APPLICATION OF SHANSEP AND HVORSLEV’S THEORIES TO EVALUATE THE SHEAR STRENGTH OF OVER-CONSOLIDATED CLAYS IN MINERALOGICAL FRAMEWORK ______

A Thesis

Presented to the

Faculty of

California State University, Fullerton ______

In Partially Fulfillment

of the Requirements for the Degree

Master of Science

in

Civil Engineering ______

By

Krishna Hari Pantha

Thesis Committee Approval:

Chair: Binod Tiwari, PhD. PE, Dept. of Civil and Environmental Engineering Co-Chair: Beena Ajmera, PhD, Dept. of Civil and Environmental Engineering Phoolendra Kumar Mishra, PhD, Dept. of Civil and Environmental Engineering

Fall, 2015

ABSTRACT

This paper presents the results of a study, whose aim was to determine the undrained shear strength at different over-consolidation ratios, which is a very important parameter to evaluate the stability of natural and man-made slopes in soft clay. The undrained shear strength of clays was determined using a laboratory test method utilizing the Direct Simple Shear (DSS) apparatus in the geotechnical engineering laboratory at

California State University, Fullerton. In this study, the change in undrained shear strength of soil with over-consolidation ratio in a mineralogical framework was studied.

Four different soil samples were prepared by mixing commercially available clay minerals such as kaolinite and montmorillonite with quartz at different proportions by their dry weight. These samples included 100% kaolinite, a mixture of 70% kaolinite with 30% quartz, a mixture of 50% kaolinite with 50% quartz and a mixture of 50% montmorillonite with 50% quartz. The plasticity characteristics of these samples were evaluated. Each of the first three samples had five different specimens representing five different over-consolidation ratios (2, 4, 8, 16 and 32). The fourth sample had only two specimens for two different over-consolidation ratios, i.e. 2 and 4. The applied consolidation stresses were 600 kPa, 300 kPa, 150 kPa, 75 kPa and 37.5 kPa for five different over-consolidation ratios of 2, 4, 8, 16 and 32, respectively. Using the direct simple shear device, the undrained shear strength of these samples were measured using a strain rate of 5%/hour.

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The pore pressures generated at different applied stresses was also back calculated from the change in total stresses. The pore water pressure continuously increased up to certain displacement and then after tended to remain constant. The results showed that it was inversely proportional to the over-consolidation ratio.

Using the results, the SHANSEP model and Hvorslev’s theory were utilized to check normalized shear strength, and true friction angle and true cohesion of each soil sample, respectively. The result showed that the shear strength depends up on the composition of clay minerals and stress history of the soil. The relationship of the normalized undrained shear strength ratio was directly proportional to the over- consolidation ratio of the soil. Similarly, the true friction angle of the soil depended up on the composition of the clay minerals, but not on the stress history. True friction angles of

19.28°, 20.63°, 21.06° and 35.24° were obtained for Sample Nos.1, 2, 3 and 4, respectively; whereas, the true cohesion of these sample were measured as 8.46°, 7.21°,

4.55° and 0.39° respectively.

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TABLE OF CONTENTS

ABSTRACT………………………………………………………………………...... ii

LIST OF TABLES……………………………………………………………………... vi

LIST OF FIGURES…………………………………………………………………..... viii

ACKNOWLEDGEMENTS………………………………………………………….... xiv

Chapter 1. INTRODUCTION……………………………………………………………... 1

2. LITERATURE REWIEW…………………………………………………….... 4

Background of Laboratory Shear Strength Testing Device……………………. 4 Shear Strength from DSS Test…………………………………………………. 8 Pore Water Pressure from DSS Test………………………………………….... 9 Effect of the Shearing Rate on the Undrained Shear Strength Properties of the Soft Saturated Clay……………………………………………………... 11 Effect of Moisture Content on Undrained Shear Strength…………………….. 12 Stress History and Normalized Soil Engineering Properties (SHANSEP)…..... 13 The Undrained Shear Strength of Over-consolidated clays…………………… 17 Hvorslev’s Theorem…………………………………………………………… 19

3. MATERIAL AND METHODOLOGY………………………………………... 22

Soils Used……………………………………………………………………… 22 Sample Preparation……………………………………………………………. 23 Preparation of Over-consolidated Samples……………………………………. 23 Direct Simple Shear Test Procedure…………………………………………... 27

4. TEST RESULTS AND DISCUSSION………………………………………... 34

Stress-Deformation Characteristics……………………………………………. 34 Pore Pressure-deformation Characteristics……………………………………. 34 Stress Path……………………………………………………………………... 36 Stress Ratio…………………………………………………………………….. 36 Shear Envelopes……………………………………………………………….. 39 Normalized Shear Strength…………………………………………………….. 41

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Equivalent Consolidation Pressure…………………………………………….. 42 True Cohesion and True Friction Angle……………………………………….. 46 Relationship between True Friction Angle, True Cohesion with Liquid Limit and Plasticity Index……………………………………………………… 50

5. CONCLUSION………………………………………………………………… 53

REFERENCES…………………………………………………………………………. 55

APPENDICES…………………………………………………………………………. 57

A. SAMPLE NO.1 (100% KAOLINITE) CURVES)…………………………….. 57 B. SAMPLE NO.2 (70% KAOLINITE WITH 30% QUARTZ) CURVES………. 68 C. SAMPLE NO.3 (50% KAOLINITE WITH 50% QUARTZ) CURVES……..... 78 D. SAMPLE NO.4 (50% MONTMORILONITE 50% QUARTZ) CURVES……. 87 E. RELATIONSHIP OF L.L., P.I. WITH TRUE FRICTION ANGLE AND TRUE COHESION…………………………………………………………….. 96

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LIST OF TABLES

Table Page

2-1 Undrained shear strength ratio ( Cu / 'vc ) and OCR relationship …………….. 18

3-1 Proportions of soil by their dry weight (%) and physical properties of the tested samples…………………………………………………………… 22

3-2 Sample details…………………………………………………………………... 24

3-3 Loading steps relative to OCR………………………………………………….. 27

4-1 Total and Effective Cohesion and Friction Angle of There Samples…………... 39

4-2 Normalized Shear Strength and OCR (Sample No.1)………………………….. 41

4-3 Effective normal stress and void ratio (Sample No.1)………………………….. 42

4-4 Effective Stress and Equivalent Consolidation Pressure……………………….. 43

4-5 Calculation of σ'3, q and σ'e (Sample No.1)…………………………………….. 45

4-6 True Cohesion and Friction Angle for Sample Nos. 1, 2, 3 and 4 ……………... 49

A-1 Relation between Effective Stress and Void Ratio……………………………... 65

A-2 Relation between q/σ'e and σ'3/σ'e………………………………………………. 66

A-3 Relation between Normalized Shear Strength and OCR……………………….. 66

A-4 L. L., P. I. and Normalized Shear Strength……………………………………... 67

B-1 Relation between Effective Stress and Void Ratio……………………………... 76

B-2 Relation between q/σ'e and σ'3/σ'e………………………………………………. 76

B-3 Relation between Normalized Shear Strength and OCR……………………….. 77

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B-4 L. L., P. I. and Normalized Shear Strength…………………………………...... 77

C-1 Relation between Effective Stress and Void Ratio…………………………….. 85

C-2 Relation between q/σ'e and σ'3/σ'e……………………………………………… 86

C-3 Relation between Normalized Shear Strength and OCR………………………. 86

C-4 L. L., P. I. and Normalized Shear Strength…………………………………….. 86

D-1 Relation between Normalized Shear Strength and OCR………………………. 91

D-2: Relation between Effective Stress and Void Ratio (Source: Tiwari and Ajmera, 2011) ………………………………………….... 92

D-3: Relation between q/σ'e and σ'3/σ'e ……………………………………………… 95

E-1: Relation between LL and PI with ɸe and ɸc ……………………………………. 98

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LIST OF FIGURES

Figure Page

2-1 Double Direct Shear as Performed by Alexander Collin in 1846 (Sower, 1963).. 4

2-2 SGI Simple Shear Device 1936 (Kjellam, 1951)……………………………….... 5

2-3 NGI DSS device (DeGroot et al, 1992)………………………………………….. 6

2-4 GeoComp Universal Shear Device (Marr, 2003)……………………………….... 7

2-5 DSS Device Set-up in Geotechnical Engineering Lab at CSUF………………… 7

2-6 Standard DSS Test Component (ASTM 2000)………………………………….. 8

2-7 Normalized undrained shear strengths for TC, DSS, and TE test results as a function of Plasticity Index (Ladd and DeGroot, 2003)………………………….. 9

2-8 Comparison of pore pressure from constant volume and undrained DSS test results (Dyvik et al. 1988)……………………………………………………….. 10

2-9 Variation of Normalized Undrained Shear strength with Axial Strain Rate and Over-consolidation Ratio (Source: Sheahan et al. (1996)……………………….. 11

2-10 Variation of Undrained Shear Strength with Moisture Content (Source: Hong et al. (2006)…………………………………………………….. 12

2-11 Variation of Normalized CKoUDSS Strength Parameters with OCRs for 5 Clays (Ladd & Foott 1974)……………………………………………………... 14

2-12 Example of Normalized Behavior Using Idealizes Triaxial Compression Test (After Ladd and Foote, 1974)…………………………………………………… 15

2-13 Normalized CKoU Direct-Simple Shear Test Data for Overconsolidated Boston Clay (After Ladd and Foote, 1974)……………………………………... 16

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2-14 Undrained shear strength ratio Cu/σ'vc versus OCR ( Strozyk and Tankiewicz {2014})...... 18

2-15 Effective Stress versus Void Ratio (Hvorslev, 1937) ………………………… 20

2-16 Effective Stress versus Shear Stress (Hvorslev, 1937) ……………………….. 21

3-1 Placement of the Batch mixture Soil into the Oedometer Ring………………... 24

3-2 Sample Set-up for Consolidation Test………………………………………….. 25

3-3 Consolidometer apparatus used in this study…………………………………… 25

3-4 Displacement versus Time Curves……………………………………………... 26

3-5 Apparatus Required to Assemble the Sample into the Shear Box……………… 28

3-6 Simple Shear Apparatus Used in This Study…………………………………… 28

3-7 Placement of Consolidated Sample into the Rubber Membrane……………….. 29

3-8 Sample inside the Rubber Membrane and Placement of Bottom O-Rings…….. 30

3-9 Placement of Teflon® Ring……………………………………………………… 30

3-10 Placement of O-Rings Arround the Top Platen………………………………… 31

3-11 Placement of Assembled Sample into the Shear Box (Top View)……………… 32

3-12 Placement of Assembled Sample into the Shear Box Filled With Water………. 32

3-13 The Complete Simple Shear Device Assembly in the Lab…………………….. 33

4-1 Typical Shear Stress versus Shear Strain Curves (Simple No.1) …………….... 35

4-2 Typical Pore Pressure versus Shear Strain Curves (Sample No.1)…………….. 35

4-3. Typical Shear Stress Paths (Sample No.1)…………………………………….... 36

4-4 Typical Total Stress Ratio versus Shear Strain Curves (Sample No.1)………… 37

4-5 Typical Effective Stress Ratio versus Shear Strain Curves (Sample No.1)……. 37

4-6 Typical Shear Envelopes for Sample No.1 ……………………………………. 38

4-7 Typical Normalized Shear Strength versus OCR Ratio (Simple No.1) ……….. 40

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4-8 Comparison for four samples for Normalized shear strength versus OCR……… 40

4-9 Typical Consolidation versus Void Ratio Curve (Sample No.1)………………. 43

4-10 q / 'e versus  '3 / 'e (Sample No.1)…………………………………………… 46

4-11 versus (Sample No.1, 2 and 3)…………………………………… 47

4-12 σ'3/σ'e versus τ/σ'e (Sample No.1)………………………………………………. 47

4-13 σ'3/σ'e versus τ/σ'e (Sample No.1, 2 and 3)……………………………………... 48

4-14 OCR versus τ/σ'e (Sample No.1)……………………………………………… 48

4-15 OCR versus τ/σ'e (Sample No.1, 2 and 3)…………………………………….. 49

4-16 Liquid Limit versus True Friction Angle ……………………………………… 51

4-17 Liquid Limit versus Base Friction Angle………………………………………. 51

4-18 Plasticity Index versus True Friction Angle………………………………….... 52

4-19 Plasticity Index versus Base Friction Angle…………………………………... 52

A-1 Shear Stress versus Shear Strain Curves………………………………………. 57

A-2 Pore Pressure versus Shear Strain Curves……………………………………… 57

A-3 Shear Stress versus Normal Stress Curves……………………………………… 58

A-4 Total Stress Ratio versus Shear Strain Curves…………………………………. 58

A-5 Effective Stress Ratio versus Shear Strain Curves……………………………… 59

A-6 Normalized Pore Pressure versus Shear Strain Curves…………………………. 59

A-7 Total Shear Envelope for OCR 1, 2, 4, 8, 16 and 32…………………………… 60

A-8 Effective Shear Envelope for OCR 1, 2, 4, 8, 16 and 32………………………. 60

A-9 Comparison of Total and Effective Shear Envelope…………………………… 60

A-10 Trend for OCR and Normalized Total Shear Strength………………………… 61

A-11 Trend for OCR and Normalized Effective Shear Strength…………………….. 61

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A-12 Comparison of Trends for OCR and Normalized T. and E. Shear Strength…… 62

A-13 Effective Normal Stress versus Void Ratio curves …………………………… 62

A-14 q/σ'e versus σ'3/σ'e ……………………………………………………………… 63

A-15 τ/σ'e versus σ'3/σ'e……………………………………………………………… 63

A-16 q/σ'e versus σ'3/σ'e (Comparison for Three Sample)…………………………… 64

A-17 τ/σ'e versus σ'3/σ'e (Comparison of Three Samples)…………………………… 64

A-18 τ/σ'e versus OCR………………………………………………………………. 65

B-1 Shear Stress versus Shear Strain Curves………………………………………. 68

B-2 Pore Water Pressure versus Shear Strain Curves……………………………… 68

B-3 Shear Stress versus Normal Stress Curves…………………………………….. 69

B-4 Total Stress Ratio versus Shear Strain Curves………………………………… 69

B-5 Effective Stress Ratio versus Shear Strain Curves…………………………….. 70

B-6 Normalized Pore Pressure versus Shear Strain Curves………………………… 70

B-7 Total Shear Envelope for OCR 1, 2, 4, 8, 16 and 32…………………………… 71

B-8 Effective Shear Envelope for OCR 1, 2, 4, 8, 16 and 32……………………… 71

B-9 Comparison of Total and Effective Shear Envelope………………………….. 72

B-10 Trend for OCR and Normalized Total Shear Strength………………………… 72

B-11 Trend for OCR and Normalized Effective Shear Strength……………………. 73

B-12 Comparison of Trends for OCR and Normalized Total and Effective Shear Strength………………………………………………………………………. 73

B-13 Effective Normal Stress versus Void Ratio curves ……………………………. 74

B-14 q/σ'e versus σ'3/σ'e……………………………………………………………… 74

B-15 σ'3/σ'e versus τ/σ'e……………………………………………………………… 75

B-16 OCR versus τ/σ'e……………………………………………………………….. 75

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C-1 Shear Stress versus Shear Strain Curves………………………………………. 78

C-2 Pore Water Pressure versus Shear Strain Curves………………………………. 78

C-3 Shear Stress versus Normal Stress Curves…………………………………….. 79

C-4 Total Stress Ratio versus Shear Strain Curves………………………………… 79

C-5 Effective Stress Ratio versus Shear Strain Curves……………………………. 80

C-6 Normalized Pore Pressure versus Shear Strain Curves……………………….. 80

C-7 Total Shear Envelope for OCR 1, 2, 4, 8, 16 and 32………………………….. 81

C-8 Effective Shear Envelope for OCR 1, 2, 4, 8, 16 and 32………………………. 81

C-9 Comparison of Total and Effective Shear Envelope…………………………… 81

C-10 Trend for OCR and Normalized Total Shear Strength………………………… 82

C-11 Trend for OCR and Normalized Effective Shear Strength……………………. 82

C-12 Comparison of Trends for OCR and Normalized Total and Effective Shear Strength………………………………………………………………………. 83

C-13 Effective Normal Stress versus Void Ratio curves……………………………. 83

C-14 σ'3/σ'e versus q/σ'e ……………………………………………………………… 84

C-15 σ'3/σ'e versus τ/σ'e………………………………………………………………. 84

C-16 OCR versus τ/σ'e……………………………………………………………….. 85

D-1 Shear Stress versus Shear Strain Curves………………………………………. 87

D-2 Pore Water Pressure versus Shear Strain Curves……………………………… 87

D-3 Shear Stress versus Normal Stress Curves…………………………………….. 88

D-4 Total Stress Ratio versus Shear Strain Curves………………………………… 88

D-5 Effective Stress Ratio versus Shear Strain Curves……………………………. 89

D-6 Total Shear Envelope for OCR 1, 2, 4, 8, 16 and 32………………………….. 89

D-7 Trend for OCR and Normalized Total Shear Strength…………………………. 90

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D-8 Trend for OCR and Normalized Effective Shear Strength…………………….. 90

D-9 Comparison of Trends for OCR and Normalized Total and Effective Shear Strength………………………………………………………………………... 91

D-10 Effective Normal Stress versus Void Ratio Curves …………………………… 92

D-11 σ'3/σ'e versus q/σ'e ……………………………………………………………… 93

D-12 σ'3/σ'e versus τ/σ'e ……………………………………………………………… 93

D-13 OCR versus τ/σ'e ………………………………………………………………. 94

D-14: OCR versus Normalized Effective Shear Strength Curves ……………………. 94

E-1 Liquid Limit versus True Friction Angle……………………………………….. 96

E-2 Liquid Limit versus Base Friction Angle……………………………………….. 96

E-3 Plasticity Index versus True Friction Angle……………………………………. 97

E-4 Plasticity Index versus Base Friction Angle……………………………………. 97

E-5 Total Stress Ratio versus OCR of Four Samples ………………………………. 98

E-6 Effective Stress Ratio versus OCR of Four Samples…………………………… 99

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ACKNOWLEDGEMENTS

I am very grateful to my thesis supervisor, Dr. Binod Tiwari, Professor of Civil

Engineering at California State University, Fullerton (CSUF), whose encouragement, guidance and support from beginning to the end has enabled me to develop understanding of the subject.

I am also very thankful to Dr. Beena Ajmera, Assistant Professor of Civil

Engineering at CSUF and co-advisor of my thesis, for her support in each and every stage of the lab test procedures and literatures review as well as the data analysis and preparation of this thesis.

I would also like to thank my thesis committee member Dr. Phoolendra Kumar

Mishra, Assistant Professor of Civil Engineering at CSUF, for his help in reviewing the thesis and valuable suggestions.

I would like to offer my thanks to Dr. Kaixi Xue, visiting faculty at CSUF, for his valuable suggestions and support. I also like to thank students from BSMP program,

Jhessyca, Arthur and Marsal for conducting some of the lab tests.

I would like to thank my seniors and colleagues Sneha Upadhyaya, Janak Koirala,

DucTran, Hari Woli, and Prakash Khanal, as well as the lab technician Hector Zazueta for their assistance and co-operation during the soil testing phase of this study.

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I would like to thank California State University, Fullerton for providing the laboratory and funding the materials used in this study via IRA Intramural Grant No.

3361.

Finally, I would like to thank my wife Laxmi Lata, daughter Kritika, and son

Kripal, for their continuous love and support.

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1

CHAPTER 1

INTRODUCTION

In geotechnical engineering practice, the two most important issues that need to be considered are whether the construction will cause deformation of the soil or instability due to shear failure. Therefore, the knowledge about the shear stress-strain behavior, deformation and shear strength of the soil is essential to ensure that the structure is safe against shear failure in the soil that supports it and that the structure does not undergo excessive settlement.

The shear strength of a soil is most important for the analysis of foundations, earthwork and slope stability problems. In general, cohesive soils like clays have very low shear strength; and as a result, more shear-induced failures occur in these materials.

The shear strength of a soil depends up on various factors such as soil type and structure, water content, stress history and stress path during the loading. The stress history (over-consolidation ratio and consolidation condition) and stress path have large effects on the undrained shear strength of a soil, which are described by SHANSEP

(Ladd, 1974). To investigate the influence of the over-consolidation ratio on undrained shear strength properties by using the SHANSEP method, we performed direct simple shear (DSS) tests on four different soil samples with five different OCRs, as described before. For this, a cylindrical soil specimen was first consolidated at the required

2 pressures in an oedometer ring. After this, the consolidated sample was set up into the shear box of the DSS device for undrained shear test.

In the second part of this thesis, the fundamental properties (true cohesion and true friction angle) of the soil were calculated, which were used to evaluate the behavior of clays. Hvorslev (1937) conducted a large numbers of direct shear tests on soils and proved that the true cohesion and true friction angle are the function of water content, but are independent of the OCR. In this study, the true cohesion and true friction angle of the samples were determined by following Hvorslev’s theorem. The relationship between the true cohesion and true friction angle with the liquid limit and plasticity index were also studied in detail.

The main objectives of this study are: (i) to determine the undrained shear strength of clays at different over-consolidation ratios using the direct simple shear apparatus, (ii) to develop both total and effective stress shear envelops at different over- consolidation ratios, (iii) to apply the SHANSEP model to determine the normalized shear strength ratios for over-consolidated soil and (iv) to evaluate the true friction angle and true cohesion of the clays using Hvorslev’s theory.

Chapter 2 will consist of a literature review, in which the theory behind the undrained shear strength of soil at different OCR is explained. Historical test results and the application of Hvorslev’s theory and the SANSEP model will be discussed.

Chapter 3 discusses in detail the properties of the soil samples used, the testing methodology performed in the laboratory including the equipment used, sample preparation and the data analysis.

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Chapter 4 presents the results of all of the DSS tests performed on the different clays at various over-consolidation ratios and a discussion of the results and their importance to geotechnical engineering.

Chapter 5 summarizes the test results and recommendations made based on this study.

All of the graphs and tables related to the soil tests are presented in the

Appendices.

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CHAPTER 2

LITERATURE REVIEW

Background of Laboratory Shear Strength Testing Device

The first shear test was performed by Collin (1846). In this test, the sample was loaded transversely in a double direct shear (simultaneous shear across two parallel planes) until failure. The soil sample for the shearing test was contained within a shearing box as shown in Figure 2-1. Leygue (1885) was the first person to use the shear box, similar to today’s shear box, to perform the soil shear test (Sowers 1963).

Figure 2-1: Double Direct Shear as Performed by Alexander Collin that was performed in 1846 (Sower, 1963), (Source: McGuire, 2011).

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The first simple shear device able to uniformly deform a soil specimen in pure shear was built by Swedish Geotechnical Institute (SGI) in 1936. This device confined the soil specimens using the rubber membrane and aluminum rings that were packed tightly together and the sample was consolidated using lead weights (Kjellam, 1951). A typical picture of the soil sample using the SGI simple shear device is presented in Figure 2-2

(Kjellam, 1951).

Figure 2-2: SGI Simple Shear Device 1936 from Kjellam (1951) (Source: McGuire, 2011).

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In 1960’s, the Norwegian Geotechnical Institute (NGI) developed a device that was able to strain in simple shear after vertical loading (DeGroot et al., 1992), which is shown in Figure 2-3.

Figure 2-3: NGI DSS device (DeGroot et al., 1992).

In 1990’s, several companies in the United States of America and United

Kingdom developed an automated direct simple shear, triaxial, consolidation and cyclic shear equipment that made data acquisition and control systems relatively inexpensive.

One of the fully automated direct simple shear device was manufactured by

GeoComp Corporation, Inc., which is able to run monotonic and cyclic direct simple shear tests under undrained conditions. This device is presented in Figure 2-4. The direct simple shear (DSS) device used in this study is presented in Figure 2-5.

7

Figure 2-4: GeoComp Universal Shear Device (Marr, 2003).

Figure 2-5: DSS Device Set-up in Geotechnical Engineering Lab of CSUF.

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Shear Strength from DSS Test

The term ‘simple shear’ relates to the state of strain in a soil sample. According to

DeGroot (1992), it is “a plane strain state where under constant volume condition an element deforms only in one direction. Through deformation the height remains constant, requiring the sides to elongate.”

The DSS test has been found to be a good representation of the shear strength along a roughly horizontal failure plane, which is applicable to many loading conditions in the actual construction field (e.g. slope stability, bearing capacity, etc.). In addition, the test results show that the values of the undrained shear strength from DSS are between the values from the triaxial compression and extension tests (Ladd and DeGroot, 2003) as

shown in Figure 2-7 below, where, su / 'vc is the undrained shear strength normalized to the vertical effective consolidation stress and PI is the plasticity index of the soil.

Figure 2-6: Standard DSS Test Component (Source: ASTM, 2000; and McGuire, 2011).

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Figure 2-7: Normalized undrained shear strengths for TC, DSS, and TE test results as a function of the plasticity index (Ladd and DeGroot, 2003).

Pore Water Pressure from DSS Test

In the DSS test, the excess pore pressure during undrained shear is calculated from the change in total stress required to maintain constant volume (i.e., height) conditions. If the total stress decreases during shear to maintain constant volume, then that change in vertical stress is assumed to be equal to positive pore pressure developed within the soil sample. This was proved by Dyvik et al. (1988) through testing of four saturated normally consolidated Drammen clay soils, as shown in Figure 2-8.

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Figure 2-8: Comparison of pore pressure from constant volume and undrained DSS test results (Source: Dyvik et al., 1988; and Ajmera, 2012).

The shear strength of a soil specimen depends on the type of the soil, consolidation stress, time of consolidation, rate of strain, and prior stress history of the soil, among other factors. The effect of these parameters is discussed later.

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Effect of the Shearing Rate on the Undrained Shear Strength Properties of the Soft Saturated Clay Sheahan et al. (1996) evaluated the effects of the shearing rate on shear strength.

They conducted twenty-five consolidated undrained triaxial compression tests on re- sedimented Boston clay. The samples were consolidated to over-consolidation ratios of 1,

2, 4 and 8 and shearing rates of 0.05%/hr, 0.5%/hr, 5%/hr and 50%/hr were applied.

Sheahan et al. (1996) found that the undrained shear strength is less dependent on the shearing rates as the applied rate decreases. They found, however, that the normalized undrained shear strength becomes higher for the lower over-consolidation ratio for a given axial strain rate (Figure 2-9).

Figure 2-9: Variation of Normalized Undrained Shear Strength with Axial Strain Rate and Over-consolidation Ratio (Source: Sheahan et al., 1996; and Ajmera, 2012).

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Effect of Moisture Content on Undrained Shear Strength

Hong et al. (2006) conducted consolidated undrained triaxial shear tests to investigate the undrained shear strength behavior of remolded and undisturbed Ariake clay samples. They applied confining pressures of 50 kPa, 100 kPa, 150 kPa and 200 kPa for the tests and found that the shear strengths of undisturbed samples were lower than the remolded shear strength. From the test results, Hong et al. (2006) found a reduction in the strength with an increase in the water content. The relationship was identical for both remolded and undisturbed samples, as presented in Figure 2-10.

Figure 2-10: Variation of Undrained Shear Strength with Moisture Content (Source: Hong et al., 2006).

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Stress History and Normalized Soil Engineering Properties (SHANSEP)

The complexity of the undrained shear behavior of soft clay is the enthusiasm for developing a new design procedure for the stability of soft clays. The current design practice with regard to stability of soft clay is still broadly dominated by the ɸ = 0 method presented by Skempton (1948). Normally, this method combined with local experiences and a conservative factor of safety has produced safe designs. However, latest research using a commercially available DSS and triaxial testing system with an automated data collection system has improved the model accuracy of the undrained shear strength behavior of clays. This improved model benefits from a theoretical

framework to correlate the pre-consolidation stress ( 'vc ), over-consolidation ratio (OCR)

and the undrained shear strength (Su ) . In this new theoretical framework, Ladd and Foott

(1974) developed an approach called the ‘Stress History and Normalized Soil

Engineering Properties’ (SHANSEP) for estimating the undrained shear strength based on the stress history of the soil. The basic theory of SHANSEP is that the undrained shear strength of soil can be normalized by the effective consolidation stress and is a function of the OCR.

Using the DSS test to perform undrained test at varying over consolidation ratios allows for the construction of the curve found in Figure 2-11 and the curve can be

expressed as shown in Equation (1), where, Su is the undrained shear strength,  'vc is the

vertical effective consolidation stress,  'p is the pre-consolidation stress, and OCR is the over-consolidation ratio, and m is the slope of SHANSEP curve.

m Su /'vc  Su /' p OCR ...... (1)

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Figure 2-11: Variation of normalized CKoUDSS strength parameters with OCRs for five clays (Source: McGuire, 2011; and Ladd and Foott, 1974).

Ladd and Foott (1974) stated that “SHANSEP is strictly applicable only to mechanically over-consolidated and truly normally consolidated soils exhibiting normalized behavior.” They tested sixteen normally consolidated clays and nine normally

consolidated silt and organic soil and found the average strength ratios ( Su / 'vc ) of

0.225 and 0.26, respectively. Figures 2-12 shows how the SHANSEP concept works.

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Figure 2-12: Example of Normalized Behavior Using Idealizes Triaxial Compression Test (Source: Ladd and Foott, 1974).

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Figure 2-13: Normalized CKoU Direct-Simple Shear Test Data for Overconsolidated Boston Blue Clay (Source: Ladd and Foott, 1974).

17

The Undrained Shear Strength of Over-consolidated clays

The mechanical properties of the clayey soils, especially shear strength, is one of the most important properties for geotechnical engineering practice. Strozyk and

Tankiewicz (2014) presented the results of laboratory tests (confined and unconfined triaxial tests) of the undrained shear strength of clayey and silty clayey soil specimen taken from the depths of 100-300 meters below the ground level. The in-situ effective vertical stress at the sampling point varied from 1.98 MPa to 5.31 MPa. The undrained

shear strength ( Cu ) was established under undrained conditions from unconfined and confined triaxial tests at different over-consolidation ratios (OCR) for each sample. The

OCR values were estimated as 3 to 28 for all tested samples. The normalized shear

strength ( Cu / 'vc ) versus OCR is presented in Figure 2-14.

The undrained shear strength ratio ( Cu / 'vc ) was obtained by following the normalized procedure described earlier by others researchers. It is clear that, in the case of soils taken from the depth, tested in the triaxial apparatus, the power law function (Equation (2)) of

OCR (SHANSEP equation) described the relationship well. In Equation (2), Cu / 'vc is

the undrained shear strength ratio, Cu is the undrained shear strength,  'vc is the effective vertical consolidation stress, m is the scaling component, S is the undrained strength ratio of the normally consolidated soil and OCR is the over-consolidation ratio.

m Cu /'vc  S(OCR) ...... ……………………………………….. (2)

18

Table 2-1: Undrained shear strength ratio (Cu / 'vc ) and OCR relationship (Adopted from Strozk and Tankiewicz, 2014)

Sample S m R2

TX7 0.4426 0.1439 0.143 TX2 0.4807 0.2566 0.945 TX27 0.2582 0.1686 0.130 TX14 0.3512 0.6796 0.661 TX12 0.6831 0.3528 0.580 TX1 0.8024 0.1494 0.976 TX22 0.5009 0.1181 0.958 TX18 0.7061 0.1973 0.944

Figure 2-14: Undrained shear strength ratio Cu / 'vc versus OCR (Source: Strozyk and Tankiewicz, 2014).

19

Strozyk and Tankiewicz (2014) found that the SHANSEP equation can be used for natural, intact, over-consolidated soil, although the values of parameters S and m of highly over-consolidated soils differ from those previously reported by Ladd and Foott

(1974), who stated that “SHANSEP is strictly applicable only to mechanically over- consolidated and truly normally consolidated soil exhibiting the normalized behavior.”

Hvorslev’s Theorem

Hvorslev’s theory explains how the true friction angle and true cohesion can be used to determine the behavior of clay. Soils from the same origin will have common properties. Hvorslev’s theorem stated that even normally consolidated soil has true cohesion. The true cohesion of the soil should be constant for the same void ratio.

Hvorslev (1937) carried out a large number of direct shear tests. He considered the water pressure, which has a great influence on the soil strength. Hence, Hvorslev extended Coulomb’s equation (S  C  tan) considering the water content, as presented in Equation (3), where,  is the effective normal stress in the failure plane, c' is the ‘true cohesion’ and  is the ‘true internal angle of friction.’ The true cohesion and true friction angle were found to be dependent on water content and this dependence can

be expressed by the equivalent consolidation pressure ( e ).

S  C    tan ……………………………………………...…… (3)

According to Hvorslev (1937), e and c are the fundamental properties of the soil that are the same for each type of soil and are irrespective of the over-consolidation

ratio (OCR). e is the true friction angle and c is base friction angle (or Hvorslev’s constant). Hvorslev explained that the cohesion is the result of a physicochemical bond

20

force and termed as the true cohesion ( Ce ). He, later, developed the equation for the

strength parameters as shown in Equation (4), where,  'e is the equivalent pre-

consolidation pressure for the same void ratio and e is the void ratio.  'e can be calculated from the consolidation curve as shown in Figure 2-15 below.

S  Ce  'tane

Ce  f (e)   'e tanc

S   'e tanc  'tane …………………………………………….. (4)

Figure 2-15: Virgin Consolidation and Swelling Curves; the Equivalent Pressure for Over-consolidated Soil is also Presented in the Figure (Hvorlev, 1937).

21

From the Equation (4), even a normally consolidated soil will have some value ofCe . For

the same void ratio, Ce should be the same, regardless of the OCR of the soil. Hence, if

e , c and consolidation curves are known, it is possible to estimate the conventional effective stress parameters. The graphical Procedure for Hvorslev’s theory is given below:

1. Estimate the major principal stress at failure,  '1 f

2. Calculate  'e from consolidation curve

3. Calculate Ce using Ce   'etanc

4. Draw an envelope with e and Ce , as shown in Figure 2-16

5. Draw the Mohr’s Circle from  '1 f until it touches the envelope

6. Repeat this for other points.

The above mentioned process is used for the data analysis in this study.

Figure 2-16: Effective Stress versus Shear Stress (Hvorslev, 1973)

22

CHAPTER 3

MATERIALS AND METHODOLOGY

Soils Used

Three different commercially available soil minerals, kaolinite, quartz, and montmorillonite, were mixed at different proportions based on their dry weight, as presented in Table 3-1. In addition to the normally consolidated samples, there were five different over-consolidation ratios (i.e. 2, 4, 8, 16, and 32) tested in case of Samples 1, 2, and 3; however, only two over-consolidation ratios (OCR of 2 and 4) were tested for sample 4.

Table 3-1: Proportions of soil by their dry weight and physical properties of the tested samples (Source: Ajmera, 2012)

Sample Kaolinite Quartz Montmorillonite L.L. P.I. OCRs Tested

No. (%) (%) (%) (%) (%)

1 100 0 0 70 25 1, 2, 4, 8, 16 and 32

2 70 30 0 50 18 1, 2, 4, 8, 16 and 32

3 50 50 0 34 9 1, 2, 4, 8, 16 and 32

4 0 50 50 209 161 1, 2 and 4

23

Sample Preparation

The following procedure was used to prepare the samples:

1. The samples were prepared by mixing the dry powdered minerals at the required

proportions based on their dry weight.

2. Sufficient deionized water was added to the dry mixture to achieve an initial

liquidity index of 1.

3. The slurried sample was stored in an air tight container and allowed to hydrate for

a period of at least 24 hours prior to start of any test.

Preparation of Over-consolidated Samples

The following step-by-step process was followed for preparation of over- consolidated samples at different OCRs:

1. A portion of the hydrated slurried batch mixed sample was placed in an

oedometer ring. The specimen was, first, subjected to a consolidation pressure

of 37.5 kPa and a real-time logarithm of time versus vertical deformation

curve was monitored to determine the completion of primary consolidation for

the sample at this stress.

 Details of the tested samples are shown in Table 3-2.

 The step by step process of the sample preparation are presented in

Figures 3-1 to 3-3.

 The example of the graph of displacement versus time is presented in

Figure 3-4. This graph has to be monitored to check whether the

primary consolidation is completed. If the curves are relatively flat, the

primary consolidation is considered to be completed.

24

Table 3-2: Sample details

Weight of Height of Diameter of Volume of Density of Sample sample sample sample sample sample No. (gm) (mm) (mm) (cm3) (gm/cm3)

1 122.41 25.4 63.5 80.440 1.522 2 129.37 25.4 63.5 80.440 1.608 3 137.76 25.4 63.5 80.440 1.713 4 97.4 25.4 63.5 80.440 1.211

Soil mixture inside the oedometer ringfilter paper

Figure 3-1: Placement of the Batch Mixed Soil into the Oedometer Ring.

25

Figure 3-2: Sample Set-up for Consolidation Test Used in This Study.

Figure 3-3: Consolidometer Apparatus Used in This Study.

26

Figure 3-4: Displacement versus Time Graph.

2. After completion of primary consolidation for the first step, the consolidation

stress was doubled and the process was repeated until a consolidation pressure

of 1200 kPa was achieved.

3. At the end of the primary consolidation at the maximum consolidation

pressure of 1200 kPa, the consolidation stress was reduced in several steps, in

each step applying a consolidation stress half of the previous step, until the

required over-consolidation ratios (i.e. 2, 4, 8, 16, and 32) were achieved. The

required steps for the consolidation pressure as per over-consolidation ratios

are presented in a tabular form in Table 3-3 below.

27

Table 3-3: Loading steps relative to OCR

Consolidation Pressure (kPa) Loading steps OCR=2 OCR=4 OCR=8 OCR=16 OCR=32

1 37.5 37.5 37.5 37.5 37.5 2 75 75 75 75 75 3 150 150 150 150 150 4 300 300 300 300 300 5 600 600 600 600 600 6 1200 1200 1200 1200 1200 7 600 600 600 600 600 8 - 300 300 300 300 9 - - 150 150 150 10 - - - 75 75 11 - - - - 37.5

4. When the specimen of desired over-consolidation ratio was obtained, the

specimen was carefully extruded from the oedometer ring.

5. The height and weight of the specimen was recorded and the specimen was

transferred to the direct simple shear apparatus to obtain its drained and

undrained shear strength properties.

Direct Simple Shear Test Procedure

The simple shear apparatus used in this study is a NGI-type device that was manufactured by GeoComp, Inc. The apparatus uses micro-stepper motors to apply both the vertical and horizontal loads to the soil specimen. The vertical and horizontal load capacities are 4448 N (1000 lbs.). The device is capable of 12.5 mm (0.5 in), resolved to

28

0.0013 mm, of horizontal and vertical displacements. Figure 3-5 shows a picture of the apparatus used and Figure 3-6 is the entire system of DSS test used in this study. The following step-by-step process was followed to complete the direct simple shear test:

Membrane Bottom platen Teflon ring Stretcher

strec

O-rings Filter paper Membrane

Top platen

Vacuum grease

Figure 3-5: Apparatus and Tools Required to Assemble the Sample into the Direct Simple Shear Box.

Figure 3-6: Simple Shear Apparatus used in this study.

29

The following step-by-step procedure was followed for the direct simple shear test:

1. The top and bottom platen of the shear box were coated with vacuum grease.

2. A filter paper was placed on the top of the lower platen.

3. The specimen obtained from the oedometer was carefully placed in a rubber

membrane, stretched around a membrane stretcher.

4. A filter paper was placed on the top of the soil specimen and then top platen

was placed on the soil specimen as shown in Figures 3-7 and 3-8.

5. The rubber membrane and specimen were, then, confined by a stack of

Teflon®-coated rings. There were total thirty-one rings, each with a thickness

of 0.94 mm, as shown in Figure 3-9.

6. The rubber membrane was secured to the top platen using the O-rings, as

shown in Figure 3-10.

Figure 3-7: Placement of Consolidated Sample into the Rubber Membrane.

30

Figure 3-8: Sample inside the Rubber Membrane and Placement of Bottom O-Rings.

Figure 3-9: Placement of Teflon® Ring.

31

Figure 3-10: Placement of O-Rings Arround the Top Platen.

7. The entire assembly was transferred to the fully automated constant volume

simple shear device (Shear Trac-II) and the shear box was filled with

deionized water as showed in Figures 3-11 and 3-12. The complete

simple shear device assembly is presented below in Figure 3-13.

8. The vertical shear pins were removed before the shearing phase started.

9. Using the computer unit and program associated to a direct simple shear

apparatus, the specimen was subjected to the final consolidation stress that

was applied in the oedometer and the real-time consolidation curve was

monitored to ensure negligible vertical deformations were measured.

32

Figure 3-11: Placement of Assembled Sample into the Shear Box (Top View).

Figure 3-12: Placement of Assembled Sample into the Shear Box, Filled with Water.

33

Figure 3-13: Complete Simple Shear Device Assembly Set Up.

10. As specified by the ASTM Standard Test Method for “Consolidated Undrained

Simple Shear Testing of Cohesive Soils” (ASTM D6528-07), the specimen was

subjected to undrained, constant volume, strain-controlled shearing at a rate of

5% per hour. The shearing phase was continued until the peak shear strength was

measured.

11. If the peak shear strength was not obtained within 25% shear strain, the test was

terminated at 25% shear strain.

12. After completion of the shearing phase, the soil specimen was removed from the

simple shear apparatus and placed into the oven for at least 24 hours to

determine its dry weight.

34

CHAPTER 4

TEST RESULTS AND DISCUSSION

Stress-Strain Characteristics

A typical shear stress versus shear strain curve for the five different OCRs (2, 4,

8, 16 and 32) for Sample No. 1 is presented in Figure 4-1. Similar figures for the remaining samples are presented in Appendix A through Appendix D for Sample No. 1 to

4, respectively. From the figure, it was found that the shear stress is inversely proportional to the OCR.

Pore Pressure-Shear Strain Characteristics

A set of typical pore water pressure versus shear displacement curves for Sample

No. 1 for different OCRs are presented in the Figure 4-2. The pore pressure versus shear strain curves for all tested samples are presented in the Appendices. The pore pressure was back calculated from the change in total stress. The results show that the pore water pressure continuously increased up to certain displacement and then tended to be constant afterwards. The relationship between OCR and pore pressure was inversely proportional, but in some cases, for the higher OCR, negative pore pressures were developed.

35

140 OCR=2 OCR=4 120 OCR=8 0CR=16 OCR=32 100

80

60

Shear Stress (kPa) Shear 40

20

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

Horizontal Displacement (mm) Figure 4-1: Typical Shear Stress versus Horizontal Displacement Curves (Sample No.1).

OCR=2 450 OCR=4 OCR=8 OCR=16 OCR=32 350

250

150

Pore Water Pressure (kPa) Pore Water Pressure 50

-50 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure 4-2: Typical Pore Pressure versus Horizontal Displacement Curves (Sample No.1).

36

Stress Paths

Presented in Figure 4-3 is the typical stress paths for Sample No. 1 for OCRs of 2,

4, 8, 16 and 32 (i.e. normal stresses of 600 kPa, 300 kPa, 150 kPa, 75 kPa and 32 kPa, respectively). Similarly, stress paths for other tested samples are provided in the

Appendices. Stress paths could be utilized to draw shear envelops. The black line and red lines are effective and total stress failure envelopes, respectively.

150 OCR=2 100 OCR=4 OCR=8 OCR=16 50 OCR=32

0

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

Figure 4-3: Typical Shear Stress Paths (Sample No.1).

Stress Ratio

Figure 4-4 shows a typical graphical presentation of the of total stress ratio (τ/σ) versus shear displacement for the Sample No. 1, whereas Figure 4-5 contains the effective stress ratio (τ/σ') for the same sample. Similar figures for all other tested samples are prepared and presented in the Appendices. In this study, the failure criteria selected was the maximum stress ratio, as suggested by Airey and Wood (1987), Dyvik et al. (1987), and Schofield and Worth (1968). Calculated values of total stress ratio and effective stress ratio for all tested samples are presented in a tabulated form in the

Appendix.

37

1.1 OCR=2 1.0 OCR=4 OCR=8 0.9 OCR=16 OCR=32 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Horizontal Displacement (mm) Figure 4-4: Typical Total Stress Ratio versus Shear Displacement Curves (Sample No.1).

1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4

0.3 OCR=2 OCR=4 0.2 OCR=8 0.1 OCR=16 OCR=32 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Horizontal Displacement (mm) Figure 4-5: Typical Effective Stress Ratio versus Horizontal Displacement Curves (Sample No.1).

38

Shear Envelopes

Typical total and effective shear envelopes for Sample No. 1 is presented in

Figure 4-6. The shear envelopes of all the other tested samples are shown in the

Appendices. From the figure, it can be concluded that the effective shearing resistance is significantly higher than the total shearing resistance for all the samples. Both the total and effective shear strengths should be considered for the design of infrastructure and slope stability purposes to determine the situation.

The shear strength parameters, cohesions and friction angles for both drained and undrained conditions for all four types of samples were calculated and are presented in a tabular form in Table 4-1. In this table, ɸ is the undrained friction angle, ɸ' is the effective friction angle, C is the total cohesion and C' is the effective cohesion. A comparative study of the strength parameters of three samples can be done through the Table 4-1. It is observed that the effective friction angle and cohesion values decreased as the percentage of kaolinite in the sample decreased.

150

100 T. Normal Stress 50 E. Normal Stress 0

Shear Stress (kPa) Shear 0 100 200 300 400 500 600 Normal Stress (kPa) Figure 4-6: Typical Shear Envelopes for Sample No.1.

39

Table 4-1: Total and Effective Cohesion and Friction Angle of the Tested Samples

Sample Kaolinite Quartz ɸ (Deg) C (kPa) ɸ' (Deg) C' (kPa) No. (%) (%) 1 100 0 9.80 31.14 21.77 15.31 2 70 30 14.26 15.17 25.35 15.03 3 50 50 10.78 28.68 26.33 10.05

Normalized Shear Strength

Figure 4-7 contains a typical plot of the normalized shear strength (τ/σ) versus over consolidation ratio from DSS test for Sample No. 1. The relationship between τ/σ

 and OCR can be explained by the power function equation (  0.8805OCR0.3298 ). The  plots for all other tested samples are shown in the Appendices. From the figures, it was observed that there was a relative increase in strength ratio with increasing OCR. The samples appear to have good normalized behavior and show consistent effects of over- consolidation ratio. The calculated normalized shear strength ratio relative to OCR for the

Sample No. 1 is presented in Table 4-2; results for other samples are presented in the

Appendices.

The shear strength parameters obtained from the tests of the same soil can be used for preliminary analysis to determine if the embankment would be stable if constructed to full height or if staged construction is required. The combined normalized shear strength versus OCR curves are presented in the Figure 4-8, through which it can be concluded that the normalized shear strength ratio increases depending on the increase of the OCR and the mineralogical composition.

40

3.0

2.5

2.0

1.5

1.0

Normalized Stress Ratio 0.5

0.0 1 10 100 OCR Figure 4-7: Typical Normalized Shear Strength versus OCR (Sample No.1).

3.5

3.0

2.5

2.0

1.5

Normalized Stress Ratio Normalized K100 K70Q30 1.0 K50Q50 M50Q50 0.5 1 10 100 OCR Figure 4-8: Comparison of the normalized shear strength versus OCR for the four samples tested.

41

Table 4-2: Normalized Shear Strength and OCR (Sample No.1)

Max. Total Effective Shear Normal Normal S OCR Strength u τ/σ τ/σ' Stress Stress (kPa) v v (kPa) (kPa) (kPa) at failure

1 100 46.54 31.34 40.09 0.40 0.67 2 600 272.71 123.85 194.52 0.32 0.45 4 300 222.61 105.53 129.47 0.43 0.47 8 150 138.17 71.17 80.45 0.54 0.52 16 75 70.60 38.32 42.66 0.57 0.54 32 37.5 33.75 34.94 36.18 0.96 1.04

Equivalent Consolidation Pressure

A change in void ratio causes changes in the consolidation characteristics and shear strength of the clays. The equation to be used to calculate the change in void ratios is given by:

e1  eo  (H1 / H s )

Where,

eo  Initial void ratio

e1  Void ratio for the first incremental loading

H s  Height of the soil solid

H1  Change in height due to the first incremental loading

42

The calculated void ratios for the Sample No. 1 are presented in Table 4-3. From the table, it is seen that when the consolidation pressure increases the void ratio decrease as excess pore pressure has been drained from the sample.

Table 4-3: Effective normal stress and void ratio (Sample No. 1)

Step No. σ'(kPa) ΔH(mm) eo H(mm) Hs(mm) e 1 37.5 3.34 1.02 25.40 22.06 0.87 2 75 4.55 1.02 25.40 20.85 0.80 3 150 5.57 1.02 25.40 19.83 0.74 4 300 6.68 1.02 25.40 18.72 0.66 5 600 7.89 1.02 25.40 17.51 0.57 6 1200 8.94 1.02 25.40 16.46 0.48 7 600 8.84 1.02 25.40 16.56 0.49 8 300 8.75 1.02 25.40 16.65 0.50 9 150 8.41 1.02 25.40 16.99 0.53 10 75 8.31 1.02 25.40 17.09 0.54 11 37.5 8.13 1.02 25.40 17.27 0.55

The equivalent consolidation pressure corresponding to the void ratio (e) is defined as

 'e for a point with the same void ratio on the virgin curve of the consolidation graph. A typical consolidation graph is presented in Figure 4-9 for Sample No.1. The consolidation curves for the other samples are available in the Appendices. In Figure 4-9, the red dotted line represents the effective stress, whereas green dotted line represent the equivalent consolidation pressure for different OCR and black solid line represents the pre- consolidation pressure. The equivalent consolidation pressures are used to calculate the true cohesion and true friction angles of soil for the tested samples. The calculated equivalent consolidation pressure at different OCRs for three different samples are presented in Table 4-4.

43

.9

.8

.7

.6

Void(e) Ratio

.5

.4 1 10 100 1000 10000

E. Normal Stress (kPa) Figure 4-9: Typical Consolidation versus Void Ratio Curve (Sample No. 1).

Table 4-4: Effective Stress and Equivalent Consolidation Pressure K100 K70Q30 K50Q50 OCR σ' (kPa) σ'e (kPa) σ' (kPa) σ'e (kPa) σ' (kPa) σ'e (kPa) 2 600 1089.43 600 1098.25 600 1117.29 4 300 975.06 300 990.31 300 1030.92 8 150 884.89 150 902.27 150 945.35 16 75 797.51 75 826.32 75 872.28 32 37.5 713.79 37.5 764.62 37.5 830.14

True Cohesion and True Friction Angle

The true cohesion and the true friction angle are the fundamental properties of the soil and it can be used to determine the clay behavior. The step-by-step procedure to

44 calculate the true cohesion and true friction angle from the data collected are provided below:

1. Using the DSS failure envelope, first calculate the ' ,  ' and c' to find confining

pressure ( '3 ) for each OCR.

2  '3 = ( '12c'tan(45 '/ 2))/ tan (45 '/ 2) …………………… (5)

2. Find the value q using:

q = ( '1 '3 )/ 2

3. Calculate the value of q / 'e and  '3 / 'e for each OCR, where,  'e is the

equivalent consolidation pressure for the same void ratio and can be calculated

from the graph of consolidation pressure versus void ratio, as explained before.

4. Plot the graph of versus and fit the trend line to get an equation of

the form y  mx  c .

5. Use m  tan  to find the value of true friction angle (e ) using the Equation (6).

1 e  sin (tan /(tan 1)) ……………………………………… (6)

6. Using the value of from Step 5 and the value of c from Step 4, calculate the

value of the true cohesion using Equation 7.

1 c  tan (c(1 sine ) / cose ) …………………………………… (7)

7. The calculated values of q , 'e and  '3 are presented below in Table 4-5 for

Sample No. 1. The corresponding results for the remaining samples are presented

in the Appendices. A typical graph of q / 'e versus  '3 / 'e for Sample No. 1 is

45

presented in Figure 4-10. Similar graphs for the remaining three samples are

presented in the Figure 4-11

Table 4-5: Calculation of σ'3, q and σ'e for Sample No.1

σ' σ' q S OCR 1 3 σ' (kPa) u τ/σ' q/σ' σ' /σ' (kPa) (kPa) (kPa) e (kPa) e e 3 e 2 272.71 104.42 84.15 1089.85 194.52 0.18 0.08 0.10 4 222.61 81.43 70.59 975.45 129.47 0.13 0.07 0.08 8 138.17 42.67 47.75 885.24 80.45 0.09 0.05 0.05 16 70.60 11.66 29.47 797.82 42.66 0.05 0.04 0.01 32 33.75 -5.25 19.50 714.07 36.18 0.05 0.03 -0.01

The relationship shown in Figure 4-11 between q / 'e and '3 / 'e can be explained by

q  ' q  ' the equations,  0.4932 3  0.0304,  0.4932 3  0.0304and  e '  e '  e '  e '

q  '  0.4932 3  0.0304for Sample Nos. 1, 2 and 3, respectively. It can be concluded  e '  e ' that the values of and highly depend on the OCR and are directly proportional to each other, but less dependent with mineralogical composition in the

same OCR. Similarly, Figures 4-12 and 4-13 show the relationship between  '3 / e and

 / 'e . All of these relationship are similar in nature as the relationship of and

, but the magnitudes of the constants are nearly double. The equations

  '   '   3 '  1.1924 3  0.0453,  1.3027 3  0.0546and 1.2145  0.0451  e '  e '  3 '  e '  e '  e ' represent the relationship between and for Sample No. 1, 2 and 3,

46

respectively. The relationship between  / 'e and OCR is presented in the Figures 4-14 and 4-15, which shows is highly dependent on OCR and inversely proportional to it. The relationship between and OCR can be defined by the power equations,

   0.565  0.2511OCR0.495 ,  0.3204OCR0.64 and  0.2664OCR for  e '  e '  e '

Sample Nos. 1, 2 and 3, respectively.

.09

.08

.07

.06

e

q/σ ` .05

.04

.03

.02 -.02 0.00 .02 .04 .06 .08 .10 .12 σ`/σ ` 3 e

Figure 4-10: q / 'e versus  '3 / 'e for Sample No.1.

47

.12

.10

.08

e .06

q/σ `

.04

K100 .02 K70Q30 K50Q50 0.00 -.02 0.00 .02 .04 .06 .08 .10 .12 .14 σ`/σ ` 3 e

Figure 4-11: q / 'e versus  '3 / 'e for Sample Nos. 1, 2 and 3.

.20

.15

e .10

τ /σ `

.05

0.00 -.02 0.00 .02 .04 .06 .08 .10 .12

σ`3/σ `e

Figure 4-12: σ'3/σ'e versus τ/σ'e for Sample No.1.

48

.25

.20

.15

e

τ /σ ` .10

K100 .05 K70Q30 K50Q50

0.00 -.02 0.00 .02 .04 .06 .08 .10 .12 .14 '/' 3 e

Figure 4-13: σ'3/σ'e versus τ/σ'e for Sample Nos. 1, 2, and 3.

.20

.18

.16

.14

e .12

τ /σ ` .10

.08

.06

.04 1 10 100 OCR

Figure 4-14: OCR versus τ/σ'e for Sample No. 1.

49

.25

K100 K70Q30 .20 K50Q50

.15

e

τ /σ ` .10

.05

0.00 1 10 100 OCR

Figure 4-15: OCR versus τ/σ'e for Sample Nos. 1, 2, and 3.

The true cohesion, true friction angle and base friction angle of the samples were calculated by using the graph in Figure 4-10 and the equations previously described. The values of these parameters are presented in Table 4-6.

Table 4-6: True Cohesion and Friction Angle for Sample Nos. 1, 2, 3 and 4.

Sample Kaolinite Quartz Montmorillonite L. L. P.I. ɸ (Deg) C e (Deg) No. (%) (%) (%) (%) e

1 100 0 0 70 25 19.3 8.5 2 70 30 0 50 18 20.6 7.2 3 50 50 0 34 9 21.1 4.6 4 0 50 50 209 161 35.2 0.39

50

From the Table 4-6 and Figure 4-10, it can be concluded that the true friction angle and true cohesion are not dependent on stress history, but depends upon the mineralogical composition of the clay as well as plasticity characteristics.

Relationship between True Cohesion, True Friction Angle with Liquid Limit and Plasticity Index

The relation between true friction angle (ɸe) and true cohesion (Cc) with the liquid limit (LL) and plasticity index (PI) are presented in the Figures 4-16 to 4-19. The true friction angle and true cohesion are highly dependent upon the liquid limit. The true friction angle is directly proportional to the liquid limit and plasticity index whereas the true cohesion is inversely proportional to the liquid limit and plasticity index. The relationship between liquid limit and plasticity index with true friction angle and base friction angle can be expressed by the following equations:

 e  0.053LL  22.911

 c  1.066LL 1.2724

 e  0.1085PI  22.211

 c  0.2464PI  2.4723

51

21.2

21.0 K100 20.8 K70Q30 K50Q50 20.6

20.4

20.2

20.0 (Deg)

e

ɸ 19.8

19.6 19.4 19.2 19.0 30 40 50 60 70

Liquid Limit (%)

Figure 4-16: Liquid Limit versus True Friction Angle.

9

8

7 (Deg)

c ɸ 6

K100 5 K70Q30 K50Q50

4 30 40 50 60 70 Liquid Limit (%) Figure 4-17: Liquid Limit versus Base Friction Angle.

52

21.2

21.0 K100 K70Q30 20.8 K50Q50 20.6

20.4

20.2 (Deg) e 20.0

ɸ 19.8 19.6 19.4 19.2 19.0 8 10 12 14 16 18 20 22 24 26

Platicity Index

Figure 4-18: Plasticity Index versus True Friction Angle.

9

8

7

6

(Deg)

c ɸ K100 5 K70Q30 K50Q50

4 8 10 12 14 16 18 20 22 24 26 Platicity Index

Figure 4-19: Plasticity Index versus Base Friction Angle.

53

CHAPTER 5

CONCLUSION

The strength of the soils depends up on its mineralogical composition and stress history. Some of the main clay minerals available in the geotechnical engineering practice are kaolinite and montmorillonite. In addition, quartz is the second most abundant minerals on the earth’s continental crust. Therefore, the evaluation of the shear strength of soils containing different composition of these minerals at different stress histories is important. In this study, three mixtures of kaolinite with quartz and one mixture of montmorillonite with quartz at different proportions based on the weight were prepared in the laboratory and tested at over-consolidation ratios of 1, 2, 4, 8, 16 and 32 for each mixture of kaolinite with quartz and at over-consolidation ratios of 1, 2 and 4 for the mixture of the montmorillonite and quartz. All the specimens from the mixture of kaolinite and quartz were used to determine the undrained shear strength and the true cohesion and true friction angle; whereas, the tested specimens prepared from montmorillonite and quartz were used to determine the shear strength only. The following conclusions can be made from the results obtained from this study:

1. As the over-consolidation ratio increased, the undrained strength ratio also

increased.

2. The increase in strength with over-consolidation ratio was dependent on the

mineralogical composition of the soil.

54

3. A greater increase in undrained strength with over-consolidation ratio was seen

in the soils with montmorillonite as the dominate clay mineral in comparison to

the soils with kaolinite as the dominate clay mineral.

4. The true cohesion and true friction angle of the soils were observed to be

independent of the over-consolidation ratio.

5. The true cohesion and true friction angle were dependent on the mineralogical

composition of the soil and plasticity characteristics.

6. As the proportion of clay mineral increased in the soil, true cohesion of the soil

also increased; whereas, the true friction angle decreased with an increase in

proportion of the clay mineral.

55

REFERENCES

ASTM (American Society of Testing and Materials) D 6528. (2007). “Standard Test

Method for Consolidated Undrained Simple Shear Testing of Cohesive Soil.”

West Conshohocken, PA: ASTM International.

Airey, D. W. and Wood, D. M. (1987). “An evaluation of direct simple shear tests on

Clays.” Geotechnique 37 (1), 25 - 35

Ajmera, B. (2012). “Undrained Shear Strength Characteristics of Normally Consolidated

Clays.” Master’s Thesis, California State University, Fullerton.

Collin, A. (1956). Landslides in clays, 1846. Toronto: University of Toronto Press.

DeGroot, D. J., Ladd, C. C., & Germaine, J. T. (1992). Direct Simple Shear Testing of

Cohesive Soils. Cambridge, MA: MIT Dept of Civil Engineering.

Dyvik R., Berre T., Lacasse S., & Raadim B. (1987). “Comparison of truly undrained

And constant volume direct simple shear tests.” Geotechnique, 37(1), 3-10.

Hvorslev, M. J. (1973). “Physical Component of the Shear Strength of Saturated Clays.”

Journal of Soil Mechanics & Foundations Div., 169-273.

Hong Z., Liu, S., & Negami, T. (2006). “Comparison in undrained shear strength

between undisturbed and remolded Arike clays.” Journal of Geotechnical and

Geoenvironmental Engineering, 132 (2), 272 – 275.

Kjellam, W. (1951). Testing the Shear Strength of Clay in Sweden.

Geotechnique, 225- 232.

56

Ladd, C. C., & Foott, R., (1974) “New Design Procedure for Stability of Soft Clay.”

Journal of the Geotechnical Engineering Division, 100. 763-786.

Ladd, C., & DeGroot, D. (2003). “Recommended Practice for the Soft Ground Site

Characterization.” Arthur Casagrande Lecture, 12th Pan-American Conference

on Soil Mechanics and Geotechnical Engineering.

Marr, W. A. (2003). Universal Shear Device. Acton, MA: GeoComp Corporation.

McGuire. (2001). “Comparison of Direct Simple Confinement Methods on Clays

and Silt Specimens.” Master’s Thesis, University of Rhode Island.

Schofield, A. N. & Worth, P. (1968). Critical State Soil Mechanics. New York: McGraw-

Hill.

Sheahan, T. C., Ladd, C. C., & Germaine, J. T. (1996). “Rate-dependent undrained shear

behavior of saturated clay.” Journal of Geotechnical Engineering, 122 (2), 99-108.

Skempton, A. W. (1948). "Undrained shear strength in stability calculation of

embankments and foundations on soft clays." Canadian Geotechnical Journal,

17 (4) 591-602.

Sowers, G. F. (1963). Strength Testing of Soils. Laboratory Shear Testing of Soils,

361, 4.

Strozyk, J., & Tankiewicz, M. (2014). “The Undrained Shear Strength of

Over-consolidated Clays.” Procedia Engineering, 91, 317 – 321.

Tiwari, B., & Ajmera, B. (2011). “Consolidation and Swelling Behavior of Major Clay

Minerals and Their Mixtures,” Applied Clay Science, 54 (3-4), 264-273.

57

APPENDIX A

SAMPLE NO. 1

140 OCR=2 120 OCR=4 OCR=8 100 OCR=16 OCR=32 80

60

40 Sear Stress (kPa) Stress Sear

20

0

Horizontal Distanceplacement (mm) Figure A-1: Shear Stress versus Horizontal Displacement Curves.

450 OCR=2 400 OCR=4 350 OCR=8 OCR=16 300 OCR=32 250 200 150 100 50 0 Pore Water Pressure (kPa) Pressure Water Pore -50 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure A-2: Pore Pressure versus Horizontal Displacement Curves.

58

150 OCR=2 100 OCR=4 OCR=8 OCR=16

(kPa) 50 OCR=32 Shear Stress Stress Shear 0 0 50 100 150 200 250 300 350 400 450 500 550 600 Normal Stress (kPa) Figure A-3: Shear Stress versus Normal Stress Curves.

1.2 OCR=2 OCR=4 OCR=8 OCR=16 1 OCR=32

0.8

0.6

σ

/ τ

0.4

0.2

0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure A-4: Total Stress Ratio versus Horizontal Displacement Curves.

59

1.2

1

0.8

σ' /

τ 0.6

0.4

0.2 OCR=2 OCR=4 OCR=8 OCR=16 OCR=32 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure A-5: Effective Stress Ratio versus Horizontal Displacement Curves.

0.7 0.6 0.5 0.4

0.3 σ

u/ 0.2 0.1 0 -0.1 OCR=2 OCR=4 -0.2 OCR=8 OCR=16 OCR=32 -0.3 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure A-6: Normalized Pore Pressure versus Horizontal Displacement Curves.

60

150

100

50

0 Shear Stress (kPa) Stress Shear 0 50 100 150 200 250 300 350 400 450 500 550 600 650 Normal Stress (kPa) Figure A. 7: Total Shear Envelope.

150

100

(kPa) (kPa) 50 Shear Stress Stress Shear 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 Normal Stress (kPa) Figure A-8: Effective Shear Envelope.

150

100 T. Normal Stress (kPa) 50

E. Normal Stress Shear Stress Stress Shear 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 Normal Stress (kPa) Figure A-9: Comparison of Total and Effective Shear Envelope (Source: Ajmera (2012) for OCR=1 Data).

61

3.2

2.7

2.2 σ

/ 1.7 τ

1.2

0.7

0.2 1 10 100 OCR

Figure A-10: Trend for OCR and Normalized Total Shear Strength.

0.7

0.6

0.5

0.4

σ'

/ τ 0.3

0.2

0.1

0 1 10 100 OCR Figure A-11: Trend for OCR and Normalized Effective Shear Strength.

62

3

2.5

2

1.5

1

Normalized Shesr Strength Strength Shesr Normalized 0.5 Total Effective 0 1 10 100 OCR

Figure A-12: Comparison of Trends for OCR and Normalized Total and Effective Shear Strength.

1

0.8

0.6

Void Ratio Void 0.4

0.2

0 1 10 100 1000

E. Normal Stress (Psi) Figure A-13: Effective Normal Stress versus Void Ratio curves (Virgin Compression and Rebound Curve).

63

0.6

0.5

0.4 e

σ' 0.3 q/

0.2

0.1

0 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 σ'3/σ'e

Figure A-14: q/σ'e versus σ'3/σ'e.

0.20

0.18

0.16

0.14

0.12

e σ'

/ 0.10 τ

0.08

0.06

0.04

0.02

0.00 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 σ'3/σ'e

Figure A-15: τ/σ'e versus σ'3/σ'e.

64

0.12

0.10

0.08

0.06

e σ' q/ K100 0.04 K70Q30

0.02 K50Q50

0.00 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 σ'3/σ'e

Figure A-16: q/σ'e versus σ'3/σ'e Comparison for Sample Nos. 1, 2, and 3.

0.25

0.20

0.15

e

σ' /

τ 0.10 K100

K70Q30 0.05

K50Q50

0.00 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 σ' /σ' 3 e

Figure A-17: τ/σ'e versus σ'3/σ'e Comparison for Sample Nos. 1, 2, and 3.

65

0.2

0.18

0.16

0.14

0.12

0.1

e 0.08

σ'

/ τ 0.06

0.04

0.02

0 1 10 100 OCR

Figure A-18: τ/σ'e versus OCR.

Table A-1: Relation between Effective Stress and Void Ratio

Step No. σ' (kPa) ΔH (mm) eo H (mm) Hs (mm) e 1 37.5 3.34 1.02 25.40 22.06 0.87 2 75 4.55 1.02 25.40 20.85 0.80 3 150 5.57 1.02 25.40 19.83 0.74 4 300 6.68 1.02 25.40 18.72 0.66 5 600 7.89 1.02 25.40 17.51 0.57 6 1200 8.94 1.02 25.40 16.46 0.48 7 600 8.84 1.02 25.40 16.56 0.49 8 300 8.75 1.02 25.40 16.65 0.50 9 150 8.41 1.02 25.40 16.99 0.53 10 75 8.31 1.02 25.40 17.09 0.54 11 37.5 8.13 1.02 25.40 17.27 0.55

66

Table A-2: Relation between q/σ'e and σ'3/σ'e

σ' σ' q S OCR 1 3 σ' (kPa) u τ/σ' q/σ' σ' /σ' (kPa) (kPa) (kPa) e (kPa) e e 3 e

2 272.71 104.42 84.15 1089.85 194.52 0.18 0.08 0.10 4 222.61 81.43 70.59 975.45 129.47 0.13 0.07 0.08 8 138.17 42.67 47.75 885.24 80.45 0.09 0.05 0.05 16 70.60 11.66 29.47 797.82 42.66 0.05 0.04 0.01 32 33.75 -5.25 19.50 714.07 36.18 0.05 0.03 -0.01

Table A-3: Relation between Normalized Shear Strength and OCR

Effective Total Max. Normal Normal Shear S OCR Stress u τ/σ τ/σ' Stress Strength (kPa) v v (kPa) (kPa) (kPa) at failure 1 100 46.54 31.34 40.09 0.40 0.67 2 600 272.71 123.85 194.52 0.32 0.45 4 300 222.61 105.53 129.47 0.43 0.47 8 150 138.17 71.17 80.45 0.54 0.52 16 75 70.60 38.32 42.66 0.57 0.54 32 37.5 33.75 34.94 36.18 0.96 1.04

67

Table A-4: L. L., P. I. and Normalized Shear Strength

Effective Total Max. Normal Normal σ' Shear L. L. OCR Stress e τ/σ' τ/σ' P.I. Stress (kPa) Strength e (%) (kPa) (kPa) (kPa) at failure

2 600 272.71 1089.43 123.85 0.45 0.11 70 25 4 300 222.61 975.06 105.53 0.47 0.11 70 25 8 150 138.17 884.89 71.17 0.52 0.08 70 25 16 75 70.60 797.51 38.32 0.54 0.05 70 25 32 37.5 33.75 713.79 34.94 1.04 0.05 70 25

68

APPENDIX B

SAMPLE NO. 2

200 OCR=2 180 OCR=4 160 OCR=8 140 OCR=16 OCR=32 120 100 80

60 Shear Stress (kPa) Stress Shear 40 20 0 0 1 2 3 4 5 6 7 8 Horizontal Displacement (mm) Figure B-1: Shear Stress versus Horizontal Displacement Curves.

350 OCR=2 300 OCR=4 250 OCR=8 OCR=16 200 OCR=32 150

100

50

0 Pore Water Pressure (kPa) Pressure Water Pore -50 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure B-2: Pore Water Pressure versus Horizontal Displacement Curves.

69

200 OCR=2 150 OCR=4 OCR=8 OCR=16 100 OCR=32

50

Shear Stress (kPa) Stress Shear 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 Normal Stress (kPa) Figure B-3: Shear Stress versus Normal Stress Curves.

0.8

0.7

0.6

0.5 σ

/ 0.4 τ

0.3

0.2 OCR=2 OCR=4 0.1 OCR=8 OCR=16 OCR=32 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure B-4: Total Stress Ratio versus Horizontal Displacement Curves.

70

1.2

1

0.8 '

σ 0.6 τ/

0.4 OCR=2 OCR=4 OCR=8 0.2 OCR=16 OCR=32 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure B-5: Effective Stress Ratio versus Horizontal Displacement Curves.

0.7 OCR=2 0.6 OCR-4

0.5 OCR=8 0.4

0.3

σ 0.2 u/ 0.1

0

-0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure B-6: Normalized Pore Pressure versus Horizontal Displacement Curves.

71

200

150

kPa) (

100 Stress

50 Shear 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 Total Normal Stress (kPa) Figure B-7: Total Shear Envelope for OCR 1, 2, 4, 8, 16 and 32.

200

150

100

Shear Stress (kPa) Stress Shear 50

0 0 50 100 150 200 250 300 350 400 Effective Normal Stress (kPa) Figure B-8: Effective Shear Envelope for OCR 1, 2, 4, 8, 16 and 32.

72

200

150

100

50 T. Normal Stress

Shear Stress (kPa) Stress Shear E. Normal Stress 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 Normal Stress (kPa) Figure B-9: Comparison of Total and Effective Shear Envelope.

3.2

2.7

2.2

1.7

σ

/ τ

1.2

0.7

0.2 1 10 100 OCR Figure B-10: Trend for OCR and Normalized Total Shear Strength.

73

0.7

0.6

0.5

0.4

' σ

/ 0.3 τ

0.2

0.1

0 1 10 100 OCR Figure B. 11: Trend for OCR and Normalized Effective Shear Strength.

3

2.5

2

' 1.5

σ

/ τ

1

0.5 Total Effective 0 1 10 100 OCR Figure B-12: Comparison of Trends for OCR and Normalized Total and Effective Shear Strength.

74

1.2

1.1

1

0.9

0.8

Void Ratio Ratio (e) Void 0.7

0.6

0.5 1 10 100 1000 E. Normal Stress (Psi) Figure B-13: Effective Normal Stress versus Void Ratio curves (Virgin Compression and Rebound Curve).

0.12

0.10

0.08 e

σ' 0.06 q/

0.04

0.02

0.00 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

σ'3/σ'e

Figure B-14: q/σ'e versus σ'3/σ'e.

75

0.25

0.20

0.15

e

σ'

/ τ 0.10

0.05

0.00 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

σ'3/σ'e

Figure B-15: σ'3/σ'e versus τ/σ'e.

0.25

0.20

0.15

e

σ'

/ τ

0.10

0.05

0.00 1 10 100 OCR

Figure B-16: OCR versus τ/σ'e.

76

Table B-1: Relation between Effective Stress and Void Ratio

Step No. σ' (kPa) ΔH (mm) eo H (mm) Hs (mm) e 1 37.5 1.21 1.15 25.40 24.19 1.10 2 75 2.33 1.15 25.40 23.07 1.04 3 150 3.02 1.15 25.40 22.38 1.01 4 300 4.01 1.15 25.40 21.39 0.96 5 600 4.91 1.15 25.40 20.49 0.91 6 1200 5.91 1.15 25.40 19.49 0.84 7 600 5.83 1.15 25.40 19.57 0.85 8 300 5.71 1.15 25.40 19.69 0.86 9 150 5.59 1.15 25.40 19.81 0.86 10 75 5.45 1.15 25.40 19.95 0.87 11 37.5 5.41 1.15 25.40 19.99 0.87

Table B-2: Relation between q/σ'e and σ'3/σ'e

σ' σ' q σ' S OCR 1 3 e u τ/σ' q/σ' σ' /σ' (kPa) (kPa) (kPa) (kPa) (kPa) e e 3 e

2 334.76 133.28 100.74 1028.87 225.58 0.22 0.10 0.13 4 116.91 33.29 41.81 990.70 115.66 0.12 0.04 0.03 8 66.44 10.13 28.15 902.62 74.24 0.08 0.03 0.01 16 80.66 16.66 32.00 826.64 53.26 0.06 0.04 0.02 32 29.59 -6.78 18.18 764.92 24.59 0.03 0.02 -0.01

77

Table B-3: Relation between Normalized Shear Strength and OCR Effective Total Max. Normal Normal Shear S OCR Stress u τ/σ τ/σ' Stress Strength (kPa) v v (kPa) (kPa) (kPa) at failure 1 100 50.62 18.77 31.26 0.31 0.37 2 600 334.76 168.48 225.58 0.38 0.50 4 300 116.91 88.05 115.66 0.39 0.75 8 150 66.44 64.07 74.24 0.49 0.96 16 75 80.66 49.85 53.26 0.71 0.62 32 37.5 29.59 22.73 24.59 0.66 0.77

Table B-4: L. L., P. I. and Normalized Shear Strength Effective Total Max. Normal Normal σ' Shear L. L. OCR Stress e τ/σ' τ/σ' P.I. Stress (kPa) Strength e (%) (kPa) (kPa) (kPa) at failure 2 600 334.76 1098.25 168.48 0.50 0.15 50 18 4 300 116.91 990.31 88.05 0.75 0.09 50 18 8 150 66.44 902.27 64.07 0.96 0.07 50 18 16 75 80.66 826.32 49.85 0.62 0.06 50 18 32 37.5 29.59 764.62 22.73 0.77 0.03 50 18

78

APPENDIX C

SAMPLE NO. 3

200 OCR=2 OCR=4 180 OCR=16 OCR=8 160 OCR=32 140 120 100 80 60 40

20 Shear Stress (kPa) Stress Shear 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure C-1: Shear Stress versus Horizontal Displacement Curves.

400 350 OCR=2 OCR=4 OCR=16 OCR=8 300 OCR=32 250 200

150 (kPa) 100 50

Pore Water Pressure Pressure Water Pore 0 -50 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure C-2: Pore Pressure versus Horizontal Displacement Curves.

79

200 OCR=2 150 OCR=4 OCR=16 OCR=8 100 OCR=32

50 Shear Stress (kPa) Stress Shear 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 E. Normal Stress (kPa) Figure C-3: Shear Stress versus Normal Stress Curves.

0.9

0.8

0.7

0.6

0.5 σ

τ/ 0.4

0.3

0.2

OCR=2 OCR=4 0.1 OCR=16 OCR=8 OCR=32 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure C-4: Total Stress Ratio versus Horizontal Displacement Curves.

80

1 '

σ 0.5 τ/

OCR=2 OCR=4 OCR=16 OCR=8 OCR=32 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure C-5: Effective Stress Ratio versus Horizontal Displacement Curves.

1

0.8

0.6

0.4

0.2 σ u/ 0

-0.2

-0.4 OCR=2 -0.6 OCR=4 OCR=8 -0.8 OCR=16 OCR=32 -1 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure C-6: Normalized Pore Pressure versus Horizontal Displacement Curves.

81

200

150

100

50

0 Shear Stress (kPa) Stress Shear 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 Total Normal Stress (kPa) Figure C-7: Total Shear Envelope for OCR 1, 2, 4, 8, 16 and 32.

200

150

100

50

0

Shear Stress (kPa) Stress Shear 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 Effective Normal Stress (kPa)

Figure C-8: Effective Shear Envelope for OCR 1, 2, 4, 8, 16 and 32.

200

150 100(kPa)

Shear Stress Stress Shear 50 T. Normal Stress E. Normal Stress 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 Normal Stress (kPa) Figure C-9: Comparison of Total and Effective Shear Envelope.

82

3.5

3

2.5

2

σ

/ τ 1.5

1

0.5

0 1 10 100 OCR Figure C-10: Trend for OCR and Normalized Total Shear Strength.

0.7

0.6

0.5

0.4

'

σ

/ τ 0.3

0.2

0.1

0 1 10 100 OCR Figure C-11: Trend for OCR and Normalized Effective Shear Strength.

83

3.5

3

2.5

2

σ / τ 1.5

1

0.5 Total Effective 0 1 10 100 OCR Figure C-12: Comparison of Trends for OCR and Normalized Total and Effective Shear Strength.

1

0.9

0.8

0.7 Void Ratio Ratio (e) Void

0.6

0.5 1 10 100 1000 E. Normal Stress (Psi) Figure A-13: Effective Normal Stress versus Void Ratio curves (Virgin Compression and Rebound Curve).

84

0.08

0.07

0.06

0.05 e

σ' 0.04 q/

0.03

0.02

0.01

0.00 -0.020 0.000 0.020 0.040 0.060 0.080 0.100 0.120 σ'3/σ'e

Figure C-14: q/σ'e versus σ'3/σ'e.

0.20

0.18

0.16

0.14

0.12

e σ'

/ 0.10 τ 0.08

0.06

0.04

0.02

0.00 -0.020 0.000 0.020 0.040 0.060 0.080 0.100 0.120 σ' /σ' 3 e

Figure C-15: σ'3/σ'e versus τ/σ'e.

85

0.20

0.18

0.16

0.14

0.12

e σ'

/ 0.10 τ 0.08

0.06

0.04

0.02

0.00 1 10 100 OCR

Figure C-16: OCR versus τ/σ'e Curve.

Table C-1: Relation between Effective Stress and Void Ratio

SN σ' (kPa) ΔH (mm) eo H (mm) Hs (mm) e 1 37.5 1.42 0.99 25.40 23.98 0.93 2 75 2.04 0.99 25.40 23.36 0.91 3 150 2.52 0.99 25.40 22.88 0.88 4 300 3.28 0.99 25.40 22.12 0.84 5 600 4.03 0.99 25.40 21.37 0.80 6 1200 4.79 0.99 25.40 20.61 0.76 7 600 4.76 0.99 25.40 20.64 0.76 8 300 4.68 0.99 25.40 20.72 0.77 9 150 4.58 0.99 25.40 20.82 0.77 10 75 4.47 0.99 25.40 20.93 0.78

86

Table C-2: Relation between q/σ'e and σ'3/σ'e σ' σ' q σ' S OCR 1 3 e u τ/σ' q/σ' σ' /σ' (kPa) (kPa) (kPa) (kPa) (kPa) e e 3 e 2 267.42 109.12 79.15 1117.72 209.85 0.19 0.07 0.10 4 79.91 23.06 28.42 1031.32 93.24 0.09 0.03 0.02 8 214.07 84.64 64.72 945.72 116.45 0.12 0.07 0.09 16 42.98 6.11 18.43 872.62 44.78 0.05 0.02 0.01 32 28.60 -0.48 14.54 830.47 29.22 0.04 0.02 0.00

Table C-3: Relation between Normalized Shear Strength and OCR Effective Total Max. Normal Normal Shear S OCR Stress u τ/σ τ/σ' Stress Strength (kPa) v v (kPa) (kPa) (kPa) at failure 1 800 355.65 166.97 260.53 0.33 0.47 2 600 267.42 146.76 209.85 0.35 0.55 4 300 79.91 55.40 93.24 0.31 0.69 8 150 214.07 110.25 116.45 0.78 0.51 16 75 42.98 40.66 44.78 0.60 0.95 32 37.5 43.36 27.67 29.22 0.78 0.64

Table C-4: L. L., P. I. and Normalized Shear Strength

Effective Total Max. Normal Normal σ' Shear OCR Stress e τ/σ' τ/σ' L. L. P.I. Stress (kPa) Strength e (kPa) (kPa) (kPa) at failure 2 600 267.42 1117.29 146.76 0.55 0.13 34 9 4 300 79.91 1030.92 55.40 0.69 0.05 34 9 8 150 214.07 945.35 110.25 0.51 0.12 34 9 16 75 42.98 872.28 40.66 0.95 0.05 34 9 32 37.5 43.36 830.14 27.67 0.64 0.03 34 9

87

APPENDIX D

SAMPLE NO. 4

100 90 80 70 60 50 40

30 Shear Stress (kPa) Stress Shear 20 OCR=2 10 OCR=4 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure D-1: Shear Stress versus Horizontal Displacement Curves.

400 OCR=2 350 OCR=4 300 250 200 150 100 50

Pore Water Pressure (kPa) Pressure Water Pore 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure D-2: Pore Pressure versus Horizontal Displacement Curves.

88

200 OCR=2 150 OCR=4

100

50

Shress Stress (kPa) Stress Shress 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 E. Normal Stress (kPa) Figure D-3: Shear Stress versus Normal Stress Curves.

0.3

0.25

0.2 σ

/ 0.15 τ

0.1

0.05 OCR=2 OCR=4 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure D-4: Total Stress Ratio versus Horizontal Displacement Curves.

89

0.4

0.35

0.3

0.25 σ'

/ 0.2 τ

0.15

0.1

0.05 OCR=2 OCR=4 0 0 1 2 3 4 5 6 7 Horizontal Displacement (mm) Figure D-5: Effective Stress Ratio versus Horizontal Displacement Curves.

150

100

50

0 Shear Shress (kPa) Shress Shear 0 50 100 150 200 250 300 350 400 450 500 550 600 650

Normal Stress (kPa) Figure D-6: Total Shear Envelope for OCR 2 and 4.

90

0.35

0.3

0.25

0.2

σ

/ τ 0.15

0.1

0.05

0 1 10

OCR Figure D-7: Trend for OCR and Normalized Total Shear Strength.

1.2

1

0.8 σ'

/ 0.6 τ

0.4

0.2

0 1 10 OCR Figure D-8: Trend for OCR and Normalized Effective Shear Strength.

91

1.2

1

0.8 σ'

/ 0.6 τ

0.4

0.2

0 1 10

OCR Figure D-9: Comparison of Trends for OCR and Normalized Total and Effective Shear Strength.

Table D-1: Relation between Normalized Shear Strength and OCR

Effective Total Max. Normal Normal Shear S OCR Stress u τ/σ τ/σ' Stress Strength (kPa) v v (kPa) (kPa) (kPa) at failure

1 800 182.29 33.06 240.00 0.30 1.00

2 600 251.29 92.56 90.00 0.15 0.53

4 300 249.26 72.50 51.00 0.17 0.42

92

10

9

8

7

6

5

Void Ratio Void 4

3

2

1

0 1 10 100 1000 10000 E. Normal Stress (kPa) Figure D-10: Effective Normal Stress versus Void Ratio curves (Source: Tiwari and Ajmera, 2011).

Table D-2: Relation between Effective Stress and Void Ratio (Source: Tiwari and Ajmera, 2011)

Step No. σ' (kPa) e0 e 1 23.93 7.55 6.05 2 47.85 7.55 5.22 3 95.77 7.55 4.38 4 191.54 7.55 3.55 5 383.09 7.55 2.71 6 766.10 7.55 1.88 7 1532.21 7.55 1.04 8 766.10 7.55 1.24 9 383.09 7.55 1.44 10 191.54 7.55 1.63 11 95.77 7.55 1.83 12 47.85 7.55 2.03 13 23.93 7.55 2.22

93

0.1

0.09

0.08

0.07

0.06 e

σ' 0.05 q/ 0.04

0.03

0.02

0.01

0 0 0.01 0.02 0.03 0.04 0.05 0.06 σ'3/σ'e

Figure D-11: q/σ'e versus σ'3/σ'e.

0.19

0.17

0.15

e 0.13

σ'

/ τ 0.11

0.09

0.07

0.05 0 0.01 0.02 0.03 0.04 0.05 0.06 σ'3/σ'e

Figure D-12: σ'3/σ'e versus τ/σ'e.

94

0.16

0.14

0.12

0.1

e

σ'

/ τ 0.08

0.06

0.04 1 10 OCR

Figure D-13: OCR versus τ/σ'e Curve.

Figure D-14: OCR versus Normalized Effective Shear Strength Curves.

95

Table D-3: Relation between q/σ'e and σ'3/σ'e

σ' σ' q OCR 1 3 σ' (kPa) S (kPa) τ/σ' q/σ' σ' /σ' (kPa) (kPa) (kPa) e u e e 3 e

1 182.29 37.59 72.35 1538.13 202.71 0.13 0.05 0.02

2 251.29 58.98 96.15 1319.24 176.26 0.13 0.07 0.04

4 249.25 58.35 95.45 1106.38 104.31 0.09 0.09 0.05

96

APPENDIX E

RELATIONSHIP OF LL AND PI WITH TRUE FRICTION ANGLE AND TRUE COHESION.

21.2 21.0 K100 20.8 K70Q30 K50Q50 20.6

20.4

20.2

20.0 (Deg)

e 19.8 ɸ

19.6

19.4 19.2 19.0 30 40 50 60 70 Liquid Limit (%)

Figure E-1: Liquid Limit versus True Friction Angle.

9

8

7

6

(Deg)

c ɸ K100 5 K70Q30 K50Q50

4 30 40 50 60 70 Liquid Limit (%) Figure E-2: Liquid Limit versus Base Friction Angle.

97

21.2

21.0 K100 K70Q30 20.8 K50Q50 20.6

20.4

20.2

(Deg)

e

20.0 ɸ

19.8

19.6

19.4 19.2 19.0 8 10 12 14 16 18 20 22 24 26 Platicity Index Figure E-3: Plasticity Index versus True Friction Angle.

9

8

7

(Deg)

c

ɸ 6

K100 5 K70Q30 K50Q50

4 8 10 12 14 16 18 20 22 24 26 Platicity Index Figure E-4: Plasticity Index versus Base Friction Angle.

98

Table E-1: Relation between LL and PI with ɸe and ɸc

Sample No. LL (%) PI ɸe (Deg) ɸc (Deg) 1 70 25 19.29 8.46 2 50 18 20.64 7.21 3 34 9 21.07 4.56 4 209 161 35.24 0.39

1.2

1

) 0.8 τ/σ

0.6

K100 Stress Ratio ( Ratio Stress 0.4 K50Q30

0.2 K70Q30

M50Q50 0 1 10 100 OCR Figure E-5: Total Stress Ratio versus OCR of Four Sample.

99

1.2

1 )

σ' 0.8

/ τ

0.6

K100 0.4 Stress Ratio ( Ratio Stress K70Q30

0.2 K50Q50 M50Q50

0 1 10 100 OCR Figure E-6: Effective Stress Ratio versus OCR of Four Sample.