## 3 Results and Discussion
### Seismic Resilience Assessment
#### 3.3.3 Effects of Different Fragility Functions on Tunnel Resilience  
A crucial issue for the resilience evaluation of tunnels is the selection of appropriate fragility functions [29; 30; 31]. Indeed, the use of different fragility functions may lead to distinct probabilities of being in a particular damage state and hence may affect the resilience index estimated for an examined tunnel. To highlight this issue, an example is provided to study the effects of different fragility functions on tunnel resilience. More specifically, the analytical fragility functions provided through this study, [PERSON] [26] and [PERSON] et al. [32], as well as the empirical fragility functions provided by ALA [33], are used to compute the resilience index \(Re\) for the examined case.  
Figure 14 illustrates the variation of the resilience index (\(Re\)) with increasing levels of the seismic intensity measure (\(PGA\)), as computed for the examined soil-tunnel configurations by employing different fragility functions. Evidently, a significant scatter is observed by comparing the \(Re\) computed for different levels of seismic \(IM\) when using different fragility functions. In particular, for a specific level of seismic intensity, the use of the empirical fragility functions provided by ALA [33] leads to the highest values of \(Re\) compared to the values computed when using the analytical fragility functions. On the contrary, the lowest \(Re\) values are obtained when using the analytical fragility functions presented by [PERSON] and [PERSON] [26]. These observations are attributed to different modelling approaches and assumptions utilized to generate the selected fragility functions. The empirical fragility functions provided by ALA [33] are derived using reports of actual damage of tunnels from past earthquakes as well as expert judgements. The numerical fragility functions provided by [PERSON] and [PERSON] [26] are developed through a couple of numerical analyses of soil-tunnel configurations, with the seismic loading being simulated by employing a quasi-static method. The numerical fragility functions proposed by [PERSON] et al. [32] are generated according to the results of a set of non-linear numerical simulations considering soil-structure interaction phenomena in a more rigorous fashion. Finally, the analytical fragility functions provided by this study are proposed by employing the results of non-linear dynamic analyses of the soil-tunnel configuration, considering the effects of local soil conditions of Shanghai city. Differences in the assumptions made regarding the geometrical properties of the soil-tunnel configuration, the implemented soil constitutive models, and the considered ground motion characteristics may have also affected the computed fragilities of the examined tunnels, hence affecting the computed resilience index of the examined configurations. The above discrepancies reveal the need for further investigation of the seismic fragility and resilience of tunnels.  
Figure 14: Resilience index (\(Re\)) of the examined tunnel using different empirical and numerical fragility functions.