Scattering And Diffraction Of A Cylindrical Cavity In Half-space Subjected To Elastic Waves

Effect of underground structures on propagation of the earthquake waves is an important topic in earthquake engineering, and its study can be divided into two aspects of situation. One of them is to investigate the effect on ground motion due to the scattering and diffraction of earthquake waves caused by underground structures. Another is to determine the response of underground structures themselves due to earthquake waves. Usually, it concerns dynamic stress concentration. Scattering and diffraction of elastic waves by an underground cavity is becoming one of the most interesting problems in elastodynamics.Scattering of incident SV and Rayleigh waves by a cylindrical lined cavity in half-space, wave conversion is complicated. Because of it, there have been no analytical solutions by now. Further more, all research work before are for two-dimensional half-space. As to three-dimensional half-space, investigation needs to be done further.Based on the previous research work, the Fourier-Bessel series expansion method is used in the dissertation. Firstly, an analytical solution for the scattering of incident SV and Rayleigh waves by a cylindrical lined cavity in the two-dimensional half-space was derived. Second, based on the solutions of two-dimensional half-space, research work is extended to three-dimensional half-space. Analytical solutions for the scattering of incident P, SV and Rayleigh waves at arbitrary angles by a cylindrical lined cavity in the three-dimensional half-space were derived. Furthermore, the effect of factors such as cavity's diameter, incident wavelength, incident angle and lining's rigidity on the surface displacement and dynamic stress concentration were also analyzed. The results indicate that the existence of a cavity affects the surface displacement of the half-space greatly. Frequency of the incident wave and lining's rigidity are two important factors which affect the surface displacement and dynamic stress concentration.When a big arc surface is used to substitute for the surface of the half-space, the model is approximate in mathematical meaning. In the dissertation, we try to find a technique to improve the model, in which Fourier-Bessel series and integral transform of Hankel function are both used. Furthermore, numerical solutions for the scattering of incident P, SV and Rayleigh waves by a cavity in the two dimensional half-space were derived. The results show that although the new technique is exact in mathematical model, errors are larger than those calculated by Fourier-Bessel series expansion method because of the precision of the numerical integration on infinite, oscillatory functions. Still, the new technique also has theoretical value and meaning.