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

Abstract

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.

A computational homogenization approach for limit analysis of heterogeneous materials

“…The behavior of cylindrical porous material was studied in using Gurson's model together with coupled kinematic and static theorems as well as homogenization theory. Based on finite elements and primal‐dual interior point optimization algorithm, the assessment of the macroscopic strength criterion and stability analysis of soils reinforced by stone columns were performed in . For periodic plates, a theoretical study on the overall homogenized Love–Kirchhoff strength domain of a rigid perfectly plastic multi‐layered plate was reported by , and numerical determination of the macroscopic bending strength criterion was presented in .…”

“…In recent years, thanks to the development of such an efficient primal‐dual interior point algorithm, implemented in a commercial optimization software Mosek , limit analysis problems have gained increasing attention. In fact, most commonly used yield criteria can be cast in the form of conic or semi‐definite constraints, and optimization problems involving such constraints can be solved efficiently by such an algorithm, evidenced by recent works .…”

A plane strain yield design approach to stability analysis of a column‐reinforced soil foundation under inclined loading

“…It might be expected (not proven by the present analysis) that this kind of reinforcement can even induce a reduction in bearing capacity with respect to that of the native soil foundation when the reinforcement ratio becomes larger. Actually, this issue has already been discussed in Hassen et al and more recently in Gueguin et al . In the latter work, the authors have obtained numerical upper bound estimates for the bearing capacity of a column‐reinforced foundation under purely horizontal load that are about 15 % lower than that of the non‐reinforced soil.…”

“…The periodic homogenization method has been applied in the context of yield design theory during the last two decades to assess the improvement of the bearing capacity of a foundation soil expected from reinforcement by a dense array of columns. Resorting either to the upper bound static or to the upper bound kinematic approach, reference to these homogenization‐based works include Jellali et al , Jellali et al , Hassen et al , Gueguin et al , or Gueguin et al .…”

Modeling Stone Columns

“…A more detailed analysis shows that the equivalent homogenous soil should be anisotropic by nature to account for the column orientation [ 50 ]. Some authors (e.g., [ 51 , 52 , 53 ]) use theories for periodic media to propose analytical transformations from the columns and the soft soil (heterogeneous periodic composite material at the microscale) to a homogeneous equivalent soil (homogenous material at a macroscale). They use a macroscopic strength criterion of the anisotropic homogeneous equivalent soil to evaluate the bearing capacity.…”