Multi-Block Failure Mechanism Approach with Broken Lines in Bearing Capacity Estimation of Spatially Variable Soil

This study presents the novel use of kinematical failure mechanisms to analyze the shallow foundation bearing capacity for spatially variable soil. The approach preserves the upper bound limit theorem. For this reason, the straight dissipation lines resulting from the multi-block failure mechanism are no longer straight lines but become broken lines. The broken lines are adjusted to the actual value of the friction angle, which is considered spatially variable. In the study, the application of the idea to bearing capacity problems is presented and discussed. The motivation for the study is to ensure numerical efficiency and the ability of failure geometry to adapt to weaker zones in spatially variable soil. The numerical efficiency comes from the similarity of the proposed approach to Vanmarcke's spatial averaging applied to dissipation regions resulting from the failure mechanism. However, the ability of the failure mechanism to adapt to weaker zones is a result of the broken lines method used together with an optimization procedure based on a subset simulation-based approach. In numerical analysis, the eleven-block failure mechanism is assumed as a reasonable compromise between numerical efficiency and accuracy. In addition, double-sided and one-sided failure mechanisms are analyzed and results obtained for both cases are compared and discussed in the study. A comparison with random finite limit analysis (RFLA) is provided; a very good agreement in the results for both methods is observed. The numerical implementation of the proposed algorithm was used to analyze a variety of cases with different values of the horizontal scale of fluctuation. Two general cases of isotropic and anisotropic correlation structures are analyzed. The proposed method is very convenient for determining the volume of the failure mechanism, for this reason, the volume of the corresponding failure mechanism is also discussed together with the corresponding bearing capacities. The proposed method is promising for applications in shallow foundation reliability analyses.

Keywords: Upper Bound, Failure Mechanism, Scale of Fluctuation, Random Field, Reliability, Shallow Foundation