## 2 Methodology  
The proposed methodology is valid for RC and masonry buildings, and has been validated for post-earthquake observations and experimental literature data. It can be developed into four key steps:  
1. Definition and characterization of the road type;
2. The road type;
3. The road type;
4. The road type;
5. The road type;
6. The road type;
7. The road type;
8. The road type;
9. The road type;
10. The road type;
11. The road type;
12. The road type;
13. The road type;
14. The road type;
15. The road type;
1  
+++ ==WARNING: Truncated because of repetitions==  
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* Assignment of vulnerability functions;
* Construction of debris graphs;
* Construction of a fragility curve for each road segment. * Definition and characterization of the road type. In order to define the type of road related to the road network segments of the urban settlement, it is necessary to identify the following:  
(i) The geometric characteristics of the analyzed road segment (the average width of the road pavement (\(w_{r}\)), the average width of the sidewalks (\(w_{br}\)), and the average distance between the opposite interfering buildings (\(w_{bb}\)) along the road sides);  
(ii) the types of interfering buildings constituting the structural aggregates or isolated structural units (structural material, number of floors, age of the building);  
(iii) the geometric characteristics of the structural aggregates or of the interfering isolated structural unit (average height of the roof covering (\(l_{b}\)) and the footprint dimensions in transversal (\(a\)) and longitudinal (\(b\)) directions). This information can be easily found in the LCE analysis of RAs, USs and Ass, as well as through satellite images. * Assignment of vulnerability functions. Once the types of interfering buildings constituting the structural aggregates or the isolated structural units are identified, two or more vulnerability functions should be assigned for each side of the road. In this way, the typological differences of the structural units constituting the aggregates and all those characteristics (structural and architectural systems, building use, and structural regularity/irregularities), not easily identifiable during the field survey necessary for the LCE analysis, can be taken into account. Vulnerability functions express the relationship between the selected _IM_ (e.g., peak ground acceleration, PGA) and the damage factor (_DF_), where the letter represents the expected average ratio of the repair cost to the replacement cost of the building. Such vulnerability functions can be defined using the methodologies and results of scientific literature (interesting approaches for structural aggregates and/or structural units can be found in [8; 9; 10]), or utilizing datasets and catalogs that are available on web platforms as resources for open risk modeling. Alternatively, they can be generated by sets of fragility curves using, for example, the following expression:  
\[DF=\sum_{i=1}^{n}DF_{{{\it{A}}_{{\it{S}}_{i}}}}\cdot P({{\it{ds}}_{i}}|{\it{IM}}) \tag{1}\]  
where \(n\) is the number of damage states considered; \(DF_{{{\it{ds}}_{i}}}\) is the mean damage factor value for a given damage state \({{\it{ds}}_{i}}\) (using, for example, the collected values from the vulnerability literature [11]); \(P({{\it{ds}}_{i}}|{\it{IM}})\) is the probability of a building of sustaining the damage state \({{\it{ds}}_{i}}\) for a specific level of _IM_. Another interesting approach to define vulnerability functions from fragility curves can be found in [PERSON] et al. [12]. Obviously, the vulnerability functions or the fragility curves used should represent the structural types and the real conditions of the analyzed buildings. * Construction of debris graphs. For each assigned vulnerability function, it is necessary to construct different graphs of debris width (\(w_{d}\)) extending further than the initial width of the structure (\(a\)), in order to consider the possible debris distributions around the damaged building.