SANISAND-Z: zero elastic range sand plasticity model

The theory of zero purely elastic range in stress space within the framework of bounding surface plasticity is applied to sand constitutive modelling. The yield surface shrinks to zero and becomes identical to the stress point itself, and plastic loading occurs for any direction of the stress ratio rate on which the loading and plastic strain rate directions now depend, rendering the model incrementally non-linear. The simplicity of the conceptual structure of the model is particularly attractive as it consists of only one surface, the bounding/failure surface, and the stress point itself in the stress ratio π-plane. The image stress point on the bounding surface is defined analytically in terms of the direction of the rate of the stress ratio, with the latter being inside, on, or outside the surface, so that the model can address consistently hardening, softening and critical state response. An updating scheme of the initial value of stress ratio at unloading–reloading events is proposed in order to avoid the overshooting phenomenon. The model follows the basic premises of the SANISAND family of models that unify the description for any pressure and density within critical state theory. The simulating capabilities of the model are shown to be comparable with those of classical models with very small yield surfaces, and additional simulations of unorthodox loading paths such as rotational shear are successfully compared with experimental data.