A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution

Soil fabric and its evolving nature underpin the non-coaxial, anisotropic mechanical behaviour of sand, which has not been adequately recognized by past studies on constitutive modelling. A novel three-dimensional constitutive model is proposed to describe the non-coaxial behaviour of sand within the framework of anisotropic critical state theory. The model features a plastic potential explicitly expressed in terms of a fabric tensor reflecting the anisotropy of soil structure and an evolution law for it. Under monotonic loading, the fabric evolution law characterizes a general trend of the fabric change to gradually become co-directional with the loading direction before the soil reaches the critical state. When sand is subjected to rotation of principal stress directions, the fabric evolves with the plastic strain increment which is further dependent on the current stress state, the current fabric and the direction of stress increment. During its evolution, the fabric rotates towards the loading direction and reaches a final degree of anisotropy proportional to a normalized stress ratio. With the incorporation of fabric and fabric evolution, the non-coaxial sand behaviour can be easily captured, and the model response converges to be coaxial at the critical state when the stress and fabric are co-directional. The model has been used to simulate the mechanical behaviour of sand subjected to either monotonic loading or continuous rotation of principal stress directions. The model predictions agree well with test data

Unified anisotropic elastoplastic model for sand

This paper presents a unified approach to model the influence of fabric anisotropy and its evolution on both the elastic and plastic responses of sand. A physically based fabric tensor is employed to characterize the anisotropic internal structure of sand. It is incorporated into the nonlinear elastic stiffness tensor to describe anisotropic elasticity, and is further included explicitly in the yield function, the dilatancy relation, and the flow rule to characterize the anisotropic plastic sand response. The physical change of fabric with loading is described by a fabric evolution law driven by plastic strain, which influences both the elastic and the plastic sand behavior. The proposed model furnishes a comprehensive consideration of both anisotropic elasticity and anisotropic plasticity, particularly the nonlinear change of elastic stiffness with the evolution of fabric during the plastic deformation of sand. It offers a natural and rational way to capture the noncoaxial behavior in sand caused by anisotropy. It also facilitates easy determination of the initial anisotropy in sand based on simple laboratory tests and avoids the various arbitrary assumptions on its value made by many previous studies. The model predictions on sand behavior compare well with test data

Cyclic Loading and Fabric Evolution in Sand: A Constitutive Investigation

An anisotropic plasticity model is proposed to describe the effect of fabric and fabric evolution on the cyclic behaviour of sand within the framework of anisotropic critical state theory. The model employs a cone-shaped bounding surface in the deviatoric stress space and a yield cap perpendicular to the mean stress axis to describe sand behaviour in constant-mean-stress shear and constant-stress-ratio compression, respectively. The model considers a fabric tensor characterizing the internal structure of sand associated with the void space system which evolves with plastic deformation. The fabric evolution law is assumed to render the fabric tensor to become co-directional with the loading direction tensor and to reach a constant magnitude of unit at the critical state. In constant-stress-ratio compres-sion, the final degree of anisotropy is proportional to a normalized stress ratio. An anisotropic variable defined by a joint invariant of the fabric tensor and the loading direction tensor is employed to describe the fabric effect on sand behaviour in constant-mean-stress monotonic and cyclic shear. Good comparison is found between the model simulations and test results on Toyoura sand in both monotonic and cyclic loadings with a single set of parameters

Dilatancy relation for overconsolidated clay

A distinct feature of overconsolidated (OC) clays is that their dilatancy behavior is dependent on the degree of overconsolidation. Typically, a heavily OC clay shows volume expansion, whereas a lightly OC clay exhibits volume contraction when subjected to shear. Proper characterization of the stress-dilatancy behavior proves to be important for constitutive modeling of OC clays. This paper presents a dilatancy relation in conjunction with a bounding surface or subloading surface model to simulate the behavior of OC clays. At the same stress ratio, the proposed relation can reasonably capture the relatively more dilative response for clay with a higher overconsolidation ratio (OCR). It may recover to the dilatancy relation of a modified Cam-clay (MCC) model when the soil becomes normally consolidated (NC). A demonstrative example is shown by integrating the dilatancy relation into a bounding surface model. With only three extra parameters in addition to those in the MCC model, the new model and the proposed dilatancy relation provide good predictions on the behavior of OC clay compared with experimental data

Constitutive modeling of anisotropic sand behavior in monotonic and cyclic loading

An anisotropic plasticity model is proposed to describe the fabric effect on sand behavior under both monotonic and cyclic loading conditions within the framework of anisotropic critical state theory. The model employs a cone-shaped bounding surface in the deviatoric stress space and a yield cap perpendicular to the mean stress axis to describe sand behavior in constant-mean-stress shear and constant-stress-ratio compression, respectively. The model considers a fabric tensor characterizing the internal structure of sand associated with the void space system and its evolution with plastic deformation. The fabric evolution law is assumed to render the fabric tensor to become co-directional with the loading direction tensor and to reach a constant magnitude of unit at the critical state. In constant-stress-ratio compression, the final degree of anisotropy is proportional to a normalized stress ratio. An anisotropic variable defined by a joint invariant of the fabric tensor and loading direction tensor is employed to describe the fabric effect on sand behavior in constant-mean-stress monotonic and cyclic shear. A systematic calibrating procedure of the model parameters is presented. Satisfactory comparison is found between the model simulations and test results on Toyoura sand in both monotonic and cyclic loadings with a single set of parameters. The important role of fabric and fabric evolution in capturing the sand behavior is highlighted. Limitations and potential improvement of the model in describing cyclic mobility of very dense sand and sand behavior in non-proportional loading have been discussed

How Evolving Fabric Affects Shear Banding in Sand?

Fabric anisotropy affects importantly the overall behaviour of sand in-cluding its strength and deformation characteristics. While both experimental and numerical evidence indicates that soil fabric evolves steadily with the applied stress/strain, how evolving fabric influences the initiation and development of shear band in sand remains an intriguing question to be fully addressed. In this pa-per, we present a numerical study on strain localization in sand, highlighting the special role played by soil fabric and its evolution. In particular, a critical state sand plasticity model accounting for the effect of fabric and its evolution is used in the finite element analysis of plane strain compression tests. It is found that the in-itiation of shear band is controlled by the initial fabric, while the development of shear band is governed by two competing physical mechanisms, namely, the struc-tural constraint and the evolution of fabric. The evolution of fabric generally makes the sand response more coaxial with the applied load, while the structural constraint induced by the sample ends leads to more inhomogeneous deformation within the sand sample when the initial fabric is non-coaxial with the applied stress. In the case of smooth boundary condition, structural constraint dominates over the fabric evolution and leads to the formation of a single shear band. When the boundary condition is rough, the structural constraint may play a comparable role with fabric evolution, which leads to symmetric cross-shape shear bands. If the fabric is prohibited from evolving in the latter case, a cross-shape shear band pattern is found with the one initiated first by the structural constraint dominant over the second one. 1 Introductio

Cyclic Loading and Fabric Evolution in Sand: A Constitutive Investigation

An anisotropic plasticity model is proposed to describe the effect of fabric and fabric evolution on the cyclic behaviour of sand within the framework of anisotropic critical state theory. The model employs a cone-shaped bounding surface in the deviatoric stress space and a yield cap perpendicular to the mean stress axis to describe sand behaviour in constant-mean-stress shear and constant-stress-ratio compression, respectively. The model considers a fabric tensor characterizing the internal structure of sand associated with the void space system which evolves with plastic deformation. The fabric evolution law is assumed to render the fabric tensor to become co-directional with the loading direction tensor and to reach a constant magnitude of unit at the critical state. In constant-stress-ratio compres-sion, the final degree of anisotropy is proportional to a normalized stress ratio. An anisotropic variable defined by a joint invariant of the fabric tensor and the loading direction tensor is employed to describe the fabric effect on sand behaviour in constant-mean-stress monotonic and cyclic shear. Good comparison is found between the model simulations and test results on Toyoura sand in both monotonic and cyclic loadings with a single set of parameters

Génération d'échantillons granulaires réalistes pour la modélisation discrète

La méthode des éléments discrets (DEM pour Discrete Element Modelling) est une approche de modélisation bien établie dans la communauté de la mécanique granulaire en général, et de la géomécanique en particulier. Une des problématiques actuelles consiste à tenir compte de la complexité morphologique des grains composant les géomatériaux réels, qui s'éloignent souvent de la forme sphérique utilisée traditionnellement en DEM. Dans l'objectif de générer des particules de formes complexes et aléatoires, tout en conservant un bon contrôle sur certaines de leurs propriétés morphologiques, une première approche fondée sur la notion de descripteur de Fourier a été proposée dans un cadre bidimensionnel [1]. Dans cette approche, les propriété morphologiques des grains sont introduites par le modélisateur par l'intermédiaire d'un spectre discret, qui décrit les fréquences et les amplitudes des irrégularités faisant dévier chaque grain de la forme circulaire. Une extension de ce travail au cadre tridimensionnel est décrite dans cette communication

The deformation and failure of strip footings on anisotropic cohesionless sloping grounds

Footing foundations are sometimes built on sloping grounds of natural sand which is highly anisotropic. The anisotropic mechanical behaviour of sand can significantly influence the bearing capacity of a foundation and the failure mechanism of its supporting slope. Neglecting sand anisotropy may lead to overestimated bearing capacity and under‐design of foundations. A numerical investigation on the response of a supporting slope under a strip footing is presented, placing a special focus on the effect of sand anisotropy. A critical state sand model accounting for fabric evolution is used. The nonlocal method has been used to regularize the mesh‐dependency of the numerical solutions. Predictions of the anisotropic model on the bearing capacity of strip footings on slopes are validated by centrifuge test data on Toyoura sand. Compared to the centrifuge test data, an isotropic model may overpredict the bearing capacity of the footing by up to 100% when the model parameters are determined based on test data on a horizontal bedding plane case. When the isotropic model parameters are determined based on test data where the bedding plane is vertical, the predictions of bearing capacity can be improved for some cases but the settlement at failure may be significantly overestimated. The soil body tends to move along the bedding plane upon the footing loading due to the non‐coaxial strain increment caused by fabric anisotropy. The slip surface appears to be deeper with lower bearing capacity when the preferred soil movement direction caused by bedding plane is towards the slope