A Characteristic State Plasticity Model for Granular Materials

TLDR: In this paper, the authors developed critical state theory in terms of a two-dimensional stress space with mean stress p and maximum shear stress 1/2q, and the ultimate stress states are located on the critical line q/p = M corresponding to a state of plastic shear without dilatation.

Abstract: The irreversible nonlinear deformation of granular materials is dominated by the effect of friction forces between grains, and therefore the ratio between shear stresses and mean stress plays a dominant role. Within the framework of plasticity theory this leads to a family of self-similar yield surfaces. Classical critical state theory was developed in terms of a two-dimensional stress space with mean stress p and maximum shear stress 1/2q. The ultimate stress states are located on the critical line q/p = M corresponding to a state of plastic shear without dilatation, (Schofield and Wroth, 1968). While representing some of the basic features of granular materials well, the critical state theory has shortcomings in its representation of the effect of triaxial stress states, seen e.g. in the triangular shape of the failure envelope, the representation of dilatation at failure, and the need for a tension cut-off of the yield surface.