Antiplane diffraction from canyon above subsurface unlined tunnel

The 2D 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: (1) The angle of incidence zeta of the plane shear horizontal waves; (2) the dimensionless frequency or wave number ka; (3) a(0)/a, the ratio of the radius of the surface canyon to that of the underground cavity; and (4) Dla, the ratio of the depth of the cavity to its radius.