Scattering Of SH Waves By a Circular Inclusion Under a Variable Circular-Arc Hill

摘要

An inclusion under a hill would amplify the ground motion tremendously. However, Few analytic solutions achieved for this problem have limitations on a special semi-cylindrical hill or a underground cavity. Here we derive one for a new model with the wave functions expansion and auxiliary functions technique. It is reduced to solving a set of infinite linear algebraic equation using Fourier expansion for auxiliary functions based on boundary condition. The solution can be degenerated to the ones of the model ignoring the hill or the inclusion. Finally, numerical solutions are obtained by truncation of the infinite equations. The results indicate that the ground motion could be seen as the superposition of the effect of the inclusion and the hill qualitatively; and when the inclusion degenerates to a cavity, amplification frequencies on the hilly boundary can be obtained by the wave speed in half-space and the vertical distance between the flat surface and the tunnel. The influence of softness and hardness of inclusion and incident angles is also discussed here.