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

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