Scattering of plane SH waves by a circulararc hill with a circular tunnel

Abstract

An analytical solution for scattering of incident SH waves by a circular-arc hill with a concentric circular tunnel was derived by Fourier-Bessel series expansion and auxiliary functions technique. The solution is reduced to solving a set of infinite linear algebraic equations finally. The accuracies of the numerical results are checked by the residual errors of boundary conditions with the truncation order increasing. The numerical results show that the existence and dimension of the tunnel have great effect on motion of the ground surface nearby and dynamic stress concentration of the tunnel.