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

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

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