A critical state two-surface plasticity model for sands

Abstract

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.

Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction

“…Microstructure (or fabric) is defined as the arrangement of particles, particle groups, and the associated pore space. Extensive research has been conducted to describe the constitutive behavior and deformation characteristics of granular materials using the theory of plasticity [1,2], micro-polar theory [3][4][5], discrete element method (DEM) [6][7][8], and coupled continuum-DEM models [9]. Some of these models provide excellent predictions of the strength behavior and deformation mode of granular materials; however, despite recent technological advances, calibration of such models using representative material parameters has always been a challenge.…”

Capturing strain localization in dense sands with random density

“…One such model, derived from the 'Nor-Sand' of Jefferies [5] and presented by Borja and Andrade [6], utilizes a variable called 'state parameter' to describe the density of a meso-element relative to that at the critical state line for the same effective mean normal stress [5,7,8]. Where the point lies below the critical state line, is negative (denser than critical), and where it lies above, is positive (looser than critical).…”

Validation of a New Elastoplastic Constitutive Model Dedicated to the Cyclic Behaviour of Brittle Rock Materials

“…Contrary to rock materials, different models exist for the cyclic behaviour of sands such as the Prevost model (Prevost, 1985;Cerfontaine et al, 2015), generalised plasticity (Mira et al, 2009) or subloading surface (Hashiguchi, 2009). The formulation proposed hereinafter is based on the bounding surface plasticity (Dafalias, 1986), the pioneering work on its application in form a two surface plasticity model for sands (Manzari & Dafalias, 1997) which was later extended further (Dafalias & Manzari, 2004;Taiebat & Dafalias, 2008;Li & Dafalias, 2012;Dafalias & Taiebat, 2016) and adopted the title of SANISAND, an acronym term for Simple ANIsotropic SAND. This framework is mainly chosen for its ability to reproduce accumulation of plastic strain upon constant amplitude cycles, for its physically based concept and relative simplicity.…”