マルコフ過程を用いた粒状体の力学モデル (1)

Abstract

In this paper a mechanical model of granular materials is proposed to analyse the variousmechanical behaviours on the granular materials such as sands. In modelling, the motion ofindividual particles is assumed to be a Markov process which is one of the well-known stochasticsprocesses. This assumption is reasonable because the irregurality of the particle in both shape andvolume, and the complicated fabric of granular materials are considered to prohibit the deter-ministic approach to the motion of individual particles in the grannlar materials.First, the Markov process is explained briefly and the basic equation of the Markov process isderived. Secondly, the Markov process is applied to the mechanical behaviours of granularmaterials, and the concepts of potential wall and potential slip plane are introduced in order todetermine the coefficients in the basic equation of the Markov process. Thirdly, the strain ofgranular materials is derived by averaging the motion of particles. Finally, the strees-strainrelationships obtained from the proposed model are compared with the results of the drainedtriaxial compression tests on Toyoura sand and the availability of the proposed model is discussed.