Stress analysis for an elastic half space containing an embedded rigid block

The plane elasticity problem of a finite, rigid rectangular block partially embedded in, and perfectly bonded to an elastic half space is investigated. The problem is formulated by the superposition of the solutions to the problems of horizontal and vertical line inclusions beneath an elastic half space. Substitution of these results into the boundary conditions appropriate for the embedded block problem leads to a system of coupled singular integral equations, whose unknowns are the normal and shear stress discontinuities between the bonded surfaces. Two distinct sets of loads are applied to the embedded block, so that it either translates without rotation in the y-direction, or rotates about an axis in the z-direction. Several important physical quantities are computed, e.g. the diffusion of the load from the block into the elastic half space for vertical translation and the rotational stiffness.