## 5 Seismic Vulnerability Assessment of Campi Alto di Norcia
### Application of Traditional Vulnerability Index (\(I_{V}\)) Methodologies and Results
The application of the GNDT method to Campi Alto di Norcia results in an average I\({}_{\rm V}\) equal to 47 with standard deviation (SD) of 14 (Figure 9). The values of the normalized I\({}_{\rm V}\)--evaluated according to [2]--are between 20 and 30 for the 6% of the SUs analysed and between 30 and 40 for the 19% of the SUs. The remaining 43% shows I\({}_{\rm V}\) within the range 40-50, 9% in the range 50-60, 7% in the range 60-70 and, finally, 12% in the range 70-80. The remaining SUs present a seismic vulnerability index value lower than 20. The Formisano method [22] was used to account for aggregate effects within SUs: isolated buildings were then neglected, leading to the analysis of only 50 SUs. The achieved normalized I\({}_{\rm V}\) values [2] are between 0 and 10 for 13% of the SUs analysed and between 10 and 20, 20 and 30, respectively, for 44% and 35% of SUs. The remaining buildings show a seismic vulnerability equally distributed in the ranges 30-40% and 40-50%. As a general remark, the Formisano method [22] provides a lower vulnerability of SAs of Campi Alto di Norcia, with an average I\({}_{\rm V}\) value of 17 and a standard deviation (SD) equal to 9 (Figure 9). For the sake of comparison, considering the same 50 SUs, the GNDT indicates an average normalized I\({}_{\rm V}\) value of 43 and an SD of 10. Finally, the adoption of the [PERSON] method (2010) led to an average normalized I\({}_{\rm V}\) equal to 41 and a standard deviation (SD) of 11; in terms of distribution, 4% of the evaluated buildings shows an I\({}_{\rm V}\) index between 10 and 20, 12% between 20 and 30, 30% between 30 and 40, and, finally, the remaining 35% between 40 and 50 (Figure 9). Again, for the sake of completeness, considering only the 50 SUs in \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Vulnerability Parameters**} & \multicolumn{2}{c}{**Short Description**} & \multicolumn{3}{c}{**Vulnerability**} & \multirow{2}{*}{**Weight**} \\ \cline{3-4} \multicolumn{2}{c}{} & & \multicolumn{1}{c}{**A**} & \multicolumn{1}{c}{**B**} & \multicolumn{1}{c}{**C**} & \multicolumn{1}{c}{**D**} \\ \hline P1 & Type of resisting system & Construction age, quality of walls’ connection & 0 & 5 & 20 & 50 & 0.75 \\ P2 & Quality of the resisting system & Vertical Element Typology & 0 & 5 & 20 & 50 & 1 \\ P3 & Conventional strength & Walls’ shear strength assuming box behaviour & 0 & 5 & 20 & 50 & 1.5 \\ P4 & Maximum distance & Spacing between walls & 0 & 5 & 20 & 50 & 0.5 \\  & between walls & Number of floors in the building & 0 & 5 & 20 & 50 & 1.5 \\ P5 & Number of floors & Number of floors in the building & 0 & 5 & 20 & 50 & 1.5 \\ P6 & Location of building and type of foundation & Slope and quality of the foundation soil & 0 & 5 & 20 & 50 & 0.75 \\ P7 & Aggregate position and interaction & Position of the SU in the SA & 0 & 5 & 20 & 50 & 1.5 \\ P8 & Plan configuration & Length/ width ratio of the building plan & 0 & 5 & 20 & 50 & 0.75 \\ P9 & Height regularity & Mass variation in elevation and the presence of arcades or towers & 0 & 5 & 20 & 50 & 0.75 \\ P10 & Wall facade openings & Influence of the misalignment & 0 & 5 & 20 & 50 & 0.5 \\ \hline P11 & Horizontal diaphragms & Quality of floor type considering stiffness and connection with the walls & 0 & 5 & 20 & 50 & 1 \\ P12 & Roof typology & Weight and the roof typology (thrust) & 0 & 5 & 20 & 50 & 1 \\ P13 & Fragilities and conservation state & Masonry quality and cracking scenario & 0 & 5 & 20 & 50 & 1 \\ P14 & Non-structural elements & Type and characteristics of the non-structural elements & 0 & 5 & 20 & 50 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._SAs used in the Formisano method, the average I\({}_{\rm V}\) value is 39 with an SD of 9. Figure 10 summarizes the I\({}_{\rm V}\) distribution in the case study of Campi Alto di Norcia. Figure 8: Vulnerability classes distribution of the different parameters, according to **(a)** the GDNT method, **(b)** the Formisano method and **(c)** the Vicente method.