Antiplane diffraction from canyon above subsurface unlined tunnel

The two-dimensional scattering and diffraction of plane shear horizontal waves by a surface semicircular canyon on top of an underground circular unlined tunnel (cavity) in a homogeneous elastic half-space has been analyzed. Using an exact analytic series solution of the problem for a general angle of wave incidence, the ground motions of the half-space surface on and near the canyon and that of the underground cavity were evaluated. These surface motions depend on the following parameters: the angle of incidence of the plane shear horizontal waves, the dimensionless frequency or wave number, the ratio of the radius of the surface canyon to that of the underground cavity, and the ratio of the depth of the cavity to its radius. The paper also provides the methodology for further studies involving other surface and subsurface topographies, such as that of a rigid foundation above rigid subway infrastructures and the case of multiple foundations above the subway.