A New Definition on Critical State of Granular Media Accounting for Fabric Anisotropy

Conventional critical state concept for granular media lacks a proper reference to the anisotropic fabric structure developed at critical state, and is thus incomplete. This paper presents a micromechanical study to identify the characteristics of fabric anisotropy when a granular assembly reaches critical state. Our study reveals a strikingly unique, path-independent relationship between the mean effective stress and a fabric anisotropy parameter, K, defined by the first joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, at critical state. Data from over 80 DEM simulations under different loading conditions and intermediate stress ratios suggest a power law for this relationship. The new finding on critical fabric anisotropy is further incorporated into the conventional critical state conditions to redefine the critical state concept for granular media. The new definition dictates that the critical state corresponds to a unique state with constant stress, constant void ratio and constant K. It defines a unique spatial critical state line for a granular medium in the three-dimensional space K-e-p'. The projection of this spatial line onto the e-p' plane is the conventional (unique) critical state line.