Seismic interaction between a semi-cylindrical hill and a nearby underground cavity under plane SH waves

Seismic waves might be unavoidably triggered during underground energy and resource exploitation. Surface irregularities and subsurface cavities have significant effects on seismic wave propagation and cause amplification or reduction of ground motion. Hence, it is significant to address the scattering problem of SH waves induced by topography features and subsurface cavities in earthquake engineering. In this paper, based on the wave function expansion method coupling with the conjunction concept and the Graf’s addition formula, a series solution to this scattering problem of SH waves induced by a semi-cylindrical hill and a nearby cylindrical cavity in a homogeneous, isotropic, linear elastic half-space is derived. The displacement amplitudes on the hill surface and its environs are calculated, and compared with the results in the existing works to verify the validity of the deriving process. Then, parametric studies are performed to analyze the effects of the cavity (its location and size), and the characteristics of incident waves (the frequency and incident angle) on the seismic response of the semi-cylindrical hill. Finally, the seismic behavior of the cylindrical cavity near or away from the hill for different frequencies and incident angles is examined.