Integration of singularities in FE/BE analyses of soil-foundation interaction with non-homogeneous elastic soils

This paper addresses the derivation of the boundary integral equations for a non-homogeneous elastic half-space subjected to constant surface tractions on an arbitrarily shaped area on the basis of the respective Green's functions. The type of non-homogeneity considered is a power law variation of Young's modulus with depth below the surface of the half-space. Two different methods, a contour integral and an integration-free approach are presented, applicable for arbitrarily and rectangular shaped boundary elements, respectively. In the first one the divergence theorem is used in order to reduce the integration of a two-dimensional surface element to an integration over the element's confining boundary only. In the second approach no integration at all is needed since the solution is found simply by evaluating functions to be determined at the boundaries of the loaded rectangle.