Upper bound solution for ultimate bearing capacity with a modified Hoek-Brown failure criterion

The first technique is the generalized tangential technique proposed by the authors. Based on a multi-wedge translation failure mechanism, a generalized tangential technique is used to formulate the bearing capacity problem as a classical optimization problem where the objective function, which is to be minimized with respects to the parameters of failure mechanism and the location of tangency point, corresponds to the dissipated power. The minimum solution is obtained by optimization. Using the technique, the effects of rock weight under the base of the footing and surcharge load can be considered. The second technique, “tangential” line technique, was originally used to analyze slope stability with a nonlinear failure criterion. In order to assess the validity of the proposed method, the “tangential” line technique is extended to evaluate the bearing capacity factor with the nonlinear failure criterion, where the effects of self-weight and surcharge load on the bearing capacity cannot considered. The second technique, however, has to utilize the previously calculated ultimate bearing capacity factor with a linear MC failure criterion. Numerical results are compared and presented for practical use in rock engineering.