Scattering Of Plane P Waves By A Semi-cylindrical Hill: Analytical Solution

Site response problem are a kind of important problems in earthquakeengineering. A lot of investigations of earthquake damage show that the existenceof local sites affects the scattering and diffraction of seismic wave greatly.Accordingly, there are sensitive change of earthquake response of ground surface,underground structure and buildings in narrow spatial dimension. The local sitesinfluence distribution of earthquake damage therefore. Hence, the investigation ofanalytical solution of scattering by local sites has great academic significance tounderstand physical essence and verify the accuracy of numerical solution. And, itsurely has distinct referenced value in practical project.Local hill site is a sort of familiar ground in practical project. It is morecomplex than that of basin site due to the multi-scattering of seismic waves. In thissituation, the solution of plane P waves is much more difficult than that of SHwaves. To date as we know, very few analytical solutions for hill site have beendone and they are all pointed to SH wave: Semi-cylindrical hill (Yuan and Liao,1992), Cylindrical hill of Circular-arc Cross-section, (Yuan and Liao, 1996). Thereare no analytical solution point to the P waves and hill.In this thesis, Fourier-Bessel series wave function expansion, auxiliaryfunction and partition division technique are used to solve this mixed-boundaryproblem. Very big circle are used to simulate the free boundary, Graf's additiontheorem is used to convert the coordinates. Finally, a set of infiniteover-determined linear algebraic equations are reduced and numerical solutionsare obtained truncation of the infinite equations and solved by singular valuedecomposition method.The accuracies of the numerical results are checked by the convergence of theground surface displacement and residual errors of boundary conditions withincreasing the truncation order. And then, the effects of the frequency and angle ofthe incident waves on the displacement amplitude of the ground surface areanalyzed.