Resolution of bearing capacity problems using the Lower Bound Theorem and linear programming

Abstract

Toe Lower Bound Theorem is a powerful tool for analysing stability problems as it assures getting in a rigorously safe solution. Nevertheless, its application to practical problems with complex geometries and stress fields is usually rather ditlicult.

Toe basic problem of any lower bound analysis turns to be constructing statically admissible stress fields conducting to solutions as close as possible to failure conditions. ln this work a rational method for this purpose is presented, admitting a discretisation of the soil mass into finite elements and using linear programming to optimise loading subjected to stress constrains. This methodology is applied to bearing capacity problems.