Оглавление
Manuel Pastor. Computational Geomechanics
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Computational Geomechanics. Theory and Applications
Preface
1 Introduction and the Concept of Effective Stress. 1.1 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. 1.3.1 A Single Fluid Present in the Pores – Historical Note
1.3.2 An Alternative Approach to Effective Stress
1.3.3 Effective Stress in the Presence of Two (or More) Pore Fluids – Partially Saturated Media
Note
References
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)
2.2.1 Equilibrium and Mass Balance Relationship (u, w, and p)
2.2.2 Simplified Equation Sets (u–p Form)
2.2.3 Limits of Validity of the Various Approximations
2.3 Partially Saturated Behavior with Air Pressure Neglected (pa = 0)
2.3.1 Why Is Inclusion of Partial Saturation Required in Practical Analysis?
2.3.2 The Modification of Equations Necessary for Partially Saturated Conditions
2.4 Partially Saturated Behavior with Air Flow Considered (pa ≥ 0) 2.4.1 The Governing Equations Including Air Flow
2.4.2 The Governing Equation
2.5 Alternative Derivation of the Governing Equation (of Sections 2.2–2.4) Based on the Hybrid Mixture Theory
2.5.1 Kinematic Equations
2.5.2 Microscopic Balance Equations
2.5.3 Macroscopic Balance Equations
2.5.4 Constitutive Equations
2.5.5 General Field Equations
2.5.6 Nomenclature for Section 2.5
Superscripts or subscripts
2.6 Conclusion
References
3 Finite Element Discretization and Solution of the Governing Equations. 3.1 The Procedure of Discretization by the Finite Element Method
3.2 u‐p Discretization for a General Geomechanics’ Finite Element Code. 3.2.1 Summary of the General Governing Equations
3.2.2 Discretization of the Governing Equation in Space
3.2.3 Discretization in Time
3.2.4 General Applicability of Transient Solution (Consolidation, Static Solution, Drained Uncoupled, and Undrained) 3.2.4.1 Time Step Length
3.2.4.2 Splitting or Partitioned Solution Procedures
3.2.4.3 The Consolidation Equation
3.2.4.4 Static Problems – Undrained and Fully Drained Behavior
3.2.5 The Structure of the Numerical Equations Illustrated by their Linear Equivalent
3.2.6 Damping Matrices
3.3 Theory: Tensorial Form of the Equations
3.4 Conclusions
References
4 Constitutive Relations: Plasticity. 4.1 Introduction
4.2 The General Framework of Plasticity. 4.2.1 Phenomenological Aspects
4.2.2 Generalized Plasticity
4.2.2.1 Basic Theory
4.2.2.2 Inversion of the Constitutive Tensor
4.2.3 Classical Theory of Plasticity. 4.2.3.1 Formulation as a Particular Case of Generalized Plasticity Theory
4.2.3.2 Yield and Failure Surfaces
4.2.3.3 Hardening, Softening, and Failure
4.2.3.4 Some Frequently Used Failure and Yield Criteria. Pressure‐Independent Criteria: von Mises–Huber Yield Criterion
Tresca Criterion
Pressure‐Dependent Criteria: Mohr–Coulomb Surface
Drucker–Prager Criterion
4.2.3.5 Consistency Condition for Strain‐Hardening Materials
4.2.3.6 Computational Aspects
4.3 Critical State Models. 4.3.1 Introduction
4.3.2 Critical State Models for Normally Consolidated Clays. 4.3.2.1 Hydrostatic Loading: Isotropic Compression Tests
4.3.2.2 Triaxial Rest
4.3.2.3 Critical State
4.3.3 Critical State Models for Sands
4.3.3.1 Hydrostatic Compression
4.3.3.2 Dense and Loose Behavior
4.3.3.3 Critical State Line
4.3.3.4 Dilatancy
4.3.3.5 A Unified Approach to Density and Pressure Dependency of Sand Behavior: The State Parameter
4.3.3.6 Constitutive Modelling of Sand Within Critical State Framework
4.4 Generalized Plasticity Modeling. 4.4.1 Introduction
4.4.2 A Generalized Plasticity Model for Clays
4.4.2.1 Normally Consolidated Clays
4.4.2.2 Overconsolidated Clays
4.4.3 The Basic Generalized Plasticity Model for Sands. 4.4.3.1 Monotonic Loading
4.4.3.2 Three‐Dimensional Behavior
4.4.3.3 Unloading and Cyclic Loading
4.4.4 Anisotropy. 4.4.4.1 Introductory Remarks
4.4.4.2 Proposed Approach
4.4.4.3 A Generalized Plasticity Model for the Anisotropic Behavior of Sand
4.4.5 A State Parameter‐Based Generalized Plasticity Model for Granular Soils
4.4.6 Generalized Plasticity Modeling of Bonded Soils
4.4.7 Generalized Plasticity Models for Unsaturated Soils
4.4.8 Recent Developments of Generalized Plasticity Models
4.4.9 A Note on Implicit Integration of Generalized Plasticity Models
4.5 Alternative Advanced Models. 4.5.1 Introduction
4.5.2 Kinematic Hardening Models
4.5.3 Bounding Surface Models and Generalized Plasticity
4.5.4 Hypoplasticity and Incrementally Nonlinear Models
4.6 Conclusion
References
5 Special Aspects of Analysis and Formulation: Radiation Boundaries, Adaptive Finite Element Requirement, and Incompressible Behavior. 5.1 Introduction
5.2 Far‐Field Solutions in Quasi‐Static Problems1
5.3 Input for Earthquake Analysis and Radiation Boundary. 5.3.1 Specified Earthquake Motion: Absolute and Relative Displacements
5.3.2 The Radiation Boundary Condition: Formulation of a One‐Dimensional Problem
5.3.3 The Radiation Boundary Condition: Treatment of Two‐Dimensional Problems
5.3.4 The Radiation Boundary Condition: Scaled Boundary‐Finite Element Method3
5.3.5 Earthquake Input and the Radiation Boundary Condition – Concluding Remarks
5.4 Adaptive Refinement for Improved Accuracy and the Capture of Localized Phenomena
5.4.1 Introduction to Adaptive Refinement
5.4.2 Adaptivity in Time4
5.4.3 Localization and Strain Softening: Possible Nonuniqueness of Numerical Solutions
5.4.4 Regularization Through Gradient‐Dependent Plasticity5
5.5 Stabilization of Computation for Nearly Incompressible Behavior with Mixed Interpolation6. 5.5.1 The Problem of Incompressible Behavior Under Undrained Conditions
5.5.2 The Velocity Correction and Stabilization Process
5.5.3 Examples Illustrating the Effectiveness of the Operator Split Procedure
5.5.4 The Reason for the Success of the Stabilizing Algorithm
5.5.5 An Operator Split Stabilizing Algorithm for the Consolidation of Saturated Porous Media
5.5.6 Examples Illustrating the Effectiveness of the Operator Split Stabilizing Algorithm for the Consolidation of Saturated Porous Media
5.5.7 Further Improvements7
5.6 Conclusion
Notes
References
6 Examples for Static, Consolidation, and Hydraulic Fracturing Problems. 6.1 Introduction
6.2 Static Problems
6.2.1 Example (a): Unconfined Situation – Small Constraint
6.2.1.1 Embankment
6.2.1.2 Footing
6.2.2 Example (b): Problems with Medium (Intermediate) Constraint on Deformation
6.2.3 Example (c): Strong Constraints – Undrained Behavior
6.2.4 Example (d): The Effect of the π Section of the Yield Criterion
6.3 Seepage1
6.3.1 Concluding Remarks
6.4 Consolidation2
6.4.1 Benchmark for a Poroelastic Column
6.4.2 Single‐Aquifer Withdrawal
6.4.3 3‐D Consolidation with Adaptivity in Time
6.5 Hydraulic Fracturing: Fracture in a Fully Saturated Porous Medium Driven By Increase in Pore Fluid Pressure3
6.5.1 2‐D and 3‐D Quasi‐Static Hydraulic Fracturing
6.5.1.1 Solid Phase: Continuous Medium
6.5.1.2 Solid Phase: Cohesive Fracture Model – Mode I Crack Opening
6.5.1.3 Solid Phase: Cohesive Fracture Model – Mode II and Mixed Mode Crack Opening
6.5.1.4 Linear Momentum Balance for the Mixture Solid + Water
6.5.1.5 Liquid Phase: Medium and Crack Permeabilities
6.5.1.6 Mass Balance Equation for Water (Incorporating Darcy’s Law)
6.5.1.7 Discretized Governing Equations and Solution Procedure
6.5.1.8 Examples
6.5.2 Dynamic Fracturing in Saturated Porous Media
6.5.3 Coupling of FEM for the Fluid with Discrete or Nonlocal Methods for the Fracturing Solid
6.6 Conclusion
References
Notes
7 Validation of Prediction by Centrifuge. 7.1 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
General Analysing Procedure
7.4.1 Description of the Precise Method of Determination of Each Coefficient in the Numerical Model
7.4.2 Modelling of the Laminar Box
7.4.3 Parameters Identified for Pastor‐Zienkiewicz Mark III Model
7.5 Comparison with the Velacs Centrifuge Experiment. 7.5.1 Description of the Models. Model No. 1
Model No. 3
Model No.11
7.5.2 Comparison of Experiment and Prediction
7.6 Centrifuge Test of a Retaining Wall (Dewooklar et al 2009)
7.7 Conclusions
References
Note
8 Applications to Unsaturated Problems. 8.1 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
8.4.1 Consolidation of Fully Saturated Soil Column
8.4.2 Consolidation of Fully and Partially Saturated Soil Column
8.4.3 Consolidation of Two‐Dimensional Soil Layer Under Fully and Partially Saturated Conditions
8.4.4 Fully Saturated Soil Column Under Earthquake Loading
8.4.5 Elastoplastic Large‐Strain Behavior of an Initially Saturated Vertical Slope Under a Gravitational Loading and Horizontal Earthquake Followed by a Partially Saturated Consolidation Phase
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 Reservoirs1
8.7 Initiation of Landslide in Partially Saturated Soil2
8.8 Conclusion
References
Notes
9 Prediction Application and Back Analysis to Earthquake Engineering: Basic Concepts, Seismic Input, Frequency, and Time Domain Analysis. 9.1 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)
9.4.1 Integration of Dynamic Equation by Half‐Cycle of Wave
9.4.2 Example of Analysis
9.5 Port Island Liquefaction Using One‐Column Nonlinear Analysis in Multi‐Direction. 9.5.1 Introductory Remarks
9.5.2 Multidirectional Loading Observed and Its Numerical Modeling – Simulation of Liquefaction Phenomena Observed at Port Island
9.5.2.1 Conditions and Modeling
9.5.2.2 Results of Simulation
9.5.2.3 Effects of Multidirectional Loading
9.6 Simulation of Liquefaction Behavior During Niigata Earthquake to Illustrate the Effect of Initial (Shear) Stress
9.6.1 Influence of Initial Shear Stress
9.6.1.1 Significance of ISS Component to the Responses. 9.6.1.1.1 Response Acceleration
9.6.1.2 Excess Pore Water Pressure
9.6.1.2.1 Theoretical Consideration
9.7 Large‐Scale Liquefaction Experiment Using Three‐Dimensional Nonlinear Analysis
9.7.1 Analytical Model and Condition
9.7.1.1 Constitutive Model
9.7.1.2 Dilatancy Modeling
9.7.1.3 Determination of the Material Parameters
9.7.2 Input Motion
9.7.3 Analysis Results
9.8 Lower San Fernando Dam Failure
References
10 Beyond Failure: Modeling of Fluidized Geomaterials: Application to Fast Catastrophic Landslides. 10.1 Introduction
10.2 Mathematical Model: A Hierarchical Set of Models for the Coupled Behavior of Fluidized Geomaterials
10.2.1 General 3D Model
10.2.2 A Two‐Phase Depth‐Integrated Model
10.2.3 A Note on Reference Systems
10.3 Behavior of Fluidized Soils: Rheological Modeling Alternatives
10.3.1 Bingham Fluid
10.3.2 Frictional Fluid
10.3.3 Cohesive‐Frictional Fluids
10.3.4 Erosion
10.4 Numerical Modeling: 2‐Phase Depth‐Integrated Coupled Models
10.4.1 SPH Fundamentals
10.4.2 An SPH Lagrangian Model for Depth‐Integrated Equations. 10.4.2.1 Introduction and Fundamentals of SPH
10.4.2.2 SPH Discretization
10.4.2.3 SPH Modeling of Two‐Phase Depth‐Integrated Equations
10.4.2.4 Boundary Conditions in Two‐Phase Depth‐Integrated Equations
10.4.2.5 Excess Pore Water Pressure Modeling in Two‐Phase Depth‐Integrated Equations
10.5 Examples and Applications
10.5.1 The Thurwieser Rock Avalanche
10.5.2 A Lahar in Popocatépetl Volcano
10.5.3 Modeling of Yu Tung Road Debris Flow
10.6 Conclusion
References
Note
Index. a
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