SH-waves scattering from a partially filled semi-circular alluvial valley

A series solution of the plane SH-waves incident on a partially filled semi-circular alluvial valley imbedded in a half-space is presented. Based on the region-matching method, the analysed region is decomposed into two subregions by the interface between two media. The antiplane displacement field of each subregion is expressed in terms of an infinite series of cylindrical wavefunctions with unknown expansion coefficients. After imposing the traction-free condition on the curved valley surface and the matching conditions on the interface with the aid of Graf's addition theorem, the unknown coefficients are obtained. Both the frequency- and time-domain responses are evaluated. In the theoretical derivation of this work, two classical exact series solutions are also included, so the present series solution is more general than those given before. Visible effects of different physical parameters on ground surface motions are illustrated in graphical form.