A flexible rectangular footing on aGibson soil: Required rigidity for full contact

Abstract

The problem of a rectangular footing or a strip footing resting on a nonhomogeneous elastic half-space is studied in this paper. The medium is assumed to be isotropic with a shear modulus linearly increasing with depth G (z) = G 0+ mz and a constant Poisson's ratio equal to 1/3. An important feature of this model is that either the Winkler foundation or the elastic homogeneous half-space can be made special cases by letting G 0 or m equal zero, respectively some results are presented for these cases. In order to investigate the necessary conditions for a footing to be considered rigid, both rigid and flexible footings have been studied. Central concentrated (column) loading, in addition to the self-weight, is treated-being the most demanding in terms of the zero uplift requirement (under conditions of symmetry in the loading with respect to the plate geometry, imposed for reasons of mathematical feasibility). The contact is assumed to be tensionless. There are three important steps in this formulation. The fundamental solution of the nonhomogeneous half-space is separated into the fundamental solution of the homogeneous half-space and a function related to the nonhomogeneity of the half-space. The latter function is approximated by an analytically tractable expression. The contact region is discretized using an adaptive scheme that accounts for the possible edge and corner singularities. The latter scheme removes the burden of most of the numerical integration. A rigid strip footing and a rigid rectangular footing are treated first to ascertain the convergence of the solution procedure and to provide information requisite for the flexibility study. The title problem is transformed into the solution of three coupled two dimensional singular integral equations. The contact regions are found iteratively since the problem is nonlinear.