SUMMARYA hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading-history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large-scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross-scale understanding of granular media. The developed framework is first benchmarked by a simulation of single-element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non-coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band.

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SUMMARY Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three‐dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void‐based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non‐coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd.

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The concept of the critical state in granular soils needs to make proper reference to the fabric structure that develops at critical state. This study identifies a unique property associated with the fabric structure relative to the stresses at critical state. A unique relationship between the mean effective stress and a fabric anisotropy parameter, K, defined by the first joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, is found at critical state, and is pathindependent. Numerical simulations using the discrete-element method under different loading conditions and intermediate principal stress ratios identify a unique power law for this relationship. Based on the findings, a new definition of critical state for granular media is proposed. In addition to the conditions of constant stress and unique void ratio required by the conventional critical state concept, the new definition imposes the additional constraint that K reaches a unique value at critical state. A unique spatial critical state curve in the three-dimensional space K-e-p9 is found for a granular medium, the projection of which onto the e-p9 plane turns out to be the conventional critical state line. The new critical state concept provides an important reference state for a soil to reach, based on which the key concepts in the constitutive modelling of granular media, including the choice of state parameters, dilatancy relation and non-coaxiality, are reassessed, and future exploratory topics are discussed.

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Soil-water characteristic curves (SWCCs) are routinely used for the estimation of unsaturated soil property functions (e.g., permeability functions, water storage functions, shear strength functions, and thermal property functions). This paper examines the possibility of using the SWCC for the estimation of in situ soil suction. The paper focuses on the limitations of estimating soil suctions from the SWCC and also suggests a context under which soil suction estimations should be used. The potential range of estimated suction values is known to be large because of hysteresis between drying and wetting SWCCs. For this, and other reasons, the estimation of in situ suctions from the SWCC has been discouraged. However, a framework is suggested in this paper for estimating the median value for in situ soil suction along with a likely range of soil suction values (i.e., maximum and minimum values). The percentage error in the estimation of soil suction from the SWCC is shown to be lowest for sand soils and highest for clay soils.

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