In-plane soil structure interaction excited by plane P/SV waves

The subject of two dimensional, in-plane soil structure interaction is studied through a classic model consisting of a shear wall resting on a rigid circular foundation embedded in an elastic homogeneous half-space. As it is known from literature, satisfying the zero stress conditions on the ground surface has been the major barrier for developing closed-form solution to any theoretical models that involve in-plane seismic wave scattering by circular inclusions in the semi-infinite half-space. The early solution to this model approximates the flat ground surface by the surface of a large cylinder. With the objective of examining the validity of such approximation, and to further understand the extent of importance and influence of these zero-stress surface conditions on the model solution, two new solution procedures with different treatments of the ground surface are presented in this work. The first solution procedure relaxes the zero-stress conditions on the ground surface, with the excitation considered to be an incident plane P or SV waves. The second solution procedure includes all boundary conditions in least square sense through the use of weighted residue method, and with the excitation of an incident plane P wave. Both formulations lead to closed-form approximated solutions. Numerical results based on these two methods are compared to each other and to those of the early published solution on the same problem.