Manuel Pastor - Computational Geomechanics

1 Cover

2 Title Page Computational Geomechanics Theory and Applications Second Edition Andrew H. C. Chan University of Tasmania Manuel Pastor ETS de Ingenieros de Caminos Universidad Politécnica de Madrid, Spain formerly at Centro de Estudios y Experimentación de Obras Públicas, Madrid, Spain Bernhard A. Schrefler University of Padua Tadahiko Shiomi Mind Inc., 3D Laboratory, Japan O. C. Zienkiewicz CINME, UNESCO former Professor of Numerical Methods in Engineering at Technical University of Catalonia (UPC), Spain Theory and Applications

3 Copyright Page

4 Preface

5 1 Introduction and the Concept of Effective Stress1.1 Preliminary Remarks 1.2 The Nature of Soils and Other Porous Media: Why a Full Deformation Analysis Is the Only Viable Approach for Prediction 1.3 Concepts of Effective Stress in Saturated or Partially Saturated Media Note References

6 2 Equations Governing the Dynamic, Soil–Pore Fluid, Interaction 2.1 General Remarks on the Presentation 2.2 Fully Saturated Behavior with a Single Pore Fluid (Water) 2.3 Partially Saturated Behavior with Air Pressure Neglected ( p a= 0) 2.4 Partially Saturated Behavior with Air Flow Considered ( p a≥ 0) 2.5 Alternative Derivation of the Governing Equation (of Sections 2.2–2.4) Based on the Hybrid Mixture Theory 2.6 Conclusion References

7 3 Finite Element Discretization and Solution of the Governing Equations3.1 The Procedure of Discretization by the Finite Element Method 3.2 u‐p Discretization for a General Geomechanics’ Finite Element Code 3.3 Theory: Tensorial Form of the Equations 3.4 Conclusions References

8 4 Constitutive Relations4.1 Introduction 4.2 The General Framework of Plasticity 4.3 Critical State Models 4.4 Generalized Plasticity Modeling 4.5 Alternative Advanced Models 4.6 Conclusion References

9 5 Special Aspects of Analysis and Formulation5.1 Introduction 5.2 Far‐Field Solutions in Quasi‐Static Problems 1 5.3 Input for Earthquake Analysis and Radiation Boundary 5.4 Adaptive Refinement for Improved Accuracy and the Capture of Localized Phenomena 5.5 Stabilization of Computation for Nearly Incompressible Behavior with Mixed Interpolation 6 5.6 Conclusion Notes References

10 6 Examples for Static, Consolidation, and Hydraulic Fracturing Problems6.1 Introduction 6.2 Static Problems 6.3 Seepage 1 6.4 Consolidation 2 6.5 Hydraulic Fracturing: Fracture in a Fully Saturated Porous Medium Driven By Increase in Pore Fluid Pressure 3 6.6 Conclusion References

11 7 Validation of Prediction by Centrifuge7.1 Introduction 7.2 Scaling Laws of Centrifuge Modelling 7.3 Centrifuge Test of a Dyke Similar to a Prototype Retaining Dyke in Venezuela 7.4 The Velacs Project 7.5 Comparison with the Velacs Centrifuge Experiment 7.6 Centrifuge Test of a Retaining Wall (Dewooklar et al 2009) 7.7 Conclusions References

12 8 Applications to Unsaturated Problems8.1 Introduction 8.2 Isothermal Drainage of Water from a Vertical Column of Sand 8.3 Air Storage Modeling in an Aquifer 8.4 Comparison of Consolidation and Dynamic Results Between Small Strain and Finite Deformation Formulation 8.5 Dynamic Analysis with a Full Two‐Phase Flow Solution of a Partially Saturated Soil Column Subjected to a Step Load 8.6 Compaction and Land Subsidence Analysis Related to the Exploitation of Gas Reservoirs 1 8.7 Initiation of Landslide in Partially Saturated Soil 2 8.8 Conclusion References

13 9 Prediction Application and Back Analysis to Earthquake Engineering9.1 Introduction 9.2 Material Properties of Soil 9.3 Characteristics of Equivalent Linear Method 9.4 Port Island Liquefaction Assessment Using the Cycle‐Wise Equivalent Linear Method (Shiomi et al. 2008) 9.5 Port Island Liquefaction Using One‐Column Nonlinear Analysis in Multi‐Direction 9.6 Simulation of Liquefaction Behavior During Niigata Earthquake to Illustrate the Effect of Initial (Shear) Stress 9.7 Large‐Scale Liquefaction Experiment Using Three‐Dimensional Nonlinear Analysis 9.8 Lower San Fernando Dam Failure References

14 10 Beyond Failure: Modeling of Fluidized Geomaterials10.1 Introduction 10.2 Mathematical Model: A Hierarchical Set of Models for the Coupled Behavior of Fluidized Geomaterials 10.3 Behavior of Fluidized Soils: Rheological Modeling Alternatives 10.4 Numerical Modeling: 2‐Phase Depth‐Integrated Coupled Models 10.5 Examples and Applications 10.6 Conclusion References

15 Index

16 End User License Agreement

1 Chapter 2 Table 2.1 Comparative sets of coupled equations governing deformation and fl... Table 2.2 Thermodynamic properties for the microscopic mass balance equatio...

2 Chapter 4Table 4.1 Parameters used in the simulationsTable 4.2 Model parameters used in simulations.

3 Chapter 6Table 6.1 Material data.Table 6.2 Material properties for a water‐injected test case.Table 6.3 Material parameters for the example of Figure 6.46.

4 Chapter 7Table 7.1 Soil Model DataTable 7.2 Material data for Finite Element analysis Table 7.3VELACS Project – Summary of centrifuge tests and class A/B predict...

5 Chapter 8Table 8.1 Material data used in the test of a saturated sand column subjecte...Table 8.2 Identified parameters for the constitutive model.Table 8.3 Geotechnical properties for soil layers (Cascini et al. 2003).

6 Chapter 9Table 9.1 Material properties of used‐for‐single DOF problem.Table 9.2 Material properties of soil layer (Shiomi et al. 2008).Table 9.3 Cases studied.Table 9.4 Soil layer and material properties.Table 9.5 Typical soil parameters (Yoshida et al. 2008b).Table 9.6 Material properties used in the Lower San Fernando dam analysis.Table 9.7 Coefficients of saturation function

1 Chapter 1 Figure 1.1 The Vajont reservoir, failure of Mant Toc in 1963 (9 October): (a... Figure 1.2 Failure and reconstruction of original conditions of Lower San Fe... Figure 1.3 Various idealized structures of fluid-saturated porous solids: (a... Figure 1.4 A porous material subject to external hydrostatic pressure increa... Figure 1.5 Two fluids in pores of a granular solid (water and air). (a) Air ... Figure 1.6 Typical relations between pore pressure head, h w= p w/ χ w, sa...

2 Chapter 2 Figure 2.1 The soil column – variation of pore pressure with depth for vario... Figure 2.2 Zones of sufficient accuracy for various approximations: Zone 1, Figure 2.3 A partially saturated dam. Initial steady‐state solution. Only sa... Figure 2.4 Test example of partially saturated flow experiment by Liakopoulo...

3 Chapter 3 Figure 3.1 Some typical two‐dimensional elements for linear and quadratic in... Figure 3.2 Elements used for coupled analysis, displacement ( u ) and pressure...

4 Chapter 4 Figure 4.1 Behavior of mild steel Figure 4.2 Behavior of soft clayFigure 4.3 Behavior of materials with damageFigure 4.4 General stress–strain behaviorFigure 4.5 Typical hardening behavior of clay. (a) Yield surfaces (b) Stress...Figure 4.6 Ideal plasticity ( κ = constant) (a) stress path; (b) stress–...Figure 4.7 Softening behavior (a) stress path; (b) stress–strain curveFigure 4.8 von Mises–Huber yield criterion. (a) In the principal stress spac...Figure 4.9 von Mises criterion for plane stress conditionsFigure 4.10 Tresca yield criterion. (a) In principal stress axes (b) in the ...Figure 4.11 Tresca criterion for plane stress conditionsFigure 4.12 Mohr–Coulomb lawFigure 4.13 Mohr–Coulomb yield surfaceFigure 4.14 Hydrostatic compression stress pathFigure 4.15 Hydrostatic compression test on a normally consolidated clay. (a...Figure 4.16 Open and closed yield surfacesFigure 4.17 Triaxial stress conditionsFigure 4.18 Consolidated drained stress pathFigure 4.19 Consolidated drained stress path in