Scattering Of SH Waves By A Circular-arc Hill Above A Circular Inclusion

A circular-arc hill above an inclusion may amplify the ground motion tremendously.However,few analytical solutions of a circular-arc hill above a circular cavity and that of a semi-cylindrical hill above an inclusion have been achieved.So we do some works as following:(1)A closed-form analytical solution of two-dimensional scattering of SH waves by a circular-arc hill and an underground circular inclusion in a half-space is presented using the wave functions expansion and the Graf's addition theorem.The solution is reduced to solving a set of infinite linear algebraic equation using Fourier expansion for auxiliary based on boundary condition.This solution can be degenerated to the ones of the model ignoring the hill or the tunnel.(2)Numerical solutions are obtained by truncation of the infinite equations.The results shows that the ground motion will be amplified obviously in areas where ground motion of the two degenerated models(one without the inclusion and the other one without the hill)is all amplified under a vertical incident SH waves.When the inclusion degenerates to a cavity,ground displacement amplitude s will be great in the hill at some periodic frequencies which can be determined based on wave speed in half-space and the distance between surface and the tunnel.(3)This paper discussed the influence of the underground inclusion and the hill.The study shows that the ground motion is closed to that of the half space as the buried depth of inclusion(cavity)increase s and the height-width ratio increas decreases.Finally,we obtain the buried depth of inclusion and the height-width ratio of hill witch can be ignored.(4)Finally,based on the theories of wave superposition,we analyzed its distribution law ignoring the effect of the second reflecting.The paper concluded that the ground position where appear great displacement amplitude and the incident frequency which cause huge displacement amplitude calculated were closed to the analytic solutions well.Besides,the motion law of the ground point over the center of cavity was same with the known conclusion.