A homogenization method for estimating the bearing capacity of soils reinforced by columns

Abstract

SUMMARYThe ultimate bearing capacity problem of a strip foundation resting on a soil reinforced by a group of regularly spaced columns is investigated in the situation when both the native soil and reinforcing material are purely cohesive. Making use of the yield design homogenization approach, it is shown that such a problem may be dealt with as a plane strain yield design problem, provided that the reinforced soil macroscopic strength condition has been previously determined. Lower and upper bound estimates for such a macroscopic criterion are obtained, thus giving evidence of the reinforced soil strong anisotropy. Performing the upper bound kinematic approach on the homogenized bearing capacity problem, by using the classical Prandtl's failure mechanism, makes it then possible to derive analytical upper bound estimates for the reinforced foundation bearing capacity, as a function of the reinforced soil parameters (volume fraction and cohesion ratio), as well as of the relative extension of the reinforced area. It is shown in particular that such an estimate is closer to the exact value of the ultimate bearing capacity, than that derived from a direct analysis which implicitly assumes that the reinforced soil is an isotropic material.

Yield design of dry‐stone masonry retaining structures—Comparisons with analytical, numerical, and experimental data

“…It can be noted that the analytic solution (19) does not depend on the block size parameters a and b, which amounts to saying that the ultimate load is independent of the slenderness ratio of the blocks in the case of dry-stone masonry retaining structures under linear pressure distribution. This result could prove to be changed for other wall geometries or different types of loading (e.g.…”

“…It results in constructing a virtual velocity field with respect to kinematic conditions and then writing the balance between external forces and maximum resisting works. This method was first devoted to soil mechanics [18,19], but it has been expanded on rock mass [20,21] and periodic masonry [15,22]. The following section describes the procedure to model a dry-stone retaining structure using this method.…”

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

“…Some authors have evaluated analytically or numerically the macroscopic strength criterion of lime-column reinforced soils (purely cohesive soil reinforced by purely cohesive solumns) by using both kinematic and static approaches of the yield design theory [27][28][29][30]. The stability analysis has been performed in such a case for different configurations of structures (embankment resting upon a reinforced soil [31] or ultimate bearing capacity of reinforced foundation under inclined loads [32]).…”

Bearing capacity charts of soft soil reinforced by deep mixing

“…This method was used to transform the three-dimensional problem to a two-dimensional plane strain idealisation. A structure having the same geometry as the initial unreinforced soil and subjected to the same loading conditions was defined whereby the composite reinforced material was replaced by an equivalent homogeneous material (Jellali et al, 2005). An example of bearing capacity solution using different homogenisation methods is given in Figure 2.…”