Broken line random failure mechanism method in foundation bearing capacity assessment for spatially variable soil

This paper presents the broken line random failure mechanism method to analyse the bearing capacity of spatially variable soil. The method uses an upper bound theorem of limit analysis. The proposed formulation is numerically efficient and provides sufficient flexibility for a failure mechanism to adapt to weaker zones in the soil domain. Two types of multiblock failure mechanisms are analyzed: one-sided and double-sided; it is shown that in the case of a spatially variable soil, one-sided (right or left) failure mechanism provides better (lower) estimates of the foundation's bearing capacity. To optimize the failure geometry, a variation of the subset simulation-based optimization scheme is proposed. The method allows to unequivocally define the volume of the failure mechanism. In the paper, a series of tests, numerical analyzes, and a comparison with laboratory results are presented. It is shown that the lowest bearing capacities are obtained for the smallest volumes of failure mechanism. The results obtained are discussed, and future development possibilities are indicated.