A thermodynamic critical state model for sands

A thermodynamics-based constitutive model predicting the critical state behavior of sands is developed in this paper. The model includes hyperelastic and plastic constitutive relations derived from thermodynamics. Using the concept of elastic potential, hyperelastic relations are derived to describe the stress- and -density dependency of the elastic stiffness of sands, which naturally lead to the elastic limit with stress-induced anisotropy in effective stress space. The plastic constitutive relations coupled with the nonlinear hyperelasticity are then derived based on the energy dissipations and the second law of thermodynamics. The model is capable of predicting the critical state behavior of sands without concepts of yield surface and plastic potential surface. The model is validated by predicting the undrained shear behavior of Toyoura sand. The modeling results show that different patterns of undrained shear response, such as the pure dilation type, the contraction-dilation type with hardening, the contraction-dilation type with softening, and the pure contraction type, can be well captured by the model, depending on the confining pressure and the void ratio. The distinctions of contraction/dilation and critical state behavior between triaxial compression and extension are also predicted. It is shown that the critical state behavior of sand is the combined results of the pressure/density/path-dependent hyperelasticity and plasticity coupled with each other.