Geotechnical Analysis Involving Cross-Anisotropic Soils Using a Generalized Anisotropic Stress Tensor

Geotechnical analysis may often involve the soil mass of cross-anisotropy, and a consideration of the cross-anisotropy of soil mass is crucial to the safety and economy of geotechnical applications. In this work, a constitutive model for cross-anisotropic soils, which relies on a generalized anisotropic stress tensor, is formulated in the SOCP format, so that the second-order cone programming optimized FEM (FEM-SOCP) can be applied to geotechnical problems involving cross-anisotropic soils. Based on a biaxial compression test of a soil specimen and a rigid strip footing resting on ground, it is found that the FEM-SOCP can predict the shear band patterns and the peak deviatoric stress of the anisotropic soil specimen in biaxial compression similar to those of the discrete-element method (DEM), and the major difference in numerical results is largely attributed to the continuum inherence of the FEM-SOCP and the discrete inherence of the DEM. The three scaling factors of stress in the proposed anisotropic stress tensor can significantly affect the ultimate bearing capacity of the ground. Given certain values of three scaling factors of stress, the ultimate bearing capacity of the ground with a bedding angle of β = 0° or 90° is evidently greater than those of grounds with other bedding angles due to the rotation of the footing caused by an asymmetric ground. Hence, the neglect of the anisotropy of the ground or a simplification of the bedding angle to β = 0° or 90° may result in an unconservative design.