Seismic analysis of a lined tunnel in a multi-layered TI saturated half-space due to qP1-and qSV-waves

Abstract

A special indirect boundary element method (IBEM) is presented to study the in-plane scattering by a lined tunnel embedded in a multi-layered TI saturated half-space. By integrating the full-space and half-space Green’s functions for the inclined distributed load and pore pressure, these singular-free kernels enables the method to treat an arbitrarily shaped tunnel with a superior flexibility and high efficiency in comparison to the traditional IBEM. For the total system, the substructure process is implemented to decompose the model into a layered TI saturated half-space region and a lining region filled with isotropic elastic medium. The dynamic stiffness matrix method developed by the authors is adopted to solve the free field of the exterior half-space, and the scattered fields existed in the exterior and interior lining regions are simulated by the half-space and full-space Green’s functions in a single-layer potential representation, respectively. Then the total wave-fields in the half-space region can be expressed as the superposition of free-field and scattered field, and the tunnel region merely contains the scattered field. The compatibility conditions on inner and outer interfaces enclosing the lining are satisfied to couple these sub-regions to the original one. The present method is calibrated by comparison with available limited cases. Displacement and dynamic hoop stress concentration at the inner surface of the lining are calculated in the frequency domain to portray the effects of anisotropy degree, drainage condition, incident angle, frequency and layering on the seismic response. Results show that the decrease of anisotropy degree generally leads to larger amplitudes of surface displacement and the stress. Prominent amplification of displacement and stress can be observed for the two-phase medium model in comparison to the one-phase model although the vertical displacement is hardly affected by the drainage condition at the lining-rock interface. When taking the layering into account, the vertical displacement maximum is increased by about 32%, while the DHSC amplitudes at different cases tend to become larger on the whole compared to those for the homogeneous half-space.