A constitutive modelling framework predicting critical state in sand undergoing crushing and dilation

This paper explains why the critical state of sand is non-unique when expressed in terms of stress and void ratio only. For this purpose, a thermodynamically consistent, micromechanically inspired constitutive modelling framework with competing grain crushing and dilation is developed. While grain crushing is described through the theory of breakage mechanics, dilation is modelled in a novel way by acknowledging its negative contribution to the overall positive rate of dissipation. The competition between dilation and grain crushing underpinned by this framework yields a unique critical state in a space of stress, void ratio and breakage, in agreement with recent experiments. As an example, a simple constitutive model with only five mechanical parameters is proposed, which not only predicts the critical state but also quantitatively connects the full constitutive behaviour to key index properties related to grading- and breakage-dependent minimum and maximum densities.