A Rational Approach to Stress-Dilatancy Modelling Using an Explicit Micromechanical Formulation

This paper presents a theoretical approach for deriving a stress-dilatancy formulation for granular materials. We first revisit Rowe’s stress-dilatancy relation by investigating two-dimensional granular assemblies with various regular particle arrangements. It is found that the energy ratio during deformation varies with particle arrangements (or fabric) with its minimum value corresponding to a particular deformation state. As such, Rowe’s stress-dilatancy equation is seen to be the lower bound of all possible dilatancy states the material can assume at various particle arrangements. Furthermore, we demonstrate that Rowe’s hypothesis of minimum energy ratio can be lifted, if we work out rigorously the local sliding planes through micromechanical analysis. Such a micromechanical approach yields a more accurate description of the dilatancy behaviour of sand. More importantly, this new approach can be readily extended to describe the dilatancy behaviour of sand under general stress conditions.