## 3 Case Study  
The proposed methodology was applied to a case study of the \"Corso Umberto I\" in Amatrice, Italy. Amatrice extends along the East-West direction with parallel roads and is crossed by Corso Umberto I, the main street of the city. Corso Umberto I is located in the historic center of the city. Although it plays a key role in the LCE analysis of the municipality of Amatrice, the earthquakes that hit Central Italy on 24 August, 26 October, and 30 October 2016 triggered major damage, mostly to buildings and architectural heritage structures along the road, causing closure of the road already with the seismic events of 24 August. More specifically, two shocks were felt on 24 August: the main shock at 3:36 a.m. (local time) with magnitude Mw = 6.2 and epicenter close to Accumoli (Rieti province), and the aftershock at 4.33 a.m. with a magnitude Mw = 5.5 and epicenter close to Norcia (Perugia province) [20]. According to the Italian Civil Protection Department [21], these seismic events caused a total of 299 fatalities, and 386 people were injured and about 4800 rendered homeless. Based on LCE analysis, Corso Umberto I consisted of two road network segments (AC1 and AC2). In addition, there were eight interfering structural aggregates and one isolated structural unit along the road. Using the LCE information available on the web-GIS platform [22], all data were found for each road segment and structural aggregate in order to identify their geometric and typological  
Figure 6: Fragility curve of a generic urban road segment in terms of (**a**) probability of closure and (**b**) probability of opening. characteristics. More specifically, AC1 and AC2 had an average width of road pavement of 5.50 m (\(w_{r}\) = 5.50 m), an average width of sidewalks of 1.00 m on each side (\(w_{br1}\) = \(w_{br2}\) = 1.00 m), and an average distance between the opposite interfering buildings along the road sides of 7.50 m (\(w_{bb}\) = 7.50 m). In terms of structural aggregates, there were 100 masonry buildings and only three RC buildings (the debris of masonry buildings was clearly prevalent). The buildings had a covered area of approximately 15,600 square meters. They varied from one to four storeys. Depending on the geometric and topological characteristics of the aggregates, the critical areas of AC1 and AC2 are circled in red in Figure 7 (road segment between aggregate 1 and 2 for AC1 and road segment between aggregate 4 and 6 for AC2). According to Equations (2)-(4), in these areas the structural aggregates reached their maximum debris widths along the infrastructures considered. These critical areas were the road portions with higher risk of loss of connectivity. The maximum area and width of the debris (\(w_{d,max}\)) for each structural aggregate in the critical areas are shown in Table 2.  
In order to describe the different seismic behaviors of the buildings constituting the structural aggregates present in the critical area of AC1 and AC2, six types of fragility curves were selected, and consequently, using Equation (1), six vulnerability functions were generated and assigned for both sides of the two road segments (Figure 8). In particular, using the OpenQuake platform [23], the fragility curves developed by [PERSON] et al. [24] were selected, which were analytical fragility functions for masonry buildings and building aggregates expressed in terms of PGA. According to these authors, the prototypical buildings represent Euro-Mediterranean buildings in general, and Italian and Slovenian buildings in particular. The fragility curves used were valid for unreinforced masonry buildings with low and high void percentages and for stone buildings of two and four storeys, respectively.