Scattering Of P And SV Waves By Alluvial Valleys With Saturated Soil Deposits

It has been shown that local sites, e.g. cavity, canyon and valley etc, have an important effect on seismic wave propagation according to abundant earthquake damage investigations. And this kind of research has become more and more attractive in recent decades. There already have been many analytical solutions to local sites by such incident seismic waves like SH, SV, P waves based on one-phased medium assumption due to many restrictions. However, it is more practical and accurate to analyze seismic wave propagation in saturated soil according to the two-phased saturated porous medium assumption. It is also significant to extend that assumption in analyzing site dynamic response during earthquake whether in theory development or in engineering application.Alluvial valley is an important local site, and a great amount of preceding research was concentrated on it. For valley, the research on SH-wave is almost perfect. For P and SV-wave, although there is conversion of wave types at boundaries, there also have many results by now. But all these results are based on the assumption of one-phased medium. In a fluid-saturated porous half-space, there exist two longitudinal waves (PⅠ, PⅡ) by incident P or SV-wave and there will be critical angles by incident SV-wave. This makes the problem very complex. Being the succession of preceding researches, on the basis of the Biot's fluid-saturated dynamic theory, an analytical solution of two-dimensional scattering and diffraction of plane P and SV waves by fluid-saturated porous valley in a elastic one-phased half-space is presented by the Fourier-Bessel series expansion technique.In this thesis, the saturated site is assumed to be two-phased saturated porous medium, and the surface is approximated by a cylindrical surface with a very large radius. And the reflected waves and scattered waves are represented by Fourier-Bessel series expansion. As for the incident SV waves, it appropriates to derive analytically the stresses and the displacements functions of incident waves from its potential functions and then to expand them in finite Fourier series. Finally, this problem is solved upon drained and undrained boundaries respectively. We can also get very accurate results when the frequency is very high (η=5.0) and the boundary conditions are satisfied very well. The solution in this thesis will be the same as the solution in one-phased medium when the porosity is very small.On the basis of these analytical solutions, the influence of porosity and Poisson's ratio on the displacement amplitude of the free surface is analyzed, and some valuable qualitative conclusions are given.