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Experimental evidence indicates that the shear localisation acts as a precursor to the failure in biaxial compression tests of granular materials. Once formed they are persistent and lead to progressive failure of most geotechnical structures. It is generally accepted that the primary mode of deformation within these shear bands is simple shear which is accompanied by rotation of principal axes. Hence, the conventional plasticity theories based on the assumption of coaxility is not sufficient to describe the behaviour within those shear bands. This paper highlights the influence of the non-coaxility on the initiation and orientation of shear bands in both drained and undrained sand. The con-coaxial plasticity theory is integrated into a critical state constitutive model enriched with the state parameter concept. The model is capable of taking account of the variation of lode angle under plane strain condition. Numerical plane strain biaxial compression tests are conducted to observe the effect of non-coaxility on shear localisation. Bifurcation criteria based on the acoustic tensor are checked to predict the onset and inclination of the shear band. Predictions from the non-coaxial model are compared with those of coaxial model. The influence of the initial void ratio for the formation of shear bands is explored. Results are compared qualitatively with experimental observations.

Summary Undrained deformation of dilative sand generates negative excess pore pressure. It enhances the strength, which is called dilative hardening. This increased suction is not permanent. The heterogeneity at the grain scale triggers localisations causing local volume changes. The negative hydraulic gradient drives fluid into dilating shear zones. It loosens the soil and diminishes the shear strength. It is essential to understand the mechanism behind this internal drainage and to capture it numerically. The purpose of this paper is to develop a macroscopic constitutive relationship for the undrained deformation of saturated dense sand in the presence of a locally fully or partially drained shear band. Separate constitutive relations are generated for the band and intact material. Both time and scale dependence during pore fluid diffusion in saturated sand are captured, eliminating the mesh dependency for finite element implementations. The model is applied to the Gauss points that satisfy the bifurcation criterion. The proposed method is calibrated to recreate the undrained macroscopic response bestowed by an extra‐small mesh. The microscopic behaviours inside and outside shear band predicted by this model are qualitatively in good agreement with individual material point behaviours inside and outside the shear band in the extra‐small mesh. Depending on the loading rate and the shear band thickness, the response inside the band can be fully or partially drained, which governs the ultimate global strength. The calibrated model is exploited to simulate an upscaled biaxial compression test with semipermeable boundaries.

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When saturated granular materials which are dilative in nature are subjected to the undrained deformation, their strength increases due to the generation of negative excess pore pressure. This phenomenon is known as dilative hardening and can be witnessed in saturated dense sand or rocks during very fast loading. However, experimental evidence of undrained biaxial compression tests of dense sand shows a limit to this dilative hardening due to the formation of shear bands. There is no consensus in the literature about the mechanism which triggers these shear bands in the dense dilative sand under isochoric constraint. The possible theoretical reasoning is the local drainage inside the specimen under the globally undrained condition, which is challenging to be monitored experimentally. Hence, both incept of localisation and post-bifurcation of the saturated undrained dense sand demand further numerical investigation. Pathological mesh dependency hinders the ability of the finite element method to represent the localisation without advanced regularisation methods. This paper attempt to provide a macroscopic constitutive behaviour of the undrained deformation of the saturated dense sand in the presence of a locally drained shear band. Discontinuation of dilatant hardening due to partial drainage between the shear band and the adjacent material is integrated into the constitutive model without changing governing equilibrium equations. Initially, a classical bifurcation analysis is conducted to detect the inception and inclination of the shear band based on the underlying drained deformation. Then a post-bifurcation analysis is carried out assuming an embedded drained or partially drained shear band at gauss points which satisfy bifurcation criterion. The smeared shear band approach is utilised to homogenise the constitutive relationship. It is observed that the dilatant hardening in the saturated undrained dense sand is reduced considerably due to the formation of shear bands.