Anti-plane seismic performance of a shallow-buried tunnel with imperfect interface in anisotropic half-space

•The seismic performance of a shallow-buried tunnel under earthquake force is investigated.•Complex variable function and multi-polar coordinate system are adopted to present the wave fields.•Spring elastic model is used to represent imperfect boundary between lining and medium.•Influence of medium anisotropy on the seismic deformation of tunnels is discussed.•Influence of imperfect interface on the seismic deformation of tunnels is discussed. The current research presents a semi-analytical solution for the anti-plane dynamic response of a shallow-buried lined tunnel. The tunnel with an imperfect interface between the tunnel lining and its surrounding medium is embedded in an anisotropic and elastic half-space medium. For anti-plane problems, three elastic constants can describe the characteristics of medium anisotropy according to the generalized Hooke’s Law. Therefore, the complex variable function method and multi-polar coordinate system were applied to express the wave fields with three unknown constants in this study. These constants also automatically satisfy the zero-stress boundary condition on the horizontal ground surface in the half-space and the Sommerfeld radiation condition at infinity. The imperfect interface is represented by a series of elastic spring model. Meanwhile, parametric sensitivity analyses indicate that both the medium anisotropy and the imperfect interface stiffness affect significantly the dynamic response of the medium-lining system including stress and ground surface displacement. Besides, the influence of both factors is also dependent on incidence direction and frequency.