Plasticity model for sand under small and large cyclic strains: a multiaxial formulation

This paper presents the multiaxial formulation of a plasticity model for sand under cyclic shearing. The model adopts a kinematic hardening circular cone as the yield surface and three non-circular conical surfaces corresponding to the deviatoric stress ratios at phase transformation, peak strength and critical state. The shape of the non-circular surfaces is formulated in accordance with the experimentally established failure criteria, while their size is related to the value of the state parameter ψ. To simulate cyclic response under small and large shear strain amplitudes without a change in model parameters, it was found necessary to introduce: (a) a non-linear hysteretic (Ramberg–Osgood type) formulation for the strain rate of elastic states and (b) an empirical index of the effect of fabric evolution during shearing which scales the plastic modulus. This index is estimated in terms of a macroscopic second-order fabric tensor, which develops as a function of the plastic volumetric strain increment and the loading direction in the deviatoric plane. Comparison of simulations to pertinent data from 27 resonant column, cyclic triaxial and cyclic direct simple shear tests provide a measure for the overall accuracy of the model.