| Foreword | p. ix |
| Preface | p. xi |
| Introduction | p. 1 |
| Characteristics of Fractured Rock Masses | p. 2 |
| Mathematical Models for Discontinuous Media | p. 7 |
| Historical Notes on DEM | p. 14 |
| References | p. 18 |
| Fundamentals | p. 23 |
| Governing Equations for Motion and Deformation of Block Systems and Heat Transfer | p. 25 |
| Newton's Equations of Motion for Particles | p. 26 |
| Newton-Euler Equations of Motion for Rigid Bodies | p. 27 |
| Newton's Equations of Motion for Rigid Body Translations | p. 29 |
| Euler's Equations of Rotational Motion - the General and Special Forms | p. 29 |
| Euler's Equations of Rotational Motion - Angular Momentum Formulation | p. 32 |
| Cauchy's Equations of Motion for Deformable Bodies | p. 34 |
| Coupling of Rigid Body Motion and Deformation for Deformable Bodies | p. 37 |
| Equations for Heat Transfer and Coupled Thermo-Mechanical Processes | p. 43 |
| References | p. 45 |
| Constitutive Models of Rock Fractures and Rock Masses - the Basics | p. 47 |
| Mechanical Behavior of Rock Fractures | p. 48 |
| Shear Strength of Rock Fractures | p. 50 |
| Constitutive Models of Rock Fractures | p. 55 |
| Constitutive Models of Fractured Rock Masses as Equivalent Continua | p. 67 |
| Summary Remarks | p. 94 |
| References | p. 103 |
| Fluid Flow and Coupled Hydro-Mechanical Behavior of Rock Fractures | p. 111 |
| Governing Equations for Fluid Flow in Porous Continua | p. 112 |
| Equation of Fluid Flow Through Smooth Fractures | p. 116 |
| Empirical Models for Fluid Flow through Rough Fractures | p. 120 |
| Flow Equations of Connected Fracture Systems | p. 126 |
| Coupling of Fluid Flow and Deformation of Fractures | p. 128 |
| Remarks on Outstanding Issues | p. 134 |
| References | p. 138 |
| Fracture System Characterization and Block Model Construction | p. 145 |
| The Basics of Fracture System Characterization - Field Mapping and Stochastic Simulations | p. 147 |
| Introduction | p. 147 |
| Field Mapping and Geometric Properties of Fractures | p. 148 |
| Statistical Distributions of the Fracture Geometry Parameters | p. 161 |
| Integrated Fracture System Characterization Under Site-Specific Conditions | p. 171 |
| References | p. 173 |
| The Basics of Combinatorial Topology for Block System Representation | p. 179 |
| Surfaces and Homeomorphism | p. 181 |
| The Polyhedron and its Characteristics | p. 182 |
| Simplex and Complex | p. 184 |
| Planar Schema of Polyhedra | p. 190 |
| Data Sets for Boundary Representation of Polyhedra | p. 195 |
| Block Tracing Using Boundary Operators | p. 196 |
| References | p. 197 |
| Numerical Techniques for Block System Construction | p. 199 |
| Introduction | p. 199 |
| Block System Construction in 2D Using a Boundary Operator Approach | p. 201 |
| Block System Construction in 3D Using the Boundary Operator Approach | p. 214 |
| Summary Remarks | p. 228 |
| References | p. 231 |
| DEM Approaches | p. 233 |
| Explicit Discrete Element Method for Block Systems - The Distinct Element Method | p. 235 |
| Introduction | p. 235 |
| Finite Difference Approximations to Derivatives | p. 237 |
| Dynamic and Static Relaxation Techniques | p. 240 |
| Dynamic Relaxation Method for Stress Analysis of Deformable Continua | p. 254 |
| Representation of Block Geometry and Internal Discretization | p. 257 |
| Strain and Stress Calculations for the Internal Elements | p. 268 |
| Representation of Block Contacts | p. 270 |
| Numerical Integration of the Equations of Motion | p. 271 |
| Contact Types and Detection in the Distinct Element Method | p. 275 |
| Damping | p. 280 |
| Linked-list Data Structure | p. 282 |
| Coupled Thermo-Hydro-Mechanical Analysis | p. 286 |
| Hybrid DEM-FEM/BEM Formulations | p. 301 |
| An Example of Comparative Modeling Using FEM and DEM | p. 302 |
| Summary Remarks | p. 303 |
| References | p. 306 |
| Implicit Discrete Element Method for Block Systems - Discontinuous Deformation Analysis (DDA) | p. 317 |
| Energy Minimization and Global Equilibrium Equations | p. 318 |
| Contact Types and Detection | p. 320 |
| The Rigid Block Formulation | p. 324 |
| Deformable Blocks with a FEM Mesh of Triangular Elements | p. 327 |
| Deformable Blocks with a FEM Mesh of Quadrilateral Elements | p. 330 |
| Evaluation of Element Stiffness Matrices and Load Vectors | p. 334 |
| Assembly of the Global Equations of Motion | p. 352 |
| Fluid Flow and Coupled Hydro-mechanical Analysis in DDA | p. 353 |
| Summary Remarks | p. 360 |
| References | p. 361 |
| Discrete Fracture Network (DFN) Method | p. 365 |
| Introduction | p. 365 |
| Representation of Fracture Networks | p. 367 |
| Solution for the Flow Fields within Fractures | p. 370 |
| Alternative Techniques - Percolation Theory | p. 381 |
| Alternative Techniques - Combinatorial Topology Theory | p. 385 |
| Summary Remarks | p. 388 |
| References | p. 390 |
| Discrete Element Methods for Granular Materials | p. 399 |
| Introduction | p. 399 |
| Basic DEM Calculation Features for Granular Materials | p. 405 |
| Demonstration Examples of the PFC Code Applications | p. 408 |
| Numerical Stability and Time Integration Issues | p. 416 |
| Cosserat Continuum Equivalence to Particle Systems | p. 427 |
| Summary Remarks | p. 434 |
| References | p. 436 |
| Application Studies | p. 445 |
| Case Studies of Discrete Element Method Applications in Geology, Geophysic and Rock Engineering | p. 447 |
| Introduction | p. 447 |
| Geologic Structures and Processes | p. 448 |
| Underground Civil Structures | p. 466 |
| Mine Structures | p. 475 |
| Radioactive Waste Disposal | p. 486 |
| Rock Reinforcement | p. 497 |
| Groundwater Flow and Geothermal Energy Extraction | p. 498 |
| Derivation of Equivalent Hydro-mechanical Properties of Fractured Rocks | p. 502 |
| References | p. 524 |
| Derivation of Expressions for Stress and Stress Couple Tensors of Particle Systems as Equivalent Cosserat Continua | p. 539 |
| Index | p. 543 |
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