Summary It is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress‐strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus‐Bauer hypoplastic model, and a scalar‐valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.

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In practical engineering, natural soil deposits often sustain an initial driving force prior to cyclic shear, owing to earthquakes, traffic and waves; such asymmetrical loading conditions may significantly affect the liquefaction susceptibility and failure mechanism of sand. To understand the typical cyclic liquefaction responses, comprehensive asymmetrical cyclic loading tests were conducted on sand samples subjected to either compressional or extensional static stress. The results indicated that different stress conditions can result in three distinct failure mechanisms: flow liquefaction, cyclic mobility and residual deformation accumulation. According to the experimental observations, an anisotropic sand model was developed within the framework of the anisotropic critical state theory. The model employed a fabric-dependent dilatancy, and accounted for the effects of the fabric evolution and accumulated loading index on the plastic hardening, in order to better reflect the cyclic degradation of the plastic modulus. The predictive capacity of the model was confirmed through undrained monotonic test results for samples with different densities. Comparisons between the model responses and experimental results indicated the excellent capabilities of the developed model in terms of capturing the typical deformation, strength and fabric characteristics of different cyclic failure mechanisms of sand under either symmetrical or asymmetrical loading conditions.

Non‐coaxial response refers to the deviation between the directions of the principal stress and plastic strain increment. In this paper, an extended hypoplastic model is proposed based on the anisotropic critical state theory, to describe the non‐coaxial and anisotropic response of sand subjected to both monotonic loading and rotation of principal stress axis. A fabric tensor that characterizes the internal structure of sand is introduced into a hypoplastic model, to reflect the effect of fabric anisotropy on the dilatancy and strength of sand. A Lode‐angle‐dependent hypoplastic potential surface is employed, rendering the flow direction no longer co‐directional with the stress tensor in the deviatoric plane. The fabric tensor is further incorporated into the flow direction, enabling the model to generate a non‐coaxial response. Upon shearing, the fabric evolves toward the loading direction following a properly defined evolution law, and the model response becomes purely coaxial at the critical state when the fabric becomes co‐directional with the loading direction. The tangential loading effect is further introduced to simulate the stiffness degradation of sand during undrained rotational shearing. The model is demonstrated to be capable of simulating the prismatic yet complex anisotropic behavior of sand under both proportional and non‐proportional loading conditions.

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This paper presented the formulation of a novel hypoplastic model for sand considering both the cyclic mobility and large accumulative shear deformation in the post‐liquefaction stage. Based on experimental observations and existing modeling response, two constitutive ingredients were incorporated into the hypoplastic model to improve its prediction accuracy. First, the fabric change effect was considered, enabling a satisfactory simulation of effective stress reduction under undrained cyclic loading. The second component was the introduction of the semifluidized state concept to reflect the modulus degradation and deviatoric strain development of sand at low‐stress state. The capability of the proposed model is demonstrated by the comparisons between the model responses and experimental results of the cyclic behavior of sand under different test conditions. Remarkably, the liquefaction phenomenon and increasing deviatoric strain amplitude during the post‐liquefaction stage were reproduced well by the model.

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