Antiplane scattering of SH waves by a shallow lined tunnel in a horizontal exponentially inhomogeneous half-space

In this study, based on the plane elastic complex variable theory, employing image technique and conformal mapping technique, an analytical solution for antiplane scattering of SH waves by a lined tunnel in an exponentially graded half-space is derived, and the dynamic stress concentration factor (DSCF) around the tunnel is investigated. The medium is a bimaterial consisting of a semi-infinite homogeneous space and an exponentially inhomogeneous half-space with a lined circular tunnel. The governing equation is normalized into a Helmholtz equation with constant coefficients in complex coordinates based on the plane complex variable theory. The conformal mapping technique is used to convert the physical plane with two half-spaces including a lined tunnel into an image region consisting of three concentric circles. By applying the boundary conditions and the principle of orthogonality of trigonometric functions, a series of infinite algebraic equation are constructed and the unknown coefficients for the scattered wave functions are calculated. The numerical calculations are performed by considering the several parameters of medium and various conditions, and then, the influences of medium parameters on the dynamic response of the tunnel are analyzed based on the calculation results.