Finite element vertical slices model: Validation and application to an embedded square footing under combined loading

This paper describes an efficient formulation for the analysis of three-dimensional (3-D) soil/structure interaction problems. The technique which is called vertical slices model (VSM) subdivides the structure and the surrounding soil into vertical slices. It takes profit of finite element 2-D numerical solutions in plane stress for building approximate 3-D solutions by replacing the inter-slice interactions by fictitious body forces. The 2-D finite element and finite difference methods are combined in a relatively simple and compact procedure, and applied iteratively to each vertical slice. The 3-D aspect of the considered problem is kept by satisfying the continuity of shear stresses developed at the inter-slices. First, the theory of the vertical slices model is presented and then a Fortran computer program is elaborated. Next, the capabilities of this program are illustrated by applying the approach to the problems of both laterally and axially loaded piles founded in both homogeneous and non-homogeneous soils. A third problem of a rigid rectangular foundation resting on top of a homogeneous elastic stratum has also been investigated. Comparisons with other numerical solutions show good agreement and consequently they prove that the model is successfully able to capture the behavior of the three boundary value problems. Finally, in terms of stiffness factors the method is used to predict the behavior of an embedded square footing under combined loading, in a half-space where the stiffness exhibits a power-law variation with depth.