Scattering Of Rayleigh Waves By Local Irregular Sites

Site response problems are a kind of important problems in earthquakeengineering. A lot of investigations of earthquake damage show that the existence oflocal irregular sites affects the scattering and diffraction of seismic waves 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. Since a large portion of thedestructive seismic energy is transmitted to the sites of important structures viasurface waves, the investigation of analytical solution of scattering of surface wavesby local sites is very useful. It also has great academic significance in understandingphysical essence and verifying the accuracy of numerical solution. And it surely hasdistinct referenced value in practical projects.In this paper, the main research work is the analytical solution of scattering ofRayleigh waves by local irregular sites. After making the coefficients of Rayleighwave's potential functions clear, we use wave function expansion method to get theanalytical solutions. In this method, the surface of the half-space is approximated by acylindrical surface with a large radius. Then the scattering waves are represented bythe series of Bessel functions expansions. As for the incident Rayleigh waves, itappropriates to derive analytically the stresses and the displacements functions ofRayleigh waves from its potential functions and then to expand them in finite Fourierseries. Finally, the problem is solved through boundary conditions. The analyticalsolutions derived by this way are preferable to present available numerical resolutions,because they can be applied to a wider range of frequency, and simpler faster incalculation, and higher precision as well.Furthermore these analytical resolutions are also utilized to analyze the effect ofrelative factors (such as the frequency of the incident waves;the ratio of site shape'sdepth to its width;the ratio of underground cavity's depth and its radii;the stiffness ofinclusion, etc.) on the site response, and some valued qualitative conclusions are got.