Non-coaxial hypoplastic model for sand with evolving fabric anisotropy including non-proportional loading

Non-coaxial response refers to the deviation between the directions of the principal stress and plastic strain increment. In this paper, an extended hypoplastic model is proposed based on the anisotropic critical state theory, to describe the non-coaxial and anisotropic response of sand subjected to both monotonic loading and rotation of principal stress axis. A fabric tensor that characterizes the internal structure of sand is introduced into a hypoplastic model, to reflect the effect of fabric anisotropy on the dilatancy and strength of sand. A Lode-angle-dependent hypoplastic potential surface is employed, rendering the flow direction no longer co-directional with the stress tensor in the deviatoric plane. The fabric tensor is further incorporated into the flow direction, enabling the model to generate a non-coaxial response. Upon shearing, the fabric evolves toward the loading direction following a properly defined evolution law, and the model response becomes purely coaxial at the critical state when the fabric becomes co-directional with the loading direction. The tangential loading effect is further introduced to simulate the stiffness degradation of sand during undrained rotational shearing. The model is demonstrated to be capable of simulating the prismatic yet complex anisotropic behavior of sand under both proportional and non-proportional loading conditions.