Bearing Capacity by Variational Method

A general limit equilibrium approach has been applied to the problem of bearing capacity of foundations. The approach is completely rigorous in the sense that the critical rupture surface and the critical stress distribution along it are derived by variational methods without any a priori assumptions. The critical rupture surface has been proven to be log-spiral, which degenerates to a circular arc in the case of the frictionless soil. The superposition principle that was assumed by Terzaghi is derived by the use of variational analysis. The values of the obtained bearing capacity factors N_c(φ) and N_q(gf) corresponds closely to that obtained from the plasticity theory. The N/dγ(φ) factor obtained corresponds rather well with De Beer's and Feda's experimental results, while Terzaghi's solution for N/dγ(φ) is too low by a factor of approximately two.