Mathematical modelling for seismic affected zoning of tunnel cavity section under SH wave incidence and shaking table verification

Abstract

Tunnel portals are particularly vulnerable during seismic events due to the influence of adjacent slope geometry and fractured rock formations. This study evaluates the seismic response of tunnel portals and determines an appropriate fortification range. Ray theory is employed to calculate the displacement field of a single-sided slope subjected to incident SH waves, while the tunnel entrance is modeled as an elastic foundation beam. An analytical expression for hoop strain is derived, accounting for the interaction between the tunnel and the surrounding rock, as well as the attenuation of seismic waves. A parametric analysis is also performed to examine the impact of slope angle, seismic wavelength, frequency, and foundation stiffness on the tunnel response. Shaking table tests are conducted to validate the theoretical results and reveal failure patterns in both the slope and tunnel. The findings show that the spandrel and arch foot exhibit the highest hoop strain responses, identifying these positions as critical points of seismic vulnerability. The seismic-affected zones of the tunnel portal are classified into three distinct regions based on the distribution of peak hoop strain. The recommended fortification range for the tunnel portal extends up to 7.5 times the tunnel span, effectively encompassing the areas of peak strain to mitigate potential damage.