Failure surface for shallow foundations in sand using a classical bearing capacity

Much effort has been made to elucidate the ultimate capacity of shallow foundations under the general cases of vertical (V), lateral (H), and moment (M) loads in soils. The nature of the dependency of the ultimate capacity of shallow foundations on the combination of V, H, and M loads, the ratio of embedment to diameter, and soil properties has has not yet been analytically revealed. In this paper, an analytical investigation into failure effect of V, H, and M loads applied to shallow foundations in nonhomogeneous sand is made using a classical bearing capacity theory. Of the bearing capacity equations proposed thus far, the most appropriate bearing capacity equation which can predict experimental results of shallow foundations in sand is presented. A no-tension interface between a foundation base and a soil and an effective diameter of the foundation are used to analyze the base failure produced by the vertical stress of the soil below the foundation base when vertical and moment loads are applied. For shallow foundations with various embedment ratios in sand under the two different loading ways, the displacement-load curves and failure envelopes in the H-M, H-V, and M?V planes and in the H-M?V space are presented. For failure envelopes in the H-M plane under a constant vertical load for shallow foundations in sand, the results obtained from experiments are well predicted by the present method.