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.

entes combinaisons de charges et de préparation des échantillons. On démontre que le modèle est en mesure de simuler, de façon harmonisée, les résultats expérimentaux reflétant les effets conjugués des méthodes de préparation des échantillons, des chemins de charge, de la densité du sol, et des pressions de confinement.

An existing platform model for inherently anisotropic sands is extended to account for deformations induced by non-proportional loadings. The platform model is within the framework of critical-state soil mechanics, and the inherent anisotropy is accounted for by rendering the critical-state line in the e-p plane and the deviatoric plastic modulus functions of a scalar-valued anisotropic parameter, A. The latter is defined in terms of joint isotropic invariants of a symmetric fabric tensor and a properly defined loading direction tensor. Proportional and some non-proportional loading responses, including stress reversals, can be successfully simulated by the platform model, but the response under loading involving significant principal stress rotations requires the introduction of an additional loading mechanism. This new mechanism is associated with components of the stress ratio rate and plastic strain rate, which are orthogonal to a loading direction coaxial with the stress ratio. The novelty in this respect is associated with the dependence of the dilatancy and plastic modulus of this new mechanism on a second anisotropic parameter, A, to account for the fabric anisotropy effect along the lines of the platform model. The resulting comprehensive model successfully simulates experimental data reflecting the complex combined effects of fabric anisotropy and non-proportional loading histories.