## 6 Retrofitting Interventions
### Intervention 1 (\(\Pi\)): Increasing the Thickness of the Concrete Walls  
The first intervention consists of concrete jacketing the walls of the RC cores, as shown in Figure 11. The external and internal thickness of the RC jacket is 10 cm. The additional longitudinal rebars were identified as suitable to increase the flexural resistance of the RC cores, while the horizontal bars were designed to improve the shear resistance of the RC cores. The diameter used for the vertical and horizontal rebars is 20 mm and the spacing ranges from 10 to 50 cm. It is important to underline that if \(\zeta_{E}\geq 0.60\) is accepted, the intervention involves only one side of the existing walls. Conversely, two sides are involved if \(\zeta_{E}\geq 1.00\) is desired. Tables 11 and 12 report the details of the rebars along the two directions for the two levels of seismic upgrading. As an example, label \(\varnothing 20/15\) indicates the diameter (20 mm) and the spacing (15 cm).  
The post-intervention flexural and shear resistance computed for the reinforced elements was reduced by the 10% according to Section C8.7.4.2.1 of Circular n.7 of 21 January 2019 [11].  
The vulnerability analysis was performed according to the assumptions presented in Section C8.7.4.2.1. In particular, the following design hypotheses were considered: (1) full bond between the new and existing concrete walls; (2) the permanent loads act only on the existing portions; and (3) the mechanical properties of the reinforced concrete are extended to the new RC walls.  
Regarding the connection between the new RC walls and the existing foundations, an epoxy resin was adopted as an anchor between the steel bars and the concrete with a design bond resistance (\(\mathrm{f_{bd,anc}}\)) of 7.95 MPa. The anchor length of the steel bars was evaluated according to the following collapse mechanisms [25]: (1) yielding of the steel bar (\(\mathrm{N_{1}}\)); (2) radial collapse of the resin (\(\mathrm{N_{2}}\)); and (3) pull-out mechanism of the steel bar (\(\mathrm{N_{3}}\)). According to Figure 12, the following results:  
\[\begin{array}{ll}\mathrm{N_{1}}=\frac{\pi\mathrm{d}^{2}}{4}\mathrm{f_{yd}}& \mathrm{N_{2}}=\mathrm{f_{bd,anc}}\pi\mathrm{d}\mathrm{I_{a}}\\ \mathrm{N_{3}}=\pi\mathrm{D}(\mathrm{L_{a}}-\mathrm{kd_{a}})\mathrm{f_{bd}}+4.4 4\mathrm{f_{cd}}\mathrm{kd_{a}}(\mathrm{kd_{a}}+\mathrm{D})\end{array} \tag{7}\]  
where \(\mathrm{f_{yd}}\) is the yield stress of the rebar; \(\mathrm{d}\) is the diameter of the rebar; \(\mathrm{f_{bd}}\) is the design bond resistance between the epoxy resin and existing concrete, which is 2.33 MPa; \(\mathrm{f_{cd}}\) is the design tension resistance of the existing concrete of 1.03 MPa; \(\mathrm{D}\) is the total diameter, which includes the steel bar and the epoxy resin; \(\mathrm{d_{a}}\) is the maximum diameter of the concrete aggregates; and \(\mathrm{L_{a}}\) is the anchor length of the steel bar. Finally, \(\mathrm{k}\) is an experimental coefficient ranging from 1.00 to 3.00 [25]. The value of \(\mathrm{k}\) is assumed to be 1.00 to err on the safe side. Regarding the vulnerability analyses, the numerical results for the seismic performance indices are reported in Section 7. They were obtained for two safety levels and based on the life safety limit state (SLV).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Direction**} & \multirow{2}{*}{**Story**} & \multicolumn{5}{c}{**RC Cores**} \\ \cline{3-6}  & & **T1 + T2 (T\({}^{\prime}\)1 + T\({}^{\prime}\)2)** & **T5** & **T3 (T\({}^{\prime}\)3)** & **T4 (T\({}^{\prime}\)4)** & **T6 (T\({}^{\prime}\)6)** \\ \hline \multirow{8}{*}{Longitudinal direction} & 1 & \(\varnothing\)20/10 & \(\varnothing\)20/10 & \(\varnothing\)20/20 & \(\varnothing\)20/20 & \(\varnothing\)20/20 \\  & 2 & \(\varnothing\)20/10 & \(\varnothing\)20/10 & \(\varnothing\)20/35 & \(\varnothing\)20/35 & \(\varnothing\)20/35 \\  & 3 & \(\varnothing\)20/20 & \(\varnothing\)20/20 & \(\varnothing\)20/35 & \(\varnothing\)20/35