Scattering of Plane SH Waves Induced by a Semicylindrical Canyon with a Subsurface Circular Lined Tunnel

Abstract

An analytical study of multiple scattering of plane shear horizontal (SH) waves induced by a semicylindrical canyon and a nearby buried circular lined tunnel in a homogeneous elastic half-space is presented using the wavefunction expansion method. The wavefields are given in terms of the wavefunction series with unknown complex coefficients in corresponding coordinate systems. Then, when the relative location between the canyon and tunnel is taken into consideration, the two wavefields induced by the tunnel and its mirror are described in the local coordinate system by applying the oblique form of Graf’s addition theorem. Finally, the unknowns are solved by taking advantage of boundary conditions. The effects of the location and size of the tunnel and the frequency of incident waves on surface-displacement amplitudes are illustrated. Based on an analysis of the numerical results, the effects of the location of the tunnel on canyon ground motions are significant. It was found that a pattern of amplification can obviously take place at the left shoulder of the canyon with a subsurface lined tunnel under horizontal incident SH waves.