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 triangle zones on the edges and a wedge shaped zone in between the triangle zones that has a logarithmic spiral form. The solution was extended by Reissner in 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 has additional correction factors for inclined loads and for non-infinite strips loads. This extended version is in some countries known 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 for 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 for.