土的三维破坏准则在颗粒流模型中的应用

Savage-Hutter(S-H)颗粒流模型用一个只与材料参数相关的土压力系数来描述颗粒流内部的应力状态，不能很好地反映颗粒体在运动时的本构关系。通过引入颗粒体应力与速度梯度之间的关系，得到了一个能够反映颗粒流本构模型的崩塌动力学模型。另外，为解除S-H模型中对横向应力大小的假定，通过引入Von Mises、Drucker-Prager、Mohr-Coulomb和Matsuoka-Nakai等土的三维破坏准则，得到了广义摩擦系数的4种表达形式。该模型的主要优势是通过引入颗粒流的本构关系，能较好地体现颗粒流体在运动中的内在机制，并且材料强度参数简单易知。分析了由Drucker-Prager准则和Mohr-Coulomb准则所得到的材料强度参数，并探讨了广义摩擦系数与应力洛德角等物理量之间的关系。用所建议的模型来模拟颗粒流的运动过程，并将数值计算与试验结果进行对比，发现两者能够较好吻合。

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.