| A distinctive feature of granular materials such as sand, beside frictional strength, is stress-dilatancy: a change in volume as grain particles override one another when sheared. Stress dilatancy plays a crucial role in granular material deformation in both monotonic and cyclic loading regimes, as well as localized deformation which is a precursor to failure. By far, most popular descriptions of stress-dilatancy still hinge on the pioneering work of Rowe in 1962. However, the stress level (barotropy), void ratio (pyknotropy) and micro-structure (anisotropy) dependency properties of granular materials cannot be captured by either Rowe's stress-dilatancy formulation or most constitutive models for sand.; In this research, Rowe's original stress-dilatancy formulation is first modified based on the physics of stress-dilatancy such as to address both pyknotropy and barotropy. Then, a comprehensive, but yet simple, constitutive model with relatively few material parameters is developed within the framework of plasticity. This model includes a novel void ratio dependent plasticity evolution law which can describe both hardening and softening by using a single expression combined with a plastic potential function driven by the modified stress-dilatancy formulation. Other salient features of the model include a failure surface governed by Mohr-Coulomb criterion, a family of shear yield surfaces and a vertical cut-off cap for hydrostatic compaction deformation mechanism.; In order to consider the microstructural dependencies of granular materials, a more general mathematical formulation of stress dilatancy is developed for an ensemble of grain particles undergoing both translational and rotational kinematics. By using homogenization technique and equating the energy dissipation calculated for an ensemble of particles to the energy per unit volume expressed in terms of macroscopic measures such as stress and strain, a stress-dilatancy formulation with embedded microstructure as well as void ratio and stress level is obtained. A fabric tensor is introduced to describe changes in microstructure during deformation history. The implementation of the resulting stress dilatancy formulation in elasto-plasticity theory produces very interesting modelling results consistent with experimental observations with respect to various microstructural aspects of granular materials.; The developed constitutive model is further extended to cyclic loading within the framework of hypo-plasticity. By considering double sliding mechanisms in granular materials during reverse loading, the modified stress-dilatancy formulation with embedded microstructure is extended so as to describe dilatancy changes in cyclic loading. It is found that combined with a kinematic hardening rule, the resulting model is very similar to one based on bounding surface plasticity. However, the major difference lies in the plastic modulus which is, herein, a function of current void ratio and fabric beside stress state. The model successfully captures most salient behaviours of granular materials related to fabric issues in cyclic loading regime in both drained and undrained conditions.; Experimental results pertaining to sands along different stress paths are used to calibrate the developed model. These include tests in drained/undrained conventional triaxial compression, triaxial compression with constant mean stress, imposed strain rate paths, triaxial extension, and cyclic loading in either drained or undrained conditions. All model results obtained are found to be consistent with experimental observations. |
