A FLEXIBLE RECTANGULAR FOOTING ON A GIBSON SOIL - REQUIRED RIGIDITY FOR FULL CONTACT

The problem of a rectangular footing or a strip footing resting on a n onhomogeneous elastic half-space is studied in this paper. The medium is assumed to be isotropic with a shear modulus linearly increasing wi th 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 foundat ion 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 ha ve 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 w ith respect to the plate geometry, imposed for reasons of mathematical feasibility). The contact is assumed to be tensionless. There are thr ee important steps in this formulation. The fundamental solution of th e nonhomogeneous half-space is separated into the fundamental solution of the homogeneous half-space and a function related to the nonhomoge neity of the half-space. The latter function is approximated by an ana lytically tractable expression. The contact region is discretized usin g an adaptive scheme that accounts for the possible edge and corner si ngularities. The latter scheme removes the burden of most of the numer ical integration. A rigid strip footing and a rigid rectangular footin g are treated first to ascertain the convergence of the solution proce dure and to provide information requisite for the flexibility study. T he title problem is transformed into the solution of three coupled two -dimensional singular integral equations. The contact regions are foun d iteratively since the problem is nonlinear.