Dynamic response of a shallow tunnel with imperfect interface in anisotropic medium

Anti-plane dynamic response of a circular lined tunnel embedded at a shallow depth in an anisotropic half-space is theoretically presented. The degree of medium anisotropy is characterized by the elastic parameters of the medium, i.e. β = C₄₄/C₅₅, k=C₄₅/C₅₅. The complex variable function method and multi-polar coordinate system are applied to express the wave fields with three unknown coefficients. By introducing an elastic spring model, imperfect boundary condition around tunnel lining can be satisfied to determine the coefficients. In numerical examples, effects of the medium anisotropy and interface stiffness on the dynamic stress and surface displacement of the medium-lining system are discussed in detail, accompanied with incident wave angle and frequency. Analytical solutions show that both the medium anisotropy and imperfect interface have considerable influence on the dynamic response of underground structures, which should be paid attention to for the design and construction of underground tunnels.