The concept of a ‘Reynolds–Taylor state’ and the mechanics of sands

Abstract

A novel conceptual model of the mechanics of sands is developed within a thermomechanical framework. Central to this model is the realisation that volume changes in granular materials are induced by two mechanisms. One is purely kinematic, and is a result of individual grains having to move over each other in a shear deformation: the ‘Reynolds effect’. This is the defining characteristic of the mechanics of granular materials. The second cause of volume changes is as a direct response to changes in stress, as in any standard continuum. These conceptual ideas are used to systematically develop a family of elastic/plastic models, involving non-associated flow rules, isotropic and kinematic hardening, and induced anisotropy. The recognition of the two distinct mechanisms of volume change shows that the classical concept of a critical state must be replaced with the more general concept of a ‘Reynolds–Taylor state’ to better explain the observed experimental behaviour in sands. In this state, which is attained early on in a deformation, the sand is still dilating but the difference between the stress and dilation ratios is constant (Taylor's stress–dilatancy relation), as is the effective pressure. In a general deformation, the shear stress, and stress and voids ratios, do not become constant until later in the deformation, when a critical state is finally attained. However, in the particular case of a drained triaxial test, the stress ratio is also constant when this state has been reached, even though the sample is still dilating. These predictions are shown to be in accord with experimental data from a series of drained tests.