DEM analysis of the influence of the intermediate stress ratio on the critical-state behaviour of granular materials

Abstract

The critical-state response of granular assemblies composed of elastic spheres under generalised three-dimensional loading conditions was investigated using the discrete element method (DEM). Simulations were performed with a simplified Hertz–Mindlin contact model using a modified version of the LAMMPS code. Initially isotropic samples were subjected to three-dimensional stress paths controlled by the intermediate stress ratio, $b=[(\sigma '_{2}-\sigma '_{3})/$ $(\sigma '_{1}-\sigma '_{3})]$. Three types of simulation were performed: drained (with $b$-value specified), constant volume and constant mean effective stress. In contrast to previous DEM observations, the position of the critical state line is shown to depend on $b$. The data also show that, upon shearing, the dilatancy post-peak increases with increasing $b$, so that at a given mean effective stress, the void ratio at the critical state increases systematically with $b$. Four commonly-used three-dimensional failure criteria are shown to give a better match to the simulation data at the critical state than at the peak state. While the void ratio at critical state is shown to vary with $b$, the coordination number showed no dependency on $b$. The variation in critical state void ratios at the same $p'$ value is apparently related to the directional fabric anisotropy which is clearly sensitive to $b$.