Fundamentals of Discrete Element Methods for Rock Engineering

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Bibliographic Details
Main Authors Jing, Lanru, Stephansson, Ove
Format eBook Book
LanguageEnglish
Published Chantilly Elsevier Science & Technology 2007
Edition1
Subjects
Methode des elements finis
Online AccessGet full text
ISBN9780444829375
0444829377

Cover

Table of Contents:
  • Chapter 5. The Basics of Fracture System Characterization - Field Mapping and Stochastic Simulations -- 5.1 Introduction -- 5.2 Field Mapping and Geometric Properties of Fractures -- 5.3 Statistical Distributions of the Fracture Geometry Parameters -- 5.4 Integrated Fracture System Characterization Under Site-Specific Conditions -- References -- Chapter 6. The Basics of Combinatorial Topology for Block System Representation -- 6.1 Surfaces and Homeomorphism -- 6.2 The Polyhedron and Its Characteristics -- 6.3 Simplex and Complex -- 6.4. Planar Schema of Polyhedra -- 6.5 Data Sets for Boundary Representation of Polyhedra -- 6.6 Block Tracing Using Boundary Operators -- References -- Chapter 7. Numerical Techniques for Block System Construction -- 7.1 Introduction -- 7.2 Block System Construction in 2D Using a Boundary Operator Approach -- 7.3 Block System Construction in 3D Using the Boundary Operator Approach -- 7.4 Summary Remarks -- References -- Part Three: DEM Approaches -- Chapter 8. Explicit Discrete Element Method for Block Systems - The Distinct Element Method -- 8.1 Introduction -- 8.2 Finite Difference Approximations to Derivatives -- 8.3 Dynamic and Static Relaxation Techniques -- 8.4 Dynamic Relaxation Method for Stress Analysis of Deformable Continua -- 8.5 Representation of Block Geometry and Internal Discretization -- 8.6 Strain and Stress Calculations for the Internal Elements -- 8.7 Representation of Block Contacts -- 8.8 Numerical Integration of the Equations of Motion -- 8.9 Contact Types and Detection in the Distinct Element Method -- 8.10 Damping -- 8.11 Linked-list Data Structure -- 8.12 Coupled Thermo-Hydro-Mechanical Analysis -- 8.13 Hybrid DEM-FEM/BEM Formulations -- 8.14 An Example of Comparative Modeling Using the FEM and DEM -- 8.15 Summary Remarks -- References
  • Front Cover -- Fundamentals of Discrete Element Methods for Rock Engineering -- Copyright Page -- Table of Contents -- Foreword -- Preface -- Chapter 1. Introduction -- 1.1 Characteristics of Fractured Rock Masses -- 1.2 Mathematical Models for Discontinuous Media -- 1.3 Historical Notes on DEM -- References -- Part One: Fundamentals -- Chapter 2. Governing Equations for Motion and Deformation of Block Systems and Heat Transfer -- 2.1 Newton's Equations of Motion for Particles -- 2.2 Newton-Euler Equations of Motion for Rigid Bodies -- 2.3 Newton's Equations of Motion for Rigid Body Translations -- 2.4 Euler's Equations of Rotational Motion - The General and Special Forms -- 2.5 Euler's Equations of Rotational Motion - Angular Momentum Formulation -- 2.6 Cauchy's Equations of Motion for Deformable Bodies -- 2.7 Coupling of Rigid Body Motion and Deformation for Deformable Bodies -- 2.8 Equations for Heat Transfer and Coupled Thermo-Mechanical Processes -- References -- Chapter 3. Constitutive Models of Rock Fractures and Rock Masses - the Basics -- 3.1 Mechanical Behavior of Rock Fractures -- 3.2 Shear Strength of Rock Fractures -- 3.3 Constitutive Models of Rock Fractures -- 3.4 Constitutive Models of Fractured Rock Masses as Equivalent Continua -- 3.5 Summary Remarks -- References -- Chapter 4. Fluid Flow and Coupled Hydro-Mechanical Behavior of Rock Fractures -- 4.1 Governing Equations for Fluid Flow in Porous Continua -- 4.2 Equation of Fluid Flow Through Smooth Fractures -- 4.3 Empirical Models for Fluid Flow Through Rough Fractures -- 4.4 Flow Equations of Connected Fracture Systems -- 4.5 Coupling of Fluid Flow and Deformation of Fractures -- 4.6 Remarks on Outstanding Issues -- References -- Part Two: Fracture System Characterization and Block Model Construction
  • A.1 Continuum Equilibrium Equations -- A.2 Moments of Equilibrium Equations -- Index
  • Chapter 9. Implicit Discrete Element Method for Block Systems - Discontinuous Deformation Analysis (DDA) -- 9.1 Energy Minimization and Global Equilibrium Equations -- 9.2 Contact Types and Detection -- 9.3 The Rigid Block Formulation -- 9.4 Deformable Blocks with a FEM Mesh of Triangular Elements -- 9.5 Deformable Blocks with a FEM Mesh of Quadrilateral Elements -- 9.6 Evaluation of Element Stiffness Matrices and Load Vectors -- 9.7 Assembly of the Global Equations of Motion -- 9.8 Fluid Flow and Coupled Hydro-mechanical Analysis in DDA -- 9.9 Summary Remarks -- References -- Chapter 10. Discrete Fracture Network (DFN) Method -- 10.1 Introduction -- 10.2 Representation of Fracture Networks -- 10.3 Solution for the Flow Fields within Fractures -- 10.4 Alternative Techniques - Percolation Theory -- 10.5 Alternative Techniques - Combinatorial Topology Theory -- 10.6 Summary Remarks -- References -- Chapter 11. Discrete Element Methods for Granular Materials -- 11.1 Introduction -- 11.2 Basic DEM Calculation Features for Granular Materials -- 11.3 Demonstration Examples of the PFC Code Applications -- 11.4 Numerical Stability and Time Integration Issues -- 11.5 Cosserat Continuum Equivalence to Particle Systems -- 11.6 Summary Remarks -- References -- Part Four: Application Studies -- Chapter 12. Case Studies of Discrete Element Method Applications in Geology, Geophysics and Rock Engineering -- 12.1 Introduction -- 12.2 Geologic Structures and Processes -- 12.3 Underground Civil Structures -- 12.4 Mine Structures -- 12.5 Radioactive Waste Disposal -- 12.6 Rock Reinforcement -- 12.7 Groundwater Flow and Geothermal Energy Extraction -- 12.8 Derivation of Equivalent Hydro-mechanical Properties of Fractured Rocks -- References -- Appendix: Derivation of Expressions for Stress and Stress Couple Tensors of Particle Systems as Equivalent Cosserat Continua