Dilatancy for cohesionless soils

Dilatancy is often considered a unique function of the stress ratio η = q/p′, in terms of the triaxial stress variables q and p′. With this assumption, the direction of plastic flow is uniquely related to η, irrespective of the material internal state. This obviously contradicts the facts. Consider two specimens of the same sand, one is in a loose state and the other in a dense state. Subjected to a loading from the same η, the loose specimen contracts and the dense one dilates. These two distinctly different responses are associated with a single η but two different values of dilatancy, one positive and the other negative. Treating the dilatancy as a unique function of η has developed into a major obstacle to unified modelling of the response of a cohesionless material over a full range of densities and stress levels (before particle crushing). A theory is presented that treats the dilatancy as a state-dependent quantity within the framework of critical state soil mechanics. Micromechanical analysis is used to justify and motivate a simple macroscopic constitutive framework. A rudimentary model is presented, and its simulative capability shown by comparison with experimental data of the response of a sand under various initial state and loading conditions.