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Strength criterion for cross-anisotropic sand under general stress conditions


By incorporating the fabric effect and Lode’s angle dependence into the Mohr–Coulomb failure criterion, a strength criterion for cross-anisotropic sand under general stress conditions was proposed. The obtained criterion has only three material parameters which can be specified by conventional triaxial tests. The formula to calculate the friction angle under any loading direction and intermediate principal stress ratio condition was deduced, and the influence of the degree of the cross-anisotropy was quantified. The friction angles of sand in triaxial, true triaxial, and hollow cylinder torsional shear tests were obtained, and a parametric analysis was used to detect the varying characteristics. The friction angle becomes smaller when the major principal stress changes from perpendicular to parallel to the bedding plane. The loading direction and intermediate principal stress ratio are unrelated in true triaxial tests, and their influences on the friction angle can be well captured by the proposed criterion. In hollow cylinder torsional shear tests with the same internal and external pressures, the loading direction and intermediate principal stress ratio are related. This property results in a lower friction angle in the hollow cylinder torsional shear test than that in the true triaxial test under the same intermediate principal stress ratio condition. By comparing the calculated friction angle with the experimental results under various loading conditions (e.g., triaxial, true triaxial, and hollow cylinder torsional shear test), the proposed criterion was verified to be able to characterize the shear strength of cross-anisotropic sand under general stress conditions.

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The financial supports by National Basic Research Program of China (through Grant No. 2014CB049100, 2012CB719803) and National Science Foundation of China (NSFC through Grant No. 11372228) are gratefully acknowledged. We are grateful to the anonymous reviewers for their helpful comments and suggestions.

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Correspondence to Xilin Lü.

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Lü, X., Huang, M. & Andrade, J.E. Strength criterion for cross-anisotropic sand under general stress conditions. Acta Geotech. 11, 1339–1350 (2016).

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  • Cross-anisotropy
  • Friction angle
  • Hollow cylinder torsional shear test
  • Intermediate principal stress ratio
  • Sand
  • True triaxial test