Mechanics of Granular Flows
The present paper deals with the flow of bulk solids comprised of discrete particles. Attention will be focused on understanding the interactions that take place between individual particles at the microstructural level as a means to establish the constit
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Stuart B. Savage Department of Civil Engineering and Applied Mechanics McGill University, 817 Sherbrooke West, Montreal, Canada
The present paper deals with the flow of bulk solids comprised of discrete particles. Attention will be focused on understanding the interactions that take place between individual particles at the microstructural level as a means to establish the constitutive relationships (expressions for stresses, energy fluxes, energy dissipation, etc.) that govern the flow of granular materials. We begin with a review of the classical papers of Bagnold and proceed to discuss the various modes and regimes of granular flow. A dimensional analysis provides a physical background for the interpretation of subsequent presentations of theoretical and experimental work. By making analogies with gases and liquids at the molecular level it is possible to develop kinetic theories of granular flows. A simple analysis of this kind is briefly outlined. Recent attempts to consider the effects of boundary conditions, to include the effects of quasi-static stresses and interstitial fluids are also discussed. Molecular dynamics type computer simulations that are related to these kinetic theories are reviewed. As an application of granular flow theories to geophysical problems we discuss some analyses of avalanches of granular materials down inclines. Continuum approaches can be used to model rockfalls and ice avalanches in a very simple, but approximate way; they appear to yield the gross features of these flows. The time dependent evolution of avalanches and other ~anular flows can also be modelled by means of molecular dynamics type computer simulat1ons. Examples of two and three-dimensional computations are described. Typically the avalanches are made up materials of different sizes. The shear that takes place over the depth of material results in a grading of particles in which larger particles move to the top and the front of the moving pile. A simple explanation of this phenomenon, based upon the segregation analysis of Savage &: Lun (1988), is given.
1. Introduction
The terms bulk solids or granular materials refer to mixtures made up of discrete solid particles which are dispersed in a fluid phase. In situations involving the flow and yielding of such bulk materials, the typical solids concentrations are quite high and the solid constituents come in contact or near contact with their neighbors. Bulk solids occur in various forms: dry grains and powders, slurries, suspensions or pastes. Some examples are sand, ore, mineral concentrate, coal, crushed oil shale, grain, animal feed, foodstuffs, pharmaceuticals, granular snow, pack ice, and metal and ceramic powders. Although there are some instances and flow regimes in which the interstitial fluid can be important, the essential mechanical aspect of bulk solids is the interaction between the solid particles. As a result of studies in the area of soil mechanics, a great deal is known about granular materials in a static state or undergoing slow deformations. Howe
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