Critical State for Anisotropic Granular Materials: A Discrete Element Perspective

Critical-state failure is a salient feature for particular materials, such as granular media and soils, whereas the critical-state theory (CST) is widely accepted for understanding and interpreting the behavior of a range of materials under complex loading conditions. In elastoplastic soil modeling, the critical state is also a favorable reference state for capturing and simulating the soils' responses, and thus many constitutive models have been developed within the CST framework. Notwithstanding this, the uniqueness of the critical state has evoked increasing debate for many years and remains an unresolved issue. The central difficulty lies in how to integrate fabric anisotropy into the delineation of the critical-state failure. Motivated by the recent development of the anisotropic critical-state theory, this paper presents a discrete element investigation of the critical-state behavior of anisotropic granular materials. Samples with different degrees of initial fabric anisotropy are sheared to the critical state under both triaxial compression and extension conditions. Based on a series of numerical simulations with varying densities and confining pressures, a unique critical-state line can be approximately obtained in the e-p plane and is found to be independent of initial fabrics and shearing modes or Lode angles. The fabric anisotropy and its evolution during the loading process can be quantified by a deviatoric fabric tensor defined based on the statistical distribution of the contact normal vectors within the granular assemblies. The most prominent observation is that the direction of the fabric tensor is codirectional with the stress at the critical state, whereas its norm has a unique value pertinent to the shear mode or Lode angle.