The inclination and shape factors for the bearing capacity of footings

In 1920, Prandtl published an analytical solution for the bearing capacity of a maximum strip load on a weightless infinite half-space. Prandtl subdivided the sliding soil component into three zones: two triangular zones on the edges and a wedge-shaped zone in between the triangular zones that has a logarithmic spiral form. The solution was extended by Reissner (1924) with a surrounding surcharge. Nowadays, a more extended version of Prandtl׳s formula exists for the bearing capacity. This extended formulation has an additional bearing capacity coefficient for the soil weight and additional correction factors for inclined loads and non-infinite strip loads. This extended version is known in some countries as “The equation of Meyerhof”, and in other countries as “The equation of Brinch Hansen”, because both men have separately published solutions for these additional correction factors. In this paper, we numerically solve the stresses in the wedge zone and derive the corresponding bearing capacity coefficients and inclination and shape factors. The inclination factors are also analytically solved.