Thermomechanical state parameter models for sands

The granular structure of sands and other geomaterials makes them amongst the most difficult engineering materials to model. In this paper a recently developed thermomechanical procedure is used to derive constitutive models for sands undergoing triaxial deformations. The well-known geomechanical state parameter is given a new significance and is taken as the fundamental thermomechanical state parameter. The logarithm of the specific volume is shown to be the plastic volume strain, and its relationship to the logarithm of the effective pressure is shown to be fractal. In addition the shear-induced volume strains, characteristic of granular materials, are introduced via a workless constraint, and the resulting deformation is seen to exhibit 'induced anisotropy' automatically. The associated reaction stress tensor is shown to be identical with the extant fabric tensor. The plastic flow rule is shown to be necessarily non-associated. Comparison with experimental data is made, together with some discussion of the model's relation to the predictions of distinct element simulations.