Critical state and ultimate state surface of soils: a granular solid hydrodynamic perspective

A model predicting the ultimate state surface and critical state of soils is established based on a non-equilibrium thermodynamic approach known as granular solid hydrodynamics. It offers a pressure- and density-dependent approach to assessing the elastic potential energy density of soils while taking soil cohesion into account. The ultimate state surface is quantitatively determined by the convex condition of the elastic potential energy density function with respect to the elastic strain and is compared with the state boundary surface in the critical state soil mechanics. The elastic stress is expressed by a hyper-elastic relationship. Both the critical state and the non-elastic deformation of soils depend on the evolution of elastic relaxation and granular fluctuation, which can be expressed in terms of dissipative forces and dissipative flows. The proposed model allows analysis of the soils critical state, its granular temperature and its effective stress. The predictions of triaxial compression tests of Toyoura sand and Q3 loess show that the model adequately predicts the ultimate state, the critical state and the dilation/contraction or hardening/softening of soils. Limitations of the proposed model in reproducing the density dependency of drained peak shear strength and the rate dependency of critical state are also discussed.