# Numerical Assessment of the Seismic Vulnerability of Bridges within the Italian Road Network
## 3 Fragility Curves
### Introduction to Multiple Stripes Analysis  
Different procedures are available to perform the fragility analysis. Incremental Dynamic Analysis (IDA) is a common approach. In the IDA, a set of ground motions is selected and scaled until the structure collapses [34]. Performing the fragility analysis employing the IDA can present challenges when ground motions must be scaled to high IM values to induce collapse. This process is computationally intensive, requiring numerous structural analyses at increasing IM levels. Furthermore, the validity of scaling typical moderate-IM ground motions to represent real instances of extreme IM levels is questionable [35]. The fragility curves associated with each case study have been derived using the so-called Multiple Stripes Analysis (MSA) [36]. This type of approach requires structural analysis to be performed at a discrete set of IM levels, using different ground motions at each level. Target properties of the ground motions vary at different IM levels and the selection  
Figure 4: Longitudinal view of the structural model—Bridge 4. Figure 5: Longitudinal view of the structural model—Bridge 5. Figure 3: Longitudinal view of the structural model—Bridge 3. Figure 2: Longitudinal view of the structural model—Bridge 2.  
of different accelerograms allows the variation of the seismic hazard parameters to be taken into consideration [37; 38]. The MSA approach is more efficient than the IDA approach since it targets a limited number of IM levels rather than requiring analysis at IM levels associated with collapse for some ground motions but not as critical for constraining the fragility function. Literature results indicate that fragility functions can be estimated in an efficient way by focusing on IM levels with lower probabilities of collapse improving the quality of the fitting on the most important region for the risk assessment [39]. The fundamental aspects of the methodology used to derive the fragility curves are reported below. A total of 10 code-based elastic spectra have been defined according to NTC2018 [40]. Each elastic spectrum takes into account the topographical and stratigraphical characteristics of the site. The spectra are characterized by an increasing value of return period \(T_{r}\), from 30 to 2475 years, as reported in Table 2. The 2475-year \(T_{r}\) for IM level 10 has been selected considering the prescriptions of the NTC2018, which indicates this value as the upper bound for the definition of seismic action. The definition of these spectra is fundamental to ensure that the selected ground motions represent a broad enough range of IM levels. The number of ground motions that have to be selected to provide reliable results is still an open issue, seven ground motions appear to be the minimum requirement [41]. For each IM level, seven pairs of natural records have been selected using the ground motion selection software REXEL [42; 43]. The selection of the ground motions required that seismic hazard disaggregation [44; 45] be undertaken first to identify, for each site, the magnitude-epicentral distance pair with the highest contribution in the definition of local seismic hazard. In the matching of the ground motions to the spectra, NTC2018 [40] has been taken as a reference for the issue of spectral compatibility. In particular, given the fundamental period \(T\), the highest value between \(2T\) and 2 s has been selected as the maximum value of the range of periods in which spectral compatibility must be ensured. The definition of the criteria used to compute capacity and demand for each structural element is crucial. A brief discussion of the criteria related to shear capacity, chord rotation capacity, and bearing displacement capacity is provided to fully describe the framework developed in this study. In terms of shear actions, considering the indications of the 2019 Commentary [46] of NTC2018, the capacity of an existing structure has to be computed taking into account the ductility demand on the elements.