Thermodynamic Constitutive Model for Sands with Consideration of Distributed Fabric

Abstract

A micromechanics-inspired fabric-dependent thermodynamic model is developed to simulate the critical-state and phase-transformation behavior of sands. A generalized fabric tensor that considers the statistical distribution of granular fabric is proposed. The fabric tensor is the sum of three families of a transversely isotropic tensor, which is assumed to be characterized by the probability density function of the normal distribution. The new tensor variable is incorporated into the reversible and irreversible thermodynamic models, and the fabric-dependent hyperelastic and plastic constitutive relations are then derived. The hyperelastic instability leads to a yield criterion that depends on fabric distribution and its evolution. Plastic strain development is linked to fabric distribution by a concept of accumulative yielding probability transitions, which in turn provides smooth transition from macroscopic elasticity to plasticity and finally to the critical state upon shearing. Using this theoretical framework, the physical mechanism underlying the phase-transformation and critical-state behavior of sands are interpreted from the evolution of fabric distribution. The performance of the model is verified by simulating various shear tests of Toyoura sand and a discrete element method (DEM)-modeled sand. The effects of b-value and principal stress direction on the stress-strain behavior are related to the evolution of fabric distribution. The noncoaxiality among stress, strain, and fabric is also captured by the model.