Scattering and amplification of SV waves by a semi-cylindrical hill in a half-space by a wavefunction-based meshless method using mapping and point-matching strategies

Abstract

The zero-stress boundary conditions along the semi-infinite surface of a half-space have always posed challenging issues for the classical wavefunction expansion method to deal with in-plane wave propagation and scattering problems. A mapping and a point matching method are both introduced in this study to overcome the issue to propose a new wavefunction series solution to the scattering of SV-waves by a semi-cylindrical hill. The semi-infinite space is divided into an open and an enclosed region with a virtual boundary. After mapping the infinite surface into a finite interval, a good match of the zero-stress conditions in the open region is achieved. The zero-stress conditions in the enclosed hill region are satisfied analytically using the orthogonality of complex exponential functions. Taking into account the stress and displacement continuity conditions on the virtual boundary, the series solution can be obtained by solving a matrix to get the unknown coefficients of the wave fields. The accuracy of the solution is verified by comparing with two existing numerical solutions. To be helpful for engineering applications, the acceleration time histories at different locations under a real earthquake input are found to be obtainable based on the transfer functions of the frequency domain solution.