Scattering of plane SH waves by a semi-circular discontinuity in an elastic half-plane

Abstract

A curved discontinuity near the ground can cause the scattering of seismic waves and significantly affect the ground and underground motions, posing some challenges in seismic design. In this paper, a series solution for the scattering and diffraction of plane SH waves from a semi-circular discontinuity in an elastic half-plane is first presented using the wave function expansion method, aiming to reveal the effects of the discontinuity properties on wave scattering and seismic motion. Based on the correspondence principle of viscoelasticity, the influence of the damping ratio of the medium on the seismic motion is also discussed. Finally, by combining the series solution and the inverse Fourier transform, the ground and underground motions induced by a transient plane SH wave are analyzed by exhibiting the wave field snapshots at different times and the waveform curves of different measurement points on the ground. The results indicate that both the stiffness of the discontinuity and the damping ratio of the medium have a great influence on the propagation of seismic waves and play an important role in seismic calculations.