Upper-bound solutions for bearing capacity of strip footings over anisotropic nonhomogeneous clays

All available solutions for the problem of bearing capacity on clays of anisotropic and nonhomogeneous strength are based on the assumption of either circular or Prandtl-type failure mechanisms. Although these solutions are rigorous within the concept of limit analysis or limit equilibrium methods, the formulations are too mathematical and exceedingly cumbersome and the bearing capacity value can only be determined through numerical optimization for each given combination of soil and failure mechanism parameters. By means of the upper bound approach of limit analysis, and adopting translational failure mechanisms, this paper presents analytical solutions for the bearing capacity of surface strip footings on clays of strength anisotropic and linearly increasing with depth. Closed-form expressions for bearing capacity factors in the case of smooth and rough footings, have been derived by considering two newly introduced kinematically admissible translational failure mechanisms with varying wedge angles. It was remarkable to find that the two mechanisms would render closed-form expressions for the bearing capacity factor if and only if the deformed region underneath the footing is set to be bounded by two vertical discontinuity surfaces. The derived formulas are expressed in terms of degree of strength anisotropy and a nondimensional parameter that reflects strength nonhomogeneity. Besides being the only closed-form solutions yet available for the bearing capacity of strip footings on clays with anisotropic and nonhomogeneous strength, the derived expressions have been found to not only provide upper bound values for the bearing capacity factor that compared favorably with available solutions, but also yield the best upper bound values when strength increase with depth becomes predominant.