Identifying suitable intensity measures for developing seismic fragility curves of horseshoe tunnels

Abstract This study presents a comprehensive framework for selecting optimal ground motion intensity measures (IMs) and developing seismic fragility curves for horseshoe tunnels. To do so, a total of 20 candidate IMs were evaluated through nonlinear time history analyses. The two-dimensional finite difference models considering soil-tunnel interaction were developed and validated using the FLAC2D program. The model incorporated varying tunnel embedment depths (10 m, 20 m, and 30 m) and different site conditions (site classes B, C, and D), with 100 input ground motions representing a wide range of seismic characteristics. The performance of each IM was examined based on four statistical criteria: goodness of fit, efficiency, practicality, and proficiency. The findings show that for stiff soil conditions (site B), the most effective intensity measures are peak ground acceleration (PGA), acceleration spectrum intensity, effective design acceleration, and the A95 parameter. In contrast, for tunnels constructed in medium to soft soils (sites C and D), velocity spectrum intensity, Housner intensity, peak ground velocity (PGV), and Arias intensity provide a better correlation with the seismic response. In comparison, predominant period, mean period, and the PGV/PGA ratio consistently exhibited weak correlation, high variability, and limited practical value, rendering them unsuitable for fragility analysis. Fragility curves were then developed based on the proposed optimal IMs. The results reveal that increasing embedment depth significantly reduces seismic vulnerability, and tunnels in soft soils exhibit higher damage probabilities under the same seismic demand. Moreover, comparisons between different tunnel shapes show that rectangular tunnels are the most vulnerable, followed by horseshoe tunnels, while circular tunnels demonstrate the highest seismic resistance. The proposed framework provides a useful reference for performance-based seismic design and risk assessment of underground structures.