Longitudinal response of tunnel lining under earthquake excitation in 2D-space simulation

This study presents a two-dimensional numerical investigation into the longitudinal seismic response of tunnel linings subjected to earthquake excitation. A simplified yet mechanically consistent modeling approach was adopted in which the annular tunnel cross-section was transformed into an equivalent rectangular section using mass and bending stiffness equivalence principles. Dynamic loading was applied in the form of a horizontally propagating shear wave, and the accuracy of wave propagation within the model was verified against analytical shear-wave relations. The analysis demonstrates that the tunnel response is predominantly bending-controlled, with longitudinal strains significantly exceeding shear strains throughout the domain. Parametric investigations were conducted to evaluate the influence of the stiffness ratio between the surrounding medium and lining (E s /E l ), peak ground acceleration (PGA), and burial depth ratio (H/D). Results indicate that increasing stiffness compatibility enhances deformation transfer, with normalized longitudinal strain approaching unity as E s /E l approaches one. Higher PGA values amplify bending response more significantly than shear distortion. The burial depth effect is governed by the relationship between tunnel depth and seismic wavelength, with maximum longitudinal strain occurring near one-quarter wavelength depth. A case study incorporating elastoplastic Mohr–Coulomb rock behavior further confirmed the global bending-dominated mechanism. Peak tensile strain exceeded the cracking strain of concrete at mid-length, while localized shear demand near portal zones approached nominal shear capacity. Nevertheless, the lining remained within a stable deformation range. The proposed framework provides an efficient tool for preliminary seismic assessment of longitudinal tunnel behavior.