Scattering of spherical P-waves by three-dimensional cavity in an elastic half-space

Abstract

This study adopts the indirect boundary integral equation method (IBIEM) to solve the scattering of spherical P-waves by a three-dimensional (3D) cavity in an elastic half-space. Specifically, the free field of the spherical wave is obtained by the method of full space superposition. Based on the single-layer potential theory, the scattered field is constructed using concentrated force sources applied on the fictitious wave source surface. Our method’s numerical accuracy and stability are verified by comparing it against existing results. Additionally, considering a spherical cavity in a half-space as an example, this study investigates the influence of the wave source orientation, incident wave frequency, distance between the wave source and the cavity, and cavity depth on the surface displacement and dynamic stress concentration factor (DSCF) on the cavity surface. The results indicate significant differences in the spatial distribution characteristics of surface displacement and DSCF on the cavity surface for different wave source orientations and cavity depths. As the incident frequency increases, the spatial oscillation of surface displacement near the cavity intensifies, and the DSCF gradually decreases. As the wave source approaches the cavity, the amplification effect of surface displacement near the cavity becomes more apparent. At the same time, the maximum DSCF shows significant non-monotonic variation, and its position also changes accordingly. When the distance between the wave source and the cavity is large, the spherical wave can be approximated as a plane wave.