State-dependent non-orthogonal elastoplastic constitutive model for sand

The mechanic characteristics of sand have obvious features of state dependence, which is mainly reflected by the fact that the deformation characteristics of sand in different stress and density states significantly differ. The reasonable description for the state-dependent hardening rule and dilatancy rule of sand is the basis to describe the state-dependent deformation characteristics of sand. A differential expression which can effectively describe the isotropic compression and critical state of sand is proposed. Based on the hardening rule under isotropic compression condition, a state-dependent hardening factor ω is proposed, and the state-dependent hardening parameter H is developed in order to reasonably decide the magnitude of plastic strain increment. In the process of determining the direction of plastic strain increment by adopting the non-orthogonal plastic flow rule, the influences of state parameter ψ on fractional order μ are introduced, and the state dependence of the direction of plastic strain increment is considered, thus reasonably describing the state-dependent dilatancy of sand. Furthermore, by introducing the state parameter into the Hooke's law, the elastic strain increment is obtained, and a non-orthogonal elastoplastic constitutive model which can describe the state dependence of sand is proposed. By reasonably predicting the results in triaxial drained and undrained tests on the Toyoura sand, it is proved that the established model can effectively capture the state-dependent mechanic characteristics of sand.