Abstract:The seismic response of a lined tunnel buried in a transversely isotropic (TI) half-space under incident qP-waves was studied by adopting the indirect boundary element method (IBEM) and the "conjunction" technique. Inheriting the advantages of both the half-space and full-space Green’s functions, a model of a lined tunnel buried in a TI-layered, viscoelastic half-space was deconstructed into the excavated layered half-space region and the enclosed circle region. First, the direct stiffness method was adopted to solve dynamic responses of the displacements and stresses due to the qP-wave incident from the underlying TI half-space (free fields). Then, a set of hypothetical distributed loads were applied both on the elements of the open surface in the layered half-space domain and on the enclosed domain boundary to calculate Green’s functions (scattered fields). Finally, densities of the hypothetical loads were determined by introducing boundary conditions, and the dynamic stress generated at the inner surface of the lining was obtained. The validity of the proposed method was verified by comparing its results with those of existing numerical solutions. By taking a lined tunnel buried in a homogeneous TI half-space and in a single TI-layered half-space as examples, numerical calculations were performed in the frequency domain, and the effects of material anisotropy, incident angle, and frequency of excitation on the dynamic stress were studied. Numerical results illustrated that the dynamic stress on the inner surface of the lined tunnel was very sensitive to the TI parameters, and there were significant difference between the TI medium and the corresponding isotropic case. The change in TI parameters altered the resonant frequency of the layer and further altered the dynamic interaction between the layer and the tunnel, which led to the change in dynamic stress in terms of magnitude and spatial distribution. Generally, the dynamic stress of the isotropic medium was litter than that of the TI medium in the two numerical examples. Therefore, the material anisotropy of the site should be considered for the seismic design of tunnels in practical engineering.
