Stability analysis of homogenized stone column reinforced foundations using a numerical yield design approach

This paper deals with the ultimate bearing capacity of soft clayey soils, reinforced by stone columns, analyzed in the framework of the yield design theory. Since such geotechnical structures are almost impossible to analyze directly due to the strong heterogeneity of the reinforced soil, an alternative homogenization approach is advocated here. First, numerical lower and upper bound estimates for the macroscopic strength criterion of the stone column reinforced soil are approximated in a rigorous way with convex ellipsoidal sets, which makes the approximated criteria much easier to handle than the initial ones. Then, both static and kinematic approaches are carried out numerically on the homogenized problem using the above approximated macroscopic strength domains in an adapted finite element method. The whole numerical procedure is applied on one classical geotechnical problem: the ultimate bearing capacity of stone column reinforced foundations. The strength capacity of the structure is rigorously framed and the efficiency of the proposed numerical method is highlighted in terms of accuracy and calculation time.