Within the critical state soil mechanics framework, the two-surface formulation of plasticity is coupled with the state parameter to construct a constitutive model for sands in a general stress space. The operation of the two-surface model takes place in the deviatoric stress-ratio space, and the state parameter is used to define the peak and dilatancy stress ratios of sand. The model is capable of realistically simulating stress–strain behaviour of sands under monotonic and cyclic, drained and undrained loading conditions. It includes features such as the softening of sands at states denser than critical as they dilate in drained loading and softening of sands looser than critical in undrained loading, and the pore-water pressure increase under undrained cyclic loading. Most important, all these simulations are achieved by a unique set of model constants at all densities and confining pressures of engineering relevance for a given sand. The numerical implementation of the model is particularly easy and efficient due to the very simple formulation. Calibration of model constants is done straightforwardly on the basis of triaxial experiments and measurements of well-known characteristics of sand stress–strain behaviour. Possibly the most attractive feature of the model is its simplicity and its foundation on concepts and data which are well established and understood by the geotechnical engineering community, with basic reference to critical state soil mechanics. Dans le contexte de la mécanique des sols à I'tat critique, on combine la formulation de la plasticité é deux surfaces et le paramétre d'état pour construire un modéle constitudf pour les sables dans un espace de tension générale. L'exploitation du modéleà deux surfaces se produit dans I'espace déviateur des rapports de tension et le paramètre d'état sert à définir les rapports de pointe et de dilatance des tensions du sable. Le modèle pent simuler réalisdquement le comportement tension/déformation des sables dans des conditions de charge uniformes et cycliques, drainées et non drainées. Il comprend des caractéristiques comme I'ameublissement de sables à des états de densité supérieurs à I'etat critique, quand ils se dilatent dans des conditions de charge drainées, et à des états de densité inférieurs à I'etat critique dans des conditions de charge non drainées, ainsi que I'augmentation de la pression interstitielle dans des conditions de charge cyclique non drainées. Plus important encore, toutes ces simulations sont réalisées à I'aide d'un seul ensemble de constantes de modèle pour toutes les densiés et pressions de confinement utiles pour un sable donné. La mise en oeuvre numérique de modèle est particulièrement facile et efficace en raison de la grande simplicité de la formulation. L'étalonnage des constantes du modèle se fait simplement à partir d'essais triaxiaux et de mesures de caractérisdques bien connues du comportement tension/déformations des sables. L'aspect le plus intéressant de ce modèle est peut-être sa simplicité et le fait qu'il repose sur des concepts et des données qui sont bien établis et qui sont bien compris des géotechniciens, avec mention sommaire de la mécanique des sols à I'tat critique.
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.
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