Failure mechanisms and corresponding shape factors of shallow foundations

In 1920 Prandtl published an analytical solution for the bearing capacity of a maximum strip load on a weightless infinite half-space. This solution was extended by Reissner in 1924 with a surrounding surcharge. In the 1940s, Keverling Buisman and Terzaghi extended the Prandtl-Reissner formula for the soil weight. Since then several people proposed equations for the soil-weight bearing capacity factor. In 1963 Meyerhof was the first to write the formula for the (vertical) bearing capacity of shallow foundations with both inclination factors and shape factors. The failure mechanisms belonging to the cohesion bearing capacity factor and the surcharge bearing capacity factor is for an infinite (2D) strip footing a Prandtl-wedge failure mechanism, but according to Finite Element Modelling (FEM) the failure mechanism belonging to the soil-weight bearing capacity factor is not. It looks more like a global failure mechanism. This means that the assumed superposition in the Terzaghi equation, and in the Meyerhof equation, is not automatically allowed. Additional FEM calculations show that in the case of a finite strip footing, and especially of round footings, the failure mechanism is again very different, and leads to much lower shape factors as factors based on a Prandtl-wedge failure mechanism. In fact the third direction, i.e. the tangential direction, which plays no important role in the failure mechanism for infinite strip footings, starts to play a major role in the failure mechanism and in the magnitude of the bearing capacity of the strip footing