General failure envelope of eccentrically and obliquely loaded strip footings resting on an inherently anisotropic granular medium

Soil is a cross anisotropic particulate medium with different strengths in various directions; this is primarily due to its geological deposition process and the very fact that particles always settle in their most stable positions. This study examines the influence of inherent anisotropy on the ultimate bearing capacity of eccentrically and obliquely loaded strip footings that rest on cohesionless granular soils using a two-dimensional plane strain finite element simulation in conjunction with the lower bound limit analysis method and second-order cone programming (SOCP). The inherent anisotropy, manifested in the so-called parameter of anisotropy ratio, is simulated by considering variable internal friction angles along different directions. The nonlinear form of the universal Mohr-Coulomb failure criterion is also used to optimize the lower bound formulation. The failure envelopes of shallow foundations that correspond to inclined and eccentric loadings are depicted and discussed for various anisotropy ratios of the underlying soil deposit. It is observed that the failure locus generally decreases in size as the anisotropy ratio increases. Based on the results of numerical simulations, a general equation that describes the general bearing capacity of shallow foundations resting on inherently anisotropic cohesionless granular medium subjected to combined vertical-horizontal-moment loadings is presented and discussed.