Anisotropic Critical State Theory: Role of Fabric

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.