Linear mathematical assumptions for procedures in other branches of engineering have little relevance for geoengineering, which must accommodate non-linear behaviors. Contributors to eight papers apply the breakthrough numerical modeling Distinct Element Method (Cundall, late 1960s).

The first single work on DEM providing the information to get started with this powerful numerical modelling approach. Provides the basic details of the numerical method and the approaches used to interpret the results of DEM simulations. It will be of use to professionals, researchers and higher level students, with a theoretical overview of DEM as well as practical guidance.Selected Contents: 1.Introduction 2.Use of DEM in Geomechanics 3.Calculation of Contact Forces 4.Particle Motion 5.Particle Types 6.Boundary Conditions 7.Initial Geometry and Specimen Generation 8.Time Integration and Discrete Element Modelling 9.DEM Interpretation: A Continuum Perspective 10.Postprocessing: Graphical Interpretation of DEM Simulations 11.Basic Statisti

Linear mathematical assumptions for procedures in other branches of engineering have little relevance for geoengineering, which must accommodate non-linear behaviors. Contributors to eight papers apply the breakthrough numerical modeling Distinct Element Method (Cundall, late 1960s). The design philosophy for structures or excavations in geotechnical engineering is different from that followed for fabricated materials like steel and concrete. The designer has little data both with regard to geological weaknesses and strength and deformation characteristics of materials before finalizing the designs. Also these characteristics vary from place to place. In-situ stresses due to gravity and tectonics and transient forces imposed due to rainfall and earthquakes make the matter more complicated. The pore waters carry the load initially before passing it on to the solids. For the analytical procedure, to be realistic, it should account for large displacements and non-linear behaviour including strain-softening. Because of these considerations, the designers have followed procedures based on simplifying assumptions such as linear, small strain, elastoplastic behaviour. Numerical procedures based on such assumptions, though very popular in other branches of engineering, have made little impact in geo-engineering. An attempt has been made in this book to compile the recent use of distinct element codes for solutions of some of the problems in geomechanics — particularly those involving excavations. It is hoped that it will provide an opportunity for the fraternity of geotechnical engineers to appreciate the opening of new frontiers in the use of computers for solving more challenging geotechnical problems.

This book is an introduction to numerical analysis in geomechanics and is intended for advanced undergraduate and beginning graduate study of the mechanics of porous, jointed rocks and soils. Although familiarity with the concepts of stress, strain and so on is assumed, a review of the fundamentals of solid mechanics including concepts of physical laws, kinematics and material laws is presented in an appendix. Emphasis is on the popular finite element method but brief explanations of the boundary element method, the distinct element method (also known as the discrete element method) and discontinuous deformation analysis are included. Familiarity with a computer programming language such as Fortran, C++ or Python is not required, although programming excerpts in Fortran are presented at the end of some chapters. This work begins with an intuitive approach to interpolation over a triangular element and thus avoids making the simple complex by not doing energy minimization via a calculus of variations approach so often found in reference books on the finite element method. The presentation then proceeds to a principal of virtual work via the well-known divergence theorem to obtain element equilibrium and then global equilibrium, both expressed as stiffness equations relating force to displacement. Solution methods for the finite element approach including elimination and iteration methods are discussed. Hydro-mechanical coupling is described and extension of the finite element method to accommodate fluid flow in porous geological media is made. Example problems illustrate important concepts throughout the text. Additional problems for a 15-week course of study are presented in an appendix; solutions are given in another appendix.

This book presents some fundamental concepts behind the basic theories and tools of discrete element methods (DEM), its historical development, and its wide scope of applications in geology, geophysics and rock engineering. Unlike almost all books available on the general subject of DEM, this book includes coverage of both explicit and implicit DEM approaches, namely the Distinct Element Methods and Discontinuous Deformation Analysis (DDA) for both rigid and deformable blocks and particle systems, and also the Discrete Fracture Network (DFN) approach for fluid flow and solute transport simulations. The latter is actually also a discrete approach of importance for rock mechanics and rock engineering. In addition, brief introductions to some alternative approaches are also provided, such as percolation theory and Cosserat micromechanics equivalence to particle systems, which often appear hand-in-hand with the DEM in the literature. Fundamentals of the particle mechanics approach using DEM for granular media is also presented. · Presents the fundamental concepts of the discrete models for fractured rocks, including constitutive models of rock fractures and rock masses for stress, deformation and fluid flow · Provides a comprehensive presentation on discrete element methods, including distinct elements, discontinuous deformation analysis, discrete fracture networks, particle mechanics and Cosserat representation of granular media · Features constitutive models of rock fractures and fracture system characterization methods detaiing their significant impacts on the performance and uncertainty of the DEM models

Proceedings of the Third International Conference on Discrete Element Methods, held in Santa Fe, New Mexico on September 23-25, 2002. This Geotechnical Special Publication contains 72 technical papers on discrete element methods (DEM), a suite of numerical techniques developed to model granular materials, rock, and other discontinua at the grain scale. Topics include: DEM formulation and implementation approaches, coupled methods, experimental validation, and techniques, including three-dimensional particle representations, efficient contact detection algorithms, particle packing schemes, and code design. Coupled methods include approaches to linking solid continuum and fluid models with DEM to simulate multiscale and multiphase phenomena. Applications include fundamental investigations of granular mechanics; micromechanical studies of powder, soil, and rock behavior; and large-scale modeling of geotechnical, material processing, mining, and petroleum engineering problems.