Upper bound rigid block analysis with rigid block subdivision

Rigid block limit analysis provides a simple method for computing rigorous upper bound solutions on the stability of geotechnical problems. The method requires the topology of a collapse mechanism to be defined a priori, from which an expression for stability is derived. For complex mechanisms optimizing these expressions using multivariate search algorithms requires enormous computational effort, and the initial feasible solution needed for local optimisation algorithms are difficult to obtain. This paper describes a method for successively subdividing blocks within a collapse mechanism, increasing its complexity gradually and allowing simple univariate optimization algorithms to be used. The performance of this technique is demonstrated by computing the bearing capacity factor for a strip footing on weightless fissured clay and the undrained stability of a circular tunnel. The techniques developed in this paper are shown to provide a robust method for solving rigid block problems with demanding material behaviour and complex geometry.