Application of a three-dimensional yield criterion to granular flow modeling

In the Savage-Hutter (S-H) granular flow model, the earth pressure coefficient that is only related to the material property is chosen to describe the internal stresses of the granular flow. However, the constitutive relation of the granular flow is not given in this model. In this paper, an avalanche dynamic model, which can well reveal the constitutive behavior of the granular flow, is developed by introducing the relationship between the stress and the velocity gradient. In order to relax the assumption for lateral stress, the Von Mises criterion, Drucker-Prager criterion, Mohr-Coulomb criterion and Matsuoka-Nakai criterion are combined to yield four expressions of the generalized friction coefficient for describing the moving properties of the granular material. As one of the advantages of the proposed model, the internal mechanism of granular flow is clearly revealed by introducing a simplified constitutive relationship, and the strength parameters used in the proposed model are readily available. The strength parameters derived by Drucker-Prager criterion and Mohr-Coulomb criterion are also analyzed, and the relationship between the generalized friction coefficient and the Lode angle is deduced. It is shown that the numerical simulations of the proposed model agree well with the experimental results.