ELASTIC SUBSURFACE STRESS-ANALYSIS FOR CIRCULAR FOUNDATIONS - I

In part I of this analysis an attempt is made to determine a simple es timate 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 quadrat ic 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 co nditions and resulting internal stress fields. The current analysis co nsists of using potential functions to derive closed form expressions for the elastic field in the half space. The half space is taken as cr oss-anisotropic (transversely isotropic), where the planes of isotropy are parallel to the free surface. The x-and y-axes are taken in the p lane of the surface with z directed into the half space. Hence the bou ndary conditions within the circular loaded area are on the shear stre ss components tau(xz), tau(yz) and normal stress sigma(zz). The soluti ons presented within actually comprise seven different boundary value problems for the transversely isotropic half space. The analytical sol utions for a point normal or shear force are first used to write the s olution for distributed loading over a circle in the form of a double integral over the loaded area. It is shown, with the aid of Hankel tra nsform analysis, that the integrals appearing in the elastic field hav e been previously evaluated in terms of complete elliptic integrals. T he necessary integral evaluations are provided in Appendix I. The limi ting form of the expressions for an isotropic material are also includ ed.