Response of an elastic half-plane with an embedded circular cavity subject to a harmonic anti-plane shear wave: A comparison of methods

Abstract

In this paper, we investigate the response of a cavity embedded in an elastic half-plane (2D) subjected to a harmonic SH wave. In previous work, the method of conformal mapping and the indirect boundary element method (indirect BEM) were employed to solve the 3D wave scattering from a cylindrical tunnel embedded in a half-space. Inaccurate results were obtained particularly at high frequencies (method of conformal mapping). Therefore, in this study we focus on a comparison of the two methods with the method of images, which serves as a benchmark solution. Through a systematic evaluation, we confirm that the two methods accurately work within the complete considered ranges of the dimensionless frequency and the embedded cavity depth. This suggests that representing the waves scattered from the free surface by cylindrical waves in the method of conformal mapping is the cause of the inaccuracies at high frequency in the 3D problem; the cylindrical waves are probably not able to fully capture all wave conversions taking place at the free surface. The presented results reveal significant effects of the system parameters on the responses. The system’s response curves display nearly equally spaced resonances, which is in line with those of the 1D shear layer subject to bedrock motion, while similar response curves for the 3D case do not have this feature.