# Vulnerability and Seismic Exposure of Residential Building Stock in the Historic Center of Alcamo
## 2 Methods
### Vulnerability and Damage Scenarios: The Macroseismic Method  
We then assessed the seismic vulnerability for both the mentioned exposure estimates, using the procedures codified in the macroseismic method [20], briefly summarized below. Among the most recognized typological-observational methods available in the literature, the macroseismic method proposed by [20] plays a predominant role. The method, unlike most typological-observational methods, is derived from an analysis by probabilistic approaches and the fuzzy set theory of the correlations between typological characteristics and expected damage per seismic event of a given intensity, implicitly contained in the European macroseismic scale EMS98 [39]. In this scale, the residential building stock is characterized through the identification of 15 main structural types (see Table 1), whose seismic vulnerabilities are described by the most probable value of the typological vulnerability index \(V_{I}\)*. The value of the macroseismic vulnerability index \(V_{I}\) for each specific building or specific sub-typology was identified by first assigning the building or sub-typology to one of the 15 typological classes, and then varying the most probable value of the vulnerability index (\(V_{I}\)*) by assigning DVI vulnerability modifiers defined according to detailed characteristics. Using the fuzzy set theory, the authors also derived from the EMS98 scale, for each typology, the range of \(V_{I}-~{}V_{I}^{+}\) values within which the modified vulnerability index was likely to stay, and the range defined by the boundary values \(V_{I\text{min}}-~{}V_{I\text{max}}\) beyond which the index value for an element of that typology could not be assigned. The assessment of building typology vulnerabilities was a necessary premise for the probabilistic description of the expected damage as a function of the seismic event intensity. In the macroseismic method [20], the damage description is identified with the description contained in the EMS98 macroseismic scale, which, in addition to the D0 level of no damage, includes the following 5 additional damage levels: D1 mild; D2 moderate; D3 severe, D4 very severe; D5 structural collapse. The qualitative descriptions of damage levels for masonry and reinforced concrete buildings are shown in Figure 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Typologies**} & \multirow{2}{*}{**Code**} & \multirow{2}{*}{**Building Type**} & \multicolumn{5}{c}{**Characteristic Values of the Vulnerability Index**} \\ \cline{3-6}  & & & \(V_{I\,\min}\) & \(V_{I}\)\({}^{-}\) & \(V_{I}\)\({}^{\star}\) & \(V_{I}\)\({}^{\star}\) & \(V_{I\,\max}\) \\ \hline \multirow{8}{*}{Masonry} & M1 & Rubble stone & 0.62 & 0.81 & 0.873 & 0.98 & 1.02 \\ \cline{2-6}  & M2 & Adobe/earth bricks & 0.62 & 0.687 & 0.84 & 0.98 & 1.02 \\ \cline{2-6}  & M3 & Simple stone & 0.46 & 0.65 & 0.74 & 0.83 & 1.02 \\ \cline{2-6}  & M4 & Massive stone & 0.3 & 0.49 & 0.616 & 0.793 & 0.86 \\ \cline{2-6}  & M5 & U Mansory (old bricks) & 0.46 & 0.65 & 0.74 & 0.83 & 1.02 \\ \cline{2-6}  & M6 & U Mansory-rc. floors & 0.3 & 0.49 & 0.616 & 0.79 & 0.86 \\ \cline{2-6}  & M7 & Reinforced /confined masonry & 0.14 & 0.33 & 0.451 & 0.633 & 0.7 \\ \hline \multirow{8}{*}{Reinforcedconcrete} & RC1 & Frame in RC (without E.R.D.) & 0.3 & 0.49 & 0.644 & 0.8 & 1.02 \\ \cline{2-6}  & RC2 & Frame in RC (moderate E.R.D.) & 0.14 & 0.33 & 0.484 & 0.64 & 0.86 \\ \cline{2-6}  & RC3 & Frame in RC (high E.R.D.) & \(-\)0.02 & 0.17 & 0.324 & 0.48 & 0.7 \\ \cline{2-6}  & RC4 & Shear walls (without E.R.D.) & 0.3 & 0.367 & 0.544 & 0.67 & 0.86 \\ \cline{2-6}  & RC5 & Shear walls (moderate E.R.D.) & 0.14 & 0.21 & 0.384 & 0.51 & 0.7 \\ \cline{2-6}  & RC6 & Shear walls (high E.R.D.) & \(-\)0.02 & 0.047 & 0.224 & 0.35 & 0.54 \\ \hline Steel & S & Steel structures & \(-\)0.02 & 0.17 & 0.324 & 0.48 & 0.7 \\ \hline Wood & W & Wood structures & 0.14 & 0.207 & 0.447 & 0.64 & 0.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristic values of the vulnerability index.