A simplified analytical framework and solution for obliquely incident seismic waves on non-circular tunnel considering soil-tunnel interface effects

Abstract

This study presents an analytical framework to evaluate the seismic response of non-circular tunnel subjected to obliquely Incident Shear Vertical (ISV) waves, considering variations in the stiffness of surrounding ground medium ($E_g$), angle of incidence ($\alpha$), soil-tunnel interface conditions (modeled via a slippage coefficient $\delta$ spanning no-slip to full-slip), and lining thickness. The pseudo-static formulation assumes that seismic wavelengths are much larger than the tunnel dimensions and employs conformal mapping to transform the irregular tunnel geometry into an equivalent circular domain. The proposed solution is validated against existing results for both circular and non-circular tunnels. A key contribution of this work is a novel representation of three-dimensional time-history representations for hoop stress and circumferential displacement that capture the spatiotemporal evolution of the tunnel response. Unlike conventional approaches that rely on peak ground acceleration (PGA), our results show that the peak structural response is phase-shifted and aligns more closely with the ground velocity. The analysis extracts absolute global maxima (maximum of maximum) along with their angular positions (${\theta }_{max}$), offering design-relevant insights that are not offered in various earlier methods reported in the literature. A systematic investigation of various factors reveals that increasing wave obliquity causes stress and displacement zones to shift along the tunnel perimeter. Higher $E_g$ reduces the deformation but may intensify stress due to reflection effects, while a greater $\delta$ leads to stress reduction and displacement amplification. Furthermore, this study shows that the lining thickness significantly influences response in soft ground, with thicker linings increasing the stress but reducing deformation. The current framework offers a practical, viable, and efficient tool for early-stage seismic design, capturing both critical response magnitudes and their spatial distribution under seismic loading conditions.