A tensor-based analysis of stress variability in granular media subjected to various loading conditions

Abstract

This paper uses a novel tensor-based approach to characterize the spatial variability and localization of stress fields in granular media derived from three-dimensional discrete element simulations. We use the Euclidean distance of the stress tensor of each particle to the bulk mean stress tensor to quantify local stress fluctuations and use the effective variance of the stress field to quantify the overall dispersion. We observe that the evolutions of both the local stress fluctuation and the bulk stress dispersion strongly depend on the stress state, packing density and shearing process. However, they become constant, and are uniquely related to the deviatoric stress and the void ratio when the sample is at critical state, under which the stress variability reaches an ultimate condition. Multifractal analysis further shows that the local stress field is highly heterogeneous and exhibits self-organized patterns.