Analytical Solution for Seismic Response of Deep Tunnels with Arbitrary Cross-Section Shape in Saturated Orthotropic Rock

Unified analytical solutions for stresses and displacements of a deep arbitrary shaped tunnel buried in saturated orthotropic rock subjected to seismic loading are presented. A pseudo-static load is used for the analysis, and the tunnel liner is isotropic and elastic and is modeled as a shell. Slip along the ground-liner interface is included. Two extreme conditions, drained and undrained, are considered in the analytical solution. The proposed analytical solution is derived using complex-variable theory and conformal mapping techniques. Validation of the solution is done by comparing its results with those obtained from a FEM, and with results from the literature. Parametric analyses are carried out for a typical section of rock tunnel, i.e. horse-shoe tunnel, to further investigate the influence of the cross-section shape on the tunnel response in orthotropic rock. In addition, the effects of the orientation of the axes of elastic symmetry with respect to the tunnel, as well as the loading conditions, namely drained and undrained, are discussed.