Lower-Bound Finite Elements Limit Analysis for Hoek-Brown Materials Using Semidefinite Programming

The lower-bound finite elements limit analysis in combination with semidefinite programming (SDP) has been used to solve stability problems involving a modified Hoek-Brown (HB) yield criterion with the exponent 𝛼=0.5. In order to demonstrate the applicability of the proposed computational approach, bearing capacities of strip and circular foundations on rock mass have been determined. The results have been given in the form of nondimensional bearing capacity factors as a function of different material input parameters. By comparing the results obtained from the present analysis with that reported in literature, it is noted that the proposed approach remains quite accurate and is highly efficient to deal with any large-scale optimization problem. The method does not require any kind of the smoothing of the yield surface and it can even be implemented to deal with any three-dimensional problem as well.