Determination of velocity and stress discontinuities in quasi-static granular flows

Abstract

In quasi-static flows of granular materials, there often exist stress and velocity discontinuities in the material. However, existing numerical techniques are generally not capable of modelling these discontinuities satisfactorily. In this paper, we develop a sophisticated numerical technique for simulating the quasi-static flow of granular materials in the presence of stress discontinuities. Based on the double-shearing model, the governing equations consist of four highly nonlinear partial differential equations with two families of characteristic lines. We firstly transform the partial differential equations into a set of ordinary differential equations using the method of characteristics. Then, a computation scheme is developed to determine the characteristic lines, the stress discontinuity lines and the stress and velocity fields. The method is then applied to study the flow of granular materials in silos.