Evolution of Various Fabric Tensors for Granular Media toward the Critical State

Abstract

The classical critical state theory of granular mechanics makes no reference to the anisotropy of the material and has thus raised questions over the uniqueness of the critical state when fabric anisotropy is taken into consideration. The recently developed anisotropic critical state theory (ACST) suggests that at a critical state the fabric anisotropy tensor acquires normwise a unique normalized critical state value, while the orientation depends on the shearing mode. Consequently it follows that for the same granular material under the same loading conditions, the fabric anisotropy tensor at the critical state should be independent of the initial fabric anisotropy. The fabric tensor in the ACST is referred to in a general sense, not specifying what entity it is constituted of. The present study investigates the evolution of three commonly used fabric tensors based on particle orientation, contact normal, and void vectors, under constant mean effective stress biaxial loading using the two-dimensional discrete element method (2D DEM). These fabric measurements provide a relatively comprehensive coverage of the fundamental characteristics of the particle-contact-void system of a granular material. Global shear banding is avoided in the biaxial simulations to keep the samples as homogeneous representative volumes during loading. The analysis confirms the existence of a unique fabric based on each of the three fabric tensor formulations for the same granular material under the same loading conditions at a critical state. The relationship between the void vector fabric tensor and the contact normal and particle orientation fabric tensors is also tentatively explored. Different fabric quantities (including scalars such as the void ratio and fabric tensor norm and orientation) are found to require different levels of deformation to reach their respective critical states.