A constitutive theory of fluid-saturated granular materials and its application in gravitational flows

Abstract

A continuum theory of fluid-saturated granular materials is presented. The microstructural effects are accounted for by additional balances of equilibrated forces. A set of constitutive equations for a viscous solid-fluid mixture with microstructure is derived by use of the Müller-Liu thermodynamic approach. This theory is applied for the description of the steady gravitational flow of a solid-fluid mixture down an inclined plate. The resulting boundary value problem is solved numerically and results are presented for various values of parameters and boundary conditions. Solutions of this problem demonstrate many of the characteristics normally assumed in the other treatments of solid-fluid mixtures. Typically, in the vicinity of the bottom, a layer of high shear rate occurs with high dilatancy, whose thickness is nearly several grain diameters. Above this layer a plug-like region develops in which the velocity is almost constant.