On Scattering & Diffraction Of Underground, Circular, Lined Tunnels Subjected To Incident Cylindrical SH Waves

Scattering and diffraction of cylindrical SH waves by the underground tunnel canaffect the ground motion near the tunnel and the hoop stress of the tunnel. So, thecylindrical waves generated by the explosion may affect the safety of the originalunderground tunnel and it is necessary to compute the impact. Up to now, theanalysis of the scattering and diffraction of cylindrical waves by tunnel(s) is stilllimited to the full space. Hence, the investigation of analytical solution ofscattering of cylindrical SH waves by underground lined tunnel in half space hasgreat significance both in theory and in engineering application.In this thesis, mirror method is used to solve this problem and analytical solution isobtained. To solve the problem with the boundary conditions, all the wave functionshould be transferred to the same coordinate in which the origin is set in the circleof the underground cavity. In this process, both the vertical form and the obliqueform of Graf's addition theorem are used. The solution of the problem is reducedto solving a set of infinite linear algebraic equations finally and numerical solutionis obtained accordingly by truncation of the infinite equations.The accuracy of the numerical result is checked up by the convergence of the hoopstress of the underground tunnel and residual errors of boundary conditions withthe increase of the truncation order. At the same time, the effects of some factorssuch as the frequency of the incident waves, the distance between the place wherethe cylindrical waves are excited and the tunnel, the depth of the tunnel and thelining's properties on the hoop stress amplitude on the wall of the tunnel areillustrated. And some useful conclusions are derived in this thesis.