A constitutive framework for anisotropic sand including non-proportional loading

An existing platform model for inherently anisotropic sands is extended to account for deformations induced by non-proportional loadings. The platform model is within the framework of critical-state soil mechanics, and the inherent anisotropy is accounted for by rendering the critical-state line in the e–p plane and the deviatoric plastic modulus functions of a scalar-valued anisotropic parameter, Ā. The latter is defined in terms of joint isotropic invariants of a symmetric fabric tensor and a properly defined loading direction tensor. Proportional and some non-proportional loading responses, including stress reversals, can be successfully simulated by the platform model, but the response under loading involving significant principal stress rotations requires the introduction of an additional loading mechanism. This new mechanism is associated with components of the stress ratio rate and plastic strain rate, which are orthogonal to a loading direction coaxial with the stress ratio. The novelty in this respect is associated with the dependence of the dilatancy and plastic modulus of this new mechanism on a second anisotropic parameter, A, to account for the fabric anisotropy effect along the lines of the plat-form model. The resulting comprehensive model success-fully simulates experimental data reflecting the complex combined effects of fabric anisotropy and non-proportional loading histories.