Đề tài A Volume-Mass constitutive model for unsaturated soils

A volume-mass constitutive model for unsaturated soils A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy in the Department of Civil and Geological Engineering University of Saskatchewan Saskatoon, Saskatchewan, Canada by Hung Q. Pham © Copyright Hung Q. Pham, July 2005. All rights reserved Copyright The author has agreed that the library, University of Saskatchewan, may make this thesis freely available for inspection. Moreover, the author has agreed that permission for extensive copying of his thesis for scholarly purposes may be granted by the professor or professors who supervised the thesis work recorded herein or in their absence, by the Head of the Department or the Dean of the College in which the thesis work was done. It is understood that due recognition will be given to the author of this thesis and to the University of Saskatchewan in any use of the material in this thesis. Copying or publication or any other use of this thesis for financial gain without approval by the University of Saskatchewan and the author’s written permission is prohibited. Requests for permission copy or to make other use of material in this thesis in whole or part should be addressed to: Head of the Department of Civil Engineering University of Saskatchewan Saskatoon, Canada S7N 5A9 i ABSTRACT Many geotechnical engineering problems involve combining two or more independent physical processes as a ‘coupled’ solution of seepage, volume change and shear strength. For any physical process being modeled, it is desirous to be able to compute any of the volume-mass soil properties. When the volume-mass soil properties are combined with the stress state of the soil, the result is a volume-mass constitutive relationship. Three volume-mass constitutive relationships (i.e., void ratio, water content and degree of saturation) are generally viewed as being the most fundamental; however, only two of the relations are independent. The unsaturated soil properties associated with seepage, volume change and shear strength problems are also related to the volume-mass soil properties. While the unsaturated soil properties are often estimated as simply being a function of the soil-water characteristic curve, it is more accurate to define the properties in a more rigorous manner in terms of the volume-mass soil properties. The advancement of computing capabilities means that it is quite easy to formulate constitutive relations for shear strength and permeability, for example, in terms of all volume-mass properties of the unsaturated soil. The objectives of this dissertation include: i) the development of volume-mass constitutive models for unsaturated soils; ii) the further study and verification of the volume-mass constitutive behavior of unsaturated soils; and iii) the development of techniques for visualization of volume-mass constitutive surfaces for unsaturated soils. To achieve these objectives, the present research study was conducted from both theoretical and experimental bases. The theoretical program commenced with a comprehensive literature review of the volume-mass constitutive relationships for unsaturated soils. A new, more rigorous volume-mass constitutive model was then proposed. Appropriate terminology was introduced for the development of the model, followed by an outline of the assumptions used and the mathematical derivation. The proposed model requires conventionally obtainable soil properties for its calibration. The model is capable of predicting both the void ratio and water content constitutive relationships for various unsaturated soils, taking into account elastic and plastic volume changes. Various stress paths can be ii simulated and hysteresis associated with the soil-water characteristic curve can be taken into account. Two closed-form equations for the volume-mass constitutive relationships were derived. A computer software program was written based on the theory of the proposed volume-mass constitutive model. Techniques for the visualization of the volume-mass constitutive surfaces were then presented. An experimental program was conducted in the laboratory. The experimental program involved the verification of a new testing apparatus. Several soils were selected for testing purposes and appropriate testing procedures were established (i.e., soil specimens were initially slurry). The testing stress paths followed in the experimental program were different from most research programs conducted in the past and reported in the research literature. Conclusions regarding the compressibility, stress path dependency, and hysteretic nature of the soil-water characteristic curve of an unsaturated soil were presented. A considerable number of test results (i.e., from both the experimental program and the research literature) were used in the verification of the new volume-mass constitutive model. This model has proven to be effective in predicting both collapse and expansion of a soil. The volume-mass constitutive model appears to predict behaviour in a satisfactory manner for a wide range of soils; however, the predictions appear to be superior for certain soils. In all cases the volume-mass predictions of the model appear to be satisfactory for geotechnical engineering practice. iii ACKNOWLEDGEMENTS First of all, I would like to sincerely thank my supervisor Professor Delwyn G. Fredlund for his brilliant supervising, consistent supports and encouragements throughout the process of completing my Ph.D. program. Without his great advices, constructive criticism, and careful review of the thesis, I would never be able to complete this work. During my study in Canada, Professor Fredlund and his wife JoAnne Fredlund treat me and my family as their family members, their cares and supports will never be forgotten. I will always feel indebted to him and his family. They are truly my Canadian family. I would like to deeply acknowledge all the committee members: Dr. S. Lee Barbour, Dr. J. Sharma, R. Fotouhi and Dr. J. Peng for their great advices, criticism, helpful comments and careful review of the thesis. I would like to especially extend my thanks to Dr. S. Lee Barbour for his continuous supports and enthusiasms. My special thanks go to Dr. James Blatz, my external examiner. His careful review and criticism help significantly improve the quality of the thesis. I am very grateful to Mr. Alex Kozlow for his valuable helps and friendship during my laboratory test program. I would like to thank my colleague Gilson Gitirana Jr. for his comments on Chapter 3 of the thesis. I must acknowledge all professors and secretaries in the department of Civil and Geological Engineering, and Vietnamese and Canadian friends at the University of Saskatchewan for their friendships and supports. I would like to thank my formal teachers Dr. Vu Cong Ngu and Dr. Nguyen Dinh Tien, and all the colleagues in the Geotechnical department, Hanoi University of Civil Engineering for their constantly supports and encouragements. This work will never be possible without helps and supports from numerous organizations: the University of Civil Engineering of Vietnam, the Ministry of Education and Training of Vietnam, and the Government of Vietnam, CIDA Canada, Department of Civil and Geological Engineering, University of Saskatchewan. Their helps and financial supports will never be forgotten. Family is always a key to all successes. I would like to express my very special thanks to my great mother, Pham Thuy Hang, for her extreme cares, supports and love throughout my life. I would like to express my thanks from the bottom of my heart to my beloved wife, Vu Hoang Lan, for her great cares, love and being a great wife. This work is also for my Daughter, Pham Lan Chi, you have strengthened your daddy’s will, thank you and love you so much. Last but not least, I would like to express my gratefulness to my big family in Vietnam for their help, supports and encouragements. Once again, I would like to thank all of you for your helps and supports. There are so much that have learned during the last five years staying in Canada: the friendship, the way to live, to work and to treat people, etc. Yes, that is even more valuable than any degrees. I hope that I will be able to pass along to my Vietnamese students what I had learned. This work is dedicated to my Grandfather Pham Gia Lang In the memory of my Grandparents and my Farther Pham Van An With best regards, Hung Quang Pham iv TABLE OF CONTENT COPYRIGHT................................................................................................................................... i ABSTRACT ................................................................................................................................... ii ACKNOWLEDGEMENT............................................................................................................... iv TABLE OF CONTENT................................................................................................................... v LIST OF TABLES ......................................................................................................................... xi LIST OF FIGURES ...................................................................................................................... xii LIST OF NOTATIONS AND SYMBOLS ................................................................................. xxvii CHAPTER 1: INTRODUCTION 1.1 BACKGROUND....................................................................................................................... 1 1.2 OBJECTIVES AND SCOPE.................................................................................................... 7 1.3 SUMMARY OF CHAPTERS.................................................................................................... 8 CHAPTER 2: LITERATURE REVIEW 2.1 GENERAL.............................................................................................................................. 10 2.2 VOLUME-MASS STATE VARIABLES ................................................................................. 11 2.2.1 Stress State Variables .................................................................................................... 12 2.2.2 State Variables................................................................................................................ 16 2.3 BASIC VOLUME-MASS CONSTITUTIVE RELATIONS ...................................................... 17 2.3.1 Volume-Mass Constitutive Relations on the Zero Soil Suction Plane. ........................... 18 2.3.2 Volume-Mass Constitutive Relationships on Non-Zero Soil Suction Planes. ................. 24 2.3.3 Volume-Mass constitutive Relations on Zero Net Mean Stress Plane ........................... 32 2.3.4 Volume-Mass constitutive Relations on the Non-Zero Net Mean Stress Planes ........... 46 2.3.5 Water Content and Soil Volume Relationship................................................................. 50 2.4 VOLUME-MASS CONSTITUTIVE SURFACES FOR UNSATURATED SOILS................... 53 2.4.1 General ........................................................................................................................... 53 2.4.2 Prediction or Estimation of the Volume-Mass Constitutive Surfaces.............................. 55 2.4.3 Uniqueness of the Volume-Mass Constitutive Surfaces................................................. 59 2.5 VOLUME-MASS CONSTITUTIVE MODELS FOR UNSATURATED SOILS....................... 61 2.5.1 General ........................................................................................................................... 61 2.5.2 Physically-Based Elastic Constitutive Models ................................................................ 61 2.5.3 Surface Fitting Constitutive Models ................................................................................ 65 2.5.4 Elasto-Plastic Models...................................................................................................... 70 v 2.6 MODELING THE EFFECT OF SHEAR STRESS TO THE VOLUME-MASS CONSTITUTIVE RELATIONS..................................................................................................... 79 2.7 MEASUREMENT OF THE VOLUME-MASS CONSTITUTIVE SURFACES........................ 81 2.7.1 Testing Equipment .......................................................................................................... 81 2.7.2 Materials and Preparation............................................................................................... 87 2.7.3 Common Testing Programs in the Literature.................................................................. 87 2.8 APPLICATIONS OF THE VOLUME-MASS CONSTITUTIVE RELATIONSHIPS IN THE PREDICTION OF SOIL PROPERTIES ....................................................................................... 91 2.8.1 Prediction of Shear Strength Function............................................................................ 91 2.8.2 Prediction of Hydraulic Conductivity Function ................................................................ 92 2.9 CHAPTER SUMMARY .......................................................................................................... 95 CHAPTER 3: THEORY 3.1 GENERAL.............................................................................................................................. 97 3.2 TERMINOLOGY FOR THE PROPOSED MODEL................................................................ 98 3.2.1 State Variables:............................................................................................................... 99 3.2.2 Pore-Size Distribution Curve......................................................................................... 101 3.2.3 Development of the Proposed Volume-Mass Constitutive Model ................................ 104 3.3 ASSUMPTIONS, SYMBOLS AND NOTATIONS................................................................ 107 3.3.1 Assumptions.................................................................................................................. 107 3.3.2 Notations and Symbols ................................................................................................. 115 3.4 STRESS-STRAIN RELATIONSHIP FOR THE SOIL STRUCTURE SURROUNDING A PORE ......................................................................................................................................... 117 3.4.1 Drying-Wetting Processes under Zero Net Mean Stress.............................................. 117 3.4.2 Drying Process under a Constant Net Mean Stress ..................................................... 119 3.4.3 Wetting Process under a Constant Net Mean Stress ................................................... 128 3.4.4 Loading-Unloading Processes at a Constant Soil Suction ........................................... 136 3.4.5 Summary Stress-Strain Relationship for the Soil Structure Surrounding a Pore ......... 136 3.5 YIELD STRESS INDUCED FROM SEVERAL SINGLE STRESS PATHS......................... 137 3.5.1 Drying and Wetting Processes under Zero Net Mean Stress....................................... 137 3.5.2 Loading-Unloading Processes at Zero Soil Suction. .................................................... 138 3.5.3 Drying and Wetting Processes at a Constant Net Mean Stress ................................... 140 3.5.4 Loading-Unloading Processes at a Constant Soil Suction. .......................................... 142 3.5.5 Compression Curve of a Soil at a Constant Soil Suction.............................................. 144 vi 3.6 MODELS FOR THE SOIL-WATER CHARACTERISTIC CURVE OF VOLUME CHANGE SOILS......................................................................................................................................... 146 3.6.1 An Equation with Independent Properties .................................................................... 147 3.6.2 A Simple Equation......................................................................................................... 150 3.7 DETERMINATION OF THE COMPRESSION INDICES OF A WATER-FILLED PORE.... 151 3.7.1 An Equation for Volume Change along the Initial Drying Process ............................... 151 3.7.2 Volume Change of Collapsible and Non-Collapsible Pores ......................................... 157 3.7.3 Summary of the Compression Indices of a Water-Filled Pore...................................... 160 3.8 A MODEL FOR HYSTERETIC SOIL-WATER CHARACTERISTIC CURVES................... 162 3.8.1 A Model for the Three Key Hysteretic Soil-Water Characteristics Curves.................... 162 3.8.2 Scanning Hysteretic Soil-Water Characteristics Curves............................................... 167 3.8.3 Hysteresis Model in the Context of the Pore-Size Distribution ..................................... 169 3.9 ANALYTICAL SOLUTION FOR THE VOLUME-MASS CONSTITUTIVE RELATIONSHIPS ................................................................................................................................................... 171 3.9.1 Yield Stresses ............................................................................................................... 174 3.9.2 Prediction of the Water Content Surface ...................................................................... 176 3.9.3 Prediction of the Void Ratio Surface............................................................................. 179 3.10 NUMERICAL SOLUTION FOR VOLUME-MASS CONSTITUTIVE RELATIONSHIPS ... 186 3.11 CONVERSION FOR ONE-DIMENSIONAL (K0) LOADING CONDITION......................... 191 3.12 DETERMINATION OF THE MODEL PARAMETERS ...................................................... 193 3.13 CHAPTER SUMMARY ...................................................................................................... 195 CHAPTER 4: VISUALIZATION 4.1 GENERAL............................................................................................................................ 197 4.2 MATERIALS ........................................................................................................................ 198 4.3 APPLICATION OF THE VOLUME-MASS CONSTITUTIVE EQUATIONS ........................ 199 4.4 VISUALIZATION OF THE VOLUME-MASS CONSTITUTIVE SURFACES....................... 207 4.4.1 Stress Paths.................................................................................................................. 207 4.4.2 Volume-Mass Constitutive Surfaces for the Three Artificial Soils................................. 209 4.4.3 Discussions ................................................................................................................... 219 4.5 VISUALIZATION OF THE UNSATURATED SOIL PROPERTY SURFACES ................... 220 4.5.1 Shear Strength Surfaces............................................................................................... 222 4.5.2 Hydraulic Conductivity Surfaces ................................................................................... 224 CHAPTER 5: LABORATORY TESTING PROGRAM vii 5.1 GENERAL............................................................................................................................ 227 5.2 OBJECTIVES OF THE TESTING PROGRAM..........................