## 3 Numerical Analysis
### Retrofitted Configuration: Intervention on Masoury Walls  
To mitigate the seismic vulnerability of the building, different retrofitting interventions have been proposed. Reinforced plaster layer and cement-based grout injections have been applied in each masonry wall of the building in order to improve their horizontal load-bearing capacity [30]. Table 5 shows the mechanical properties of the masonry considered after the execution of the retrofitting interventions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mechanism** & \(\text{PGA}_{\text{CLM}}\) & \(\text{PGA}_{\text{D}}\) & \(\text{RI}_{\text{PGA}}\  
An additional wall (45 cm thick) made in Poroton blocks and M10 cement mortar has been built adjacent to the central stairwell (Figure 8). To avoid the activation of local collapse mechanisms, a concrete curb adjacent to the roof has been realized and the interlocking between orthogonal masonry walls has been improved through the application of steel ties. Furthermore, the wooden slabs have been reinforced with the construction of new wood-concrete slabs connected to the existing structural elements by means of shear connectors to improve the box behavior of the building, realizing a rigid diaphragm at each floor (Figure 9). Equivalent frame model representing the retrofitted configuration has been implemented considering the same hypotheses used for the equivalent frame model implementation of the current configuration (Figure 10). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\gamma\) & E & G & \(\mathbf{f_{m}}\) & \(\mathbf{\tau_{0}}\) \\
[**kN/m\({}^{3}\)]** & [**MPa**] & [**MPa**] & [**MPa**] & [**MPa**] \\ \hline
20 & 2091 & 697 & 3.40 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mechanical properties of the masonry after the retrofitting interventions. Figure 8: The new wall made in Poroton blocks and M10 cement mortar. Pushover analysis has been carried out considering the same horizontal load profiles used for the evaluation of the seismic behavior of the current configuration. Figure 11 shows the capacity curves obtained for X (red curves) and Y (green curves) direction considering the retrofitted configuration. Figure 11: Capacity curves (retrofitted configuration). Figure 9: Retrofitted configuration of the wooden slabs (unit of measure in cm). Table 6 summarizes the results of the non-linear static analysis performed for the retrofitted configuration in terms of minimum value of risk indices calculated considering the different capacity curves shown in Figure 11.  
It is possible to notice that the minimum value of the risk indices obtained by the execution of the pushover analysis, both in terms of peak ground acceleration and return period, is greater than one. It is important to highlight that the 2475 year-mark (which corresponds to a value of peak ground acceleration equal to 0.427 g for the area where the case study is built) represents the maximum return period that can be considered for the evaluation of the seismic vulnerability of this type of construction according to what is reported in [25; 26]. In addition, for the retrofitted configuration, the activation of the local collapse mechanisms has been evaluated through the kinematic approach. Figure 12 shows the possible local collapse mechanisms that can occur for the retrofitted configuration while Table 7 summarizes the related results obtained expressed in terms of the same risk indices. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PGA\({}_{\text{C}}\)** & **PGA\({}_{\text{D}}\)** & **RI\({}_{\text{PGA}}\)** & **RP\({}_{\text{C}}\)** & **RP\({}_{\text{D}}\)** & **RI\({}_{\text{RP}}\)** \\ \hline
**[g]** & **[g]** & **[-]** & **[year]** & **[year]** & **[-]** \\ \hline
0.427 & 0.299 & 1.428 & 2475 & 475 & 5.211 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Risk indices obtained from pushover analysis (retrofitted configuration).