Finite difference analysis of vertically loaded raft foundation based on the plate theory with boundary concern

Abstract

This paper introduces the finite difference formulations for the deformations of a surface raft foundation under vertically uniform loads. The thin-plate theory and central difference scheme were adopted to derive the equations in which the finite raft was affected by boundary conditions. With the use of approximate soil springs underneath the raft, none-uniform settlements of the foundation can be analyzed through the newly proposed method. A computer program WERAFT-S is suggested accordingly. Solutions of the analysis were examined with the three-dimensional finite element analysis on numerical models. It was found that the foundation settlements of the newly proposed analysis can be rational by modeling the soils underneath raft as the axial forced elements providing that their stiffness were calibrated carefully prior to the analysis. If the Lysmer's analog model was adopted for the soil springs, much smaller foundation settlements would be resulted at the corners since the analog model is more adequate for rigid footing analysis. Applicability and details of the newly proposed solution are introduced.