Elastic Subsurface Stress Analysis for Circular Foundations. I

Abstract

In part I of this analysis an attempt is made to determine a simple estimate of the stresses resulting from a circular foundation subjected to concentric or eccentric loading. It is assumed that the foundation loading can be modeled as combinations of uniform, linear, and quadratic tractions applied over a circular area on the surface of an elastic half space. The present analysis for quadratic and linear loading are combined with a uniform loading solution (normal or shear traction), previously derived by the authors, to provide the requisite loading conditions and resulting internal stress fields. The current analysis consists of using potential functions to derive closed form expressions for the elastic field in the half space. The half space is taken as cross-anisotropic (transversely isotropic), where the planes of isotropy are parallel to the free surface. The x- and y-axes are taken in the plane of the surface with z directed into the half space. Hence the boundary conditions within the circular lo...