Analytical solution for seismic response of deep fluid-filled tunnel subjected to P and SV waves

Abstract

A novel analytical solution is derived that provides closed-form formulations for seismic response of a deep fluid-filled tunnel subjected to incident plane P and SV waves. For the derivation, the tunnel is assumed to be fully filled with an incompressible, inviscid, and irrotational fluid. Under such conditions, only P-waves can propagate in the infilled fluid. It is also assumed that the ground and liner are homogeneous, isotropic and linear elastic, with a no-slip condition at all contact interfaces. The incident P and SV waves is assumed to be perpendicular to the tunnel axis, and thus the plane strain condition is applied. The potentials of the diffracted waves by the tunnel and infilled water are expanded by Bessel-Fourier series to obtain the solution. The analytical solution is verified by comparing its results with those obtained from the finite element method. The interaction between the hydrodynamic pressure and soil pressure on the fluid-filled tunnel under SV wave and P wave is analyzed to investigate the coupling mechanisms among the internal fluid, tunnel, and surrounding ground, and a non-fluid tunnel is included, serving as a benchmark for comparative analysis to understand the influence of hydrodynamic pressures on the fluid-filled tunnel. Parametric analyses are carried out to investigate the influence of frequency of the incident SV and P waves and flexibility ratio of the ground and tunnel on the seismic performance of fluid-filled tunnels.