Propagation of Nonplanar SH Waves Emanating from a Fault Source around a Lined Tunnel

An analytical solution is presented for scattering nonplanar SH waves emanating from a fault source using a lined tunnel. The lined tunnel is assumed to be an annular elastic solid in half-space. A simplified circular arc fault model is employed to represent the wave source. By means of the separation of variables method, all wave fields are given in terms of the wave function series with unknown coefficients. Taking advantage of the method of images, the zero-stress boundary condition on the horizontal ground surface is satisfied automatically. By applying Graf's addition formula, a system of equations for seeking the unknowns is derived by taking advantage of the boundary conditions. The problem of wave scattering is finally solved after seeking solutions for the system of equations through standard matrix techniques. The effects of fault distance, fault curvature, and fault orientation are revealed with numerical results. It is found that the plane waves provide a good approximation to the fault-induced cylindrical waves when the source-receiver distance or fault radius of curvature is larger enough. Fault-induced topographic effects are strongly affected by source orientation.