe a uniaxial stress experimental by nonlinear hereditary theory (Feda, 1992). 54

83 Table 2.1. The Mannville Group sub-units in Athabasca region (Glass, 1997) Sub-unit Age Lithology Maximum thickness (m) Grand Rapids Formation Albian ( ma) Bituminous fine to medium sand 125 Clearwater Formation Albian ( ma) Black and green shales and sand 85 - Wabiskaw Member Glauconitic sands with black fissile shale 35 McMurray Formation Late Barremian to Aptian ( ma) Fine grained bituminous sands 60 Table 2.2. The subdivisions of Wabiskaw Member (Haug, et al., 2014). Subdivision Description Note Wabiskaw A sandstone Wabiskaw B shale Wabiskaw C sandstone Wabiskaw D sandstone and shale A typically thin unit of water-saturated sandstone and silty mudstone A 2-5 m unit with similar lithology to that of the lower Clearwater A thin glauconitic water sand unit Typically contains wavy interbeds of bitumen rich sand and thin steely grey mud Top of Wabiskaw member Can be interpreted as uppermost unit May be absent in Wabiskaw member 55

84 Table 2.3. Facies classification for the Horizon oil sand project (Moore, 2007) Stratigraphy Facies unit code Facies Description Silty clay to clayey silt. Generally laminated with Kcc 720 Silt to clay bioturbated silt-rich laminae/lenses. Medium-todark-grey in colour. Silty-mud with fine-grained glauconitic sand Kcc 710 the presence of Glossifungites surface. Glauconitic interbeds and interlaminae. Sand decreases sandy clay upward. Lower boundary is commonly marked by Kcb 700 Low density Dark grey to black, fissile low-density clay with clay to silty rare to moderate silt laminae/lenses. clay Kcb 650 Glauconitic sandy/silty clay Consist of glauconitic light, medium greenish grey sandy-silty clay. Overlain by black, low-density clay marking the Wabiskaw/Clearwater boundary. Kca 625 Silt to clay Silt dark grey clay to clayey silt. Generally laminated with churned silt-rich laminae/lenses. Minor glauconite. Kcw 600 Glauconitic silty/sandy clay Thinly interbedded to churned/ bioturbated glauconitic silty/sandy dark grey clay. Rare thin indurated beds, commonly near contacts. 56

85 Table 2.4. Relation between investigated clay shale facies and the other stratigraphy units and formations (Moore, 2007) Period Epoch/Formation Stratigraphy unit Facies code Quaternary Holocene Pleistocene Grand rapids Cretaceous Devonian Clearwater McMurray Waterways Wabiskaw member Upper McMurray Middle McMurray Lower McMurray Kce 750 Kce 745 Kcd 740 Kcc 730 Kcc 725 Kcc 720 Kcc 710 Kcb 700 Kcb 650 Kca 625 Kcw

86 Shale Table 2.5. Shale geological classification (Underwood, 1967) Clayey shale (clay 50% or more clay sized particle which shale) may or may not be true clay minerals. 25% to 45% silt sized particles. Silt may Silty shale be in thin layers between clayey shale Soil-like shale bonds. (Compaction or 25%to 45% sand sized particles. Sand sub-shale) Sandy shale may be in thin layers between clayey shale bonds Organic rich, split into thin semi-flexible Black shale sheets. 20% to 35% Ca2Co3 (Marls and shaly Calcareous shale chalk 35% to 65% Ca2Co3) 70% to 85 % amorphous silica often Siliceous shale highly siliceous volcanic ash (quartzose shale detrital quartz) Rock-like shale 25% to 35% Fe2o3 (potassic shale - 5% (cemented or Ferruginous shale to 10% potash) bonded) Carbonaceous matter (3% to 15%) tends Carbonaceous shale to bond constituents together and (oil shale bone coal) imparts a certain degree of toughness Welded by recrystallization of clay Clay bonded shale minerals, or by other digenetic bonds. 58

87 Table 2.6. Classification by British Standard Institute (1957) Consistency Field indication q u (kpa) Very stiff Brittle or very tough >150 Stiff Cannot be molded in fingers Firm Molded in fingers by firm pressure Soft Easily molded in fingers Very soft Extrudes between fingers 20 q u : Undrained shear strength 59

88 Table 2.7. Morgenstern and Eigenbrod (1974) classification Cu0 < 1.7 MPa t50 < 1 hr Medium to soft Cu > 0.6 Cu0 Clay t50 < 1 day Stiff Argillaceous materials w > 1% t50 > 1 day Hard (clay shale) (clay sized particles > 50%) Cu0 > 1.7 MPa Claystone Cu < 0.6 Cu0 w < 1% Mudstone Siltstone LL < 20 Very low Amount of slaking WS = LL 20 < LL < 50 Low 50 < LL < 90 Medium 90 < LL < 140 High LL < 140 Very high Rate of slaking (2 hr water immersion) LI < 0.75 Slow 0.75 < LI < 1.25 Fast LI > 1.25 Very fast Cu0 = Undrained shear strength at natural water content (Q test using 345 kpa chamber pressure) Cu = Strength loss after softening to equilibrium water content w = Change in water content after softening t50 = Time of softening for loss of 50% of Cu0 LL = liquid limit WS = Maximum water content due to slaking LI = Change in liquidity index 60

89 Table 2.8. Porosity, depth, and densities of shales of Eau Claire Formation and Maquoketa Formation (Wisconsin Geological and Natural History Survey, 2013) Formation Depth(ft) Porosity Dry Wet Grain density (g/cm 3 ) Eau Claire Eau Claire Eau Claire Eau Claire Maquoketa Table 2.9. Porosity of undisturbed shale of Oligocene and Miocene age from Eastern Venezuela (Hedberg, 1936) Depth (m) Porosity minimum maximum average

90 Table Porosity and depth of shales of Cretaceous age Stratigraphic unit Location Depth (m) Porosity Min. Max. Ave. Reference Bearpaw shale (siltstone) Mancos Shale (Ferron sandstone) Graneros shale Graneros shale Graneros shale Shale Mentor Formation (shale) Adaville Formation (shale) Adaville Formation (shale) Adaville Formation (shale) Hilliard Formation (shale) Shale Shale Shale Shale Shale Rosebud County, Montana Wasatch Plateau gas field, Utah Hamilton County, Kansas Hamilton County, Kansas Hamilton County, Kansas Hamilton County, Kansas outcrop outcrop Falun, Kansas outcrop Afton quadrangle, Wyoming Sublette County, Wyoming Sublette County, Wyoming Afton quadrangle, Wyoming Black Hills, Wyoming Black Hills, Wyoming Black Hills, Wyoming Black Hills, Wyoming Black Hills, Wyoming outcrop outcrop Stearns (1927) Walton (1955) Hedberg (1926) Birch et al. (1942) Allison et al. (1946) Rubey (1930) 62

91 Table Swelling rate of shales and shaly limestones measured in free swell test (Lo et al., 1978) Age Unite Locality Swelling rate* Number of tests Horizontal Vertical Horizontal Vertical Lockport Gasport Dolomitic Limestone Silurian Lockport Gasport Shaly Limestone Rochester Shale Niagara Cabot Head Shale Hamilton-Wennorth Queenston Shale Oakville Niagara Georgian Bay** Shaly limestone West of Toronto Ordovician Georgian Bay Shale with 7% calcite Georgian Bay Shale with 1% calcite Etobicoke Creek, Downtown Toronto CN Tower, Downtown Toronto Collingwood Black shale Duffin Creek Trenton-Black River Shaly limestone * percent strain per log cycle of time ** also Dundas-Meaford Formation Wesleyville

92 Table Index parameters of Kca samples (Wedage et al., 1998) Liquid limit 135% Plasticity Index 107% Clay size fraction 49% Natural moisture content 23% Table Results of direct shear tests on Kca material (Wedage et al., 1998) Sample type Average internal friction angle at peak Average residual internal friction angle Effective cohesion Intact Slickensided

93 Table Grain size distribution, Atterberg s limits, and moisture content of the Clearwater facies at the West Tank Farm (Pinheiro et al., 2013) Facies Clay (%) Silt (%) Sand (%) LL (%) PL (%) PI (%) W N (%) LI Kcc to to 0.35 Kcb to to 0.16 Kcb to to 0.15 Kca to to 0.13 Kcw-600 No grain size distribution testing

94 Table Direct shear test results of the Clearwater facies at the West Tank Farm (Pinheiro et al., 2013) Facies Sample depth (m) Normal stress (kpa) Friction angle ( ) peak residual Kcc Kcb Kca Kcw

95 Table Initial estimates of soil parameters for FLAC analysis (Moore, 2007) Facies K (MPa) G (MPa) E (MPa) n e φ ( ) ρ (kg/m 3 ) ν Sand Pl Clay Clay till Kcc Kcb Kcb Kca-625u Kca-625l Kcw K: Bulk modulus, G: shear modulus, E: Young s modulus, n: porosity, e: void ratio, φ : friction angle, ρ: density, and ν: Poisson s ratio. 67

96 Table Best fit soil properties for FLAC analysis (Moore et al., 2011) Facies K (MPa) G (MPa) E (MPa) n e φ ( ) ρ (kg/m 3 ) ν Sand Pl Clay Clay till Kcc Kcb Kcb Kca-625u Kca-625l Kcw K: Bulk modulus, G: shear modulus, E: Young s modulus, n: porosity, e: void ratio, φ : friction angle, ρ: density, and ν: Poisson s ratio. 68

97 Table Range of allowable temperature fluctuation for creep tests Allowable temperature fluctuation range Reference ±0. 5 Lo (1961) ±2. 5 Esu and Grisola (1977) ±1. 0 Schiffman et al. (1966) ±0. 3 Campanella and Mitchell (1968) ±0. 1 Najder and Werno (1968) ±0. 3 Johnson (1976) ±2. 0 Baleshta and Dusseault (1988) ±1. 15 Feda (1992) 69

98 Figure 2.1. Phanerozoic rocks thickness east of the Cordilleran Foreland Thrust Belt (Porte et al., 1982) Figure 2.2. Shallow inland seaways in North America during the mid-cretaceous period (Cobban and McKinney, 2015) 70

99 Figure 2.3. The Athabasca Oil Sands area bitumen outline (Teare et al., 2014) and Fort McMurray area map (Haug et al., 2014). 71

100 Figure 2.4. Fort McMurray area stratigraphic (Haug et al., 2014). 72

101 Figure 2.5. Schematic representation of stratigraphic units of the interbedded soil layer at the test fill site (Moore, 2007). Figure 2.6. The effect of change in structure of shale and sand on porosity-depth relationship (Schön, 2011). 73

102 Figure 2.7. Porosity-depth field data (Fowler et al., 1985) and relationship (Revil et al., 2002) Figure 2.8. Variation of porosity with depths of undisturbed shale of Oligocene and Miocene age from Eastern Venezuela (Hedberg, 1936) 74

103 Figure 2.9. Uniaxial compressive strength versus water content for various clay shales (Hsu and Nelson, 1993) Figure Permeability range of shale in comparison with other geomaterials (Schon, 2011; Hearst et al., 2000) 75

104 Figure Schematic change of water content with depth of burial and stages of clay shale formation (Bjerrum, 1967) Figure Schematic of clay shale fabric (Wong, 1998) 76

105 Figure Residual strength of the Kca clay shale from direct shear test (El-Ramly et al., 2003) Figure Layout of slope inclinometers and wire piezometers (Moore et al., 2006) 77

106 Figure Cumulative and incremental deformations perpendicular to fill face measured 10 m off the west face by SI01 (Moore et al., 2006) Figure Schematic representation of the stress-strain behavior: a. isochronic stressstrain diagrams at different time periods); b. creep curve. c. stress relaxation curve (Feda, 1992). 78

107 Figure Stress relaxation: (a) Stress strain diagrams of three different relaxation tests (A, B, and C) where the strain rate prior to relaxation varies and (b) the normalized deviator stress versus log time for the three relaxation tests. q is the deviator stress and q 0 is the stress at the beginning of relaxation (Augustesen, 2004). 79

108 Figure Rheological model of a Zener s material: a) creep. b) relaxation. c) set of isochronic linear stress-strain curves (Feda, 1992). 80

109 Chapter 3: Experimental work 3.1. Test material The shale samples for this project were obtained from tanks farms, which were constructed at an oil sand plant near Fort McMurray, Alberta. Clearwater Formation is relatively shallow in the area and the samples are from depths of between 8-21 m below the ground surface Atterberg s limit and moisture content Atterberg s limits were obtained by performing tests following ASTM D4318 procedure on six samples from each facies (a total of 24 tests). The results of index tests are reported in Table 3.1. The value of liquidity index provides a reliable indication of the degree of consolidation of clayey soils (Rominger and Rutledge 1952; Means and Parcher 1963). The values near zero are indicators of overconsolidated clay. Negative values are found for in-situ weathered stiff clays and highly overconsolidated clays, which are the case for clay shale samples of this study (Nagaraj, et al., 2003). Liquidity indices are still near zero with even considering 10 % moisture loss. A total of 28 tests, following ASTM D2216 procedure, have been done in order to determine the water content of soil samples. The results of the tests are shown in Figure Specific gravity Specific gravity, G s, is defined as the ratio of the mass of unit volume of soil grains to the mass of unit volume of deaired distilled water at a stated temperature. General range of G s is for clay and silty clay soils. Specific gravity of the Clearwater clay shale was determined by means of 81

110 a water pycnometer according to the ASTM D The tests were carried out on four samples, one from each facies, at 20 C and. The measured values of G s are reported in Table 3.2 and are in the range of with an average value of Organic content Organic content is defined as the ratio of the mass of organic material to the total mass of the dry soil. The tests were performed according to the ASTM D 2974 Standard test methods for moisture, ash, and organic matter of peat and organic soils. The measured organic content of Clearwater clay shale facies are presented in Table Dimensions and densities of the samples Dimensions of each sample along with its weight were measured prior to triaxial testing. Measured dimensions and calculated densities of samples used in triaxial testing are presented in Table 3.4. Average values of density for facies of clay shale are presented in Table Swell tests Geomaterial swelling anisotropy can be identified by carrying out swell test. A straightforward way to do this is the free swell test. This test gives a first indication of the expandability of the candidate clay. Three samples from each facies, with an average diameter and height of 62 and 50 mm, respectively, were prepared for free swell tests. Then, the sample and two circular perforated plastic plates, attached to each end of the sample, were enclosed in a membrane. Finally, 82

111 the samples were submerged in water. The height, diameter, and mass of the samples were measured and recorded over specific time intervals. Based on recorded data, strain in axial and two perpendicular radial directions were calculated. Then, the volumetric strain was calculated from axial and radial strains. The variation of volumetric strains with time is very close to a power function of time (Figure 3.2): ε V = at b (3.1) where, ε V is the volumetric strain. t is the time from the start of the test in days and a and b are experimental coefficients. The resulting power functions of different samples are similar to one another. Hence, an attempt was made to correlate these curves with a third parameter. The clay content was initially selected as the third parameter. Graphs of volumetric strain versus clay content at different constant times were drawn, which demonstrated good linear correlation between these two parameters. Then, this procedure was repeated using smectite content as the third parameter instead of clay content that led to an even better correlation with volumetric strains at different times. Therefore, the volumetric strains and smectite contents of different samples are found to be related through the formula below at different constant times (Figure 3.3): ε V = cs + d (3.2) where, s is the smectite content; c and d are experimental coefficients. In the next stage, the coefficients of trend lines (c and d) were drawn versus time. The coefficients c and d demonstrated very good power function trends with time in the following equations, respectively (Figure 3.4): 83

112 c = t , R 2 = 0.93 (3.3) d = t.3329, R 2 = 0.97 (3.4) By introducing the above equations in the equation ε V = cs + d, an explicit relationship between volumetric strain with smectite content and time is obtained: ε V = (1.2814t )s + ( t.3329 ) = st t (3.5) Volumetric strains predicted by the above formula along with measured volumetric strains are plotted versus time in Figure 3.5. Experimental results clearly show anisotropic behaviour of clay shale. Comparison of radial strains in two directions implies the existence of horizontal isotropy planes. Anisotropy ratio (ratio of axial strain to radial strain due to swelling) increases with smectite content (Figure 3.6) and decreases with time (Figure 3.7). The anisotropy ratios at the end of the test are between 3.45 and There is a correlation between axial and radial strains (Figure 3.8): ε a = ε r (3.6) in which, ε a is the axial strain and ε r is the radial strain Swelling anisotropy and its variation with smectite content The performed free swell tests demonstrated the anisotropic nature of swelling behaviour of Clearwater clay shale. Moreover, the results of these tests showed the dependence of swelling potential (Figure 3.3) and swelling anisotropy (Figure 3.6) on clay content and smectite content. Hicher et al. (2000) demonstrated the dependence of mechanical behaviour of the clays on their structural characteristics. Sedimentary rocks, formed by deposits of clay and silt sediment, exhibit 84

113 strong inherent anisotropy, which manifests itself in a directional dependence of deformation characteristics. The anisotropy is strongly related to the microstructure, in particular the existence of bedding planes which mark the limits of strata and can be easily identified by a visual examination (Pietruszczak et al., 2002). Considering the origin of formation of Clearwater clay shale, deposition in a shallow marine environment (Kosar, 1992), and approximately horizontal bedding planes were observed in the logging of recovered cores, anisotropy with horizontal preferential direction is expected in this material. Avsar et al. (2009) investigated the swelling anisotropy of Ankara clay, an overconsolidated fissured clay, using a thin wall oedometer ring (providing synchronized measurement of swelling parameters in both directions 1 ). They measured greater swelling pressures in the direction normal to sheeting than in the direction parallel to sheeting in the scanning electron microscopy micrographs. They inferred that preferred orientation of clay plates and silt grains may cause anisotropic swelling behavior. In addition, Chen and Huang (1987) also reported that swelling pressures in the direction perpendicular to the particle orientation is greater than that in the direction parallel to the particle orientation. Considering the studies of Avsar et al. (2009) and Chen and Huang (1987), the swelling in Clearwater clay shale samples is expected to be markedly anisotropic (a large swelling anisotropy 1 Lateral swelling pressure applied to the thin wall of the oedometer were computed from the amount of strain recorded by the strain gauges installed on the outer surface of the wall of the oedometer ring and the calibration data of the strain gauges (relating applied pressures to measured strains). 85

114 factor), i.e. swelling strains develop mostly in axial direction perpendicular to preferred orientation of clay particle cluster (radial direction). In addition, it is well-known that smectite has the most contribution to the swelling among various clay minerals (Olson and Mesri, 1970). Based on the role of preferential direction of clay plates, increase in smectite content of a sample is expected to result in both larger swelling strains, Figure 3.3, and more anisotropy in swelling, which in turn results in larger ratio of axial to radial swelling (larger swelling anisotropy factor), Figure Variation of swelling anisotropy with time (or swelling strain) The results of free swell tests on Clearwater clay shale revealed reduction of the swelling anisotropy with the elapsed time or swelling strain (Figure 3.7). Katti and Katti (2003) investigated the swelling of Wyoming bentonite, a sodium montmorillonite clay. They measured swelling pressure at various levels of swelling (0, 25, 50, and 75 % volumetric strains) and examined samples using scanning electron microscopy and fourier transform infrared spectroscopy. They observed that 0 %-swelled samples are highly oriented as compared to 50 %-swelled samples although the dry compacted sample before saturation was prepared from randomly oriented particles. The clay platelets are most oriented at 0 % swelling. Then, clay platelets move apart due 86

115 to swelling, which in turn leads to increased misorientation 1 of the clay platelets. Therefore, misorientation of the clay platelets increases with increased swelling strain. Similarly, the variation of the anisotropy ratio with time in Figure 3.7 can be explained. With more elapsed time since start of swelling (more swelling taking place), array of particle assemblages in Clearwater clay shale samples changes from a predominantly radial direction to a more random distribution. As a result, the swelling anisotropy factor decreases with the elapsed time Mineralogy Shale generally contains quartz, feldspar, micacalcite, iron minerals, clay minerals (illite, smectite, chlorite and kaolinite) and organic matter. High percentage of illite and smectite in a shale leads to lower shear strengths and higher swelling potential than a shale with a high percentage of kaolinite and/or only low percentage of illite, smectite, or other mixed-layer minerals (Underwood, 1967). Behaviour of shale is largely controlled by amount and type of its clay minerals. Clay content determines the specific surface area of soils and thus their plasticity is dependent to a great extent by clay content. Results of tests on illite-rich shale recovered from the Wilcox formation showed 1 Misorientation is the difference in orientations between two neighboring platelets. It is common to use an angle-axis representation based on the fact that one orientation can be matched to another using rotation by an angle around an axis (Sedivy et al., 2013). 87

116 that permeability depends on clay content (Kuwano, et al., 2000; Kwon, et al., 2004). Dependence of elastic parameters on clay content had been reported elsewhere in literature (Vanorio, et al., 2003). Different methods had been used to determine the amount and type of clay minerals of shale such as X-ray diffraction (XRD), scanning electron microscopy (SEM), dielectric constant measurement (DCM), and cation exchange capacity (CEC). XRD was used for semi-quantitative mineralogical analysis of the different facies of the Cretaceous Clearwater Formation X-ray diffraction (XRD) analysis In this method, X-rays are used to probe the crystal structure of minerals. The various atoms in a mineral are ordered in a regular fashion and form layers with a definite interatomic spacing. From the difference in the paths travelled by the X-rays reflected by the various layers of the crystal, the diffraction angle is calculated (based on the Bragg s Law). The intensities of the diffracted X-rays as a function of measured angle for each mineral are unique and thus the mineralogical composition of each sample can be identified (Mah, 2005). Details of principle and application of this method can be found in literature (Reynolds, 1989a; Reynolds, 1989b; Srodoi, et al., 2001; Harris and Norman, 2008; Hubert, et al., 2009). A total of twenty-four samples, six samples from each facies, were used for XRD analyses. Two types of XRD analyses, bulk sample analysis and clay fraction analysis, were carried out on each sample. The bulk sample analyses were conducted on powder samples. This analysis 88

117 identifies the clay and non-clay minerals and the relative proportions of clay and non-clay minerals in each sample. Samples of less than 2 μm were used for the clay fraction analyses XRD analyses results Detailed mineralogy of samples from various facies of clay shale from XRD analyses is presented in Table 3.6. Average values for mineralogy of each facies of Clearwater clay shale from bulk sample analyses are presented in Table 3.9. The results of bulk sample analyses show the existence of at least 39 % of quartz (45 % in average). Other major non-clay minerals in the bulk are plagioclase (9 %), dolomite (5 %), K-feldspar (5 %), and pyrite (1 %). The clay content varies between 23 % and 45 % with an average of 34 %. Kcc-710 facies (shallowest facies) has the lowest clay content with an average of 25 % and Kca-625 facies (deepest facies) has the highest percentage of clay (39 %). Clay content of Kcc-700 and Kcb-650 are close, 37 % and 35 %, respectively. Percentage of minerals constituting clay content of samples are presented in Table 3.7, where the percentage of illite and smectite mixture in inter-layer is given as a whole. The average values of the clay fractions for each facies are presented Table The clay fractions are at least 55 % of illite/smectite inter-layer (66 % in average) and 11 % of illite (18 % in average) and some minor minerals, 10 % kaolinite and 5 % chlorite on average. The amount of both kaolinite and illite decreases with depth for each facies. In Table 3.8, the percentage of smectite in interlayer has been estimated. Therefore, the total percentage of illite has been reported in this table. Averages of clay fractions (smectite and illite 89

118 divided) for each facies are presented in Table Smectite, the most swelling mineral group, is 40 % of clay fraction and 14 % of the bulk in average while illite forms 44 % of clay fraction and 15 % of the bulk in average. The amount of smectite both in the bulk and as clay fraction increases with depth for each facies One-dimensional consolidation tests Oedometer consolidation tests Two oedometer consolidation tests were carried out on samples from Clearwater clay shale. The first test was performed on the clay shale sample from Kcb-700 facies. Fresh water was used as pore fluid in this test and was added to the cell, completely submerging both the sample and upper porous disc. The test consisted of 5-minute loading stages and 24-hour holding stages in between (to allow for consolidation). The sample was loaded in increments to 200, 400, 800, 1600, 3200, 4800, and 7200 kpa. After which, the sample was unloaded to 4800 and 3200 kpa in stages and reloaded back to 4800 and 7200 kpa. Volumetric strain was measured and drawn versus time at each stage (Figure 3.10). Then, The coefficient of consolidation was calculated for each stress level (Table 3.12), which are in the range of to cm 2 s. The measured values of coefficient of consolidation, presented in Figure 3.12, increase with increase in axial stress (and consequently the confining pressure) and are comparable with the measured value in test #7 on the same facies ( cm 2 s). The variation of the coefficient of consolidation with confining pressures is discussed in section Moreover, the secondary compression index for each stress level is 90

119 presented in Table 3.12, which are in the range of The ratio between the secondary compression and compression indices is almost constant for a given soil. Considering the calculated compression index of for the current test, these ratios are in the range of with an average of 0.04 (Table 3.12). Mersri and Godlewski (1977) compiled data from a number of natural clays and suggested this ratio to be 0.04±1 for inorganic clays. The variation of void ratio versus axial stress is plotted in Figure The value of compression index was determined to be while, the value of swelling index was estimated as based on the results of unloading and reloading stages. The second test was also conducted on a Kcb-700 sample with an initial water content of 18.5 %. The saline water, with three percent concentration, was used as pore fluid in this experiment. The sample was loaded in increments to 100, 300, 500, 800, and 1200 kpa. The load was held constant in each stage until the measured vertical displacements attained a constant value, which took between two to four days. Then, the sample was unloaded and reloaded following similar increments. The load was held constant for one day during these stages. The variation of void ratio versus axial stress is plotted in Figure The compression index was estimated as in this test, while the swelling index was determined as The compression and swelling indices measured in two conventional oedometer tests, conducted on Kcb-700 samples, are consistent with each other. The test saturated with fresh water lies above the one with saline water due to swelling (Figure 3.11). 91

120 Constant-rate-of-strain consolidation tests Two constant-rate-of-strain (CRS) consolidation tests were performed on Clearwater clay shale. Hamilton and Crawford (1959) introduced the CRS test as a rapid means of determining the preconsolidation pressure. Imposed boundary conditions in the CRS test are similar to those in the conventional incremental-loading test. The specimen is confined laterally by the same type of ring used in the conventional test apparatus (oedometer), and drainage of pore water is only permitted at the top. The strain rate is chosen such that significant pore pressure does not develop in the specimen; then, the effective stress is considered equal to the applied stress. The main advantage to the conventional oedometer test is that a well-defined stress-strain curve is provided by continuous stress-strain points (Gorman et al., 1977). In both conventional oedometer tests, the preconsolidation pressure was not captured. This was attributed to swelling due to using of 3 % saline or fresh water as pore fluid, which induced a physicochemical change in pore fluid chemistry. Therefore, the CSR tests were conducted on intact samples with no pore fluid. The preconsolidation pressure has been estimated to be 860 kpa from a CSR test on a Kcb-700 sample in an oedometer cell. The variation of void ratio versus axial stress is plotted in Figure Based on this test, the compression and swelling indices were calculated and 0.024, respectively. Another test was conducted on a Kcb-650 sample with no pore fluid, in which the preconsolidation pressure has been estimated to be 1280 kpa. Unloading and reloading staged were performed in this test while various strain rates were applied. The variation of void ratio versus axial stress is plotted in Figure The compression index was calculated as in this test, 92

121 while the swelling index is estimated in a range of Based on the estimated preconsolidation values and calculated effective vertical stress in layers, the OCRs were calculated for each facies (Table 3.13). A summary of one-dimensional consolidation tests conducted on the Clearwater clay shale is presented in Table Triaxial tests detail and procedure Sample preparation Sample disturbance could affect the results of geotechnical laboratory tests on a soil sample (Olsen, 1986). Therefore, measures were taken to have minimum sample disturbance and moisture loss during handling, storage, and preparation of samples. A geotechnical investigation was carried out by Thurber Engineering Limited at thickener tanks 1001 and 2001 at the Horizon oil sands site located near Fort Mackay, Alberta. As part of this investigation, six core holes along the perimeter of thickener tanks 1001 and 2001 was drilled (Figure 3.9). Cores from these boreholes, except borehole F, were recovered. Approximately 1.5 m long fissured cores were covered by plastic wrap in the field. Then, cores were tightly sealed in polyvinyl chloride (PVC) tubes and were transported to the laboratory. The shale cores, 63 mm in diameter, were cut into mm in length using a band saw for triaxial tests (therefore, samples had an height to diameter ratio of approximately two). To prevent any moisture loss, the cut sample pieces were wrapped with two layers of plastic cling wraps and, then, with two layers of aluminum foil. In next step, the wrapped samples were vacuum sealed in 93

122 plastic food saver bags. These sealed samples were put in a container and maintained inside a moisture room Test apparatus and setup Test apparatus The GDS Standard Triaxial Automated System is used in this study. The equipment consists of: - A 2 MPa triaxial cell, constructed from aluminum with perspex wall, with a base pedestal for 63 mm diameter samples. - A 2 MPa pore pressure transducer with an accuracy of 0.15% of the full range output, which is equal to 3 kpa. - A 50 kn load frame with a velocity controlling device. Its built-in actuator has a speed range of to mm/min. - Two 3 MPa pressure/volume controllers with 200 cc volumetric capacity, one for applying confining pressure and measuring cell volume change and the other one for applying backpressure and measuring sample volume change. o Pressure is measured by an integral pressure transducer. The resolution of pressure measurement is 1 kpa while the pressure accuracy is less than 0.15 % of full range, equal to 3 kpa. o Volume change is measured by counting the steps of the incremental motor. Volume accuracy is 0.25 % of measured value with ± 30 mm 3 backlash (volume resolution is 1 mm 3 ). 94

123 - A 16 bit standard GDS 8-channel data acquisition device. - A 25 kn internal submersible load cell, which has a unique feature in that pressure does not affect the load reading. Therefore, corrections for ram upthrust and friction of the ram do not need to be made. It has an axial force accuracy of less than 0.1 % of full-scale output, equal to 25 N. Its non-linearity and hysteresis are less than ± 0.05 and ± 0.1 % of full scale output, respectively. The cell pressure, back pressure, and strain/stress rate are directly controlled by a computer. Either load-controlled or displacement-controlled loading for a conventional triaxial compression test may be specified. In addition to saving these parameters to a hard drive, the computer also logs axial displacement, axial load, pore pressure, and volume change Sample setup Filter papers were attached to both ends of the trimmed sample. Filter paper was cut in 10 mm wide and approximately 100 mm long (30 mm shorter than the sample length) strips and attached to the sides of the sample to provide radial drainage. Porous stones were placed on bottom and top ends of the sample. Then, the sample was covered with a neoprene membrane (with internal diameter of 60 mm and thickness of 0.6 mm). The membrane was sealed against the top and bottom platens by two O-rings in each end to prevent the leakage of confining fluid into the sample. 95

124 Load and displacement transducers The displacement measurement system is composed of three local strain transducers in radial and axial directions and an external axial displacement transducer. Local strain transducers are used for on-sample measurement of strain. Two vertically oriented local strain transducers were needed to measure small axial strain of the sample. These axial linear variable differential transformers, LVDTs, are suspended from an upper pad bonded to the sample membrane by adhesive. The weighted rounded brass end of the LVDT armature rests freely on the lower pad anvil, which is glued to the membrane. A radial local strain transducer, mounted directly on the sample, measures the strain in radial direction. A caliper is mounted on two diametrically opposed pads, which are bonded to the membrane by adhesive. The radial LVDT is positioned across the opening of the caliper where it measures the opening and closing of the jaws. It should be noted that the external LVDT measurement was used to calculate the axial displacement and the axial strain. The local LVDTs measurements were implemented in calculation of the Poisson s ratio (with assumption of elastic behaviour). To avoid errors induced by friction between the loading rod and the triaxial cell, an internal load cell was placed inside the triaxial cell to measure the axial load Triaxial tests detail and data reduction Different triaxial tests have been designed to investigate the effect of various parameters (confining pressure, strain rate) on stress-strain behavior of various Clearwater clay shale facies. In addition, 96

125 stress relaxation tests were conducted at different axial strains to study time-dependent behaviour. The specifications of these triaxial tests are summarized in Table In group A, the stress-strain behavior of the clay shale along with its volumetric behavior was investigated. In group B, the time dependent behaviour of the various facies of the clay shale has been investigated by conducting 23 stress relaxation tests during five drained consolidated compression triaxial tests. All tests, except Test #2, were conducted under a confining pressure of 100 kpa. All the samples in this group were sheared with 5.32 %/day strain rate. Only in Test #1, five different strain rates were applied in the post-peak region, to investigate its effect on the postpeak strength of the material. In group C, the effect of the strain rate (0.27 %/day, 1.33 %/day, and 5.32 %/day) on the stressstrain behaviour of the clay shale was investigated. In group D, a multistage triaxial test at various confining pressures (100, 300, and 500 kpa) were performed on a single specimen to reduce the variability in results caused by testing multiple samples with the natural variation in the mineralogy and structure. Both strain rate effect and stress relaxation phenomena were investigated in this group. Tests of group E are the only ones, in which back pressure were applied and were conducted in undrained condition. The rest of triaxial tests were conducted in drained condition without applying any back pressure. Drainage conditions of triaxial tests are specified in Table In group A, drainage was provided from top and bottom of the sample during both consolidation and triaxial shearing. In the rest of drained tests (groups B, C, and D), drainage was provided at the bottom end and side of 97

126 the sample during consolidation/shear while the pore pressure was measured at the top end of the sample to ensure a fully drained condition. In triaxial tests, the deviatoric stress was calculated based on confining pressure measured at cell pressure pump and axial load measured via an internal load cell. The axial strain was measured by an external LVDT. The secant Young s modulus was calculated by dividing the measured axial stress by the axial strain. In drained tests, volumetric strain was calculated based on the cell volume change. In each stress relaxation stage, the axial displacement was held constant for a specific period of time, at least 2280 min, and the changes in the deviatoric stress were recorded. The normalized deviatoric stress curves were obtained from dividing the deviatoric stress values by the deviatoric stress at the beginning of each stress relaxation test. Volumetric strains were normalized in a similar way, i.e., measured volumetric strains were divided by the volumetric strains at the beginning of each stress relaxation test. Change of volumetric strain from the start of relaxation was also reported Results of consolidation tests In group E (undrained tests), the volume of pore fluid flowed out of the sample was measured via backpressure pump and was used to calculate the volumetric strain. In rest of tests (drained tests), the volumetric strain is estimated based on the cell volume change. In analyzing the consolidation stage data, the coefficient of consolidation in isotropic consolidation is calculated from the following formula (Head, 1998): 98

127 c v = π D2 λ t 100 (3.7) where D is the diameter of the sample, λ is a constant depending on drainage boundary condition (equal to 80 when drainage is provided from radial boundary and one end for samples with length to diameter ratio of two), and t 100 is the time representing theoretical 100 % consolidation. Based on the consolidation results, the value of t 100 was estimated from the graph of volumetric strain (or the degree of consolidation) versus square-root of time for each test; then, the coefficient of consolidation in isotropic compression was calculated. The estimated values of t 100 along with the calculated coefficients of consolidation are presented in Table The calculated values of coefficients of consolidation are comparable with those reported by Gautam (2004) for Colorado shale, which are in the range of cm 2 s to cm 2 s Consolidated drained triaxial compression tests - Group A Test #6: consolidated drained triaxial compression test For this test, a Kca-625 facies clay shale sample was prepared from borehole C. The sample was consolidated at a confining pressure of 500 kpa and sheared at an axial strain rate of 2.66 %/day in a drained condition. The stress-strain behavior of the sample along with its volumetric behavior was investigated during the test. 99

128 Saturation and consolidation After installation of the sample in the triaxial cell set up, the confining pressure was increased to 500 kpa instantaneously. Drainage was provided from both ends of the sample at this stage. Volumetric strain is plotted versus square-root of time in Figure Drained shearing The sample was sheared in a drained condition (drained from both ends) after completion of the consolidation stage. The axial strain rate of 2.66 %/day was applied during shearing. The variation of deviatoric stress with axial strain is shown in Figure The sample exhibits a maximum deviatoric stress of 1132 kpa at an axial strain of 3.47 %. The shearing stopped at an axial strain of 12 % after the deviatoric stress reduced to 582 kpa. The measured volumetric strain is plotted versus axial strain in Figure As illustrated in this figure, the sample initially contracted during shearing to demonstrate a maximum volumetric strain of 1.77 % at an axial strain of 2.21 % and dilated afterwards to reach to a volumetric strain of % at the end of the test (axial strain of 12 %). Secant Young s modulus was calculated for the strain in pre-peak region and plotted versus axial strain in logarithmic axis in Figure For axial strains between 0.01 % and 0.1 %, secant Young s modulus is drawn in Figure Secant Young s modulus for axial strains greater than 0.1 % up to the axial strain for the peak strength is shown in Figure Using local LVDTs measurements in vertical and horizontal directions, the Poisson s ratio was also determined at prepeak axial strains and demonstrated in Figure

129 Test #5: consolidated drained triaxial compression test A Kcb-650 facies clay shale sample was cut from cores recovered from borehole B. The sample was consolidated at a confining pressure of 100 kpa. Then, the sample was sheared at an axial strain rate of 1.33 %/day in a drained condition. The stress-strain and volumetric behavior of the sample was investigated during the test Saturation and consolidation Drainage was provided from both ends of the sample during the saturation-consolidation stage. In the first step, the confining pressure was increased to 100 kpa after setting up the sample in the triaxial cell. In the second step, the cell pressure was reduced to 50 kpa. In the next steps of saturation-consolidation process, the cell pressure was increased to 150 kpa and decreased to 100 and 50 kpa. Initially, it was planned to continue this process up to 2000 kpa of confining pressure. Since the saturation-consolidation steps took longer than the planned time (for example, 34 and 44 hr for unloading to confining pressures of 100 and 50 kpa, respectively), this process of saturationconsolidation was stopped. In the new process of saturation-consolidation, the confining pressure was increased in increments of 100 kpa up to a confining pressure of 2000 kpa and was kept constant for 90 min in each pressure level. Then, the cell pressure was decreased in decrements of 100 kpa from 2000 kpa to 100 kpa with 75 min hold period in each pressure level. 101

130 Drained shearing The sample was sheared in a drained condition after saturation-consolidation stage was completed. Drainage was provided from top and bottom ends during shearing. The axial strain rate of 1.33 %/day was applied during shearing. The variation of deviatoric stress with axial strain is plotted in Figure 3.22, in which a maximum deviatoric stress of 381 kpa is observed at an axial strain of 9.13 %. The shearing ended at an axial strain of % after the sample strength reduced to 367 kpa. The measured volumetric strain is plotted versus axial strain in Figure The sample contracted during shearing to a maximum volumetric strain of 1.66 % at an axial strain of %. In addition, Secant Young s modulus was calculated for strains in pre-peak region and plotted versus axial strain in a logarithmic axis in Figure Consolidated drained triaxial compression tests - Group B Test #12: consolidated drained triaxial compression test For this test, a Kcc-710 facies clay shale sample was prepared from borehole D. The sample was consolidated at a confining pressure of 100 kpa and sheared at an axial strain rate of 5.32 %/day in drained condition. Four stress relaxation stages were conducted at different axial strains. The stress-strain behavior of the sample along with its volumetric behavior was investigated during the test. 102

131 Saturation and consolidation After installation of the sample in the triaxial cell set up, the confining pressure was increased to 100 kpa instantaneously. While the pore pressure was measured at the top end, drainage was provided from the radial boundary and the bottom end of the sample. Volumetric strain is plotted versus square-root of time in Figure Drained shearing The sample was sheared in a drained condition, after completion of consolidation stage, while drainage was provided at the bottom and the side boundary of the sample. The pore pressure measurement was made at top of the sample. The axial strain rate of 5.32 %/day was applied in shearing stages. Details of different shearing stages are presented in Table The variation of deviatoric stress with axial strain is shown in Figure The sample exhibits a maximum deviatoric stress of 868 kpa at an axial strain of 5.3 % (consolidated under 100 kpa confining pressure). The sample showed a stiffer behavior in comparison to the other test on the same facies of clay shale at the same confining pressure (test #11 on kcc-710) in which the deviatoric stress was equal to 158 kpa at 2.5 % axial strain. Samples consolidated at higher confining pressures showed higher peak stresses. For instance, a peak stress of 1045 kpa was observed on test #9 with a confining pressure of 300 kpa. The variation of volumetric strain versus axial strain is shown in Figure The sample initially contracted during shearing to demonstrate a maximum volumetric strain of 2.3 % at axial strain of 4.3 % and dilated afterwards to reach to a volumetric strain of -0.6 % at the end of the 103

132 test. The shearing stopped at an axial strain of 15.4 % after the sample strength became approximately constant at 228 kpa Relaxation stages Details of stress relaxation tests are presented in Table The stress relaxation tests were conducted before and after the peak stress. In each stress relaxation stage, the axial displacement was held constant for at least 2280 min and the changes in the deviatoric stress were recorded. The normalized deviatoric stress curves, obtained from dividing the deviatoric stress values by the deviatoric stress at the beginning of each stress relaxation test, are plotted versus the logarithm of time in Figure The stress relaxation curve of stage #6 indicates a notable reduction in slope (deviation from the linear variation with the logarithm of time), implying the existence of a final relaxed stress level. This deviation from the straight line (reduction in slope) was also observed in three stress relaxation stages in test #11. A final relaxed level of stress was observed in previous stress relaxation studies (Oda and Mitachi, 1988). By comparing the stress relaxation curves of stages #2 and #4, it can be found that the percentage of change in deviatoric stress (23.1 % and 15.4 %, respectively) decreased with increase in axial strain (2.4 % and 3.9 %) in pre-peak domain. The same trend is observed in the results of test #11. The details of stress relaxation stages of #8 and #15 from test #11 are presented in Table The comparison of these two stages indicates that the percentage of change in 104

133 deviatoric stress (33.8 % and 14.6 %) during the stress relaxation stage decreased with axial strain (3 % and 7.7 %) Test #1: consolidated drained triaxial compression test This test was conducted on a clay shale sample cut from a core recovered from borehole C. The sample, from Kca-625 facies, was initially consolidated at a confining pressure of 100 kpa and consequently sheared in a drained condition. In addition, six stress relaxation tests were performed at different axial strains Saturation and consolidation The confining pressure was raised to 100 kpa instantaneously following the installation of the sample in the triaxial cell set up. Volumetric strain, calculated based on the cell volume change, is plotted versus square-root of time in Figure Drained shearing Upon completion of consolidation stage, the sample was sheared in a drained condition. The axial strain rate of 5.32 %/day was applied during shearing before the peak deviatoric stress. Five different rates of axial strain were applied in the post-peak domain. Details of different shearing stages are presented in Table The variation of deviatoric stress with axial strain is presented in Figure A maximum deviatoric stress of 714 kpa occurs at an axial strain of 4.25 %. The drained triaxial test at the same 105

134 confining pressure (100 kpa) but on a different facies (Kcc-710 facies) resulted in a maximum deviatoric stress of 868 kpa at an axial strain of 5.3 % (test #12). The variation of volumetric strain, calculated from the changes in cell volume, with axial strain is plotted in Figure As demonstrated in this figure, the sample volumetric strain reaches 2.34 % at an axial strain of 3.73 % as a result of initial contraction, which is followed by dilation. To investigate strain rate effect on the post-peak strength of the material, the sample was sheared further and five different strain rates were applied. The deviatoric stress is plotted versus axial strain in Figure The deviatoric stress has reduced to 213, 209, 215, and 216 kpa at the end of stages #11, #12, #14, and #15, respectively. These values are normalized by the deviatoric stress at the end of the relaxation stage (stage #16), 165 kpa, and drawn versus the logarithm of the axial strain rate of each stage in Figure Based on observed change in axial displacement during the relaxation time, an average strain rate of %/day was calculated and considered for the stress relaxation stage. The results indicate the decrease of post-peak strength with the decrease in axial strain rate according to the following expression: q qr = log 10 ε a (q is in kpa and ε a is in %/day) (3.8) where ε a is the axial strain rate; q and q r are deviatoric stresses at the end of each stage and the relaxation stage, respectively. Moreover, Figure 3.34 shows that the stress relaxation can be considered as a shearing stage with a very slow strain rate. Note that stage #13 was not considered in this figure because of its short shearing time (only 54 min). 106

135 The volumetric strain is plotted versus axial strain in Figure The sample volumetric strain attains a value of 1.23 % at the end of shearing (at an axial strain of 18.0 %). Moreover, the sample dilates further to a volumetric strain of % in the last stress relaxation, stage # Relaxation stages Details of stress relaxation tests are presented in Table Six stress relaxation tests were carried out before and after the peak stress. The axial displacement was held constant for at least 1750 min in each stress relaxation stage while the changes in the deviatoric stress were recorded. The normalized deviatoric stress curves are plotted versus the logarithm of time in Figure Similar to the results of stress relaxation stages in tests #10, #11, and #12, a linear trend could be found in each normalized stress relaxation curve after an initial time period in Figure Reductions in slope of this line near the end of the stage, implying the existence of a final relaxed stress level where no more stress relaxation happens (Oda and Mitachi, 1988), were observed in previous stress relaxation stages (for example, three stress relaxation stages in test #11). This is not observed in stress relaxation stages in this test except in stress relaxation at axial strain of 4.5 %. The volumetric strain of the sample was recorded during the stress relaxation stages. Changes in volumetric strains from the beginning of each stress relaxation test are plotted versus the logarithm of time in Figure For relaxation stages #2, #4, #8, and #10, the changes in volumetric strain is less than 0.5 % and contractive; while the relaxation stages #6 and #16 exhibit relatively higher dilative changes in volumetric strains up to 1 % and 1.5 %, respectively. The 107

136 highest reduction in deviatoric stress as well as the largest change in volumetric strain is observed in stress relaxation #6; this stress relaxation was conducted at an axial strain (4.5 %) which is the closest to the axial strain at the peak strength (4.25 %) among the six relaxation stages Test #2: consolidated drained triaxial compression test This test was carried out on a Kca-625 facies clay shale sample cut from a core recovered from borehole C. The sample was initially consolidated at a confining pressure of 300 kpa and consequently sheared in a drained condition. In addition, four stress relaxation tests were performed at different axial strains Saturation and consolidation The confining pressure was raised to 300 kpa instantaneously following the installation of the sample in the triaxial cell set up. Volumetric strain is plotted versus square-root of time in Figure Drained shearing Upon completion of consolidation stage, the sample was sheared in a drained condition. The axial strain rate of 5.32 %/day was applied during shearing. Details of different shearing stages are presented in Table The variations of deviatoric stress with axial strain is drawn in Figure A maximum deviatoric stress of 1055 kpa occurs at an axial strain of 4.38 %. The strength has reduced to 298 kpa at an axial strain of 16 % at the end of the test. 108

137 The drained triaxial test at a same confining pressure (300 kpa) but on a different facies (Kcb- 700 facies) resulted in a maximum deviatoric stress of 1052 kpa at an axial strain of 6 % (test #9). Although these two tests showed comparable maximum deviatoric stresses, the pre-peak stressstrain behavior of the current test is stiffer than the one in the test #9. Secant Young s moduli for this test and other tests on the same facies or with the same confining pressure are presented in Table The variations of volumetric strain with axial strain is plotted in Figure As demonstrated in this figure, the sample initially contracts up to a volumetric strain of 2.54 % at an axial strain of 4.87 %. Then, the sample dilates and volumetric strain decreases to 0.28 % at the end of shearing (at an axial strain of 16.0 %) Relaxation stages Details of stress relaxation tests are presented in Table Four stress relaxation tests were conducted before and after the peak deviatoric stress. The axial displacement was held constant for a period of 1800 min (30 hr) in each stress relaxation stage while the changes in the deviatoric stress were recorded. The normalized deviatoric stress curves are plotted versus the logarithm of time in Figure Three stress relaxation stages have been conducted before the peak strength. The deviatoric stresses at the start and end of these stress relaxation stages were plotted versus axial strain in Figure Then, a straight line is passed through the points corresponding to shearing at 5.32 %/day (the start of relaxation) to calculate the tangent Young s modulus. Similarly, another 109

138 straight line is passed through the points corresponding to the stresses at the end of relaxation stages to calculate the tangent Young s modulus corresponding to the long-term stress-strain behaviour. Comparison of the slope of these two lines reveal that the tangent Young s moduli decreases from 25.3 MPa to 17.9 MPa from shearing at 5.32 %/day to shearing at a very slow rate, respectively. Moreover, the comparison of the secant Young s moduli of shearing at 5.32 %/day and those of the long-term stress-strain curve (end of the relaxation stages) at various axial strain before the peak deviatoric stress, Table 3.26, shows similar decreases in modulus values. The volumetric strain of the sample, calculated based on the cell volume changes, was recorded during the stress relaxation stages. Changes in volumetric strains from the beginning of each stress relaxation test are plotted versus the logarithm of time in Figure Volumetric strains were also normalized similar to the deviatoric stresses, from dividing volumetric strains by the volumetric strains at the beginning of each stress relaxation test, and plotted versus the logarithm of time in Figure For relaxation stages #2, #4, and #6 (all before the peak in deviatoric stress), the changes in volumetric strain are less than 0.3 % and contractive; while the relaxation stages #8 (after the peak in deviatoric stress) exhibits relatively higher dilative change in volumetric strains. The highest reduction in deviatoric stress as well as the largest contractive change in volumetric strain is observed in stress relaxation #2. 110

139 Test #3: consolidated drained triaxial compression test This test was carried out on a Kcb-700 facies clay shale sample cut from a core recovered from borehole E. The sample was initially consolidated at a confining pressure of 100 kpa and consequently sheared in a drained condition. In addition, six stress relaxation tests (five before the peak stress and one after that) were performed at different axial strains intervals Saturation and consolidation The confining pressure was raised to 100 kpa instantaneously following the installation of the sample in the triaxial cell set up. Volumetric strain is plotted versus square-root of time in Figure Drained shearing Upon completion of consolidation stage, the sample was sheared at axial strain rate of 5.32 %/day in a drained condition. Details of different shearing stages are presented in Table The variation of deviatoric stress with axial strain is drawn in Figure A maximum deviatoric stress of 227 kpa occurs at an axial strain of 8.53 %. The strength has reduced to 126 kpa at an axial strain of % at the end of the test. The drained triaxial test at a same confining pressure, 100 kpa, but on different facies (Kca- 625, Kcb-650, and Kcc-710 facies) has been conducted. Results of these tests show a stiffer stressstrain behavior than that of the current test (#3) in pre-peak region. Secant Young s moduli for this test and other tests with same confining pressure are presented in Table

140 The variation of volumetric strain with axial strain is plotted in Figure As demonstrated in this figure, the sample volumetric strain reaches 2.18 % at an axial strain of 8.54 % as a result of initial contraction. Thereafter, the sample dilates to a volumetric strain of 1.30 % at the end of shearing (at an axial strain of 17.0 %) Relaxation stages Details of stress relaxation tests are presented in Table Five stress relaxation tests were conducted before and one after the peak stress. The axial displacement was held constant for 1800 min (30 hr) in each stress relaxation stage (except 24 hr for the last one) while the changes in the deviatoric stress were recorded. The normalized deviatoric stress curves are plotted versus the logarithm of time in Figure Similar to the results of stress relaxation stages in tests #10, #11, and #12, a linear trend could be found in each normalized stress relaxation curve an initial time period in Figure Reduction in slope of this line is clearly observed in stress relaxation curves at axial strains of 1.5 % and 3 %. This implies the existence of a final relaxed stress level, similar to observation in previous stress relaxation stages (for example, three stress relaxation stages in test #11) and stress relaxation studies in literature (Sheahan et al., 1994). Five stress relaxation stages have been conducted before the peak strength. The deviatoric stresses at the start and end of these stress relaxation stages are plotted in Figure These points can be approximated with a hyperbola with a high degree of accuracy following Duncan and Chang s (1970) method. To obtain the related hyperbolic equation for each case, the stress-strain 112

141 data are plotted on transformed axes in Figure Based on the equations of lines drawn on Figure 3.49, the hyperbola approximations of these two curves are as follows: - For the start of stress relaxation stages: q = ε a ε a (q is in kpa and ε a is in percent) (3.9) - For the end of the stress relaxation stages: q = ε a ε a (q is in kpa and ε a is in percent) (3.10) where q is the deviatoric stress and ε a is the axial strain. Changes in volumetric strain from the beginning of each stress relaxation test are plotted versus the logarithm of time in Figure Normalized volumetric strains are plotted versus the logarithm of time in Figure All the stress relaxation results showed small contraction (less than 0.1 %) after 167 min (10000 seconds in Figure 3.50) of relaxation. Relaxation stages #2, #4, #10 and #12 exhibited a similar pattern of initial contraction followed by dilation. The relaxation stage #8 contracted up to the end of stage while the relaxation stage #6 oscillates between contraction and dilation Test #4: consolidated drained triaxial compression test A clay shale sample of Kcb-650 facies was cut from cores recovered from borehole A. After consolidation at a confining pressure of 100 kpa, the sample was sheared at an axial strain rate of 5.32 %/day in a drained condition. Moreover, stress relaxation tests were carried out at three different axial strains before (1.0 %) and after the peak strength (3.0 % and 4.5 %). In addition, 113

142 unloading and reloading of the sample was conducted to investigate the loading and unloading modulus of elasticity Saturation and consolidation Confining pressure of 100 kpa was applied to the sample in the consolidation stage. The variation of volumetric strain with the square-root of time is plotted in Figure Shearing stages The sample was sheared at an axial strain rates of 5.32 %/day in a drained condition after consolidated under 100 kpa effective confining pressure. After shearing to an axial strain of 2.5 %, the sample was unloaded to investigate the unloading modulus. Stress relaxation tests were carried out at three different axial stains (1 %, 3 %, and 4.5 %). Details of shearing stages (the range of axial strains and the applied axial strain rate) are presented in Table The variation of the deviatoric stress with axial strain is shown in Figure The sample reached a maximum deviatoric stress of 287 kpa at an axial strain of 2.47 %. The samples (from other facies) consolidated to a same confining pressure exhibits higher peak deviatoric stresses in drained tests. A sample from Kca-625 showed a maximum deviatoric stress of 714 kpa at an axial strain of 4.25 % in another test while consolidated under 100 kpa confining pressure (test #1). The other test with the same confining pressure on a sample from Kcc-710 resulted in a peak deviatoric stress of 868 kpa at an axial strain of 5.30 % (test #12). 114

143 To compare the pre-peak stress-strain behavior of these three tests, the Secant Young s moduli have been calculated at different strain levels (Table 3.31). The stress-strain behavior of the current test is similar to that of Kcc-710 facies but softer than that of Kca-625 facies. The volumetric strain, for shearing and the stress relaxation stages, is plotted versus axial strain in Figure As demonstrated in this figure, the sample volumetric strain reaches 1.14 % at an axial strain of 2.50 % as a result of initial contraction and thereafter reduces to 0.15 % at the end of shearing (at an axial strain of %). Secant Young s modulus versus axial strain is shown in Figure 3.55 for loading, unloading, and reloading stages. As demonstrated in this figure, secant Young s moduli for reloading stage are larger than those for loading stage. Secant Young s moduli for unloading fall in between those for loading and reloading. Secant Young s moduli for unloading is approximately equal to those for loading at low strains (about %) and those for reloading at higher strains (about 0.5 %) Relaxation stages Details of stress relaxation tests are presented in Table Two stress relaxation tests have been carried out after the peak strength in addition to one before the peak strength. The axial displacement was held constant for 1800 min in these stress relaxation stages at axial strains of 1.0 %, 3.0 % and 4.5 %, respectively; while the changes in the deviatoric stress were measured. Normalized deviatoric stress curves are plotted versus the logarithm of time in Figure Volume change of the sample was recorded during the stress relaxation stages. Changes in volumetric strains from the beginning of each stress relaxation test are plotted versus the logarithm 115

144 of time in Figure Volumetric strains were also normalized and plotted versus the logarithm of time in Figure The sample exhibited a different volumetric response in stress relaxation stages in pre-peak (stage #2 at axial strain of 1.0 %) and post-peak stress (stage #6 and #8 at axial strains of 3.0 % and 4.5 %, respectively) in first 167 min of relaxation (10000 seconds in Figure 3.57). During this period, the stress relaxation at axial strain of 1.0 % contracted steadily from the start of the relaxation, while those at axial strains of 3.0 % and 4.5 % had no significant change in volumetric strain. The stress relaxation at axial strain of 3 % dilated less than 0.1 % after first 167 min of relaxation, while the one at axial strain of 4.5 % contracted more than 0.1 %. The stress relaxation at axial strain of 1 % initially contracted to about 0.1 % and, then, dilated near the end of the stage Consolidated drained triaxial compression tests - Group C Test #9: consolidated drained triaxial compression test A clay shale sample of Kcb-700 facies from borehole D was consolidated at a confining pressure of 300 kpa. Then, the sample was sheared in a drained condition at different axial strain rates: 0.27 %/day, 1.33 %/day, 5.32 %/day, and %/day. Stress relaxation tests were conducted at two axial strains (6.5 % and 9.6 %) after the peak strength Saturation and consolidation The confining pressure was increased to 300 kpa instantaneously after installation of the sample in the triaxial cell. While the pore pressure was measured at the top end of the sample, drainage 116

145 was provided from the radial boundary and the bottom end of the sample. The variation of volumetric strain with the square-root of time is shown in Figure The volumetric strain was calculated based on: first, the changes in cell volume; second, the local LVDTs measurements (two axial LVDTs and a radial one, mounted on the sample inside the triaxial cell). The axial strains calculated from the local LVDTs measurements during the consolidation stage are presented in Figure Shearing stages Shearing of the sample in the drained condition was initiated after the completion of consolidation. Details of shearing stages, the range of axial strains and the applied axial strain rate, are presented in Table The duration of stress relaxation stages along with the related axial strains are also listed in Table The variation of the deviatoric stress with axial strain is shown in Figure The sample showed a maximum deviatoric stress of 1052 kpa at an axial strain of 6.0 %. The samples consolidated at a lower confining pressure exhibited lower peak stresses. For example, in test #12 (on Kcc-710), consolidated at 100 kpa confining pressure, the maximum deviatoric stress was 869 kpa. Higher peak stresses were observed in the samples consolidated at a higher confining pressure. For instance, a peak stress of 1071 kpa was observed on test #7 (on the same facies) at a confining pressure of 500 kpa. The variation of the volumetric strain is shown in Figure The sample exhibited a contractive volumetric behavior and reached a maximum volumetric strain of 2.82 % at an axial strain of 6.23 %. 117

146 The strength has reduced to 463 kpa at an axial strain of 14.5 % at the end of the test at an axial strain rate of %/day. The deviatoric stress has reduced to 410, 433, and 463 kpa at the end of stages #10, #11, and #12, respectively. These values are normalized by the smallest value, the deviatoric stress at the end of the relaxation stage (stage #10), and drawn versus the logarithm of the axial strain rate of each stage in Figure The result implies the decrease of post-peak strength with the decrease in axial strain rate Relaxation stages Details of stress relaxation tests are presented in Table Two stress relaxation tests have been carried out after the peak strength. The axial displacement was held constant for 6480 and 4800 min in these stress relaxation stages at axial strains of 6.5 % and 9.6 %, respectively; while the changes in the deviatoric stress were measured. Normalized deviatoric stress curves are plotted versus logarithm of time in Figure Volume change of the sample was recorded during the stress relaxation stages. Normalized volumetric strains are plotted versus logarithm of time in Figure Both tests show a slight and smooth increase in volumetric strain (dilation) till 27.8 hr since the start of the relaxation (corresponding to the end of the linear part in the graph of deviatoric stress versus logarithm of time) and fluctuate after that. In both stress relaxation stages, a slight and smooth increase in volumetric strain (dilation) was observed till 27.8 hr since the start of the relaxation (corresponding to the end of the linear part in the graph of deviatoric stress versus logarithm of time). Fluctuations in volumetric strain was observed in both stress relaxation stages after 27.8 hr. 118

147 Test #10: consolidated drained triaxial compression test A clay shale sample of Kcb-650 facies from borehole E was consolidated at a confining pressure of 500 kpa. Then, the sample was sheared in a drained condition at three strain rates: 0.27 %/day, 1.33 %/day, and 5.32 %/day. Moreover, stress relaxation tests were conducted at five axial strains Saturation and consolidation A confining pressure of 500 kpa was applied to the sample while drainage was provided from side and the bottom of the sample to allow the sample to consolidate. During this stage, the induced pore pressure was measured at the top end of the sample. Since the nature of the pore fluid was not known exactly, back pressure was not applied during saturation-consolidation stage to prevent occurrence of any swelling. The dissipation of excess pore pressure versus time in logarithmic axis is illustrated in Figure Then, the degree of consolidation, U, is calculated and plotted versus square-root of time in Figure Finally, the value of t 100 is readily estimated from Figure 3.67 to calculate c v Shearing stages After the completion of consolidation at an effective confining pressure of 500 kpa (without any back pressure), shearing of the sample in a drained condition was initiated. Details of shearing stages, the range of axial strains and the applied axial strain rate, are presented in Table The 119

148 duration of stress relaxation tests and axial strains corresponding to them are also included in Table The variation of deviatoric stress is shown in Figure 3.68, where the sample shows a maximum deviatoric stress of 1343 kpa at an axial strain of 4.18 %. The measured volumetric strain is plotted versus axial strain in Figure The volume of the sample decreased (contracted) up to an axial strain of 3.2 % and increased (dilated) afterwards. The samples reached a maximum volumetric strain of 2 % at an axial strain of 3.2 %. The shearing continued to an axial strain of 29 % to measure the residual (or the post-peak) strength of the soil sample. The measured deviatoric stress is plotted versus axial strain in Figure 3.70 and the variation of volumetric strain with axial strain is shown in Figure According to these figures, the rate of change in volumetric strain of the sample with axial strain becomes approximately constant in stage #15, while the deviatoric stress is still decreasing even at the end of this stage. Based on Figure 3.70, the post-peak strength of the sample has reduced to 349 kpa, one-fourth of the peak strength, at an axial strain of 29 % Relaxation stages Four stress relaxation stages have been carried out after the peak strength in addition to the one before the peak strength. Details of stress relaxation tests are presented in Table Normalized deviatoric stress curves are plotted versus logarithm of time in Figure 3.72 (data related to stress relaxations in stages #8 and #12 were not recorded). 120

149 Changes in volumetric strains from the beginning of each stress relaxation test are plotted versus logarithm of time in Figure Volumetric strains were also normalized and plotted versus logarithm of time in Figure The sample showed different volumetric responses in stress relaxation stages before and after peak deviatoric stress. During 27.8 hr after start of relaxation, the sample exhibited an approximately contractive behaviour in stage #5 (conducted before peak deviatoric stress), while it showed dilative behaviour at the same period in stages #10 and #14 (carried out after peak deviatoric stress). After this period, the sample contracts in all the mentioned three relaxation stages Multistage consolidated drained triaxial compression test - Group D Test #11: consolidated drained triaxial compression test A clay shale sample of kcc-710 facies from borehole C was prepared. This consolidated drained triaxial compression test includes multiple stages of consolidation at different levels of confining pressures (100, 300, and 500 kpa). This was done to eliminate the potential discrepancy in results due to samples heterogeneity. In addition, effects of axial strain rates (5.32 %/day, 1.33 %/day, and 0.27 %/day) during shearing were also studied in this test. Stress relaxation tests were also conducted at seven different axial strains Consolidation The test involved five stages of consolidation which are presented in Table The sample was completely unloaded before application of the desired confining pressure in each stage. The 121

150 coefficient of consolidation in isotropic consolidation was calculated for each stage and plotted versus confining pressure in Figure It is evident from this figure that the coefficient of consolidation increases with increase in confining pressure. Varatharajan (2011) experimentally measured the coefficient of consolidation of water-saturated kaolinite clay sample in axial and radial direction. The reported values of the coefficient of consolidation also increases with confining pressure in both directions. The coefficient of consolidation depends on: the coefficients of hydraulic conductivity and volumetric compressibility, which both depend on confining pressure. These two factors both decrease with increase in confining pressure, therefore, the variation of the coefficient of consolidation with confining pressure depends on the rates of decrease of the coefficients of hydraulic conductivity and volumetric compressibility with confining pressure. The variation of coefficient of volumetric compressibility versus axial pressure from a constant rate of strain consolidation test on Kcb-700 is shown in Figure Delage and Lefebvre (1984) studied the microstructure of a Champlain clay using the of electron microscopy and mercury intrusion porosimetry. They found that only the largest existing pores collapse during consolidation and small intra-aggregate pores were not compressed until large pressures and until all macro pores have been collapsed. They concluded that the compression index should be related to the largest existing pore size for a given consolidation pressure increment. Porosity and permeability decrease with increase in effective pressure because of preferential collapse of large pores in shales (Gautem, 2005). Pender et al. (2009) suggested the sensitivity of 122

151 permeability to inhomogeneities in soil fabric. Therefore, the permeability of shale is more dependent on preferential fabric than pore volume. Considering dependence of shale permeability on preferential fabric and volumetric compressibility on the largest pore size, the range of applied effective pressure in consolidation stages should have been enough to change significantly the size of the largest pore (or proportion of large pore) of clay shale but not enough to change preferential fabric of clay shale. This resulted in more decrease in volumetric compressibility than the permeability, which means increase of coefficient of consolidation with effective stress Shearing stages After the completion of each consolidation stage, the sample was sheared in different stages. Specification of each shearing stage is presented in Table Different strain rates were used to shear the sample after consolidation at confining pressure of 100 kpa (stages #1, #3, and #4). The strain rate of 5.32 %/day was applied in the rest of shearing stages (consolidated and sheared at 300 or 500 kpa confining pressure), except the last one (stage #22) that was sheared at an axial strain rate of %/day. The variation of the deviatoric stress versus axial strain, up to an axial strain of 10 %, is plotted in Figure The sample, consolidated at 500 kpa confining pressure, showed a peak deviatoric stress of 1330 kpa at an axial strain of % (3.93 % after reloading). The axial strains corresponding to the peak deviatoric stresses for triaxial tests (test #1-12 except test #5) are in the range of 2.47 %-6.00 % with an average of 4.66 %. Therefore, the measured axial strain of the 123

152 peak strength in the current test is comparable with the rest of the triaxial tests in this study. The relaxation stages are seen as vertical lines in Figure The volumetric behavior of the sample is shown in Figure The sample exhibited a maximum contraction (5 % of volumetric strain) at an axial strain of 8 %. The variation of the volumetric strain versus time is also plotted in Figure 3.81 to clarify the changes in volumetric strain. The test continued with shearing and stress relaxation stages. The measured deviatoric stress is plotted versus axial strain in Figure 3.79, in which the post-peak strength decreases to 692 kpa at an axial strain of 23.7 %. The measured volumetric strain is also plotted in Figure The sample exhibits very small changes in volume for axial strains larger than 10 %. Finally, the deviatoric stress is plotted versus the mean effective principal stress in Figure Relaxation stages Details of stress relaxation tests are presented in Table One stress relaxation test has been carried out before each unloading stage (four tests). Additional stress relaxation tests have been carried out at axial strains of 3 %, 7.7 %, and 12.7 %. Normalized deviatoric stress curves of various stress relaxation stages are plotted versus logarithm of time in Figure As illustrated in Figure 3.83, the variation of the normalized deviatoric stress is linear with the logarithm of time after an initial time period. This was also observed in previous studies by Murayama and Shibata (1961), Vyalov and Skibitsky (1961), and Lacerda and Houston (1973). The mentioned initial time period or the time delay of initiation of deviatoric stress decay is longer in stress relaxation at axial strain of 2.5 % (stage #5) in comparison with other stress relaxation 124

153 stages. This is consistent with observation of Lacerda and Houston (1973) that the strain rate prior to the stress relaxation stage has an influence on the time at which stress relaxation begins. The slower strain rate (0.27 %/day) applied in stage #4 before stress relaxation in stage #5 led to this longer time delay before initiation of decay in normalized deviatoric stress. The stress relaxation stages conducted in this test can be divided into two groups: - Group I: The first, third, and fourth stress relaxation stages. - Group II: The second, fifth, sixth, and seventh stress relaxation stages. Based on this division, the following observations can be made: - A reduction in slope is seen in stress relaxation of Group I, implying the existence of a final relaxed stress level. A final relaxed level of stress was reported by Oda and Mitachi (1988). - The normalized deviatoric stress has relaxed to lower levels in Group I than in Group II. - Stress relaxation stages of group I were conducted at axial strains of 1.5 %, 3 %, and 3.8 %. In Group II, stress relaxations were carried out at axial strains of 2.5 %, 7.7 %, 9.7%, and 12.7 %. Excluding the stress relaxation at axial strain of 2.5 %, the stress relaxations of Group II were conducted at larger axial strains than those in Group I. - Stress relaxation tests of Group I were carried out at axial strains after reloading (1.5 %, 1 %, and 1 %) smaller than those of Group II (2.5 %, 2 %, 4 %, and 4.6 %). - The last two observations imply that axial strain after reloading is a better criterion to divide stress relaxation stages rather than the axial strain. 125

154 Percent of change in deviatoric stress versus axial strain for these two groups of stress relaxation stages are plotted versus axial strain in Figure It is observed that the percent of change in deviatoric stress increases with axial strain in each group. In addition, the percent of change in deviatoric stress increases with the increase in confining pressure in each group (Figure 3.85). In other words, the relaxed normalized deviatoric stress (the normalized deviatoric stress at the end of the relaxation stage) decreases with the increase in confining pressure in each group Consolidated undrained triaxial compression tests - Group E Test #7: consolidated undrained triaxial compression test A clay shale sample of Kcb-700 facies from borehole D was consolidated at a confining pressure of 500 kpa and was sheared using different axial strain rates (0.53 %/day, 5.32 %/day, and %/day) in an undrained condition. The stress-strain response of the sample and the generated excess pore fluid pressure was investigated Saturation and consolidation Three percent saline water was used as pore fluid to prevent clay shale sample from swelling during saturation stage. This was decided based on the comparison of the results of free swell tests on clay shale samples submerged in water with different salinity content (1 %, 3 %, 5 %, and 10%). Initially, a back pressure of 250 kpa was applied to saturate the sample. In next step, the B-test was conducted and resulted in a B-value equal to Then, the back-pressure was increased in 126

155 stages, to 500, 1000, 1250, and 1450 kpa, and kept constant for 4 hours in each stage to ensure the full saturation of the sample. During these stages cell pressure were increased to keep a constant 20 kpa pressure difference (effective stress). The B-values measured at different levels of back pressure are shown in Figure The B- value reached 0.89 and 0.9 at 1250 and 1450 kpa of back-pressure, respectively. The saturation process ceased after the B-value reached 0.9. Stiff soils at full saturation can have B-values significantly less than unity. Head (1998) recommended to relate the required B-value as a criterion for saturation to the properties of soil instead of using the traditional arbitrary B-value of about 0.95 in all cases. Black and Lee (1973) defined different soil categories for the study of saturation effects in Table They presented a graphical relationship of B-value to degree of saturation and soil stiffness, shown in Figure Assuming the clay shale sample, tested in this research, is a lightly overconsolidated clay, it will belong to the medium soil category according to Table Thus, the degree of saturation is approximately 98.5 % for the observed B-value of 0.90 from Figure By increasing the cell pressure to 1930 kpa, the consolidation at effective confining pressure of 500 kpa began. The pore pressure initially increased from 1430 to 1884 kpa which means B- value reached Drainage was provided from both the top and bottom ends of the sample during the consolidation. The variations of volumetric strain with the square-root of time is plotted in Figure The volumetric strain was calculated based on the amount of fluid flowed out of the sample during saturation (measured by back-pressure pump). 127

156 Shearing stages The sample was sheared in an undrained condition after consolidated at 500 kpa effective confining pressure. Different axial strain rates (0.53 %/day, 5.32 %/day, and %/day) were implemented in different shearing stages in this test to investigate the effect of axial strain rates on the stress-strain response. Details of shearing stages (the range of axial strains and the applied axial strain rate) are presented in Table The variation of the deviatoric stress with axial strain is shown in Figure The sample reached a maximum deviatoric stress of kpa at an axial strain of 5.39 %. The samples (from other facies) consolidated at a same confining pressure exhibited higher peak deviatoric stresses in drained tests. A sample from Kca-625 facies showed a maximum deviatoric stress of 1132 kpa at an axial strain of 3.47 % while sheared in a drained condition (test #6). The other drained test on a sample from Kcb-650 facies showed a peak deviatoric stress of 1343 kpa at an axial strain of 4.18 % (test #10). Both tests conducted in drained condition showed a stiffer pre-peak stress-strain behavior than the undrained response (Table 3.42). The generated excess pore fluid pressure, measured at the top end of the sample, versus axial strain is shown in Figure The excess pore fluid pressure reaches a maximum of 361 kpa at an axial strain of 4.34 %, about one percent before the peak strength. The excess pore fluid pressure decreases and reaches negative values after axial strain of %. This is due to the flow of water toward the dilated shear band from the top end of the sample. The variation of pore pressure coefficient A, calculated from dividing the excess pore fluid pressure by the deviatoric stress, with the axial strain is demonstrated in Figure The value of 128

157 the pore pressure coefficient A at failure depends on the soil type and its past stress history (Head, 1998). The A-value at failure for the current test is calculated equal to 0.28, which is a typical value for lightly overconsolidated clays according to Table A typical relationship between the A-value at failure and the overconsolidation ratio (OCR) is demonstrated in Figure The observed pore pressure coefficient A at failure, equal to 0.28, is related to an OCR of about 2.5 based on this figure. The value of OCR implies a preconsolidation of 1250 kpa, which is close to the preconsolidation pressures estimated in constant-rate-of-strain consolidation tests, 860 and 1280 kpa. The variation of the deviatoric stress versus the mean effective stress is plotted in Figure 3.93 for different rates of axial strain during shearing. In addition, secant Young s modulus versus axial strain is shown in Figure 3.94 for the axial strains before peak strength. In Figure 3.95, values of secant Young s modulus are plotted versus axial strains greater than 0.1 % Test #8: consolidated undrained triaxial compression test A sample of Kcb-700 facies from borehole D was consolidated at a confining pressure of 500 kpa and was sheared in an undrained condition. Three different axial strain rates (0.53 %/day, 5.32 %/day, and %/day) were applied during the shearing stages. The undrained stress-strain response of the sample was studied. 129

158 Saturation and consolidation Saturation and consolidation of the sample were performed in a single stage by increasing the cell pressure and the back pressure to 1930 and 1430 kpa, respectively. To prevent any potential swelling of the sample during saturation-consolidation stage, three percent saline water was employed as pore fluid. Radial drainage was provided in addition to drainage from both bottom and top end of the sample. At the end of saturation-consolidation process, the B-test was conducted and resulted in a B-value equal to The measured B-value is correlated with 95 % degree of saturation according to Figure The variations of volumetric strain with the square-root of time is plotted in Figure The volumetric strain was calculated from both the amount of fluid flowed out of the sample and the cell volume change Shearing stages After consolidated at 500 kpa effective confining pressure, the sample was sheared in an undrained condition. Different rates of axial strain (0.53 %/day, 5.32 %/day, and %/day) were applied in shearing stages to examine the effect of axial strain rate on the stress-strain response. The variation of the deviatoric stress with axial strain is plotted in Figure A maximum deviatoric stress of 827 kpa occurs at an axial strain of 3.06 %. The sample exhibited a lower maximum deviatoric stress at a smaller axial strain in comparison with the one in test #7 (undrained test on the same facies and at the same confining pressure), which showed maximum deviatoric stress of 1067 kpa at an axial strain of 5.39 %. The calculated secant s young modulus versus axial 130

159 strain is shown in Figure 3.98 for the axial strains before peak strength. The calculated elastic moduli are compared with those in other tests at 500 kpa confining pressure in Table The measured excess pore pressure versus axial strain is shown in Figure The excess pore pressure attained a maximum of 296 kpa at an axial strain of 3.06, the same axial strain that the peak strength occurred. The excess pore fluid pressure decreased to 181 kpa at the end of the test at axial strain of %. The pore pressure coefficient A is calculated and plotted versus axial strain in Figure The A-value at failure is 0.36, which is a typical value for lightly overconsolidated clays according to Table 3.43 with an OCR of about 2 based on Figure The value of OCR implies a preconsolidation pressure of 1000 kpa, while the preconsolidation pressure was estimated in constant-rate-of-strain consolidation tests as 860 and 1280 kpa. The variation of the deviatoric stress versus the mean effective stress is plotted in Figure for different rates of axial strain during shearing Corrections to triaxial test data Area corrections Barrelling The correction for the increasing area due to axial strain in a triaxial test is called barrelling correction. The corrected deviatoric stress in an undrained test is given by: q = P A c (1 ε a ) (3.11) 131

160 where q is the corrected deviatoric stress, P is the applied axial force, A c is the initial area of the consolidated specimen, and ε a is the axial strain. In a drained test, the change in volume due to drainage, V, should be taken into consideration to calculate the corrected area and subsequently the corrected deviatoric stress. If the volume at the start of shearing is V c, then, the corrected deviatoric stress will be: q = P A c (1 ε a ) (1 V V c ) (3.12) The above corrections were applied to the measured deviatoric stresses in pre-peak regions of the tests Single-plane slip The effective plane area, used for calculation of axial stress, decreases when a slip surface forms and two generated wedges move along each other. The shear band had been developed at the postpeak region, therefore, the mentioned reduction in the effective plane area should be considered in calculation of the deviatoric stress at this region. To apply this correction, Head (1998) suggested multiplying the calculated deviatoric stress by the following slip area factor: f s = π 2(β sinβ cosβ) (3.13) in which β is expressed in radians and: cosβ = L D tanθ (3.14) 132

161 where D is the sample diameter, L is the vertical movement of the upper part of the sample from the start of slip, and θ is the angle of the slip plan with vertical direction. In the above formula, it is assumed that the slip begins at the strain corresponding to the peak deviatoric stress and thus L becomes the upper part vertical movement after occurrence of the peak strength. The values of θ were measured in laboratory at the end of each test and are presented in Table The single-plane slip correction was calculated and applied to all the tests except test# 8 in which two shear bands were developed. The calculated slip area factors at axial strain of 15 % have an average of 1.17 (Table 3.46) Membrane corrections The rubber membrane, enclosing the triaxial sample, applies a restraining effect on the sample and contributes to the resistance offered against compression. A correction, depending upon the mode of deformation, has to be subtracted from measured axial (deviatoric) stresses Barrelling A correction has to be deducted from the measured stress at failure to take account of the restraining effect of the rubber membrane enclosing a triaxial sample. The membrane correction, is specified in BS 1377:Part 7:1990 in a graph for 38 mm diameter samples fitted into 0.2 mm thick membrane. The correction from the mentioned graph is multiplied by 38 D t 0.2 (3.15) 133

162 where D is the diameter of the sample and t is the membrane thickness both in mm. The calculated membrane correction changes linearly from zero at the beginning of the shearing up to 1.3 kpa at an axial strain of 5 % Slip plane After formation of a slip plane, the movement of one portion of the sample along the other one distorts the membrane. A small contribution to the measured axial (deviatoric) stress is made by the distorted membrane. Therefore, it becomes necessary to apply a membrane correction to the measured axial (deviatoric) stress after the peak strength. Meehan et al. (2011) evaluated the membrane correction by testing on a cylindrical Lucite (Plexiglas) specimen with a diameter of 35 mm and height of 85 mm having a slickensided surface at an angle of 35 with vertical direction. They suggested the following expression for the correction value in kpa: ε s ( σ 3 ) (3.16) where ε s is the axial strain after start of slip in percent and σ 3 is the effective cell pressure in kpa. For any other sample direction or any other slip plane inclination, the calculated correction should be multiplied by 38 D t 0.2 L 2D (3.17) where L is the length of the sample. Considering D = 63 mm, t = 0.6 mm, and L = 2, the multiplier D will be equal to 1.4. Therefore, the original equation transforms to 134

163 ε s ( σ 3 ) (3.18) The value of correction at an axial strain of 10 % after slip, implementing the above equation, will be equal to 17.9, 31.3, and 44.7 kpa for confining pressures of 100, 300, and 500 kpa, respectively. Considering average deviatoric stresses at the end of the tests, the membrane corrections account for 8.8 %, 8.2 %, and 8.3 % of the measured deviatoric stresses at the end of tests for confining pressures of 100, 300, and 500 kpa, respectively Side drain corrections Barrelling A correction is deducted from the measured deviatoric stress to allow for the restraint imposed by filter paper 1 side drains. The value of correction, according to the sample diameter, are specified in BS 1377: Part 8:1990 that is equal to 5.7 kpa for a 63 mm diameter sample. This correction should be applied to strains from 2 % up to the strain corresponding to the peak strength. For strains from zero up to 2 %, the correction should increase linearly from zero to 5.7 kpa with increasing strain. 1 Whatman No.54 filter paper 135

164 Slip plane La Rochelle (1967) and Balkir and Marsh (1974) have studied the correction for side drains under condition of single-slip and found evidence of a small increase in resistance with increasing cell pressure. Head (1998) provided simplified drain correction curves, after data from La Rochelle (1967), for various effective cell pressure. According to which, the correction value increases approximately linearly with axial strain after slip with rate of 0.72 kpa/%, 0.96 kpa/%, and 1.20 kpa/% for effective confining pressures of 100, 300, and 500 kpa, respectively. Therefore, the values of side drain correction at an axial strain of 10 % after slip will be equal to 7.2, 9.6, and 12.0 kpa for effective confining pressures of 100, 300, and 500 kpa, respectively. Considering average deviatoric stresses at the end of the tests, the side drain corrections account for 3.5 %, 2.5 %, and 2.2 % of the measured deviatoric stresses at the end of tests for confining pressures of 100, 300, and 500 kpa, respectively Summary Correction to triaxial data, discussed in previous sections, are summarized in Table As expected, the values of correction that should be applied are greater in the post-peak region. For area corrections, the correction factor in the pre-peak region reaches a maximum of 0.95 at the strain corresponded to the peak deviatoric stress while this factor reaches a range of at an axial strain of 10 % after the strain corresponding to the peak strength. For membrane and side drain corrections, the correction values are less than 5.7 kpa in pre-peak region while these value are much higher in post peak region. The single-plane slip corrections of membrane and side drain 136

165 increase with increase of confining pressure, while the barreling corrections do not show any dependence on confining pressure Analysis of triaxial test data Secant Young s modulus and Poisson s ratio To compare pre-peak response of samples at different tests, secant Young s moduli are calculated from dividing the axial stress by the axial strain for each test at axial strains of 1 %, 2 %, and one corresponded to the peak strength (Table 3.48). In addition, average values of secant Young s modulus at different axial strains for different facies are presented in Table Using displacement recorded by local LVDTs, Poisson s ratio has been calculated for various facies of Clearwater clay shale at axial strains of 1 %, 2 %, 3 %, and 4 % (Table 3.50) Dependence of secant Young s modulus on confining pressure Secant Young s moduli for all the test were calculated for each axial strain. Five tests have been conducted on samples (from four different facies) consolidated at a confining pressure of 100 kpa. Calculated secant Young s moduli from these tests verses axial strain are demonstrated in Figure in a log-log scale. The secant Young s moduli from different facies lie within a relatively narrow band and the curve of each test in this log-log graph can be approximated with: log 10 E = A log 10 ε a + B (3.19) 137

166 in which E is the secant Young s modulus in MPa, ε a is the axial strain in percent, A, and B are coefficients. For instance, the secant Young s moduli related to the test #3, conducted on Kcb-700 facies at a confining pressure of 100 kpa, can be approximated with the following straight line: log 10 E = log 10 ε a (3.20) where E is in MPa and ε a is in percent. The secant Young s moduli for the test on Kca-625 facies at three different confining pressures (100, 300, and 500 kpa) are plotted versus axial strain in a log-log scale in Figure As expected, the sample consolidated at higher confinig pressure showed higher stifness at each axial strain level. Curve fitting of the results of each test yields: - Test #1: - Test #2: log 10 E = log 10 ε a (3.21) - Test #6: log 10 E = log 10 ε a (3.22) log 10 E = log 10 ε a (3.23) In next step, the calculated coefficients for these straight lines are plotted versus the related confining pressure. These coefficients depict a clear dependency on confining pressure (Figure 3.104): A = σ c (3.24) B = σ c (3.25) where σ c is the confining pressure in kpa. Therfore, for Kca-625: 138

167 log 10 E = ( σ c ) log 10 ε a σ c (3.26) Estimation of Mohr-Coulomb shear parameters The triaxial stresses at-failure can be plotted in the q p plane. The Mohr-Coulomb failure criterion is obtained by fitting the best line: q = M p p + c (3.27) where M p is the slope of the failure line and c is the cohesion intercept. Then, the internal friction angle at the peak deviatoric stress, φ p, can be obtained from the following expression: sinφ p = and the cohesion, c, from the following equation: 3M p 6 + M p (3.28) c = c (3 sinφ ) 6 cosφ (3.29) If the values corresponding to the end of the tests are plotted in the p q plane, a line can be fitted to the data: q = M r p (3.30) in which M r is the slope of the post-peak strength line. Then, the internal friction angle at post-peak (end of the test), φ r, can be obtained from the following equation: sinφ r = 3M r 6 + M r (3.31) The stress states at-failure and the end of triaxial tests are plotted in the q p plane in Figure The internal friction angle at peak strength and post-peak along with cohesion for 139

168 various facies of Clearwater clay shale were calculated, based on the results of triaxial tests, and listed in Table In addition, all triaxial tests, except tests #5 and #8, were included in Figure and the friction angle values at peak and end of the test along with cohesion was calculated for Clearwater clay shale (Table 3.51) Correlations between results of triaxial tests and properties of samples Correlations with clay content Friction angle at the end of the test and clay content The calculated friction angles at the end of the tests were plotted versus clay content in Figure As expected, the overall trend is a decrease in strength (the friction angles) with increasing clay content. Test #5 was not considered because of early termination of the test at an axial strain of %. Shearing in Test#10 continued up to an axial strain of %, while the rest of the tests ended in an axial strain in range of % %. Therefore, the value of q and p at the axial strain of % (average of axial strains at the end of the rest of the tests) was used for Test#10. In Figure 3.108, friction angles at the end of the tests are plotted versus clay contents of the samples at different confining pressures. In Clearwater clay shale, 31 % - 53 % of the clay fraction consists of smectite. Friction angles at the end of the tests are plotted versus smectite contents and smectite portion of clay fraction of the samples in Figures and 3.110, respectively. Illite constitutes 39 % - 46 % of the clay fraction of the samples. Friction angles at the end of the tests are plotted versus sample illite contents in Figure

169 A general correlation between saturated residual friction angle of a soil and its clay content, seemingly independent of clay mineralogy, was suggested by Skempton (1964). Lupini et al. (1981) underlined that the reduction of friction angle with increase in clay content is nonlinear, following a sigmoidal curve. Tembe et al. (2010) investigated the degradation of friction angle with increasing content of clay minerals content by conducting triaxial compression tests and found that the decrease in friction angle follows a sigmoidal trend with the fraction of montmorillonite, while follows an approximately linear trend with the fraction of illite. Dimitrova and Yanful (2011) found that an increase in clay content generally caused a decrease in the frictional angle; however, the decrease was greater when the clay fraction mostly consisted of bentonite and lesser when the clay fraction mostly consisted of kaolinite Depth of the samples and clay content The estimated depths of triaxial samples were plotted versus their clay content in Figure Considering the samples of Kcc-710 and Kcb-700 together and Kcb-650 and Kca-625 together reveals that the clay content of the samples slightly increases with increase in depth Surface hardness and clay content Surface hardness of samples used in tests #5, #6, #7, #9, and # 10 have been measured, via the Leeb rebound hardness test (Equotip impact device D with hardness unit HLD), and were plotted versus their clay content in Figure It is clear from the figure that the surface hardness increases with clay content. 141

170 Liquid limit and clay content The values of the liquid limit of facies of Clearwater clay shale, from index tests, are plotted versus clay content of these facies, from XRD analysis, in Figure Moreover, clay and smectite content of triaxial samples, estimated from XRD analysis, are plotted versus their liquid limit in Figure Density and clay content Densities of samples used in triaxial testing, presented in Table 3.4, are plotted versus clay contents of these samples in Figure Sample for test #3 has the lowest density, which explains its low peak deviatoric stress, 227 kpa, and deviatoric stress at the end of the test, 126 kpa. The sample for test #3 is the only sample cut from cores recovered from borehole E, which had lots of slickensided surfaces and visible cracks Correlations with peak strength Peak strength and density Peak strength of samples measured in triaxial tests are plotted versus density of each sample at different confining pressures in Figure The peak strength of samples sheared at the same confining pressure increases with increase in density. Four triaxial tests have been conducted on samples from facies Kcb-700. Peak strength versus density of those tests were plotted in Figure 3.118, which shows increase in strength with increase in sample density. 142

171 Peak strength and shear band angles The values of measured shear band angle at the end of each test are presented in Table The values of maximum deviatoric stress in triaxial tests are plotted versus measured shear band angles at the end of the tests in Figure In Figure 3.120, the tests have been divided into three groups: - Group I: all the tests sheared under 100 kpa confining pressures except test #4. - Group II: tests on Kcb-700 facies. - Group III: rest of the tests, including those on Kcc-710, Kcb-650, and Kca-625 at confining pressures of 300 kpa and 500 kpa in addition to test #4 on Kcb-650 at a confining pressure of 100 kpa. In each group, the maximum deviatoric stress increases with the increase in measured shear band angle. Moreover, the samples with an approximately same shear band angle exhibit higher values of maximum deviatoric stresses at higher confining pressures Analysis of results of stress relaxation tests A total of 37 stress relaxation tests were carried out in triaxial tests in groups B, C, and D (20 and 17 stress relaxation tests before and after the peak strength, respectively). Effect of different parameters on change in normalized deviatoric stress versus time was studied. These parameters were: sample facies, axial strain, relation to the peak deviatoric stress, axial strain difference with the axial strain corresponding to the peak deviatoric stress, axial strain rate prior to relaxation, 143

172 confining pressure, relaxation time, and deviatoric stress range (deviatoric stress at the start and the end of the stress relaxation stage). For test #11, which was a multistage triaxial test with unloading, consolidation, and reloading, and test #4, with unloading and reloading stages, the axial strain after reloading was also considered as a parameter. Among mentioned parameters, the axial strain rate, the pre-relaxation strain rate and the relation to peak deviatoric stress showed the most influence on the change in normalized deviatoric stress. In general, the stress relaxation tests performed at larger axial strains experienced more decrease in deviatoric stress than those performed at smaller axial strains. Lacerda and Houston (1973) approximated the variation of the normalized deviatoric stress versus with the logarithm of time with a straight line, with the slop of s, after an initial time period, t 0 (Figure 3.121). Similarly, the variation of the normalized deviatoric stress versus with the logarithm of time was approximated with a straight line after an initial time period in this research. The decay of the deviatoric stress in stress relaxation is associated with a delay (the mentioned initial time period), which depends on the strain rate prior to the stress relaxation. The influence of prior strain rate on the time to start of stress relaxation is demonstrated in Figure As seen in this figure, the higher pre-relaxation strain rate leads to shorter delay before start of the relaxation. In the pre-peak strength region, 18 stress relaxations were carried out after sample had been sheared with an axial strain rate of 5.32 %/day, results of which are demonstrated in Figure in a graph of change in deviatoric stress versus axial strain. A line is fitted into the points 144

173 corresponded to stress relaxation tests on each facies at a specific confining pressure. The fitted lines are in the form of: (1 q r) 100 = nε a + q n (ε a is in percent) (3.32) where q r is the normalized deviatoric stress at the end of the stress relaxation stage (normalized relaxed stress), n is the slope of this line, and q n is a constant. The value of n and q n for stress relaxation tests conducted before the peak-strength, presented in Figure 3.123, on different facies and at different confining pressures are listed in Table It is observed that the stress relaxation lines corresponding to each facies have an approximately similar slope (n value) in different confining pressures. Moreover, the stress relaxation line corresponded to a higher confining pressure is above the one corresponded to a lower confining pressure (has a larger q n value), i.e. a lower stress relaxation is observed in tests at a higher confining pressure. In the post-peak strength region, 17 stress relaxation were carried out. Two stress relaxation tests were performed on each facies after shearing with an axial strain rate of 5.32 %/day, which are demonstrated in Figure A line is fitted into results of each facies and the calculated parameters are presents in Table In addition, results of stress relaxation tests on Kcb-650 facies with pre-relaxation axial strain rate of 1.33 %/day at a confining pressure 500 kpa are included in Figure Considering stress relaxation tests at a confining pressure of 100 kpa in Figure 3.124, five of them are almost located on a straight line, while the other two corresponded to kcb-650 are placed significantly lower. It is worth to mention that these two tests were performed after unloading- 145

174 reloading in test #4. Thus, the unloading-reloading stage may contributed to the decrease in the amount of deviatoric stress changes during these relaxations. Results of four more stress relaxation tests are shown in Figure in comparison with those presented in Figure Based on this comparison, the following observation can be made: - The point corresponding to the stress relaxation on kcc-710 at confining pressure of 500 kpa is located above the line for kcc-710 at a confining pressure of 100 kpa. - The point corresponding to stress relaxation on kca-625 at a confining pressure of 300 kpa lies slightly above the line for kca-625 at a confining pressure of 100 kpa. This implies that the influence of confining pressure on q s may be smaller in the post-peak region than that in the pre-peak region. Therefore, the two tests on kcb-700 at confining pressures of 100 and 300 kpa are considered together. - The result of the other test on kcb-700 facies at a confining pressure of 300 kpa but with a lower pre-relaxation strain rate (1.33 %/day) is below the line for stress relaxation tests on kcb-700 facies with a higher pre-relaxation strain rate (5.32 %/day). - Similarly, the point corresponding to the stress relaxation test on kca-625 at a confining pressure of 100 kpa with a pre-relaxation strain rate of 0.53 %/day lies below the line corresponded to the same facies at the same confining pressure but with a higher prerelaxation strain rate (5.32 %/day). Last two observations suggest that the lower pre-relaxation strain rate leads to a smaller decrease in the deviatoric stress in a stress relaxation test than that in a stress relaxation test with higher prior strain rate but at the same confining pressure and on the same facies. The smaller 146

175 decrease in the deviatoric stress in a stress relaxation after a smaller strain rate may be also due to the mentioned delay in start of the relaxation. In about half the stress relaxation tests, the slope of the normalized deviatoric stress versus the logarithm of time decreased towards the end of the stage, implying the existence of a final relaxed stress level (Figure 3.121). This phenomenon was observed in 13 of 19 stress relaxations carried out before the peak-strength and 5 of 16 stress relaxations performed after the peak-strength. Volume changes of samples during stress relaxation stages were measured. Considering the volume change of samples in the relaxed state in comparison with the start of the relaxation, the following observation are made: - In general, stress relaxation tests performed before the pre-peak exhibited contraction, consistent with the volumetric behavior of samples during shear in this region. - In the post-peak strength region, stress relaxation tests showed both contractive and dilative volumetric behavior. - Two stress relaxation tests, one performed before the peak-strength and the other after the peak-strength, exhibited approximately zero volume change. 147

176 Table 3.1. Results of Atterberg s limits and moisture content tests Stratigraphy unit Facies code LL (%) PL (%) PI (%) Organic content (%) Soil classification W N (%) LI (%) Kcc CH Kcb CH Kcb CH 20-6 Kca CH LL: liquid limit, PL: plastic limit, PI: plastic index, CH: clay of high plasticity, W N : natural water content, and LI: liquidity index. 148

177 Table 3.2. Specific gravity of facies of Clearwater clay shale Facies Sample # Specific gravity Kcc-710 C Kcb-700 D Kcb-650 C Kca-625 C Clearwater clay shale average 2.86 Table 3.3. Organic content of facies of Clearwater clay shale Facies Sample Organic content (%) Average organic content (%) Kcc-710 B Kcb-700 C D D Kcb-650 C C C Kca-625 C

178 Table 3.4. Dimensions and densities of clay shale samples used in triaxial testing Test Number #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 Sample facies Kca- 625 Kca- 625 Kcb- 700 Kcb- 650 Kcb- 650 Kca- 625 Kcb- 700 Kcb- 700 Kcb- 700 Kcb- 650 Kcc- 710 Kcc- 710 Depth (m) Diameter (mm) Height (mm) Density (g/cm 3 )

179 Table 3.5. Average values of density for facies of Clearwater clay shale Facies Kca-625 Kcb-650 Kcb-700 Kcc-710 Average density (g/cm 3 )

180 Facies Table 3.6. Mineralogy of Clearwater clay shale samples from XRD analyses Sample # Depth (m) Q (%) K-f (%) P (%) D (%) G (%) Py (%) Clay content (%) Kcc Kcb Kcb Kca Q: quartz, K-f: k-feldspar, P: plagioclase, D: dolomite, G: gypsum, and Py: pyrite. 152

181 Table 3.7. Clay mineral content of samples of clay shale facies from XRD analyses Facies Test Depth K Ch I I-S mix K Ch I I-S mix Clay content # (m) % of clay (%) Kcc Kcb Kcb Kca K: kaolinite, Ch: chlorite, I: illite, and I-S mix: illite and smectite mixture in inter-layer. 153

182 Table 3.8. Clay mineral content from XRD analyses (illite and smectite separated) Facies Test Depth K Ch S Total I K Ch S Total I Clay content # (m) % of clay (%) Kcc Kcb Kcb Kca K: kaolinite, Ch: chlorite, Total I: illite in and out of interlayer mixture with smectite, and S: smectite in inter-layer. 154

183 Facies Kcc- 710 Kcb- 700 Kcb- 650 Kca- 625 Table 3.9. Average mineralogy of facies of clay shale from XRD analyses Depth (m) Quartz (%) K- feldspar (%) Plagioclase (%) Dolomite (%) Gypsum (%) Pyrite (%) Clay content (%) Table Average content of clay minerals of clay shale facies from XRD analyses (illite and smectite not separated) Facies Depth K Ch I I-S mix K Ch I I-S mix Clay content (m) % of clay (%) Kcc Kcb Kcb Kca K: kaolinite, Ch: chlorite, I: illite, and I-S mix: illite and smectite mixture in inter-layer. 155

184 Table Average content of clay minerals of facies of clay shale from XRD analyses Facies Depth K Ch S Total I K Ch S Total I Clay content (m) % of clay (%) Kcc Kcb Kcb Kca K: kaolinite, Ch: chlorite, Total I: illite in and out of interlayer mixture with smectite, and S: smectite in inter-layer 156

185 Table Estimated coefficient of consolidation and secondary compression index for each stress level in oedometer test (Kcb-700 facies) Axial stress (kpa) c v (10 6 cm2 s) C α C α C c c v : coefficient of consolidation, C α : secondary compression index, and C c : compression index. 157

186 Table Estimated OCRs of clay shale layers Facies OCR (based on CRS test) on Kcb-700 on Kcb-650 Kcc Kcb Kcb Kca-625u Kca-625l Kcw Table Summary of one-dimensional consolidation tests on the Clearwater clay shale Type of consolidation test Facies Pore fluid Compression index Swelling index Preconsolidation pressure (kpa) Oedometer Kcb-700 fresh water Oedometer Kcb-700 saline water Constant-rate-ofstrain Kcb Kcb Constant-rate-ofstrain

187 Table Triaxial tests matrix Test Axial strain rate (%/day) Number of Group # Loading Unloading relaxation Drainage condition Confining pressure (kpa) Facies A B C D E Drained 100 kcb Drained 500 kca (0.53, 1.33, 5.32, 13.29, and at post-peak region) - 6 Drained 100 kca Drained 300 kca Drained 100 kcb Drained 100 kcb Drained 100 kcc , 1.33, and Drained 300 kcb , 1.33, and Drained 500 kcb , 1.33, and Drained 100 kcc and Drained 300 kcc and Drained 500 kcc , 5.32, and Undrained 500 kcb , 5.32, and Undrained 500 kcb

188 Table Drainage conditions and pore pressure measurement methods in triaxial tests Test Top/bottom drainage Group # Consolidation Shearing Side drainage Pore pressure measurement Back pressure (kpa) Borehole A B C D E 5 B Both Both No No No 6 C 1 C 2 C 3 Bottom Bottom Yes Top No E 4 A 12 C 9 D Bottom Bottom Yes Top No 10 C Bottom Bottom Yes Top No D 11 7 No Both No 8 Yes (consolidation only) Top (shearing) Yes D 160

189 Table Estimated consolidation parameters from the consolidation stage of triaxial tests Test # Confining pressure (kpa) Facies t 100 (h) c v (10 6 cm2 s) Kcb Kcb Kca Kca Kca Kcb Kcb Kcc Kcc Kcb Kcc Kcc Kcc Kcc Kcc Kcb Kcb * Sample was unloaded before applying the confining pressure corresponding to the new consolidation stage. 161

190 Table List of different stages in test #12, kcc-710 facies Stage number Stage Type Axial strain rate (%/day) Time (min) Axial strain\axial strain range (%) 1 Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Table List of different stress relaxation stages in test #12, kcc-710 facies Stage number Relation to peak Axial strain (%) Axial strain rate prior to relaxation (%/day) Time (min) Deviatoric stress range (kpa) Deviatoric stress changes (%) 2 Pre-peak Pre-peak Post-peak Post-peak

191 Table List of different stress relaxation stages in test #11, kcc-710 facies Stage number Relation to peak Axial strain (%) Axial strain rate prior to relaxation (%/day) Confining pressure (kpa) Time (min) Deviatoric stress range (kpa) Deviatoric stress change (%) 8 Pre-peak Pre-peak

192 Table List of stages in test #1, Kca-625 facies Stage number Stage Type Axial strain rate (%/day) Time (min) Axial strain\axial strain range (%) 1 Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Shearing Shearing Shearing Shearing Stress relaxation

193 Table List of stress relaxation stages in test #1, Kca-625 facies Stage number Relation to peak Axial strain (%) Axial strain rate prior to relaxation (%/day) Time (min) Deviatoric stress range (kpa) change (%) 2 Pre-peak Pre-peak Post-peak Post-peak Post-peak Post-peak Table List of stages in test #2, Kca-625 facies Stage number Stage Type Axial strain rate (%/day) Time (min) Axial strain\axial strain range (%) 1 Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing

194 Table Secant Young s modulus at different axial strains for different facies and confining pressures # Test Secant Young s modulus (MPa) Sample facies Kca-625 Kca-625 Kcb-700 Kcb-700 Confining pressure (kpa) At 1 % axial strain At 2 % axial strain At peak strength Table List of stress relaxation stages in test #2, Kca-625 facies Stage number Relation to peak Axial strain (%) Axial strain rate prior to relaxation (%/day) Time (min) Deviatoric stress changes range (kpa) (kpa) (%) 2 Pre-peak Pre-peak Pre-peak Post-peak

195 Table Secant Young s modulus at different axial strains at the start and end of the stress relaxation stages Axial strain (%) At shearing at 5.32 %/day Secant Young s modulus (MPa) At the end of the stress relaxation

196 Table List of stages in test #3, Kcb-700 facies Stage number Stage Type Axial strain rate (%/day) Time (min) Axial strain\axial strain range (%) 1 Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing

197 Table Secant Young s modulus at different axial strains for tests under 100 kpa confining pressure Test Secant Young s modulus (MPa) Number #3 #4 #1 #12 Sample facies Kcb-700 Kcb-650 Kca-625 Kcc-710 At 1 % axial strain At 2 % axial strain At peak strength Table List of stress relaxation stages in test #3, Kcb-700 Stage number Relation to peak Axial strain (%) Axial strain rate prior to relaxation (%/day) Time (min) Deviatoric stress changes range (kpa) (kpa) (%) 2 Pre-peak Pre-peak Pre-peak Pre-peak Pre-peak Post-peak

198 Table List of different stages in test #4, Kcb-650 facies Stage number Stage Type Axial strain rate (%/day) Time (min) Axial strain range (%) 1 Shearing Stress relaxation Shearing Shearing (unloading) Shearing Stress relaxation Shearing Stress relaxation Shearing Table Secant Young s modulus at different axial strains for tests under 100 kpa confining pressure Test Secant Young s modulus (MPa) Number #4 #1 #12 Sample facies Kcb-650 Kca-625 Kcc-710 At 1 % axial strain At 2 % axial strain At peak strength

199 Table List of different stress relaxation stages in test #4, Kcb-650 facies Stage number Relation to peak Axial strain (%) Axial strain rate prior to relaxation (%/day) Time (min) Deviatoric stress changes range (kpa) (kpa) (%) 2 Pre-peak Post-peak Post-peak

200 Table List of different stages in test #9, Kcb-700 facies Stage number Stage Type Axial strain rate (%/day) Time (min) Axial strain\axial strain range (%) 1 Shearing Shearing Shearing Shearing Shearing Shearing Shearing Stress relaxation Shearing Stress relaxation Shearing Shearing Table List of different stress relaxation stages in test #9, Kcb-700 facies Stage number Relation to peak Axial strain (%) Axial strain rate prior to relaxation (%/day) Time (min) Deviatoric stress range (kpa) Deviatoric stress decrease (%) 8 Post-peak Post-peak

201 Table List of different stages in test #10, Kcb-650 facies Stage number Stage Type Axial strain rate (%/day) Time (min) Axial strain\axial strain range (%) 1 Shearing Shearing Shearing Shearing Stress relaxation Shearing Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing Stress relaxation Shearing

202 Table List of stress relaxation stages in test #10, Kcb-650 facies Stage number Relation to the peak Axial strain (%) Axial strain rate prior to relaxation (%/day) Time (min) Deviatoric stress changes range (kpa) (kpa) (%) 5 Pre-peak Post-peak Post-peak Post-peak Post-peak Table List of different consolidation stages in test#11, kcc-710 facies Before stage Confining pressure (kpa) t 100 (h) c vi (10 6 cm2 s) Axial strain before consolidation* (%) * Sample was unloaded before applying the confining pressure corresponding to the new consolidation stage. 174

203 Stage # Table List of different stages in test#11, kcc-710 facies Stage Type Confining pressure (kpa) Axial strain rate (%/day) Time (min) Axial strain\axial strain range (%) 1 Shearing Stress relaxation Shearing Shearing Stress relaxation Unloading Shearing Stress relaxation Unloading Shearing Stress relaxation Shearing Unloading Shearing Stress relaxation Shearing Stress relaxation Unloading Shearing Stress relaxation Shearing Shearing

204 Table List of different stress relaxation stages in test #11, kcc-710 facies Stage number Relation to peak Axial strain (%) Axial strain after reloading (%) Axial strain rate prior to relaxation (%/day) Confining pressure (kpa) Time (min) Deviatoric stress range changes (kpa) (kpa) % 2 1 st stress relaxation Pre-peak nd stress relaxation Pre-peak rd stress relaxation Pre-peak th stress relaxation Pre-peak th stress relaxation Pre-peak th stress relaxation Pre-peak th stress relaxation Post-peak

205 Table Soil categories according to Black and Lee (1973) for the study of saturation effect Soil category Soft soils Medium soils Stiff soils Description Soft normally consolidated clays Lightly overconsolidated clays Compacted clays and silts Overconsolidated stiff clays Average sands Very stiff clays Very dense sands Very stiff soils Soils consolidated to a high effective stress Compacted clays with stiff structure Soils with a cementing agent, even if only very weak 177

206 Table List of different stages in test #7, Kcb-700 Stage number Axial strain rate (%/day) Time (min) Axial strain range (%)

207 Table Secant Young s modulus at different axial strains for tests under 500 kpa confining pressure. Test Secant Young s modulus (MPa) # Sample facies Kca-625 Kcb-700 Kcb-650 At 1 % axial strain At 2 % axial strain At peak strength Table Typical A-values at failure (Skempton, 1954) Soil type Shear induced volume change A-value at failure Highly sensitive clays Large contraction 0.75 to 1.5 Normally consolidated clays Contraction 0.5 to 1 Compacted sandy clays Slight contraction 0.25 to 0.75 Lightly overconsolidated clays None 0 to 0.5 Compacted clay graves Expansion to 0.25 Heavily overconsolidated clays Expansion -0.5 to 0 179

208 Table List of different stages in test #8, Kcb-700 Stage number Axial strain rate (%/day) Time (min) Axial strain range (%) Stress relaxation* * Shearing was paused for a short interval of time and sample experienced an unplanned stress relaxation. 180

209 Table Secant Young s modulus at different axial strains for tests under 500 kpa confining pressure. Drainage condition Drained Undrained Test # Sample facies Kca-625 Kcb-650 Kcb-700 Kcb-700 Secant Young s modulus (MPa) At 1 % axial strain At 2 % axial strain At peak strength

210 Table Measured shear band angles and calculated single-plane slip correction coefficient Test # Facies Confining pressure (kpa) left ( ) Measured shear band angle* right ( ) average ( ) β (rad) f s Tests with confining pressure of Average : Average value for all the tests * Shear band angle was measured with respect to horizontal direction and at two side of the sample, indicated here as right and left. 182

211 Table Summary of corrections to triaxial data Single-plane slip (post-peak region) Barrelling (pre-peak region) equation at an axial strain of 10 % after slip at confining pressure of 100 kpa 300 kpa 500 kpa Area corrections Undrained condition: (3.11), f b = 0.95* Drained condition: (3.12), f b = ** (3.13) f s =1.20 f s =1.15 f s =1.16 Membrane corrections Change linearly from 0 at the beginning of the shearing up to 1.3 kpa at 5 % axial strain (3.18) 17.9 kpa or 8.8 %*** 31.3 kpa or 8.2 % 44.7 kpa or 8.3 % Side drain corrections Change linearly from 0 at the beginning of the shearing to 5.7 kpa at 2 % axial strain and constant thereafter up to the strain corresponding to the peak strength kpa or 3.5 % 9.6 kpa or 2.5 % 12.0 kpa or 2.2 % f b : correction factor for area due to barrelling and f s : slip area factor. * At an axial strain of 4.51 % (average of axial strains corresponding to peak deviatoric stresses in tests #7 and #8), deviatoric stress should be multiplied by this value. ** At an axial strain of 5.13 % (average strains corresponding to peak deviatoric stress in drained tests), deviatoric stress should be multiplied by this value (based on volumetric strain in range of 1-4 %). *** Percentage are calculated based on average of deviatoric stresses at the end of the tests at each confining pressure. 183

212 Table Secant Young s modulus at different axial strains for different facies and confining pressures Test Number #1 #2 #3 #4 #6 #7 #9 #10 #11 #11 #11 #12 Sample facies Kca- 625 Kca- 625 Kcb- 700 Kcb- 650 Kca- 625 Kcb- 700 Kcb- 700 Kcb- 650 Kcc- 710 Kcc- 710 Kcc- 710 Kcc- 710 Confining pressure (kpa) Axial strain at peak strength (%) * 4.00* Secant Young s modulus (MPa) At 1 % axial strain At 2 % axial strain At peak strength * Test #11 was a multi-stage test, therefore, the sample was sheared up to axial strains of 2.5 % and 4.0 % at confining pressures of 100 and 300 kpa, respectively, without exhibiting a peak in deviatoric stress. 184

213 Table Average secant Young s modulus at different axial strains for different facies at confining pressures range of kpa Sample facies Kca- 625 Kcb- 650 Kcb- 700 Kcc- 710 Axial strain of the peak strength (%) Secant Young s modulus (MPa) At 1 % axial strain At 2 % axial strain At peak strength Table Poisson s ratio calculated for facies of Clearwater clay shale at various axial strains Sample facies Axial strain (%) Kca-625 Kcb-650 Kcb-700 Kcc % Poisson s ratio 2 % % %

214 Table Internal friction angle (at peak strength and post-peak) and cohesion for facies of Clearwater clay shale Sample facies Kca- 625 Kcb- 650 Kcb- 700 Kcc- 710 All Friction angle (φ ) At peak strength At post-peak (end of the test) Cohesion (kpa) Table Parameters of lines fitted into results of stress relaxation tests conducted before the peak-strength (presented in Figure 3.123) Facies Confining pressure (kpa) n q n Number of stress relaxation tests Kcb Kcc Kcc Kcc * Kca Kca * Average of values of s for Kcc-710 at confining pressures of 100 and 300 kpa. 186

215 Table Parameters of lines fitted into results of stress relaxation tests conducted before the peak-strength (presented in Figure 3.124) Facies Confining pressure (kpa) n q n Number of stress relaxation tests Pre-relaxation strain rate (%/day) Kcb Kcb * 5.32 Kcc Kcb and Kca * Both after unloading and reloading. 187

216 Volumetric strain (%) Water content (%) Average depth of sample (m) Figure 3.1. Water content of Clearwater clay shale samples Time (day) y = x , R² = 0.98 y = x , R² = 0.97 y = x , R² = 0.97 D331 (700) D334 (700) C92 (625) Figure 3.2. Variation of volumetric strains with time in free swell tests (approximated with power function) 188

217 Values of coefficients Volumetric strain (%) y = x R² = y = x R² = t=10 days t=17 days Smectite content (%) Figure 3.3. Linear variation of volumetric strain with smectite content in free swell tests y = x R² = y = x R² = coefficient c coefficients d Time (day) Figure 3.4. Power function trends of coefficients c and d with time in free swell tests 189

218 Ratio of axial strain to radial strain Figure 3.5. Comparison of experimental and predicted values of volumetric strain versus time in free swell tests (Kca-625 facies from borehole C) Smectite content (%) Figure 3.6. Variation of anisotropy ratio (ratio of axial strain to radial strain due to swelling) with smectite content in free swell tests 190

219 Vertical strain (%) Ratio of axial strain to radial strain C64 (650) C63 (650) E51 (650) Time (day) Figure 3.7. Variation of anisotropy ratio (ratio of axial strain to radial strain due to swelling) with time in free swell tests y = 4.715x R² = Radial strain (%) Figure 3.8. Correlation between axial and radial strains in free swell tests 191

220 Figure 3.9. Schematic of borehole locations in the perimeter of thickener tanks 1001 and 2001 Figure Volumetric strain versus time from oedometer test using fresh water (Kcb-700 facies) 192

221 Figure Results of oedometer tests using fresh and saline water (Kcb-700 facies) Figure Coefficient of consolidation versus axial pressure in the oedometer test using fresh water (Kcb-700 facies) 193

222 Figure Void ratio versus axial stress in the CRS consolidation test (Kcb-700 facies) Figure Void ratio versus axial stress in the CRS consolidation test (Kcb-650 facies) 194

223 Figure Volumetric strain versus square-root of time (test #6, Kca-625 facies) Figure Deviatoric stress versus axial strain (test #6, Kca-625 facies) 195

224 Figure Volumetric strain versus axial strain (test #6, Kca-625 facies) Figure Secant Young s modulus versus axial strain (test #6, Kca-625 facies) 196

225 Figure Secant Young s modulus versus axial strains between 0.01 % and 0.1 % (test #6, Kca-625 facies) Figure Secant Young s modulus versus axial strains greater than 0.1 % (test #6, Kca- 625 facies) 197

226 Figure Poisson s ratio versus axial strain (test #6, Kca-625 facies) Figure Deviatoric stress versus axial strain (test #5, Kcb-650 facies) 198

227 Figure Volumetric strain versus axial strain (test #5, Kcb-650 facies) Figure Secant Young s modulus versus axial strain (test #5, Kcb-650 facies) 199

228 Figure Volumetric strain versus square-root of time (test #12, kcc-710 facies) Figure Deviatoric stress versus axial strain for different shearing and stress relaxation stages (test #12, kcc-710 facies) 200

229 Figure Volumetric strain versus axial strain for different shearing and stress relaxation stages (test #12, kcc-710 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #12, kcc-710 facies) 201

230 Figure Volumetric strain versus square-root of time (test #1, Kca-625 facies) Figure Deviatoric stress versus axial strain for shearing and stress relaxation stages (test #1, Kca-625 facies) 202

231 Figure Volumetric strain versus axial strain for shearing and stress relaxation stages (test #1, Kca-625 facies) Figure Deviatoric stress versus axial strain for different shearing and stress relaxation stages (test #1, Kca-625 facies) 203

232 Figure Volumetric strain versus axial strain for different shearing and stress relaxation stages (test #1, Kca-625 facies) Figure Normalized deviatoric stress versus axial strain rate (test #1, Kca-625 facies) 204

233 Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #1, Kca-625 facies) Figure Changes in volumetric strain versus time for different stress relaxation stages (test #1, Kca-625 facies) 205

234 Figure Volumetric strain versus square-root of time (test #2, Kca-625 facies) Figure Deviatoric stress versus axial strain for different shearing and stress relaxation stages (test #2, Kca-625 facies) 206

235 Figure Volumetric strain versus axial strain for different shearing and stress relaxation stages (test #2, Kca-625 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #2, Kca-625 facies) 207

236 Figure Deviatoric stress versus axial strain at the start and end of stress relaxation stages before the peak strength (test #2, Kca-625 facies) Figure Changes in volumetric strain versus time for different stress relaxation stages (test #2, Kca-625 facies) 208

237 Figure Normalized volumetric strain versus time for different stress relaxation stages (test #2, Kca-625 facies) Figure Volumetric strain versus square-root of time (test #3, Kcb-700 facies) 209

238 Figure Deviatoric stress versus axial strain for different shearing and stress relaxation stages (test #3, Kcb-700 facies) Figure Volumetric strain versus axial strain for different shearing and stress relaxation stages (test #3, Kcb-700 facies) 210

239 Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #3, Kcb-700 facies) Figure Deviatoric stress versus axial strain at the start and end of stress relaxation stages before the peak strength (test #3, Kcb-700 facies) 211

240 Figure Ratio of axial strain to deviatoric stress versus axial strain at the start and end of stress relaxation stages before the peak strength (test #3, Kcb-700 facies) Figure Changes in volumetric strain versus time for different stress relaxation stages (test #3, Kcb-700 facies) 212

241 Figure Normalized volumetric strain versus time for different stress relaxation stages (test #3, Kcb-700 facies) Figure Volumetric strain versus square-root of time (test #4, Kcb-650 facies) 213

242 Figure Deviatoric stress versus axial strain for shearing (loading, unloading, and reloading) and stress relaxation stages (test #4, Kcb-650 facies) Figure Volumetric strain versus axial strain for shearing (loading, unloading, and reloading) and stress relaxation stages (test #4, Kcb-650 facies) 214

243 Figure Secant Young s modulus versus axial strain for loading, unloading, and reloading stages (test #4, Kcb-650 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test #4, Kcb-650 facies) 215

244 Figure Changes in volumetric strain versus time for different stress relaxation stages (test #4, Kcb-650 facies) Figure Normalized volumetric strain versus time for different stress relaxation stages (test #4, Kcb-650 facies) 216

245 Figure Volumetric strain versus square-root of time (test #9, Kcb-700 facies) Figure Local axial strains versus square-root of time (test #9, Kcb-700 facies) 217

246 Figure Deviatoric stress versus axial strain for different strain rates and the stress relaxation stages (test #9, Kcb-700 facies) Figure Volumetric strain versus axial strain for different strain rates and stress relaxation stages (test #9, Kcb-700 facies) 218

247 Figure Normalized deviatoric stress versus axial strain rate (test #9, Kcb-700 facies) Figure Normalized deviatoric stress versus logarithm of time for stress relaxation stages (test #9, Kcb-700 facies) 219

248 Figure Normalized volumetric strain versus time for stress relaxation stages (test #9, Kcb-700 facies) Figure Dissipation of excess pore pressure with time during consolidation stage (test #10, Kcb-650 facies) 220

249 Figure Degree of consolidation, U, versus square-root of time (test #10, Kcb-650 facies) Figure Deviatoric stress versus axial strain for different strain rates and stress relaxation stages (test#10, Kcb-650 facies) 221

250 Figure Volumetric strain versus axial strain for different strain rates and stress relaxation stages (test #10, Kcb-650 facies) Figure Deviatoric stress versus axial strain (test#10, Kcb-650 facies) 222

251 Figure Volumetric strain versus axial strain (test #10, Kcb-650 facies) Figure Normalized deviatoric stress versus time for different stress relaxation stages (test#10, Kcb-650 facies) 223

252 Figure Changes in volumetric strain versus time for different stress relaxation stages (test #10, Kcb-650 facies) Figure Normalized volumetric strain versus time for different stress relaxation stages (test #10, Kcb-650 facies) 224

253 Figure Coefficient of consolidation versus confining pressure (test#11, kcc-710 facies) Figure Coefficient of volumetric compressibility versus axial pressure from a constant rate of strain consolidation test on Kcb

254 Figure Deviatoric stress versus axial strain for different strain rates and stress relaxation stages before peak (test#11, kcc-710 facies) Figure Volumetric strain versus external axial strain for different strain rates and stress relaxation stages before peak (test#11, kcc-710 facies) 226

255 Figure Deviatoric stress versus external axial strain for different strain rates and stress relaxation stages (test#11, kcc-710 facies) Figure Volumetric strain versus external axial strain for different strain rates and stress relaxation stages (test#11, kcc-710 facies) 227

256 Figure Volumetric strain versus time for different strain rates and stress relaxation stages (test#11, kcc-710 facies) Figure Deviatoric stress versus mean effective stress (test#11, kcc-710 facies) 228

257 Figure Normalized deviatoric stress versus time for different stress relaxation stages (test#11, kcc-710 facies) Figure Change in deviatoric stress versus axial strain for stress relaxation stages (test#11, kcc-710 facies) 229

258 Figure Change in deviatoric stress versus confining pressure for different stress relaxation stages (test#11, kcc-710 facies) Figure B-values measured at different levels of back pressure (test #7, Kcb-700) 230

259 Figure B-values related to degree of saturation and soil stiffness (Black and Lee, 1973) Figure Volumetric strain versus square-root of time (test #7, Kcb-700) 231

260 Figure Deviatoric stress versus axial strain for different strain rates (test #7, Kcb-700) Figure Excess pore pressure versus axial strain for different strain rates during shearing stages (test #7, Kcb-700) 232

261 Figure A-values measured at different strain rates during shearing stages (test #7, Kcb-700) Figure Typical relationship between A-values at failure and overconsolidation ratio (Head, 1998) 233

262 Figure Deviatoric stress versus mean effective stress (test #7, Kcb-700) Figure Secant Young s modulus versus axial strain (test #7, Kcb-700) 234

263 Figure Secant Young s modulus versus axial strains greater than 0.1 % (test #7, Kcb- 700) Figure Volumetric strain versus square-root of time (test #8, Kcb-700) 235

264 Figure Deviatoric stress versus axial strain for different strain rates (test #8, Kcb-700) Figure Secant Young s modulus versus axial strain (test #8, Kcb-700) 236

265 Figure Excess pore pressure versus axial strain (test #8, Kcb-700) Figure A-values measured during shearing stages (test #8, Kcb-700) 237

266 Figure Deviatoric stress versus mean effective stress (test #8, Kcb-700) Figure Secant Young s moduli verses axial strain in log-log scale at confining pressure of 100 kpa 238

267 Figure Secant Young s modulus versus axial strain at different confining pressure of Kca-625 facies Figure Coefficients A and B versus confining pressure from tests on Kca-625 facies 239

268 Figure Stress states at the peak and post-peak deviatoric stress in q p plane Figure Deviatoric stress, q, versus mean effective stress, p, at the end of the triaxial tests 240

269 Figure Friction angle at the end of the tests versus clay contents of the samples Figure Friction angle at the end of the tests versus clay contents of the samples at different confining pressures 241

270 Figure Friction angle at the end of the tests versus smectite contents of the samples Figure Friction angle at the end of the tests versus smectite portion of clay fraction 242

271 Figure Friction angle at the end of the tests versus illite contents of the samples at different confining pressures Figure Estimated depth of the samples versus clay content 243

272 Figure Surface hardness versus clay content of Clearwater clay shale samples Figure Liquid limit versus clay contents for facies of Clearwater clay shale 244

273 Figure Clay and smectite content of triaxial samples versus liquid limit Figure Density versus clay content of samples used in triaxial testing 245

274 Figure Peak strength versus density for confining pressures of 100, 300, and 500 kpa. Figure Peak strength versus density for samples of facies Kcb

275 Figure Maximum deviatoric stress versus measured shear band angles Figure Maximum deviatoric stress versus measured shear band angles (divided in groups) 247

276 Figure Approximation of actual relaxation curve with a line (Lacerda and Houston, 1973) Figure Influence of prior strain rate on the time to start of stress relaxation 248

277 Figure Normalized deviatoric stress change in relaxation tests with pre-relaxation axial strain rate of 5.32 %/day at axial strains before peak strength Figure Normalized deviatoric stress change in relaxation tests at axial strains after peak strength 249

278 Figure Normalized deviatoric stress change in relaxation tests at axial strains after peak strength in comparison with those presented in Figure

279 Chapter 4: FLAC simulation of test fill based on triaxial tests data 4.1. Model description Model geometry The field stratigraphy is a layered system of soils. Layers are assumed to be horizontal and uniform in thickness, and the depth of each layer is specified in Table 1. A fifteen meters thick layer of the Clearwater Formation is overlain by a three meters thick clay/clay till layer and a two meters thick sand layer. The Clearwater Formation in the field consisting of five different facies: Kcc-710, Kcb- 700, Kcb-650, Kca-625, and Kcw-600. The Kca-625 layer has been divided into two layers in the FLAC analyses, one is the top 5 m and the other is the bottom 1 m. Patrick and Sisson (2010) has reported that extensive pre-shearing is found along the bedding planes of the Kcc-710, Kcb-700, and lower part of Kca-625. Moreover, Moore (2007) mentioned that the Kcc-720, Kcc-710, Kcb-700, and lower part of Kca-625 are weaker than the other Clearwater units (Kcb-650, upper part of Kcb-625, and Kcw-600). The division of Kca-625 into two weak and strong layers is also justified based on the existence of an indurated zone at the bottom of Kca-625 layer described in the logging report of recovered cores from previous boreholes drilled in 2004 and 2006 (Uffen and Martinez, 2013). The triaxial samples from Kca-625 tested in the current study all belong to the lower part of the Kca-625. The McMurray Formation, found in the depth greater than 20 m, is assumed to be bedrock because significant lateral displacement was not observed in the field measurements. The model is constructed axisymmetrically about the center of the fill, given the symmetrical loading pattern applied by the tank and the assumed geology for the field. Model dimensions are: 20 m deep and 251

280 80 m wide, the latter being four times of the width of uniformly distributed applied load (20 m) to limit boundary effects. The model, gridded in 0.5 m intervals in both directions, consists of 40 zones in vertical direction and 160 zones in horizontal direction (a total of 6400 zones, Figure 4.1). In other words, the model is a grid of 6601 gridpoints (41 rows and 161 columns) Fluid properties Water table is specified to be at 2 m deep at the interface of sand and clay layers according to the field observation and assumed to be constant during and after loading. Permeability 1 of the clay shale materials to water is assumed 1e-13 m 2 /(Pa. s), which does not have any effect in geostatic stage and undrained loading stage since FLAC is run in No flow mode but it plays an important role in consolidation analysis and coupled creep-consolidation analysis (coupled flow-mechanical analysis of a viscous material). Fluid density is specified as 1000 kg/m 3, and the acceleration of gravity has been set equal to 9.8 m/s 2. Fluid bulk modulus, or water-gas mixture, is specified as 100 MPa, which is significantly lower than that of the pure water (around 2 GPa). Due to water level fluctuation in the field, the air is entrapped in the pores even below the phreatic line. Therefore, water degree of saturation in the 1 The permeability required by FLAC is the mobility coefficient (the coefficient of the pore pressure term in Darcy s low). The relation between hydraulic conductivity, k H, the coefficient of the head term in Darcy s low, and permeability, k, is expressed as: k H = kgρ w 252

281 field lies in a range of 90-99% (Fredlund et al., 2012). The compressibility of water-gas mixture can be estimated by the following expression neglecting the solubility of gaseous phase in water (Richart et al., 1970): C gw = 1 K gw = S w K w + 1 S w K g (4.1) where C gw and K gw are the compressibility and bulk modulus of water-gas mixture, respectively, S w is the degree of water saturation, K w is the bulk modulus of water, and K g is the gas bulk modulus which is equal to the total pressure, the sum of atmospheric pressure and gas pressure in the relevant depth under the phreatic surface (for small value of entrapped gas, gas and water pressures can be considered equal). Given that K g K w, K gw, calculated from the above equation, remains much smaller than K w at all saturation degrees except those very close to 100%. In other word, the compressibility of the water-air mixture significantly increases (and becomes considerably greater than that of the pure water) even with inclusion of a small amount of gas Boundary conditions The model bottom boundary is fixed against displacements in both vertical and horizontal directions. Lateral sides of the model are fixed against displacement in horizontal direction only. The degree of saturation is set to be fixed during analysis: the zones above the water table (sand layer) are set to be completely unsaturated (with degree of saturation equal to 0) while the zone below the water table are set to be fully saturated (with 100% degree of saturation). 253

282 The geostatic vertical stresses are estimated based on the profile of effective overburden stress with depth. In absence of any direct field measurement of the in-situ horizontal stresses, those stresses are calculated using the coefficient of the earth pressure at rest that represents the ratio of horizontal to vertical effective stresses. Several theoretical and empirical relationships for the coefficient of the earth pressure at rest have been postulated for normally-consolidated clays and sands. The simplest approximation is the Jaky s (1944) formula: K 0nc = 1 sinφ (4.2) where K 0nc is the coefficient of the earth pressure at rest of a normally-consolidated soil and φ is the effective stress friction angle. The coefficient of the earth pressure at rest increases with overconsolidation ratio (OCR) and its variation with OCR may be expressed by the relationship proposed by Schmidt (1966): K 0oc K 0nc = OCR α (4.3) where K 0oc is the coefficient of the earth pressure at rest of an overconsolidated soil, and α is an exponent defined as the at-rest rebound parameter of the soil, which was suggested to be equal to α = sinφ by Mayne and Kulhawy (1982). Therefore, the coefficient of the earth pressure at rest of an overconsolidated clay may be estimated by knowing OCR and the effective stress friction angle: K 0oc = (1 sinφ )OCR sinφ (4.4) Two constant-rate-of-strain (CRS) consolidation tests were performed on Clearwater clay shale. The preconsolidation pressure has been estimated to be 860 kpa from the test on Kcb

283 sample and 1280 kpa from the test on Kcb-650 sample. Based on the first estimated preconsolidation values and calculated effective vertical stress in layers, the OCRs were calculated for each facies. Finally, the coefficient of the earth pressure at rest for each layer was determined using the above formula along with the calculated OCRs from CRS consolidation tests and measured effective frictional angle from triaxial tests (Table 4.1). The weighted average (with respect to layer thickness) of the coefficients of the earth pressure at rest of all clay shales layers is equal to one, same as the assumed value in Moore (2007) and Moore et al. (2011). Using the second estimate of the preconsolidation pressure (1280 kpa) results in increase of the weighted average of the coefficients of the earth pressure at rest to 1.2. The first estimate was preferred because of the consistency of the average value of K 0oc with that mentioned in previous studies Material properties The porosity and dry density of clay shale facies (Kcc-710, Kcb-700, Kcb-650, Kca-625u, and Kca-625l) have been specified based on the average values of the samples measured from triaxial experiments (Table 4.2). For the rest of soil layers (sand, clay, clay till, and Kcw-600) the values reported in previous analyses (Moore, 2007) were implemented (Table 4.2). The solid bulk density (total density), ρ, is calculated from the following expression: ρ = ρ d + nρ w (4.5) where ρ d and ρ w are the bulk density of the dry matrix and the density of the fluid phase, respectively, and n is the porosity. 255

284 Elastic properties Elastic properties of the different soil layers are presented in Table 4.2. Average values of secant Young s modulus at 2% of axial strain, measured in different triaxial tests at confining pressures of 100 kpa, 300 kpa, and 500 kpa, were used in elastic and elastoplastic analyses. The samples in triaxial tests showed the peak strength at an average axial strain of about 4%. Since it is common practice to evaluate the Young s modulus at a half of the peak strength for elastic analyses (Lambe and Whitman, 1969), the Young s moduli at axial strain of 2% were selected in the current analyses. For the Kcc-710, results of Test#12 and Test#11 at the confining pressure of 100 kpa was considered. Results of Test#11 at confining pressures of 300 kpa and 500 kpa were disregarded, because unloading-reloading stages during this test lead to stiffer pre-peak response (relative to an intact sample) at these confining pressures. Values of Young s modulus selected for Pl Clay 880 and Clay till 830 are similar and in the range of values implemented in previous analyses, MPa. The Kca-625 is modelled as two layers similar to previous analyses. Therefore, the Young s modulus value measured in laboratory for Kca-625 was specified for the lower part of Kca-625 (Kca-625l) and the Young s modulus value for the upper part of Kca-625 (Kca-625u) was set similar to that in Moore et al. (2011). The values of Young s modulus for Kcw-600 and sand was adopted from Moore et al. (2011) and Moore (2007), respectively. A Poisson s ratio of 0.4 was selected for all the soil layers except Kcb-650 and Kca-625u which have shown near zero lateral displacements in the field. 256

285 Plastic properties (Mohr-Coulomb shear parameters) Values of friction angles corresponding to the end of triaxial tests (about 14% of axial strain on average) were calculated for each facies and inputted into the model (Table 4.2). The friction angles were calculated based on the slope of best fitted line passing through the origin, implying zero cohesion, in q-p graph (values of dilatancy angles were set as zero for all the layers). Note that drained parameters, both elastic and plastic ones, are inputted into the FLAC. In case of an undrained analyses, the undrained parameters are calculated based on saturation degree and porosity of zones along with provided bulk modulus of water Undrained analyses A uniformly distributed load (20 m wide) is applied gradually to the model. In order to prevent from inducing large amount of unbalanced force into the model during analyses, the load is applied with an average rate of 20 Pa/step. Different patterns of applying loads over steps -linear, quadratic, and cubic- were investigated to minimize the number of run-steps required to keep the unbalanced force small, among which the cubic one required the smallest number of steps and was implemented in the model. The results of analyses are recorded in intervals when the load magnitude reaches 50 kpa, 80 kpa, 100 kpa, 134 kpa, 150 kpa, or 180 kpa Verification of geostatic stresses and hydrostatic pore pressure Vertical stresses and pore pressures have been calculated manually and compared with values presented by FLAC (Table 4.3). 257

286 Numerical modeling cases To investigate the short-term and long-term responses of clay shale layers in the field subjected to the test fill loading, the following cases of analyses have been defined: Case 1: Poro-elastic analysis of a homogenous soil layer in undrained condition. o Isotropic elastic model with no fluid-flow Case 2: Poro-elasto-plastic analysis of a homogenous soil layer in undrained condition. o Mohr-Coulomb model with no fluid-flow Case 3: Poro-elastic analysis of a layered soil profile in undrained condition. o Isotropic elastic model with no fluid-flow Case 4: Poro-elasto-plastic analysis of a layered soil profile in undrained condition. o Mohr-Coulomb model with no fluid-flow Cases 5, 6, and 7: Analyses with a quasilinear model in undrained condition. o Chsoil model with no fluid-flow Case 8: Poro-elasto-visco-plastic (creep) analysis in undrained condition o Burgers-creep viscoplastic model (combining the Burgers-creep model and the Mohr-Coulomb model) with no fluid-flow Case 9: Poro-elasto-plastic analysis in drained condition (consolidation analysis) o Mohr-Coulomb model with fluid-flow Case 10: Poro-elasto-visco-plastic analysis in drained condition (coupled creepconsolidation analysis) 258

287 o Burgers-creep viscoplastic model with fluid-flow 4.2. Case 1: Poro-elastic analysis of a homogenous soil layer in undrained condition A single layer of soil, with the elastic properties specified in Table 4.4, was loaded in undrained condition. A weighted average, based on the layer thickness, of values of each parameter in all layers (Table 4.2) is used in the current analysis. The results corresponded to a vertical load of 150 KPa are shown in Figures 4.2 to 4.8. Horizontal displacements are all positive in Figure 4.3, which means soil elements are moving away from the tank centerline (moving to the right of the figure). Note that compressive stresses are considered negative in FLAC. Therefore, negative changes in normal stresses mean increase in normal stresses in Figures 4.6 and 4.8. Moreover, the water table is assumed at two meters deep and thus the top two meters of soil is unsaturated. Therefore, no excess pore pressure is generated at this region (Figure 4.7) Case 2: Poro-elasto-plastic analysis of a homogenous soil layer in undrained condition The model was initially composed of a single layer with Mohr-Coulomb as its constitutive law. Input parameters of the model are presented in Table 4.5. A weighted average, based on the layer thickness, of values of each parameter in all layers (Table 4.2) is used in the current analysis. After applying load the model failed at the edge of the tank. Therefore, top two meters of the model is 259

288 modeled as a different layer with same properties except that the friction angle has been increased (Table 4.5). Results corresponding to the applied load of 150 kpa are shown in Figures 4.9 to The results are generally similar to the elastic model except that yielding in 2 m to 6 m depth has changed the excess pore pressure pattern Case 3: Poro-elastic analysis of a layered soil profile in undrained condition A Poisson s ratio of 0.4 was selected for all the soil layers except for Kcb-650 and Kca-625u which have shown near zero lateral displacements in the field and therefore a Poisson s ratio of 0.01 was set for them (Table 4.6). The value of the Poisson s ratio up to 0.45 has been reported in literature for dense sand (the Sand 860 layer can be considered a dense sand). In addition, saturated cohesive soils (Pl Clay 880 and Clay till 830) can be considered almost incompressible and have a Poisson s ratio of up to 0.5 (Das, 2002). The result of analysis for this case is presented in Figures 4.16 to 4.23.The shape of the vertical displacements contours (Figure 4.16) is different than that of the homogenous case (Case 1, Figure 4.2) in which the maximum vertical displacement occurs at the center of the tank. The reason for this difference in pattern is the layered soil profile with different properties. The variation of the porosity and elastic parameters with depth alters the patterns of the change in vertical stress contours (Figure 4.6 versus Figure 4.20) and the excess pore pressure contours (Figure 4.7 versus Figure 4.21) and consequently contours of change in effective stress (Figure 4.8 versus Figure 4.23). 260

289 To better understand the excess pore pressure contours generated in FLAC in response to the loading (Figure 4.21), the formulation used in fluid-mechanical processes in FLAC are briefly discussed here. The response equation for the pore fluid depends on the degree of saturation. For the case of fully saturated soils, the induced pore pressure is calculated from: P t = M( ζ ε α t t ) (4.6) where M is the Biot modulus (calculated from expression below), ζ is the variation of fluid volume per unit volume of porous material, α is the Biot coefficient, and ε is the volumetric strain (negative strain indicates compression). The Biot modulus could be determined from the following expression: M = K w n + (α n)(1 α) K w K (4.7) where K is the drained bulk modulus of the porous medium and K w is the fluid bulk modulus. For the case of no fluid-flow (undrained analyses) ζ is equal to zero. Therefore, the response equation becomes: P t = K w n + (α n)(1 α) K w K ( α ε t ) (4.8) If the compressibility of grains assumed to be negligible compared to that of the drained bulk material, α = 1, then the response equation will be simplified to: P t = K w ε n t (4.9) 261

290 According to the above expression, the induced excess pore pressure in a zone depends on the both porosity of the zone and the amount of volumetric strain in the zone. In Figure 4.21, the largest increase in pore pressure happens in Clay till and Kcc-710 layers (excess pore pressure > 125 kpa). On the contrary, the Kca-625u exhibits relatively small pore pressure response to the loading. The Kca-625u has a porosity value of 0.33 which is 6%, 15%, 3% smaller than the porosity values of the Kcb-650, Kcb-700, and Kcc-710, respectively, but bulk modulus of the Kca-625u is 39.8 MPa, that is 4.5, 1.5, and 2.2 times larger than the bulk modulus of the Kcb-650, Kcb-700, and Kcc-710, respectively. Therefore, the Kca-625u with much larger bulk modulus than those facies and locating deeper (less increase in vertical pressure) is expected to have less volumetric strain (less than one third, Figure 4.22). Thus, considering the approximately equal porosity values of the Kca-625u and the mentioned upper facies, less increase in pore pressure than the rest of the facies is anticipated for Kca-625u Case 4: Poro-elasto-plastic analysis of a layered soil profile in undrained condition Same values of elastic parameters, Young s modulus and Poisson s ratio, as previous analysis have been used. Values of friction angles calculated at the end of triaxial test (about 14% of axial strain on average) were inputted into the model (Table 4.7). Cohesion and dilatancy were set as zero for all the layers. Results of the current analysis are presented in Figures 4.24 to Recalling that the undrained pore pressure response of a saturated soil, neglecting the compressibility of grains versus that of the drained bulk material (assuming α = 1), is calculated from the following expression: 262

291 P t = M ε t & M = K w n (4.10) In an elastoplastic half-space, if any element yields then plastic deformations will occur and ε t will change and P will be different for each element, though the Biot modulus (M) is the same for all t element. Similar to the elastic analysis (case 3), the variations in excess pore pressure contours between different layers (Figure 4.29) is related to the amount of volumetric strain (Figure 4.30). In the current model, the yielding and plastic deformation has contributed to the resulted volumetric strain and thus has an effect on the amount of induced excess pore pressure (Figures 4.32 and 4.33). In other words, yielding leads to an increase in compressive volumetric strain (compressive strain are considered negative in FLAC) and consequently an increase in pore pressure (in absence of dilation) in comparison with the elastic analysis Comparison of results of Cases 1-4 with field data and previous analyses Previous analyses by Moore (2007) and Moore et al. (2011) Moore (2007) and Moore et al. (2011) used Mohr-Coulomb constitutive model in conjunction with a strain-softening function to update the elastic parameters with changes in stress and strain. The function updates the secant shear modulus with change in shear stress based on the relationship suggested by Fahey and Carter (1993). G = G i [1 f ( τ g ) ] (4.11) τ max 263

292 in which G and G i are the current and initial secant shear moduli, respectively. τ and τ max are the current shear stress and its maximum value, respectively. The tangent bulk modulus is updated with change in mean effective stress according to the expression presented by Duncan et al. (1980). K t = k B P a ( p m ) P a (4.12) where K t and m are the bulk modulus number and exponent, respectively. P a is the atmospheric pressure and p is the mean effective stress. The data from the full-scale load test was used to calibrate the mentioned model in FLAC to obtain a reasonable set of parameters. An iterative process was followed to obtain a reasonable match between FLAC and observed behaviour of the test fill foundation, including profiles of horizontal displacement and pore pressure measurements (Moore, 2007) Comparison of models predictions with field data The tank 72-TK-1A, constructed in the West Tank Farm in Canadian Natural Resources Limited oil sands mine and plant near Fort McMurray, Alberta, Canada, was instrumented during hydrotesting to monitor its performance. This tank was located in a place where the Clearwater formation was thick and shallow in comparison with the other tanks. Sixty equally spaced monitoring points were located around the perimeter of the tank, which were surveyed to determine the settlement of the tank foundation. Settlements at the center of the tanks were determined by observing the displacements of the center post of the tank. The tank foundation settlements were also monitored 264

293 using four settlement plates installed around the inside edge of the tank. The measured center post settlement versus the applied fluid pressure and the prediction of various models are shown in Figure The average measured edge settlement and different model predictions at various levels of applied load are shown on Figure At full tank load, the edge settlement was about 17 mm, reaching to 20 mm after 32 hours hold period. All out-of-plane settlements were less than 4 mm at 200 kpa load. The accuracy of the tank settlement predictions has been improved in comparison with the previous analysis (Figures 4.34 and 4.35). The single-layer models (Case 1 and 2) have predicted the tank center and edge settlement slightly better than the multilayer models (Cases 3 and 4). The cumulative horizontal displacement was measured by a slope inclinometer located at 10 m offset from the tank edge. Comparison of field measured lateral displacement and various model predictions are shown in Figure Field measured data indicate two zones with large lateral displacements: one at 5 m to 8.5 m depth, correspond to the Kcc-710 and Kcb-700 facies, and the other at 17 m to 18 m depth in Kca-625l layer. Single-layer models, whether elastic or elastoplastic, show smooth lateral displacement curves and are not able to capture concentrated zones of horizontal movements (Figure 4.36). Expectedly, the multilayer models predicted more accurate lateral displacements than the single-layer models. The predicted responses of Kcc-710, Kcb-700, and Kca-625l facies are stiffer than the real behavior, lead to underestimation of lateral displacements in field. Multilayer elastoplastic model shows slightly larger displacements in Kcc-710, Kcb-700, and Kcb-650 layers. 265

294 The foundation pore pressure response was monitored using vibrating piezometer installed at 12 m depth in the Kcb-650 facies and is compared with models predictions in Figure The multilayer Mohr-Coulomb model prediction for excess pore pressure is higher than the rest of the predictions, which are approximately equal. This is due to the occurrence of yielding in Mohr- Coulomb model, which leads to a higher compressive volume change and, therefore, a higher induced excess pore pressure when loaded (this point has been discussed in Case 4). In summary, considering the results presented in Figures 4.34 to 4.37, Case 3 (multilayer elastic model) seems to provide better predictions than the rest of cases Numerical simulation implementing the Chsoil model (Cases 5, 6, and 7) Geotechnical investigations consistently indicate that the stress-strain relationship of soils is nonlinear (Lamb and Whitman, 1969). Soil stiffness is not constant, decreases under deviatoric stress, and the plot of the deviatoric stress versus axial strain in a drained triaxial test is nonlinear. The nonlinear stress-strain response of a soil sample may be approximated by a hyperbola, which is used by Duncan and Chang (1970) to formulate their nonlinear elastic model. Despite some improvement in comparison with linear elastic model and its simplicity, Duncan and Chang s hyperbolic model has drawbacks such as difficulty in characterizing unloading/reloading and producing a physically unrealistic bulk modulus that can lead to erroneous energy generation in the model in specific cases. Duncan et al. (1980) summarized the limitation of nonlinear elastic hyperbolic relations as follows: 266

295 - Relations are just applicable to pre-peak stage and may display unrealistic behavior after the peak. - They do not incorporate volume changes from shear stress changes and shear dilatancy. Therefore, deformations in dilatant soils are not predicted accurately. - An isotropic behavior is predicted in the π plane, which may not be true (soil behaviors are different in compression and extension). Chsoil model is formulated in a strain-hardening plasticity frame work, therefore it is capable of producing nonlinear (hyperbolic) behavior implementing friction hardening and addressing some of the problems associated with Duncan and Chang s model. The Chsoil model provides a realistic stress-strain relation at both pre- and post-peak regions, although the model does not have a volumetric cap. The unloading and reloading up to the outermost previously reached yield envelope is elastic. The elastic behavior of the model is based on the incremental elastic law (Itasca Consulting Group. 2011) Chsoil model description Mohr-Coulomb parameters Shear yielding is determined by the Mohr-Coulomb yield envelope which is a composite of a shear and a tensile criteria. The criteria are formulated as follows: f = σ 1 σ 3 N φm + 2c N φm N φm = 1+sinφ m 1 sinφ m (4.13) f = σ t σ 3 (4.14) 267

296 where φ m is the mobilized friction angle, c is the cohesion, σ t is the tensile strength, and σ 1 and σ 3 are the minimum and maximum principal stresses, respectively (the compressive stresses are negative). The potential function, g, has the following form in shear and tension yielding, respectively: g = σ 1 σ 3 N ψm N ψm = 1+sinψ m 1 sinψ m (4.15) g = σ 3 (4.16) where ψ m is the mobilized dilation angle. Cohesion, c, and internal friction angle, φ, are input parameters to define the frictional Mohr- Coulomb shear yield envelope. These parameters were determined by passing a best fitted straight line through the point corresponding to the peak strength of each test in p-q space for each facies (Table 4.8). Then, these shear parameters were kept constant during the calibration process Model specific parameters The mobilized elastic bulk modulus, K e, and the mobilized elastic shear modulus, G e, are calculated from the following expression, respectively: K e = K ref p ref ( p i m ) p ref G e = G ref p ref ( p i n ) p ref (4.17) (4.18) 268

297 where K ref and G ref are the bulk and the shear modulus numbers, respectively; p ref and p i are the reference and initial effective pressures; m and n are bulk modulus and shear modulus exponents. Alternatively, the Young s modulus number, E ref and the Poisson s ratio, ν can be specified instead of the bulk and the shear modulus numbers, since we have: K ref = G ref = E ref 3(1 2ν ) E ref 2(1 + ν ) (4.19) (4.20) The failure ratio, R f, which is a constant (smaller than unity, 0.9 in most cases) should be specified to assign a lower bound for shear modulus Dilation law The mobilized dilation angle, ψ m, is needed to be specified in order to define the previously mentioned nonassociated potential function. A simple stepped function is used to characterize the mobilized dilation angle: { ψ m = 0 for φ m < φ d ψ m = ψ f for φ m φ d (4.21) where ψ f is the dilation angle and φ d is the dilation law constant. 269

298 Friction hardening A friction strain-hardening law, similar to the one incorporated in UBCSAND liquefaction model by Byrne et al (2004), is implemented in the Chsoil model to develop the mobilized friction angle, φ m, with the induced plastic shear strain, γ p. As a result, the plot of deviatoric stress versus axial strain obtained in a drained triaxial test will be similar to a hyperbola. The following expression is used to calibrate the mobilized friction angle in terms of the plastic shear strain: Sinφ m = Sinφ f R f ( γ p G ref ( p i n 1 ) R f p ) ref Sinφ f (4.22) Calibration of the Chsoil model parameters using the results of the triaxial tests A single-element model was built, with the Chsoil model as the constitutive law, to predict each triaxial test result in the calibration process. The confining pressure, equal to the confining pressure used in the lab, was applied to the element. Then, the element was sheared with applying a constant velocity to the top of the element (a displacement-controlled test) and the variation of the deviatoric stress along with the volumetric strain versus axial strain was plotted. The predicted results were compared with the experimental one, and the input parameters were adjusted to attain the best fit possible. For instance, the predicted stress-strain curves for tests at different confining pressures on Kca-625 samples are presented in Figure 4.38 along with the results obtained in laboratory. Additionally, the volumetric behavior of the same tests and FLAC predictions are presented in Figure 4.39 (the calibration results for the rest of the facies are presented in Figures 4.40 to 4.45 at the end of this section). 270

299 Selected parameters Shear parameters specified for the Chsoil model in FLAC analyses are presented in Table 4.9. The shear parameters of all the soil layer except Kcb-700 were assigned same as those value obtained in triaxial tests, Table 4.8, and were kept constant during the calibration process. Although four triaxial tests have been carried out on samples from Kcb-700 facies, the results of only tests #3 and #9 were used in calibration process. The test#7 was not used in calibration because the test showed peak strength approximately equal to that in test #9, while these two tests were carried out at different confining pressures (500 kpa and 300 kpa, respectively). The test#8 was not also used in calibration because the failure pattern of the sample was different from the rest of samples (formation of two shear surfaces instead of a single one). Therefore, the friction angle was recalculated based on the results of tests #3 and # Calibrated parameters Soil properties inputted into FLAC for analysis using the Chsoil model are presented in Table The calibrated parameters are the Poisson s ratio, the Young s modulus number, the bulk modulus exponent, the shear modulus exponent, the dilation angle, and the dilation law constant. The failure ratio was selected equal to 0.9 and kept constant for all the calibration models. The reference pressure was fixed equal to 1 kpa. The Poisson s ratios resulted from calibration process are the same as those value used in elastic and elastoplastic analyses except for Kcc-710, which increases from 0.40 to

300 Investigation of characteristics of the Kca-625u, Kcw-600, clay till 830, Pl Clay 880, and sand 860 units were not in the scope of the current study and hence were not studied experimentally. Therefore, the values of the bulk modulus exponent and the shear modulus exponent for those mentioned layers (with the exception of the Kca-625u) were assumed to be same as those values for Kcb-650. For the Kca-625u, shear-related parameters (φ d and ψ f ) were specified same as those values for the Kca-625l similar to the shear parameters selection of elastoplastic analysis. The values of the Young s modulus number for the Kca-625u was selected such that the value of the Young s modulus corresponding to its initial effective stress to be same as the one assigned in elastic and elastoplastic analyses (the bulk modulus and the Shear modulus exponents were specified same as the Kca-625l). For the Kcw-600, the Poisson s ratio, the Young s modulus number, and ψ f were selected similar to those values for the Kca-650 (φ d was set equal to φ f similar to the Kca-650). For the Pl Clay 880 layer, the Young s modulus number was selected such as the resulting elastic Young s modulus to be equal to the value used in Moore et al. (2011), 35 MPa. Moore (2007) mentioned that the clay till was often difficult to distinguish conclusively from the overlying glaciolacustrine clay, and in many cases, the engineering properties of the material are similar. Therefore, the Young s modulus number for Pl Clay 880 was selected same as those of Clay till 830 layer. The selected Young s modulus number for the sand layer leads to the Young s modulus of 25 MPa in the middle of the layer, consistent with the estimation in Moore (2007). The Poisson s ratio for these layers was specified to be 0.4, the same value used in the elastic and elastoplastic analyses. 272

301 For the top three layers, Sand 860, Clay 880, and Clay till 830, the dilation law constant was approximated with friction angle at constant volume, φ cv. Moore (2007) has reported liquid limit of 43.1% and clay fraction of 19.6% for clay/clay till layer. Based on these properties along with effective normal stress, the drained residual friction angle is estimated 25 from the graph provided by Stark and Eid (1994). The Sand 860 layer is described as a fine-grained sand, with traces of silt, consisting of 94% sand, 0.8% gravel, and 5.2% silt and clay. The average SPT number was 13, while higher values up to 36 were recorded (Moore, 2007). According to British Standard 8002 (1994), the critical state friction angle is estimated to be at least 30. The dilation angles for these layers were calculated from formula provided by Bolton (1986) for the case of triaxial (i.e., axisymmetrical) condition: φ f φ cv 0.5ψ f (4.23) 4.8. Case 5: Test fill analysis using the Chsoil model Soil properties for the Chsoil model in FLAC analysis, obtained from triaxial tests and calibration process, are presented in Table The current model predictions are presented in comparison with the predictions of the Mohr-Coulomb model (Case 4) in addition to the field measurements in Table Comparison of the analyses results with field measurements reveals that the model predicts larger settlements than what occurred in the field. Moreover, the model predicts smaller lateral displacements than the field measurements for the Kc-625l and Kc-710 and larger horizontal movements than the field measurements for the Kc-600 and Kc-650 (Figure 4.46). 273

302 The results of this analysis are compared with the field measurements under various applied fluid pressure in the tank in Figures 4.46 to Case 6: Test fill analysis using the modified Chsoil model To improve the quality of the predictions of the fields measured parameters, the Chsoil model was scrutinized. The main advantages of this model (relative to Mohr-Coulomb model) are: - First, the elastic parameters are correlated with the mean effective stress (they are constant and independent of the mean effective stress in Mohr-Coulomb model). - Second, the mobilized friction angle is not constant and increases from zero to the ultimate friction angle with the induced plastic shear strain. The hardening law does not add new parameters to the model and the shear modulus exponent controls the evolution of the friction angle. - Third, a step function for the mobilized dilation angle, with two values of zero and ultimate friction angle, is used. The angle of dilation controls the amount of plastic volumetric strain developed during plastic shearing. The value of ψ m = 0 corresponds to the volume preserving deformation while in shear (zero volumetric strain). Therefore, the volumetric strains are result of only elastic compressive strains while φ m < φ d and the produced compressive volumetric strains at small strains are larger than those in the Mohr-Coulomb model with a constant dilation angle. Considering these advantages of Chsoil model relative to Mohr-Coulomb model, the prediction of the field behavior does not improve substantially with the change of the constitutive model 274

303 (Figure 4.46) 1. Comparison of the Chsoil model result with the field measurement shows that the Kcb-650 and Kcw-600 exhibit larger horizontal displacement than the measured value in the field while the lateral responses of Kcc-710, Kcb-700, Kca-625u, and Kca-625l are smaller than horizontal displacements measured in the field. Patrick and Sisson (2010) reported that extensive pre-shearing is found along the bedding planes of high plastic layers of the Clearwater Formation. In the West Tank Farm, the units of the Kcc-710, Kcb-700, and the lower part of the Kca-625 (specified as the Kca-625l in the current study) are in particular of high plasticity and known to be slickensided (Moore, 2007). To account the effect of pre-sheared and slickensided bedding planes, the shearing parameters of post-peak (end of the test) are assigned for Kcc-710, Kcb-700, and Kca-625l (Table 4.12) while for the rest of facies (Kcb-650, Kca-625u, and Kcw-600) the shear parameters calculated from peak-strengths are specified (same as those in the previous analysis). Properties assigned to different soil layers for the current analysis using the Chsoil model are presented in Table Note that the dilation law constant for the Kcb-700 was reduced to a value of its ultimate friction angle. The Chsoil specific parameters were kept same as those in the previous analysis which were obtained from the calibration process. The predicted results of this 1 The root-mean-square deviation, frequently used as a measure of the differences between values predicted by a model and the values actually observed, was calculated for each case to compare predictions of the lateral displacement quantitatively. The root-mean-square deviation of the lateral displacement predictions was calculated as 2.0 mm and 3.0 mm for cases 4 and 5, respectively. Therefore, the Mohr-Coulomb model (case 4) has smaller forecasting error in comparison with the Chsoil model (case 5). 275

304 analysis, presented in Figures 4.46 to 4.50 and Table 4.17, has improved in comparison to those of the previous analysis (Case 5) 1. The concentrated zones of horizontal movements, observed in the field measured data, at Kcc-710/Kcb-700 and Kca-625l layers, are captured in predicted results, but the lateral displacements of the Kcb-650 and Kcw-600 are still overestimated Case 7: Test fill analysis using the improved Chsoil model With the modification made in input parameters of the Chsoil model in previous analysis (Case 6), the accuracy of the field predictions improved. Another factor contributing to the accuracy of the prediction of the Chsoil model may be that the shear parameters specified for the Kcc-710, Kcb- 700, and Kcb-650 are each determined from the results of just two tests. Considering the nonhomogeneity across each facies, the shear parameters may not be representative. Therefore, one may consider all the tests on different facies together and obtain two sets of shear parameters for the Clearwater clay shale (at the peak-strength and post-peak state). The shear parameters corresponding to the post-peak state are assigned for Kcc-710, Kcb-700, and Kca-625l, because of being pre-sheared and having slickensided bedding planes in the field. For the rest of facies (Kcb-650, Kca-625u, and Kcw-600) the shear parameters calculated from peak-strengths are specified (Table 4.15). 1 The root-mean-square deviation of the lateral displacement predictions was calculated as 1.7 mm case 6. Moreover, the root-mean-square deviation of the lateral displacement predictions was calculated as 2.0 mm and 3.0 mm for cases 4 and 5, respectively. Therefore, the accuracy of the prediction of lateral displacements in case 6 has improved in comparison with cases 4 and

305 Properties assigned to different soil layers for the current analysis using Chsoil are presented in Table In addition to the ultimate friction angle and cohesion for all clay shales layers, the dilation law constants for the Kcc-710, Kcb-700, and Kcb-650 were reduced from the values obtained in calibration process to the ultimate friction angle for each of those facies. The Chsoil specific parameters were kept same as those in previous analysis which were obtained from calibration process. The results of current analysis are compared with field measurements and results of Cases 5 and 6 in Figures 4.47 to 4.50 and Table The lateral displacements of various layers are predicted accurately, in particular, the accuracy of the prediction of lateral displacements of the Kcb-650 and Kcw-600 are improved in comparison to the previous analyses (Case 6) 1. The results of the current analysis corresponded to a vertical load of 150 KPa are shown in Figures 4.51 to The root-mean-square deviation of the lateral displacement predictions was calculated as 0.8 mm for case 7, while the root-mean-square deviation of the lateral displacement predictions was calculated as 2.0 mm, 3.0 mm, and 1.6 mm for cases 4, 5, and 6, respectively. Therefore, the prediction of lateral displacement is the most accurate in case 7 among the mentioned cases. 277

306 4.11. Analysis of the creep effects in the field using the FLAC Selection of the creep constitutive law Several models have been incorporated in the FLAC to simulate the time-dependent behavior of materials. These essential creep models are: - Maxwell viscoelastic model: Materials that behave both viscous and elastic are called viscoelastic. The rate of strain is considered to be proportional to stress in the Newtonian viscosity. The simplest form of representing such material in one dimension is by a spring (elastic or Hookean element) in series with a dashpot (viscous or Newtonian element). Therefore, shear and bulk moduli and viscosity are the required material properties for this model (three input parameters). - Kelvin (or Kelvin-Voigt) viscoelastic model: Similar to the Maxwell model, this model can be represented one-dimensionally by a spring in parallel with a dashpot. Hence, shear modulus and viscosity are required to characterize the deviatoric behavior of this model while bulk modulus is required for characterization of the volumetric behavior (three input parameters). - The two-component power law model: The model consists of two creep law mechanisms which follow the Norton s power law (Norton, 1929). Creep strain rate is given by a power function of the von Mises equivalent stress which reduces to the deviatoric stress in case of cylindrical symmetry. - Waste Isolation Pilot Plant (WIPP) creep reference law: The WIPP-creep model is an empirical creep law originally developed to describe time-dependent and 278

307 temperature-dependent creep of natural rock salt for nuclear-waste isolation studies. Detailed descriptions of the model can be found in the literature e.g., Herrmann et al. (1980a and b) and Senseny (1985). - Burgers-creep viscoplastic model: In this model, the deviatoric behavior is viscoelastoplastic while the volumetric behavior is just elasto-plastic. The viscoelastic and plastic components of strain-rate act in series. A Burgers model, consisted of a Maxwell mechanism in series with a Kelvin cell, forms the viscoelastic model and a Mohr- Coulomb model serves as the plastic constitutive law. The following parameters are required for this model: Kelvin shear modulus, Kelvin viscosity, Maxwell shear modulus, and Maxwell viscosity for the viscoelastic deviatoric behavior, bulk modulus for the volumetric behavior, and internal angle of friction, cohesion, dilation angle, and tension limit for the plastic behavior. - WIPP-creep viscoelastic model: The mentioned viscoelastic WIPP model is combined with the Drucker-Prager plasticity model. - Crushed-salt constitutive model: It is a variation of the WIPP-reference creep law based on the model described by Sjaardema and Krieg (1987) with addition of the proposed deviatoric component of Callahan and DeVries (1991). The number of parameters needed for various creep models are presented in Table Among different models that include plastic yielding, the Burgers-creep viscoplastic model needs the fewest parameters, nine. 279

308 Maxwell viscoelastic model For a Maxwell viscoelastic model, composed of a Newton unit in series with a Hook unit: u = F k + F η (4.24) where u is the velocity, and F is the change in force with time, k is the elastic constant, F is the force, and η is the viscosity. In three-dimensional isotropic Maxwell model, when the viscous strains are incompressible and the volume changes are purely elastic (Ottosen & Ristinmaa, 2005): ε ij d = S ij 2G + 3S ij 2η (4.25) Therefore, in triaxial condition: ε q = q 2G + 3q 2η (4.26) where ε q is the shear strain rate, q is the deviatoric stress rate, G is the shear modulus, and q is the deviatoric stress. In triaxial condition: ε q = 2 3 (ε a ε r) (4.27) In the stress relaxation test, ε a = 0. Therefore, 2 3 ε r = q 2G + 3q 2η (4.28) or ε r = 3q 4G 9q 4η (4.29) 280

309 The Maxwell shear modulus and viscosity can be obtained from a graph of radial strain rate versus the rate of change in deviatoric stress. This model has the disadvantage of the unlimited stress relaxation and the result of element test showed stress reduction to almost zero Burgers-creep viscoplastic model Deviatoric behavior of a Burgers model is visco-elasto-plastic. A Maxwell mechanism in series with a Kelvin cell (Figure 4.58) acts as the viscoelastic model while the plastic component is a Mohr-Coulomb model (acting in series with the viscoelastic model). Volumetric behavior is just elasto-plastic Zener s viscoplastic model The existence of the viscous component (dashpot) of the Maxwell mechanism in series with other components in a Burger s model leads to reduction of the deviatoric stress to zero in the simulation of triaxial stress relaxation tests at large times. However, the final relaxed stresses in laboratory tests were nonzero and in the range of 55%-85% of the initial deviatoric stresses. Therefore, the Maxwell dashpot component was omitted from the model by attributing infinity (default value) as the Maxwell viscosity value and practically transform the Burger model to the Zener model (Figure 4.59). Specifying a finite value for the Maxwell viscosity introduces an infinite strain in the case of creep. 281

310 Description of the deviatoric behavior of the Zener s viscoplastic model Kelvin, Maxwell, and plastic components act in a series. Therefore, strain rate can be partitioned to: e ij = e ij K + e ij H + e ij P (4.30) where e ij denotes the deviatoric strain rate while e ij K, e ij H and, e ij P are contributions of Kelvin, Hookean, and plastic components, respectively. For Kelvin component S ij = 2η K e ij K K + 2G K e ij (4.31) where S ij is the deviatoric stress, η K is the (Kelvin) dynamic viscosity, and G K is shear modulus of Kelvin mechanism. For Hookean component e ij H = S ij 2G (4.32) where G is the (Hookean) shear modulus. Therefore, η K, G K, and G are needed to be known to describe the viscoelastic component of the deviatoric behavior of the Zener model (Table 4.19). The Mohr-Coulomb yield envelope is a composite of shear and tensile criteria which are as follows, respectively: f = σ 1 σ 3 N φ + 2c N φ N φ = 1+sinφ 1 sinφ (4.33) f = σ t σ 3 (4.34) 282

311 where φ is the internal friction angle, c is the cohesion, σ t is the tensile strength, and σ 1 and σ 3 are the minimum and maximum principal stresses. The potential function, g, has the following form in shear and tension yielding, respectively: g = σ 1 σ 3 N ψ N ψ = 1+sinψ 1 sinψ (4.35) g = σ 3 (4.36) where ψ is the dilation angle. Accordingly, φ, c, σ t, and ψ are required to characterize the plastic component of the deviatoric behavior of the Zener model (Table 4.19). Mohr-Coulomb contribution is e ij P = λ g 1 σ ij 3 e vol P δ ij (4.37) e vol P = λ [ g σ 11 + g σ 22 + g σ 33 ] (4.38) where λ is the plastic multiplayer, which is nonzero only during plastic flow and may be defined from the consistency condition Description of the volumetric behavior of the Zener s viscoplastic model The volumetric behavior is elasto-plastic and is given by σ 0 = K (e vol e vol P ) (4.39) in which σ P 0 is the mean effective stress. K is the bulk modulus. e vol and e vol are the total and plastic volumetric strain rates, respectively. 283

312 Estimation of the maximum creep time step The deviatoric stress state governs the creep process. The maximum creep time step, satisfying the numerical accuracy, can be estimated from the ratio of the material viscosity, η, to the shear modulus, G, for Maxwell s model: cr t max = η M G M (4.40) For the Burgers viscoplastic model, the equation transforms to: cr t max = min ( η K G K, η M G M ) (4.41) where the superscripts K and M refer to Kelvin and Maxwell properties, respectively. For the Zener s viscoplastic model, the maximum creep time step is: cr t max = min ( η K G K ) (4.42) Burgers and Zener model formulation Stress relaxation and creep functions for Burgers model are (Nielsen, 2005): r(t) = E M [(m m 1 m 1 1)e m 1 t τ K (m 2 1)e m 2t τ K ] (4.43) 2 c(t) = 1 E M (1 + t τ M + α [1 exp ( t τ K )]) (4.44) τ M = η M E M, τ K = η K E K, α = E M E K (4.45) 284

313 m 1, m 2 = 1 2 (1 + α + τ K τ M ± (1 + α + τ K τ M ) 2 4 τ K τ M ) (4.46) where E M and E K are Maxwell and Kelvin Young s moduli, respectively. η M and η K are Maxwell and Kelvin viscosity values, respectively. Zener model is obtained by removing the Newton element of the Maxwell unit from the Burger mechanism and its formulation can be obtained by specifying infinite Maxwell viscosity: Therefore And then It can be rewritten as: And then It can be rewritten as: σ(t) ε if η M then τ M (4.47) r(t) = m 1, m 2 = 1 + α, 0 (4.48) E (1+α)t M 1 + α [αe τ K + 1] (4.49) = E ME K [ E M e (E M +E K )t η K + 1] (4.50) E K + E M E K c(t) = 1 E M (1 + α [1 exp ( t τ K )]) (4.51) ε(t) σ = 1 E M (1 + E M E K [1 exp ( E Kt η K )]) (4.52) Stress relaxation formula, normalizing by the stress value at the start of the relaxation, transforms to: 285

314 σ (t) = σ(t) σ(0) = ε E M σ(0) 1 + α (αe If t = 0, then σ(t) = σ(0) = εe M and σ (0) = 1. Therefore, the normalized relaxed stress will be: (1+α)t τ K + 1) (4.53) σ (t) = 1 (1+α)t 1 + α (αe τ K + 1) (4.54) Stress relaxation formula for the case of triaxial condition, transforms to: q (t) = 1 (1+α)t 1 + α (αe τ K + 1) (4.55) τ K = η K G K and α = G G K (4.56) in which α is the ratio of the Maxwell shear modulus to the Kelvin shear modulus. G and G K are the Hookean and Kelvin shear moduli, respectively. η K and τ K are Kelvin viscosity and the ratio of Kelvin viscosity over Kelvin shear modulus, respectively Calibration of creep parameters of the Burgers-creep viscoplastic model using the relaxation test results The values of the bulk and shear moduli implemented in the elastic analysis (Case 3) were used as the bulk modulus and Hookean shear modulus, respectively (Table 4.20). Plastic parameters for Zener s model, φ, c, ψ, and σ t, were specified same as those in elastoplastic analyses (Case 4). The remaining parameters, G K and η K, were estimated using stress relaxation tests performed in triaxial equipment (Table 4.20). Although only a single relaxation test is needed to determine G K and η K, two relaxation tests at axial strains of 1.5% and 3% have been used in the calibration 286

315 process of each facies. The results of a total of eight tests from four triaxial tests on samples from four different facies under 100 kpa confining pressure are used. The process to estimate the values of shear modulus and viscosity of Kelvin components for each facies from laboratory results is described below. Examining the different stress relaxation data from experiments shows they can be best fitted with the following curve: a d q = d ( t (4.57) c )d Then q (0) = q 0 = a and q ( ) = q r = d, rewriting the above equation: q = q r + q 0 q r 1 + ( t )q r (4.58) c Scrutinizing the curve fitted to the laboratory stress relaxation data, a physical meaning can also be attributed to the constant c. If t = c, then it is obtained that q t=c = q 0 + q r 2 (4.59) Therefore, c, termed as half relaxation time, t h, is the elapsed time in which the stress decreases to the half of the total relaxed stress (i.e. q = q 0+q r ). In other words, t 2 h is the time elapsed for half the stress relaxation in term of stress takes place (half the stress relaxation occurs before and half afterward). So, the curve fitted to the triaxial relaxation data can be rewritten: q = q r + q 0 q r 1 + ( t t h ) q r (4.60) 287

316 or q = q r + 1 q r 1 + ( t t h ) q r (4.61) Recalling the expression for the stress relaxation of a Zener model (a Kelvin component in series with a spring): If t then q (t) = 1 (1+α)t 1 + α (αe τ K + 1) (4.62) q ( ) = α = q relaxed (4.63) Hence, the value of α can be estimated from the final relaxed stress level. α = 1 q r 1 (4.64) Recalling the definition of α as the ratio of the shear modulus to the Kelvin shear modulus, the value of the Kelvin shear modulus can be calculated from: G K = G α (4.65) or G K = Gq r 1 q r (4.66) If the viscosity is assumed to be a function of time, comparing the model formula and the fitted curve equation results in: 288

317 q r + 1 q r 1 + ( t t h ) q r = 1 + αe (1+α)t τ K (t) 1 + α (4.67) Knowing q r = 1 1+α = 1 1+ G G K simplifying the above equation and rewriting the above equation to find τ K : (1 + α)t τ K (t) = Ln(1 + ( t 1 (4.68) 1+α t ) ) h Recalling the definition of τ K as the ratio of Kelvin viscosity to Kelvin shear modulus, Kelvin viscosity is readily calculated as: or η K (t) = (1 + α)g Kt Ln(1 + ( t 1 (4.69) 1+α t ) ) h η K (t) = (G + G K )t Ln(1 + ( t t ) h G K G+G K ) (4.70) Implementing the above equation in the FLAC, providing G, G K, and t h, the viscosity is calculated as a function of the time. In conclusion, to find G K and η K for a facies following the procedure described above, the values of q r and t h related to the curve fitted to a single relaxation tests are required. Since two relaxation curves have been used to calibrate the creep parameters for each facies, the average values of t h and q r were considered. Therefore, the stress relaxation curve of the element test 289

318 simulation lies between two experimental curves in each case. Results of the calibration process along with the experimental results for different facies are presented in Figures 4.60 to The parameters resulted from calibration process for each facies are presented in Table Poro-elasto-visco-plastic (creep) analysis in undrained condition (Case 8) A creep analysis was performed following the undrained loading stage (Case 4). For the Kcc-710, Kcb-700, Kcb-650, and Kca-625l parameters resulted from the calibration process were inputted into the FLAC (Table 4.20). The values of t h and α (or alternatively q r) for the Kca-625u and the Kcw-600 were selected same as those for the Kca-625l and the Kcw-600 (Table 4.20). Recalling that α is the ratios of the shear modulus to Kelvin shear modulus, then G K = G α (4.71) and knowing values of G from elastic analysis (Case 3), the Kelvin shear moduli has been calculated for the Kca-625u and the Kcw-600 (Table 4.20). The behavior of the top three layers (Sand 860, Pl Clay 880, and Clay till 830) is governed by the Mohr-Coulomb constitutive law (without consideration of any time dependent behavior). Since the analysis has been performed after the undrained loading stage, the displacements include those during the undrained loading stage. The input parameters for each facies for the current analysis are presented in Table The results of the analysis are presented in Figures 64 to 68. The vertical displacements contours (Figure 4.64) are similar to those of the Case 4 290

319 (Figure 4.24), but the differential settlement has increased from 19.2 mm to 21.1 mm (Table 4.25). The rest of the contours are also similar to those of the Mohr-Coulomb analysis (Case 4). In most practical cases, settlement from secondary consolidation, S c, at time t can be estimated from (Mesri and Godlewski, 1977): S c = C α H 1 + e 0 log 10 ( t ) (4.72) 0 t p where C α is the secondary compression index, t p is the duration of primary consolidation, and H 0 is the thickness of compressible layer. Based on secondary compression indices measured in the conducted oedometer test on a Kcb-700 sample and the creep settlement after 10 years is calculated and presented in Table According to the results of Case 9, the duration of primary consolidation is considered as 3.5 years. The estimated creep settlements are in the range of mm and have an average of 34.2 mm, while the creep analysis (Case 8) predict settlements of 52.8 and 12.8 mm at the tank center and edge, respectively Poro-elasto-plastic analysis in drained condition (Case 9: consolidation analysis) FLAC can model flow of fluid through a permeable solid in parallel with the mechanical modeling, in order to capture the effects of fluid/solid interaction such as consolidation. The consolidation has two mechanical effects: first, change in pore pressure leads to the change in effective stress that affects the response of the solid; second, the fluid in a zone reacts to the mechanical volume change by a change in pore pressure. 291

320 The saturated fast-flow technique, which is applicable to a fully saturated and coupled fluidmechanical simulation, is implemented to speed up the analysis. In this logic, the fluid is considered as incompressible compared to the drained compressibility of the soil. Mechanical effects take place almost instantaneously, but, the fluid flow and the dissipation associated with consolidation is a long-term process. Therefore, it is adopted in FLAC that no time is associated with any of the mechanical sub-steps taken in association with fluid-flow steps in order to satisfy quasi-static equilibrium. On the other hand, each fluid step does correspond to a real period of time. FLAC alternates mechanical steps and fluid steps in the saturated fluid-flow scheme. At the beginning, one fluid step may induce large unbalanced forces and place the system substantially out of equilibrium. Consequently, many mechanical steps is needed for each fluid step. In later stages, the change in fluid pressure decreases and the system will remain in equilibrium. Therefore, several fluid steps may be taken for each mechanical step Consolidation parameters Based on the consolidation results of triaxial tests, the coefficient of consolidation, c v, for different facies have been calculated. The coefficient of volume compressibility, m v, has been estimated from the constant-rate-of-strain consolidation test for stresses corresponded to the confining pressures applied in triaxial tests according to British Standard 1377 (1990). Then, hydraulic conductivity, k H, is calculated through the following equation: k H = c v γ m v (4.73) 292

321 in which, γ is the unit weight of fluid and m v is the coefficient of volume compressibility. The hydraulic properties of samples tested in triaxial equipment and the average permeability of each facies are presented in Table The estimated coefficients of permeability are consistent with the values reported in literature. For example, Gautam (2004) reported the coefficients of permeability to be in a range of m/s for Colorado shale, with a clay content in range of 30% to 57% (Smith et al., 2003). The estimated permeability values in Table 4.22 are based on the results of triaxial compression and odometer tests on intact samples of the Clearwater clay shale. Hence, the reported permeability values represent that of the intact shale materials, while slickensided surfaces and sand lenses have been observed during the logging of the recovered cores from the field. Therefore, the permeability of the clay shale in the field was estimated to be higher, 10 9 m/s (Moore & Sobkowicz, 2005). Accordingly, the permeability of clay shale facies are specified as m 2 /(Pa s) in drained analysis in FLAC, while 10 9 m 2 /(Pa s) was assigned as the permeability of clay and clay till layers (Table 4.23) Consolidation analysis results The parameters inputted to FLAC for this analysis is similar to those of Case 4, while the permeability was specified for each layer and fluid flow was permitted (Table 4.23). The results of analysis are presented in Figures 69 to 72. The vertical displacements contours due to the consolidation are presented in Figure 4.69, which show a more uniform settlement comparing to Case 4 (Figure 4.24) and Case 8 293

322 (Figure 4.64). The differential settlement is just 7.3 mm compared with 19.2 mm and 21.1 mm settlements of the undrained loading stage and creep analysis, respectively. The displacements vectors, Figure 4.71, are aligned in a more vertical direction compared to Case 4 (Figure 4.26) and Case 8 (Figure 4.71). The reason may be attributed to the fact that fluid flow is in vertical direction and consolidation is essentially one-dimensionally. The sand layer acts as drainage while bottom and sides boundaries are no-flow boundaries Poro-elasto-visco-plastic analysis in drained condition (Case 10: coupled creep-consolidation analysis) Laboratory and field data suggest that secondary consolidation occurs simultaneously with primary consolidation in fine-grained soils. Particularly on highly compressible clays, viscous effects may contribute significantly to the settlement during the time frame of primary consolidation (Leroueil, 1996). Consequently, creep during primary consolidation need to be explicitly calculated. A coupled consolidation and creep analysis was performed after the undrained stage. Biot consolidation theory is implemented to calculate the soil deformation from consolidation, while a elasto-viscoplastic rheological model is needed to consider settlements due to the secondary consolidation. Therefore, a coupled ground water flow analysis is conducted to take into account both excess pore water dissipation and the resulted settlement along with that from creep phenomenon. Values of soil properties used in the coupled creep-consolidation analysis in FLAC are presented in Table

323 Analysis results The coupled creep-consolidation analysis of the test fill was carried out after the undrained analysis for a duration of about 10 years. The implementation of the creep model along with the calibrated parameters to the field model leads to occurrences of a maximum settlement at tank center, equal to of mm (Figure 4.73). Horizontal displacements contours are shown in Figure 4.74 and the displacement vectors are demonstrated in Figure In addition, shear stresses contours are shown in Figure Finally, the settlement at center and edge of the tank and lateral displacement predictions of Cases 8 to 10 along with those of Case 4 are presented in Table The predicted settlements at tank center and edge are smaller than sum of those settlements in creep and consolidation analysis, while the differential settlement between the tank center and edge is predicted 44.8 mm, larger than sum of the differential settlements in creep and consolidation analysis (21.1 mm and 7.3 mm, respectively). Therefore, it is necessary to perform a coupled consolidation-creep analysis to have a realistic prediction of both vertical and lateral displacements. The results showed a maximum settlement of mm occurs at the tank center in long-term. Poulos et al. (2001) specified the tolerable limit for foundations on clay in a range of mm. 295

324 Table 4.1. Estimate of the coefficients of the earth pressure at rest of clay shale layers Facies Thickness (m) Friction angle ( ) OCR K 0oc Kcc Kcb Kcb Kca-625u Kca-625l Kcw Weighted average with respect to layer thickness

325 Table 4.2. Layers properties and specifications in addition to the total stresses, effective stresses, and hydrostatic pore pressure at bottom of each layer Facies E (MPa) Thickness (m) Average depth (m) ν φ ( ) n K (MPa) G (MPa) Dry Total density (kg/m 3 ) Layer stress (kpa) Total stress Pore pressure Effective stress at bottom of the layer (kpa) Sand Pl Clay Clay till Kcc Kcb Kcb Kca-625u Kca-625l Kcw E: Young s modulus, ν: Poisson s ratio, φ : friction angle, n: porosity, K: bulk modulus, and G: shear modulus. 297

326 Table 4.3. Comparison of hand-calculated values of vertical total stresses and pore pressures with those calculated by FLAC Grid point Total density (kg/m 3 ) Change in stress (kpa) Depth (m) Total stress (kpa) Pore pressure (kpa) Pore pressure FLAC (kpa) Pore pressure difference (kpa) Zone Total stress (kpa) Total stress FLAC (kpa) Total stress difference (kpa)

327 Grid point Total density (kg/m 3 ) Change in stress (kpa) Depth (m) Total stress (kpa) Pore pressure (kpa) Pore pressure FLAC (kpa) Pore pressure difference (kpa) Zone Total stress (kpa) Total stress FLAC (kpa) Total stress difference (kpa) Note: Pore pressures are calculated at grid points in FLAC while stresses are calculated at each zone. 299

328 Table 4.4. Soil properties for FLAC analyses (Case 1) Facies Thickness (m) E K G (MPa) ν Density (kg/m 3 ) n Sand, clay and clay shale E: Young s modulus, K: bulk modulus, G: shear modulus, ν: Poisson s ratio, and n: porosity. Table 4.5. Soil properties for FLAC analyses (Case 2) Facies Thickness (m) E K G (MPa) ν φ ( ) Density (kg/ m 3 ) n Sand Clay and clay shale E: Young s modulus, K: bulk modulus, G: shear modulus, ν: Poisson s ratio, φ : friction angle, n: porosity. 300

329 Table 4.6. Soil properties for FLAC analyses (Case 3) Facies Thickness (m) E K G (MPa) ν Dry density (kg/m 3 ) n Source Sand Moore (2007) Pl Clay 880 Clay till Moore (2007) Moore (2007) Kcc Current study Kcb Current study Kcb Current study Kca- 625u Current study Moore et al. (2011) Kca-625l Current study Kcw Moore et al. (2011) E: Young s modulus, K: bulk modulus, G: shear modulus, ν: Poisson s ratio, n: porosity. 301

330 Table 4.7. Soil properties for FLAC analyses (Case 4) Facies Thickness (m) E (MPa) ν K (MPa) G (MPa) φ ( ) ρ d (kg/ m 3 ) n Source Sand Moore (2007) Pl Clay Moore (2007) Clay till Moore (2007) Kcc Current study Kcb Current study Kcb Current study Kca-625u Current study Moore et al. (2011) Kca-625l Current study Kcw Moore et al. (2011) E: Young s modulus, ν: Poisson s ratio, K: bulk modulus, G: shear modulus, φ : friction angle, ρ d : dry density, n: porosity. 302

331 Table 4.8. Shear parameters determined from the triaxial tests Sample facies Kca-625 Kcb-650 Kcb-700 Kcc-710 Friction angle at peak strength Cohesion (kpa) Tests 1, 2, and 6 4 and 10 3, 7, 8, and 9 11 and 12 Table 4.9. Shear parameters used in Chsoil model for fill test simulation after calibration Sample facies Friction angle at peak strength Cohesion (kpa) Tests Sand Moore et al. (2011) Pl Clay Moore et al. (2011) Clay till Moore et al. (2011) Kcc and 12 (at peak) Kcb and 9 (at peak) Kcb and 10 (at peak) Kca-625u Similar to Kc-625w Kca-625l , 2, and 6 (at peak) Kcw Moore et al. (2011) 303

332 Table Model predictions under 150 kpa applied load (Case 5) Model Field measurements Elastic (Case 3) Mohr- Coulomb (Case 4) Chsoil (Case 5) Settlement at tank center post (mm) Pore pressure at tank center post (kpa) (depth of 12 m) Lateral displacement at top of the clay shale layer (mm) (10 m from tank edge and depth of 5m) Lateral displacement (mm) (10 m from tank edge at surface)

333 Table Soil properties for FLAC analysis using the Chsoil model (Case 5: original Chsoil model) Facies E ref ν φ f c (kpa) φ d ψ f m n R f K ref G ref p i (kpa) Tests* Sand Pl Clay Clay till Kcc and 12 Kcb and 9 Kcb and 10 Kca-625u Kca-625l , 2 and 6 Kcw E ref : Young s modulus number, ν: Poisson s ratio, φ f : friction angle, c: cohesion, φ d : dilation law constant, ψ f : dilation angle, m: bulk modulus exponent, n: shear modulus exponent, R f : failure ratio, K ref : bulk modulus number, G ref : shear modulus number, p i : initial effective pressure. * The number of the tests used in calibration process are shown in last column. 305

334 Table Shear parameters used in the modified Chsoil model for fill test simulation Sample facies Friction angle at peak strength Cohesion (kpa) Tests Sand Moore et al. (2011) Pl Clay Moore et al. (2011) Clay till Moore et al. (2011) Kcc and 12 (at post-peak) Kcb and 9 (at post-peak) Kcb and 10 (at peak) Kca-625u , 2, and 6 (at peak) Kca-625l , 2, and 6 (at post-peak) Kcw Moore et al. (2011) 306

335 Table Model predictions under 150 kpa applied load (Case 6) Model Field measurements Elastic (Case 3) Mohr- Coulomb (Case 4) Chsoil (Case 5) Chsoil (Case 6) Settlement at tank center post (mm) Pore pressure at tank center post (kpa) (depth of 12 m) Lateral displacement at top of the clay shale layer (mm) (10 m from tank edge and depth of 5m) Lateral displacement (mm) (10 m from tank edge at surface)

336 Table Soil properties for FLAC analysis using the Chsoil model (Case 6: modified Chsoil model) Facies E ref ν φ f c (kpa) φ d ψ f m n R f K ref G ref p i (kpa) Tests* Sand Pl Clay Clay till Kcc and 12 Kcb and 9 Kcb and 10 Kca-625u Kca-625l , 2 and 6 Kcw E ref : Young s modulus number, ν: Poisson s ratio, φ f : friction angle, c: cohesion, φ d : dilation law constant, ψ f : dilation angle, m: bulk modulus exponent, n: shear modulus exponent, R f : failure ratio, K ref : bulk modulus number, G ref : shear modulus number, p i : initial effective pressure. * The number of the tests used in calibration process are shown in last column. 308

337 Table Shear parameters used in the improved Chsoil model for fill test simulation (Case 7) Sample facies Friction angle at peak strength Cohesion (kpa) Tests Sand Moore et al. (2011) Pl Clay Moore et al. (2011) Clay till Moore et al. (2011) Kcc All tests (at post-peak) Kcb All tests (at post-peak) Kcb All tests (at peak) Kca-625u All tests (at peak) Kca-625l All tests (at post-peak) Kcw All tests (at peak) 309

338 Table Soil properties for FLAC analysis using the Chsoil model (Case 7: improved Chsoil model) Facies E ref ν φ f c (kpa) φ d ψ f m n R f K ref G ref p i (kpa) Tests* Sand Pl Clay Clay till Kcc and 12 Kcb and 9 Kcb and 10 Kca-625u Kca-625l , 2 and 6 Kcw E ref : Young s modulus number, ν: Poisson s ratio, φ f : friction angle, c: cohesion, φ d : dilation law constant, ψ f : dilation angle, m: bulk modulus exponent, n: shear modulus exponent, R f : failure ratio, K ref : bulk modulus number, G ref : shear modulus number, p i Initial effective pressure. * The number of the tests used in calibration process are shown in last column. 310

339 Table Different model predictions under 150 kpa applied load Model Field measurements Elastic (Case 3) Mohr- Coulomb (Case 4) Chsoil (Case 5) Chsoil (Case 6) Chsoil (Case 7) Settlement at tank center post (mm) Pore pressure at tank center post (kpa) (depth of 12 m) Lateral displacement at top of the clay shale layer (mm) (10 m from tank edge and depth of 5m) Lateral displacement (mm) (10 m from tank edge at surface)

340 Table List of creep models incorporated in the FLAC and the number of input parameters for each one Model Number of parameter needed Maxwell viscoelastic model 3 Kelvin viscoelastic model 3 The one-component power law model 5 The two-component power law model 8 Burgers-creep viscoplastic model 9 WIPP-creep reference model 10 WIPP-creep viscoelastic model 14 Crushed-salt constitutive model 17 Table Parameters needed for Zener s viscoplastic model Behavior Component Symbol Model specific parameter viscoelastic G K η K G Kelvin shear modulus Kelvin viscosity Hookean shear modulus Deviatoric φ internal friction angle plastic c ψ σ t cohesion dilation angle tensile strength Volumetric elasto-plastic K bulk modulus 312

341 Table Soil properties for calibrating creep parameters using relaxation data in FLAC (Case 8) Parameters Elastic (Case 3) Mohr-Coulomb (Case4) Viscous (calibration with relaxation data) Facies ρ (kg/m 3 ) n E (MPa) ν K (MPa) G (MPa) φ ( ) Test# q r α G K (MPa) t h (s) Sand Pl Clay Clay till Kcc Kcb Kcb Kca-625u Kca-625l Kcw ρ: density. n: porosity, E: Young s modulus, ν: Poisson s ratio, K: bulk modulus, G: shear modulus, φ : friction angle, q r: relaxed stress, α: the ratio of the Maxwell shear modulus to the Kelvin shear modulus, G K : Kelvin shear modulus, and t h : half relaxation time. Input parameters for the Zener s viscoplastic model are bold in the table above (K, G, G K, t h, and φ ). Cohesion, dilation angle, and tension limit are the other three input parameters for the Mohr-Coulomb component of the model. Similar to Case 4, cohesion and dilation angle are set as zero for all the layers. Tension limit was set equal to 1 kpa for all the layers. 313

342 Table Estimated coefficient of consolidation and secondary compression index for each stress level in oedometer test (Kcb-700 facies) Axial stress in oedometer test (kpa) C α C α C c S c (mm) Average C α : secondary compression index, and C c : compression index. 314

343 Table Hydraulic properties of different facies of Clearwater clay shale Facies Test# c v (cm 2 /s) Confining pressure (kpa) m v (1/MPa) k H (m/s) k H average (m/s) k average (m 2 /(Pa s)) Kcc-710 Kcb-700 Kcb-650 Kca k H : coefficient of permeability or hydraulic conductivity, m v : coefficient of volume compressibility, and k: permeability or the mobility coefficient (k = k H gρ w, g is the gravitational acceleration, and ρ w is the density of water). 315

344 Table Soil properties for the consolidation analysis in FLAC (Case 9) Parameters Elastic (Case 3) Mohr-Coulomb (Case 4) Facies ρ(kg/m 3 ) K (MPa) G (MPa) φ ( ) Flow-related (Case 9) k (m 2 /(Pa s)) n Sand Pl Clay Clay till Kcc Kcb Kcb Kca-625u Kca-625l Kcw ρ: density, K: bulk modulus, G: shear modulus, φ : friction angle, k: permeability, and n: Porosity. 316

345 Table Soil properties for the coupled creep-consolidation analysis in FLAC (Case 10) Parameters Elastic (Case 3) Mohr-Coulomb (Case 4) Viscous (Case 8) Flow-related (Case 9) Facies ρ(kg/m 3 ) K (MPa) G (MPa) φ ( ) G K (MPa) t h (s) k (m 2 /(Pa s)) n Sand Pl Clay Clay till Kcc Kcb Kcb Kca-625u Kca-625l Kcw ρ: density, K: bulk modulus, G: shear modulus, φ : friction angle, G K : Kelvin shear modulus, t h : half relaxation time, k: permeability, and n: Porosity. 317

346 Table Different model predictions under 150 kpa applied load Model Field data Case 4 Case 8 Case 9 Case 10 Drainage condition Undrained Undrained Undrained Drained Drained Time frame Instantaneously After 10 years Settlement at tank center post (mm) Settlement at 15m from tank center post (mm) (52.5) 71.4(31.1) 120.2(79.9) (31.4) 94.0(38.3) 120.1(64.4) Settlement at tank edge (mm) (12.8) 44.9(23.8) 56.2(35.1) Differential settlement between the tank center and edge (mm) Pore pressure at tank center post (kpa) (depth of 12 m) Lateral displacement at top of the clay shale layer (mm) (10 m from tank edge and depth of 5m) Lateral displacement (mm) (10 m from tank edge at surface) (39.7) 26.5(7.3) 64(44.8) Lateral displacement at top of the clay shale layer (mm) (at tank edge and depth of 5m) Each of Cases 8 to 10 were performed after Case 4: For Case 8, viscous (time-dependent) effects was considered after short term elastoplastic analysis (the constitutive model changed from Mohr-Coulomb to the Burgers-creep viscoplastic model while the drainage was still not allowed). - For Case 9, drainage was provided after elastoplastic analysis while the constitutive model was kept constant. - For Case 10, both the constitutive model changed from Mohr-Coulomb to the Burgerscreep viscoplastic model and the drainage was provided after short term analysis. The number in parentheses shows the amount of the settlement in excess of the settlement due to the undrained loading. 318

347 JOB TITLE :. (*10^1) FLAC (Version 7.00) LEGEND 1-Apr-16 16:13 step E-01 <x< 2.690E E+00 <y< 2.367E+01 User-defined Groups Clay:600 Clay:625weak Clay:625strong Clay:650 Clay:700 Clay:710 Clay:Till Clay:Clay Sand:Sand Grid plot 0 5E 0 Boundary plot 0 5E 0 Fixed Gridpoints X X-direction X X X X X X X X X X X X X X X X X X X X X BBBBB BBBBBB BBBBB BBBBBB BBBBB BBBBBB BBBBBB BBBBB BBBBBB BBBB (*10^1) Figure 4.1. Grids of finite difference model and layered soil profile 319

348 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 17-Dec-15 12:01 step E-01 <x< 4.047E E+01 <y< 2.283E+01 Y-displacement contours -2.50E E E E E E Contour interval= 5.00E (*10^1) Figure 4.2. Vertical displacements contours in meter (Case 1) 320

349 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 17-Dec-15 12:02 step E-01 <x< 4.047E E+01 <y< 2.297E+01 X-displacement contours 0.00E E E E E E E-02 Contour interval= 2.00E (*10^1) Figure 4.3. Horizontal displacements contours in meter (Case 1) 321

350 Figure 4.4. Displacements vectors contours in meter (Case 1) 322

351 Figure 4.5. Shear stresses contours in Pa (Case 1) 323

352 Figure 4.6. Change in vertical stresses contours in Pa due to loading (Case 1) 324

353 Figure 4.7. Excess pore pressure contours in Pa due to loading (Case 1) 325

354 Figure 4.8. Change in effective vertical stresses contours in Pa due to loading (Case 1) 326

355 Figure 4.9. Vertical displacements contours in meter (Case 2) 327

356 Figure Horizontal displacements contours in meter (Case 2) 328

357 Figure Displacements vectors contours in meter (Case 2) 329

358 Figure Shear stresses contours in Pa (Case 2) 330

359 Figure Change in vertical stresses contours in Pa due to loading (Case 2) 331

360 Figure Excess pore pressure contours in Pa due to loading (Case 2) 332

361 Figure Change in effective vertical stresses contours in Pa due to loading (Case 2) 333

362 Figure Vertical displacements contours in meter (Case 3) 334

363 Figure Horizontal displacements contours in meter (Case 3) 335

364 Figure Displacements vectors contours in meter (Case 3) 336

365 Figure Shear stresses contours in Pa (Case 3) 337

366 Figure Change in vertical stresses contours in Pa due to loading (Case 3) 338

367 Figure Excess pore pressure contours in Pa due to loading (Case 3) 339

368 Figure Magnitude of compressive volumetric strain versus depth at tank centerline, 10 m and 20 offset from tank centerline (Case 3) Figure Change in effective vertical stresses contours in Pa due to loading (Case 3) 340

369 Figure Vertical displacements contours in meter (Case 4) 341

370 Figure Horizontal displacements contours in meter (Case 4) 342

371 Figure Displacements vectors contours in meter (Case 4) 343

372 Figure Shear stresses contours in Pa (Case 4) 344

373 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 16-Dec-15 15:28 step E-01 <x< 4.061E E+01 <y< 2.286E+01 EX_ 3 Contours -1.50E E E E E E E+00 Contour interval= 2.50E (*10^1) Figure Change in vertical stresses contours in Pa due to loading (Case 4) 345

374 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 16-Dec-15 15:26 step E-01 <x< 4.065E E+01 <y< 2.315E+01 EX_ 4 Contours 0.00E E E E E E E+05 Contour interval= 2.00E (*10^1) Figure Excess pore pressure contours in Pa due to loading (Case 4) Figure Magnitude of compressive volumetric strain versus depth at tank centerline, 10 m and 20 offset from tank centerline (Case 4) 346

375 Figure Change in effective vertical stresses contours in Pa due to loading (Case 4) 347

376 Depth (m) Figure Comparison of magnitude of compressive volumetric strain versus depth at tank centerline (Cases 3 and 4) 2 Accumulated volumetric strain (%) Mohr-Coulomb analysis Elastic analysis Figure Comparison of magnitude of compressive volumetric strain versus depth at 10 m offset from tank centerline (Cases 3 and 4) 348

377 Figure Measured settlement at tank center post and different model predictions (MC stands for Mohr-Coulomb model) Figure Average measured settlement at tank edge and different model predictions 349

378 Figure Measured horizontal displacement at 10 meter offset from tank edge and different model predictions 350

379 Figure Measured excess pore pressure in center of tank at 12 m depth and different model predictions 351

380 Figure Measured and simulated stress-strain behavior of Kca-625 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated volumetric behavior of Kca-625 facies in drained triaxial compression test at various confining pressures 352

381 Figure Measured and simulated stress-strain behavior of Kcc-710 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated volumetric behavior of Kcc-710 facies in drained triaxial compression test at various confining pressures 353

382 Figure Measured and simulated stress-strain behavior of Kcb-700 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated volumetric behavior of Kcb-700 facies in drained triaxial compression test at various confining pressures 354

383 Figure Measured and simulated stress-strain behavior of Kcb-650 facies in drained triaxial compression test at various confining pressures Figure Measured and simulated volumetric behavior of Kcb-650 facies in drained triaxial compression test at various confining pressures 355

384 Figure Measured horizontal displacement at 10 meter offset from tank edge and different model predictions 356

385 Figure Measured horizontal displacement at 10 meter offset from tank edge and different Chsoil model predictions 357

386 Figure Measured settlement at the tank center post and different model predictions (MC stands for Mohr-Coulomb model) Figure Average measured settlement at the tank edge and different model predictions 358

387 Figure Measured excess pore pressure in center of the tank at 12 m depth and different model predictions JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 21-Dec-15 12:36 step E-01 <x< 4.050E E+01 <y< 2.401E+01 Y-displacement contours -6.00E E E E E E E E-02 Contour interval= 1.00E (*10^1) Figure Vertical displacements contours in meter (Case 7) 359

388 JOB TITLE :. (*10^1) FLAC (Version 7.00) LEGEND 21-Dec-15 13:03 step E-01 <x< 4.169E E+01 <y< 2.395E+01 X-displacement contours 0.00E E E E E E E-02 Contour interval= 1.00E (*10^1) Figure Horizontal displacements contours in meter (Case 7) 360

389 JOB TITLE :. (*10^1) FLAC (Version 7.00) LEGEND 21-Dec-15 13:04 step E+00 <x< 4.169E E+01 <y< 2.467E+01 Displacement vectors max vector = 7.704E E (*10^1) Figure Displacements vectors contours in meter (Case 7) 361

390 JOB TITLE :. (*10^1) FLAC (Version 7.00) LEGEND 21-Dec-15 13:04 step E-01 <x< 4.144E E+01 <y< 2.422E+01 XY-stress contours -5.00E E E E E E E E E+04 Contour interval= 5.00E+03 Extrap. by averaging (*10^1) Figure Shear stresses contours in Pa (Case 7) 362

391 JOB TITLE :. (*10^1) FLAC (Version 7.00) LEGEND 21-Dec-15 13:05 step E-01 <x< 3.077E E+00 <y< 2.326E+01 EX_ 3 Contours -1.50E E E E E E E Contour interval= 2.50E (*10^1) Figure Change in vertical stresses contours in Pa due to loading (Case 7) 363

392 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 21-Dec-15 13:05 step E-01 <x< 4.089E E+01 <y< 2.388E+01 EX_ 4 Contours 0.00E E E E E E+05 Contour interval= 2.50E (*10^1) Figure Excess pore pressure contours in Pa due to loading (Case 7) 364

393 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 21-Dec-15 13:06 step E-01 <x< 4.078E E+01 <y< 2.402E+01 EX_ 5 Contours -1.50E E E E E E E+00 Contour interval= 2.50E (*10^1) Figure Change in effective vertical stresses contours in Pa due to loading (Case 7) 365

394 Figure Burger s viscoelastic model schematic (Itasca Consulting Group, 2011) Figure Zener s viscoelastic model schematic 366

395 Figure Stress relaxations from Test#12 on Kcc-710 and the FLAC result (Zener model) Figure Stress relaxations from Test#3 on Kcb-700 and the FLAC result (Zener model) 367

396 Figure Stress relaxations from Test#4 on Kcb-650 and the FLAC result (Zener model) Figure Stress relaxations from Test#1 on Kca-625l and the FLAC result (Zener model) 368

397 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 13-Apr-16 11:51 step Creep Time E E-01 <x< 4.086E E+00 <y< 3.726E+01 Y-displacement contours -8.00E E E E E+00 Contour interval= 2.00E (*10^1) Figure Vertical displacements contours in meter (Case 8) 369

398 JOB TITLE :. (*10^1) FLAC (Version 7.00) LEGEND 13-Apr-16 11:52 step Creep Time E E-01 <x< 4.362E E+00 <y< 3.999E+01 X-displacement contours 0.00E E E E E E E E-02 Contour interval= 1.00E (*10^1) Figure Horizontal displacements contours in meter (Case 8) 370

399 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 13-Apr-16 11:53 step Creep Time E E-01 <x< 4.548E E+00 <y< 4.029E+01 Displacement vectors max vector = 9.768E E (*10^1) Figure Displacements vectors contours in meter (Case 8) 371

400 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND Apr-16 11:54 step Creep Time E E-01 <x< 4.463E E+00 <y< 3.830E+01 XY-stress contours -1.00E E E E E E+04 Contour interval= 1.00E+04 Extrap. by averaging (*10^1) Figure Shear stresses contours in Pa (Case 8) 372

401 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 13-Apr-16 11:55 step Creep Time E E-01 <x< 4.073E E+00 <y< 3.750E+01 Pore pressure contours 0.00E E E E E E+05 Contour interval= 5.00E (*10^1) Figure Pore pressure contours in Pa due to loading (Case 8) 373

402 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 12-Apr-16 12:36 step Flow Time E E-01 <x< 4.086E E+00 <y< 3.726E+01 Y-displacement contours -8.00E E E E E+00 Contour interval= 2.00E (*10^1) Figure Vertical displacements contours in meter (Case 9) 374

403 JOB TITLE :. (*10^1) FLAC (Version 7.00) LEGEND 12-Apr-16 12:36 step Flow Time E E-01 <x< 4.365E E+00 <y< 4.003E+01 X-displacement contours 0.00E E E E E E E E-02 Contour interval= 5.00E (*10^1) Figure Horizontal displacements contours in meter (Case 9) 375

404 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND 12-Apr-16 12:37 step Flow Time E E-01 <x< 4.552E E+00 <y< 4.033E+01 Displacement vectors max vector = 9.821E E (*10^1) Figure Displacements vectors contours in meter (Case 9) 376

405 JOB TITLE :. FLAC (Version 7.00) (*10^1) LEGEND Apr-16 12:37 step Flow Time E E-01 <x< 4.463E E+00 <y< 3.830E+01 XY-stress contours 0.00E E E E E+04 Contour interval= 1.00E+04 Extrap. by averaging (*10^1) Figure Shear stresses contours in Pa (Case 9) 377

406 Figure Vertical displacements contours in meter (Case 10) 378

407 Figure Horizontal displacements contours in meter (Case 10) 379

408 Figure Displacements vectors contours in meter (Case 10) 380

409 Figure Shear stresses contours in Pa (Case 10) 381