# Vulnerability and Seismic Exposure of Residential Building Stock in the Historic Center of Alcamo
## 4 Seismic Vulnerability
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Behaviour Modifier**} & \multirow{2}{*}{**Masonry**} & \multicolumn{5}{c}{**Reinforced Concrete**} \\ \cline{3-8}  & & **Devlm** & \multicolumn{2}{c}{**Seismic**} & \multicolumn{2}{c}{**Without**} & **Moderate** & **High** \\ \cline{3-8}  & & **DVIm** & **Design Level** & **DVIm** & **DVIm** & **DVIm** \\ \hline \multirow{2}{*}{State of preservation} & Good & \(-0.04\) & Good & - & - & - \\ \cline{2-8}  & Bad & \(0.04\) & Bad & \(+0.04\) & \(+0.02\) & \(0\) \\ \hline \multirow{3}{*}{Number of floors} & Low (1–2) & \(-0.08\) & Low (1–3) & \(-0.02\) & \(-0.02\) & \(-0.02\) \\ \cline{2-8}  & Medium (3–5) & \(0\) & Medium (4–7) & \(0\) & \(0\) & \(0\) \\ \cline{2-8}  & High (\(\geq\)6) & \(0.08\) & High (\(\geq\)8) & \(+0.04\) & \(+0.04\) & \(+0.04\) \\ \hline \multirow{3}{*}{Structural system} & Wall thickness & \multirow{3}{*}{\(-0.04-+0.04\)} & Short columns & \(+0.02\) & \(+0.01\) & \(0\) \\ \cline{2-8}  & Wall distance & & Bow-windows & \(+0.04\) & \(+0.02\) & \(0\) \\ \cline{2-8}  & Wall connection & & & & & \\ \hline \multirow{2}{*}{Plan irregularity} & Geometry & \multirow{2}{*}{\(+0.04\)} & Geometry & \(+0.04\) & \(+0.02\) & \(0\) \\ \cline{2-8}  & Mass distribution & & Mass & \(+0.02\) & \(+0.01\) & \(0\) \\ \hline \multirow{2}{*}{Vertical irregularity} & Geometry & \multirow{2}{*}{\(+0.04\)} & Geometry & \multirow{2}{*}{\(+0.04\)} & \multirow{2}{*}{\(+0.02\)} & \multirow{2}{*}{\(0\)} \\ \cline{2-8}  & Mass distribution & & Mass & & & \\ \hline \multicolumn{2}{c}{Superimposed floors} & \multicolumn{2}{c}{\(+0.04\)} & \multirow{2}{*}{\(+0.04\)} & \multirow{2}{*}{\(+0.04\)} & \multirow{2}{*}{\(+0.04\)} & \multirow{2}{*}{\(0\)} \\ \cline{2-8}  & Roof & Weight, thrust and connections & & & & \\ \hline \multirow{2}{*}{Retrofitting interventions} & \multirow{2}{*}{\(-0.08-+0.08\)} & \multirow{2}{*}{\(+0.04\)} & \multirow{2}{*}{\(+0.04\)} & \multirow{2}{*}{\(0\)} & \multirow{2}{*}{\(0\)} \\ \cline{2-8}  & Raprican, Foil arches, Buttresses & & & & & \\ \hline \multirow{3}{*}{Aggregate building position} & Middle & \(-0.04\) & \multirow{3}{*}{\(+0.04\)} & Insufficient & \multirow{3}{*}{\(+0.04\)} & \multirow{3}{*}{\(0\)} \\ \cline{2-8}  & Corner & \(+0.04\) & & aseismic joints & & \\ \cline{2-8}  & Header & \(+0.06\) & & & & \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Typological discontinuity \\ \end{tabular} } & \multirow{3}{*}{\(+0.03\)} & \multirow{3}{*}{\(+0.04\)} & \multirow{3}{*}{\(+0.02\)} & \multirow{3}{*}{\(+0.04\)} & \multirow{3}{*}{\(0\)} \\ \cline{2-8}  & Taller on 2 sides & & & & \\ \cline{2-8}  & Taller on 1 side & & & & \\ \cline{2-8}  & Shorter on 2 sides & \(-0.04\) & & & \\ \cline{2-8}  & Shorter on 1 side & \(-0.02\) & & & \\ \hline \multirow{3}{*}{Foundation} & Different level & \(+0.04\) &
\begin{tabular}{c} Plinths \\ Isolated beams \\ \end{tabular} & \(-0.04\) & \(0\) & \(0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(\text{DVI}_{\text{M}}\) vulnerability index modifiers. index of confined masonry was particularly significant (38%), due to the presence of the regional modifier \(\mathrm{DVI_{R,M^{\prime}}}\). The increases in the vulnerability index in Compartment C02 were smaller, thanks to the reduced irregularities in the plan and elevation and the better connection of roofs to the masonry walls, especially for the MUR2 and MUR 3 types. The changes in the vulnerability index for reinforced concrete types, in both compartments, were extremely small and all negative, except for CAR1 in Compartment C02, due to the absence of seismic joints in accordance with the standards and the presence of a significant percentage of buildings that were irregular in plan and/or elevation or had an irregular distribution of infill. In order to summarize the difference in seismic vulnerability between the two compartments, it was possible to estimate an average vulnerability index of the compartment through a weighted average, according to the percentages of the presence of the vulnerability indexes of each type.