Instabilities in sands

Introduction

1.1. The problem
1.2. Aim
1.3. Outline

2. Theoretical Framework of Instabilities in Sands
2.1. Second-Order Work
2.1.1. First and Second Law of Thermodynamics
2.1.2. Total Energy and Helmholtz Free Energy
2.1.3. Instability Criterion for Symmetric Stiffness Matrix
2.1.4. Instability Criterion for Nonsymmetric Stiffness
Matrix
2.1.5. Second-Order Work in an Undrained Triaxial Test

2.2. Loss of Uniqueness - Bifurcation

2.3. Shear Bands - Bifurcation
2.3.1. Compatibility and equilibrium conditions

3. Constitutive Models 35

3.1. Von Wolffersdorff Hypoplastic Constitutive Model
3.2. Manzari - Dafalias Elastoplastic Constitutive Model
3.2.1. Critical State Line
3.2.2. Elasticity
3.2.3. Yield Function
3.2.4. Plastic Potential
3.2.5. Evolution Laws

4. Strain Localization Based on the Bifurcation Theory: An Application for use with the Hypoplastic Constitutive Model

4.1. Aspects Affecting Shear Bands in Finite Element
Simulations
4.1.1. Plane Strain Biaxial Test
4.1.2. Biaxial Simulations using FEM
4.1.3. Aspects of the Shear Band studied
4.1.4. Discussion
4.1.5. Concluding Remarks

4.2. Bifurcation Analysis under Plane Strain Conditions

4.3. Bifurcation Analysis for a General Stress Path
4.3.1. Numerical Results in Element Test
4.3.2. Concluding Remarks

5. Diffuse Instability in Sand under Undrained Loading Conditions - Liquefaction

5.1. Definitions of Liquefaction
5.1.1. Cyclic Mobility
5.1.2. Flow Liquefaction

5.2. Flow Liquefaction Criterion

5.3. Applicability of Criterion for Detecting the Onset of Flow Liquefaction
5.3.1. Monotonic Loading Conditions
5.3.2. Cyclic Loading Conditions

5.4. Predictions of Flow Liquefaction
5.4.1. Experiments by Verdugo and Ishihara (1996)
5.4.2. Experiments by Yamamuro and Covert (2001)
5.4.3. Experiments by Qadimi and Coop (2007)
5.4.4. Experiments by Pradahn (1989)
5.4.5. Concluding Remarks

5.5. Numerical Analysis of the Influence of Picnotropy, Barotropy and Anisotropy of Initial Stresses on the Onset of Flow Liquefaction under Static Loading Conditions
5.5.1. Introduction
5.5.2. Validation of the Criterion for Detecting Static Liquefaction under Anisotropic Initial
Conditions of Stress
5.5.3. Numerical Simulations
5.5.4. Concluding Remarks

6. Diffuse Instability in Sand Under Drained Loading Conditions

6.1. Introduction
6.2. Drained Instability Criterion

6.3. Numerical Predictions
6.3.1. Instability Predictions in Dilative Sand
6.3.2. Instability Predictions of Contractive Sand

6.4. Discussion
6.5. Concluding Remarks

7. Conclusions

7.1. Summary
7.2. Recommendations for Further Study

Appendix A. Loss of Uniqueness under Mixed Controlled Test
A.1. Loss of Uniqueness on Stress Controlled Test
A.2. Loss of Uniqueness in Strain Controlled Test
A.3. Test under Mixed Stress and Strain Control
A.4. Shear Band Analysis Based on Nov Concept

Appendix B. Integration of Hypoplastic Constitutive Model 181

Appendix C. Integration of the Manzari Dafalias Constitutive
Model
C.1. Midpoint Rule Algorithm
C.2. Back Euler Algorithm. Implicit Integration
C.3. Analytical Derivatives for the Implicit Algorithm

References