This volume introduces both theory and applications in detail. It includes differential dynamical models of granular shearing, dynamical strength characteristics and the excited response of granules subject to vibration. The book is a useful reference for both theoretical researchers and engineers in the fields of mining engineering and geotechnical engineering. Engineers in fields ranging from metallurgy to water conservancy and hydroelectricity will also benefit from the book.

This book is devoted to the Discrete Element Method (DEM) technique, a discontinuum modelling approach that takes into account the fact that granular materials are composed of discrete particles which interact with each other at the microscale level. This numerical simulation technique can be used both for dispersed systems in which the particle-particle interactions are collisional and compact systems of particles with multiple enduring contacts. The book provides an extensive and detailed explanation of the theoretical background of DEM. Contact mechanics theories for elastic, elastic-plastic, adhesive elastic and adhesive elastic-plastic particle-particle interactions are presented. Other contact force models are also discussed, including corrections to some of these models as described in the literature, and important areas of further research are identified. A key issue in DEM simulations is whether or not a code can reliably simulate the simplest of systems, namely the single particle oblique impact with a wall. This is discussed using the output obtained from the contact force models described earlier, which are compared for elastic and inelastic collisions. In addition, further insight is provided for the impact of adhesive particles. The author then moves on to provide the results of selected DEM applications to agglomerate impacts, fluidised beds and quasi-static deformation, demonstrating that the DEM technique can be used (i) to mimic experiments, (ii) explore parameter sweeps, including limiting values, or (iii) identify new, previously unknown, phenomena at the microscale. In the DEM applications the emphasis is on discovering new information that enhances our rational understanding of particle systems, which may be more significant than developing a new continuum model that encompasses all microstructural aspects, which would most likely prove too complicated for practical implementation. The book will be of interest to academic and industrial researchers working in particle technology/process engineering and geomechanics, both experimentalists and theoreticians.

This title serves as an introduction to the application of numerical methods to systems of granular particles. Accordingly, emphasis is on a general understanding of the subject rather than on the presentation of latest advances in numerical algorithms.

This IMA Volume in Mathematics and its Applications TWO PHASE FLOWS AND WAVES is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshop focussed on the development of waves in flowing composites. We thank the Coordinating Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing the stimulating year-long program. We especially thank the Workshop Organizers, Daniel D. Joseph and David G. Schaeffer for their efforts in bringing together many of the major figures in those research fields in which modelling of granular flows and suspensions is used. Avner Friedman Willard Miller, Jr. PREFACE This Workshop, held from January 3-10,1989 at IMA, focused on the properties of materials which consist of many small solid particles or grains. Let us distinguish the terms granular material and suspension. In the former, the material consists exclusively of solid particles interacting through direct contact with one another, either sustained frictional contacts in the case of slow shearing or collisions in the case of rapid shearing. In suspensions, also called two phase flow, the grains interact with one another primarily through the influence of a viscous fluid which occupies the interstitial space and participates in the flow. (As shown by the lecture of I. Vardoulakis (not included in this volume), the distinction between these two idealized cases is not always clear.

This volume presents basic notions and fundamental properties of granular materials covering a wide spectrum of granular material mechanics. The granular materials may behave as fluids or solids or both. The grain size may span from microscopic to macroscopic scale. From the wet sand effect, Reynolds inspired in 1885 the notion of granular universe introducing the term "dilatancy." Bak, Tan, and Wisenfeld (1987, 1988) used the sand pile as a representative model of complex systems. In this collection of chapters, granular dynamics, granular flow from dilute to jammed states, dynamics of granular gas in microgravity, particle jetting induced by impulsive loadings, particle migration phenomena in embankment dams, and the grading entropy-based criteria of granular materials and filters are presented.

This book provides an overview of covered karst types, covered karst features, functioning of covered karst features, the evolution of covered karst features and the development of covered karst reliefs. The introductory chapters present the characteristics of karst, the investigated areas and the applied methods. The covered karsts are categorized according to the quality and development of the superficial deposit and its geomorphological position and environment. The morphology, development, functioning, sediment development and the transformation of the karst features are presented. The relationship between the covered karst formation and climate is analyzed; including the covered karst formation of the tundra climate, taiga climate, temperate zone climate, subtropical, tropical climate and the high mountains. The manifestation of the human activity on covered karsts is presented.