study of the undrained static response of sandy soils in the critical state framework

PURDUE UNIVERSITY GRADUATE SCHOOL Thesis Acceptance This is to certify that the thesis prepared By Entitled Complies with University regulations and meets the standards of the Graduate School for originality and quality Forthedegreeof Final examining committee members , Chair Approved by Major Professor(s): Approved by Head of Graduate Program: Date of Graduate Program Head's Approval: Tejas Gorur S. Murthy Study of the Undrained Static Response of Sandy Soils in the Critical State Framework Doctor of Philosophy Monica Prezzi Co-Chair Rodrigo Salgado Co-Chair Adolph G. Altschaeffl Laura J. Pyrak-Nolte July 26, 2006 Monica Prezzi Rodrigo Salgado Darcy M. Bullock STUDY OF THE UNDRAINED STATIC RESPONSE OF SANDY SOILS IN THE CRITICAL STATE FRAMEWORK A Dissertation Submitted to the Faculty of Purdue University by Tejas Gorur S Murthy In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2006 Purdue University West Lafayette, Indiana UMI Number: 3239785 3239785 2007 UMI Microform Copyright All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 by ProQuest Information and Learning Company. ii For my parents, Ranganayaki and Sreenivasa Murthy iii ACKNOWLEDGMENTS I am grateful to my advisors Professors Rodrigo Salgado and Monica Prezzi for their tutelage. It was my privilege to work on this project. I am especially grateful for their guidance, advice and patience throughout graduate school. I thank Professors Adolph Altschaeffl and Laura Pyrak-Nolte for serving on my committee. I am indebted to Professor Adolph Altshcaeffl for providing me with funding all through my stay at Purdue. Working with him on the projects from Purdue Physical Plant Services was truly enjoyable. I am very obliged to Professor Altschaeffl for providing valuable suggestions during the course of my research. His insights into experimentation and soil behavior are truly remarkable and it was my good fortune that I got a chance to interact with him. I will treasure all his kind words, cryptic emails, and advice always. I especially want to thank my colleague Dr. D. Loukidis for permitting me to use our joint work in Chapter 4. Dr. P. Bandini and Dr. A. Carraro helped me with basic specimen reconstitution techniques. I would also like to thank Dr. M. Santagata for giving me a chance to be her TA so many times. It was a remarkable experience. I express my deepest gratitude to Ms. J. Lovell for all her assistance, guidance and discussions during my experimentation and, often at 4:25 pm. I would like to thank Dr. C. K. Chan for providing clarifications on the design and implementation of the triaxial machine. A few triaxial extension tests were performed by Ms. I. Z. Yildirim, I acknowledge her help. I am very thankful to Drs. Srinivasan, and Veda Chandrasekar for their kindness and hospitality. I also thank Dr. A. Shah, Dr. P. Banada and Euridice Oware for their friendship. Finally I am very grateful to my brother Koustuba for his love, support and encouragement throughout my life. iv TABLE OF CONTENTS Page LIST OF TABLES vii LIST OF FIGURES x ABSTRACT xiii LIST OF SYMBOLS xv CHAPTER 1. INTRODUCTION 1 1.1. Project Rationale 1 1.2. Thesis Scope and Objectives 3 1.3. Organization 4 CHAPTER 2. BACKGROUND 6 2.1. Introduction 6 2.2. Laboratory Element Testing 6 2.3. Stress And Strain Variables 8 2.4. Interpretation of P and Q 13 2.5. Critical-State Soil Mechanics 15 2.6. Mechanical Behavior Of Sands 15 2.6.1. Behavior of Sand Under 1-D and Isotropic Compression 16 2.6.2. Shear Behavior of Sands 17 2.6.3. Stress-Dilatancy Relationships 20 2.6.4. Critical State of Sands 25 2.7. Rationale Behind Laboratory Programs 31 2.8. Summary 32 CHAPTER 3. MATERIALS, EQUIPMENT, AND TESTING PROGRAM 34 3.1. Introduction 34 3.2. Advantages of the Triaxial Test 35 3.3. Equipment Description 37 3.3.1. Application And Measurement of Axial Load 39 3.3.2. Measurement of Axial Displacement 40 3.3.3. Measurement of Pore Pressure 40 3.3.4. Measurement of Volume Change 41 3.3.5. Modifications to the Triaxial Apparatus 41 3.4. Materials Used 44 3.5. Density Characterization of The Soils Studied 48 v Page 3.5.1. E max And E min of Silty and Clayey Sands 49 3.6. Methods of Sample Preparation 50 3.6.1. Moist Tamping (MT) 51 3.6.2. Water Pluviation Method (WP) 54 3.6.3. Modified Slurry Deposition (SD) 55 3.7. Saturation 58 3.7.1. Vacuum Saturation Method 58 3.7.2. Back-Pressure Saturation 59 3.8. Consolidation 60 3.9. Undrained Triaxial Shear 61 3.10. Disassembly and Water Content Analysis 61 3.11. Corrections to Triaxial Test Data 62 3.12. Summary 64 CHAPTER 4. UNDRAINED RESPONSE OF CLEAN AND SILTY SANDS IN TRIAXIAL COMPRESSION 65 4.1. Introduction 65 4.2. Previous Work 66 4.3. Materials and Equipment 68 4.4. Specimen Preparation 69 4.5. Results 70 4.5.1. Isotropic Compression 70 4.5.2. Undrained Shear in Triaxial Compression 75 4.5.3. Critical State 77 4.5.4. Phase-Transformation State 80 4.5.5. Quasi-Steady State 83 4.5.6. Undrained-Instability State 86 4.6. Discussion of Test Results 89 4.6.1. Critical State 89 4.6.2. Phase Transformation 97 4.6.3. Quasi-Steady State 104 4.6.4. Undrained Instability State 107 4.7. Conclusions 116 CHAPTER 5. EFFECTS OF PLASTICITY OF FINES ON THE UNDRAINED BEHAVIOR OF SANDY SOILS 118 5.1. Introduction 118 5.2. Previous Work 119 5.3. Experimental Program 122 5.3.1. Sample Preparation 122 5.3.2. Test Procedure 123 5.4. Results 123 5.4.1. Critical State 124 5.4.2. Phase-Transformation and Quasi-Steady States 125 5.4.3. Undrained Instability State 127 vi Page 5.5. Discussion of the Results 128 5.5.1. Critical State 128 5.5.2. Phase-Transformation State 133 5.5.3. Quasi-Steady State 138 5.5.4. Undrained Instability State 139 5.6. Parameters for Comparison of Densities 140 5.6.1. Intergranular Void Ratio 141 5.6.2. Relative Density and Relative State Parameter 145 5.7. Micromechanical Considerations of the Fabric of Sands with Fines 150 5.8. Conclusions 151 CHAPTER 6. UNDRAINED RESPONSE OF SANDY SOILS IN TRIAXIAL EXTENSION 153 6.1. Introduction 153 6.2. Previous Work 154 6.3. Experimental Details 156 6.4. Results 157 6.4.1. Critical State 158 6.4.2. Phase-Transformation State 159 6.4.3. Quasi-Steady State 160 6.4.4. Undrained Instability State 161 6.5. Discussion 162 6.5.1. Critical State 162 6.5.2. Phase-Transformation State 167 6.5.3. Quasi-Steady State 171 6.5.4. Undrained Instability State 172 6.6. Conclusions 175 CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS 176 7.1. Summary of Results 176 7.1.1. Overview of Research Program 176 7.1.2. Effects of Silt on the Undrained Behavior 177 7.1.3. Effects of Plasticity of Fines 178 7.1.4. Effects of Deformation Mode 178 7.2. Recommendations for Future Research 179 7.2.1. Overview 179 7.2.2. Expansion of the Current Project 180 7.2.3. Evaluation of Microstructure During Shearing 180 7.2.4. Detailed Investigation Deformation Mode 181 7.2.5. Correlation Between Laboratory Behavior and Field Performance 181 LIST OF REFERENCES 183 APPENDIX 193 VITA 227 vii LIST OF TABLES Table Page Table 2-1 Summary of Stress-Dilatancy Relationships (Been and Jefferies 2004) 24 Table 3-1–Maximum and minimum void ratios obtained for sands with fines (from ASTM procedures) 50 Table 3-2– Dry mixture proportion for target fines content (revised from Carraro 2004). 57 Table 4-1–Results of static undrained triaxial compression tests at critical state (Clean Sand) 78 Table 4-2– Results of static undrained triaxial compression tests at critical state (5% silty sand). 79 Table 4-3–Results of static undrained triaxial compression tests at critical state (10% silty sand). 79 Table 4-4– Results of static undrained triaxial compression tests at critical state (15% silty sand). 80 Table 4-5– Stresses and strain at phase transformation from undrained triaxial compression tests (clean sand) 81 Table 4-6– Stresses and strain at phase transformation from undrained triaxial compression tests (5% silty sand) 82 Table 4-7–Stresses and strain at phase transformation from undrained triaxial compression tests (10% silty sand) 82 Table 4-8– Stresses and strain at phase transformation from undrained triaxial compression tests (15% silty sand) 83 [...]... context of the critical- state framework The critical state was found to be independent of the initial fabric and of the pre-shear stress history of the sand The critical- state friction angle increased slightly with the addition of small percentages of silt The effect of silt on the characteristic states of undrained shear was evaluated and ways to relate the critical state with these states of behavior... percentage of fines in the sand matrix, plasticity of the fines, and the mode of deformation only under isotropically consolidated, and static loading triaxial conditions Four characteristic states were identified in the undrained response of the soils investigated: the undrained instability state, quasi-steady state, phasetransformation state and critical state The experimental data was analyzed in the context... both undrained and drained conditions In the case of undrained tests, this state of pre-yield straining can be identified when excess pore pressure develops In drained tests, this stage is determined at the onset of permanent volumetric strains A change of slope in a stress-strain curve, defines the point of yielding The strains generated beyond the yielding point are fully plastic The behavior of soil... Professors: Monica Prezzi and Rodrigo Salgado The thesis reports on experimental research on the static undrained response of silty and clayey sands The purpose of this testing program was to understand the stress-strain response of sands with small percentages of fines With this objective in sight, the testing program involved understanding and delineating the effect of four variables: density of the. .. studied the implications of multiple compression lines on the application of the critical- state theories They propose separating the state parameter (state parameter defined as the difference between the current void ratio and the critical state void ratio at a given state of stress) and overconsolidation ratio In case of clays these two variables have been treated as alternative forms of the same... strains at the undrained instability state in undrained triaxial extension (clean sand) 161 Table 6-8-Stress and strains at the undrained instability state in undrained triaxial extension (5% silty sand) 162 Table 6-9- Critical- state parameters for sandy soils tested under undrained triaxial extension conditions 165 Table 6-10- Stress ratios at critical state and at PT state. .. interactions and the elastic stiffness of the soil grains At such small levels of strains, there is no sliding of the soil grains relative to each other The behavior of sands at these small strain ranges are studied in the laboratory using Bender Element tests Studies on the small strain behavior of sands with silty and clayey fines were done by Carraro (2004) Linear Elastic Stiffness G or E Non-Linear... proposed The concepts used in constitutive modeling of sands can be extended to silty sands using the suitable input parameters The plasticity of the fines had an impact on the response of the sand The variables conventionally used in understanding the behavior of sands with small xiv amounts of fines were evaluated, and the validity of the different variables was assessed It was found that extension of. .. instability state for undrained triaxial compression and extension (clean and 5% silty sands) (continued) 173 Figure 6-8– Initial mean stress vs mean stress at the undrained instability state under triaxial extension conditions 174 xiii ABSTRACT Murthy, Tejas Gorur S Ph.D., Purdue University, August, 2006 Study of the Undrained Static Response of Sandy Soils in the Critical State Framework. .. for the silty and clayey sands investigated 1.3 Organization The thesis is composed of 7 chapters, including this chapter Chapter 1 describes the goals and the scope of the work done Chapter 2 deals with the basics of stress and strain analysis It also discusses the fundamental concepts of the critical- state framework and some important research carried out to date on the critical- state behavior of . 2006. Study of the Undrained Static Response of Sandy Soils in the Critical State Framework Major Professors: Monica Prezzi and Rodrigo Salgado The thesis reports on experimental research on the. the undrained instability state, quasi-steady state, phase- transformation state and critical state. The experimental data was analyzed in the context of the critical- state framework. The critical. Bullock STUDY OF THE UNDRAINED STATIC RESPONSE OF SANDY SOILS IN THE CRITICAL STATE FRAMEWORK A Dissertation Submitted to the Faculty of Purdue University by Tejas Gorur S Murthy In Partial