An Efficient Pseudo Three-Dimensional Finite Element Model: Presentation and Analysis of Two Soil/Foundation Interaction Problems

Abstract

A pseudo-three-dimensional numerical model has been developed for the analysis of full 3D soil problems under combined loading. The procedure called Vertical Slices Model takes advantage of finite element (FE) 2D numerical solutions in plane stress for building approximate 3D solutions by replacing the inter-slice interactions by fictitious body forces. Continuum slices are successively analyzed by the combination of the explicit 2D finite element (FE) method and finite difference (FD) method in iterative process. The three-dimensional aspect of the considered problem is preserved by satisfying the continuity of shear stresses developed at the inter-slices. The theory of the vertical slices model is developed first, and then encoded in a Fortran computer program. Next, the prediction capabilities of this program are illustrated with two classical geotechnical applications, namely; the laterally and the axially loaded single piles embedded in homogeneous and non-homogeneous elastic soils. Although approximate, the model proved its ability to capture the behavior of the two boundary value problems. Then, in terms of stiffness factors the approach is used to predict the behavior of an embedded rigid square footing and a pile under combined loading in a half-space where the stiffness shows a power law variation with depth. Keywords: Finite element analysis; finite difference method; vertical slices; iterative process. 231 Int. J. Comput. Methods 2005.02:231-253. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/24/15. For personal use only. 232 D. A. Bouzid et al.

Response prediction of horizontally loaded single piles using a pseudo 3-D nonlinear FE procedure

“…The procedure involves the combination of the finite element (FE) method and the finite difference (FD) method for analysing the vertical pile and the surrounding soil sub-structured into vertical panels. The theory on which the present approach is based has been presented elsewhere by Amar Bouzid et al (2005aBouzid et al ( , 2005b for elastic problems involving other structures interacting with soil. Hence, the elastic version of the pseudo-3D model is not detailed herein; only a brief description is presented.…”