Anisotropic Critical State Theory: Role of Fabric

TLDR

The authors introduce an Anisotropic Critical State Theory (ACST) for granular media that incorporates anisotropic fabric at critical state. ACST extends classical Critical State Theory by adding a critical value requirement for a fabric‑anisotropy measure, introduces a fabric tensor whose norm‑wise and direction‑wise evolution is tracked, defines a scalar fabric‑anisotropy variable linking the tensor to loading direction, and uses a triaxial model to simulate anisotropic material response. When the fabric‑anisotropy variable reaches its critical value, the dilatancy state line coincides with the critical state line, the dilatancy parameter ζ equals the state parameter ψ, the critical state line is proven unique thermodynamically, and static liquefaction occurs at ζ = 0 with critical stress ratio but unchanged void ratio and fabric.

Abstract

An Anisotropic Critical State Theory (ACST) for granular media is presented, which accounts for the role of anisotropic fabric at critical state. It enhances the requirements of critical values for the stress and void ratio of the classical Critical State Theory (CST) by an additional requirement of critical value for an appropriate measure of fabric-anisotropy. A fabric tensor and its evolution toward a critical value, norm-wise and direction-wise, is introduced motivated by micromechanical and experimental studies. On the basis of a scalar-valued fabric-anisotropy variable relating the evolving fabric tensor to the loading direction, a dilatancy state line is defined in the void ratio—pressure plane which determines a dilatancy state parameter ζ that characterizes the contracting or dilating trends of the current state. When the fabric-anisotropy variable reaches its critical state value, the dilatancy state line becomes identical to the critical state line and the ζ identical to the well-known state parameter ψ. An immediate corollary is the uniqueness of the critical state line, for which a thermodynamic proof is provided on the basis of the Gibbs condition. Static liquefaction is obtained when ζ=0 with the stress ratio reaching its critical value but not the void ratio and the fabric. Simulations of anisotropic material response by a triaxial model are used to illustrate the effectiveness of the novel ACST.