Mechanical Model of Particulate Material Based on Markov Process

Abstract

In this paper a mechanical model for particulate materials, such as sand, is proposed to analyse their stress-strain behaviours during shear. In modelling, the motion of individual particles is assumed to be a Markov process, which is one of the well-known stochastic processes, because the irregularity of particles in both shape and volume, and the complicated fabric of particulate material are considered to prohibit the deterministic approach to the motion of individual particles in a particulate material. The strain of the particulate material is then derived by the motion of particles. It is shown that the stress-strain relationships of a particulate material derived from the proposed model compare favorably with those of Toyoura sand which are obtained from the drained compression tests and the proposed model can comprehensively evaluate the inherent anisotropy due to the fabric of particulate material, the extrinsic anisotropy due to the stress history and the non-linearity of stress-strain relationship.