## 5 Seismic Vulnerability Assessment of Campi Alto di Norcia  
### Application of Traditional Vulnerability Index (\(I_{V}\)) Methodologies and Results  
The statistical approach used for the seismic vulnerability assessment of masonry buildings at urban scale is the vulnerability index method (I\({}_{V}\) method), originally developed by [30] and later revisited by [31; 32; 33]. The method is based on defining the seismic vulnerability of an SU within an SA through the analysis of several parameters--selected in relation to the structural typology--provided by a \"weight\" and finally defining a vulnerability index (1). Resulting values are usually normalized in the range \(0\div 100\)[34] (2). The I\({}_{V}\) evaluation is performed based on a comprehensive survey of the building, where the relevance of each parameter, measured by its weight, is defined based on post-earthquake damage observation. Having determined the hazard level of the territory resorting to an intensity scale, it is possible to evaluate the expected damage scenarios of a specific area using semi-empirical methods [35]. \[\mathrm{I}_{V}^{*}=\sum\mathrm{p}_{i}\cdot\mathrm{c}_{i}\quad\mathrm{where} \left\{ \begin{array}{c}\mathrm{c}_{i}=\mathrm{vulnerability}\ \mathrm{class}\ \mathrm{``i}^{\mathrm{ \prime}}\\ \mathrm{P}_{i}=\mathrm{weight}\ \mathrm{i}\end{array} \right. \tag{1}\]  
\[\mathrm{I}_{V}=\mathrm{I}_{V}^{*}\ \mathrm{normalized}\ \mathrm{to}\ 100\% \tag{2}\]  
Current vulnerability index methodologies were developed and calibrated basing on specific constructions' typologies, being then provided by good reliability for buildings belonging to those categories but decreasing their if relevant differences are present. In the present research work, three traditional approaches were used: the GNTD method [21], the Formisano method [22] and the Vicente approach [35], being more appropriate for the considered context. The GDNT method [21] adopts for the I\({}_{V}\) evaluation eleven parameters (namely P1 to P11) and four vulnerability classes (A to D, being A the best condition and D the worst one); the method was developed for isolated buildings, taking into account their geometry, structural and non-structural features, the floors and roof typologies, walls thickness and maintenance conditions. The maximum value of the achievable non-normalized I\({}^{*}\)\({}_{V}\) is equal to 382.5. With the aim of improving the [21] procedure by considering the SA effect and the interaction among SUs, [PERSON] [22] introduced five additional parameters: the position of the SU in the aggregate, the percentage of openings in the facade walls, the presence of staggered slabs, the structural difference between adjoining SUs and the interaction of neighbouring SUs with different heights. Compared to the GDNT method, this approach disregarded, at least in an explicit manner, the qualitative resistance of the walls. Some of the weights were also redefined. Negative values were assigned with the aim of reducing the vulnerability. The maximum value of the achievable non-normalized I\({}^{*}\)\({}_{V}\) is equal to 515.25. The [PERSON] method [35] introduced 4 macro-classes of parameters related to the structural building system (P1 to P4), to the irregularities and interaction (P7 to P10), to floor slabs and roof (P11 to P12), to conservation status and other elements (P13 to P14); 3 new parameters (P4, P6 and P7) were also introduced. The maximum value of the achievable non-normalized I\({}^{*}\)\({}_{V}\) is equal to 650. Table 5 summarizes the parameters adopted in the different methods, vulnerability classes and weights associated. As visible, the three approaches have several common parameters even if the weight associated can slightly vary.