# Climate Change Impact on Corrosion of Reinforced Concrete Bridges and Their Seismic Performance
## 4 Case Study  
As mentioned before, the approach illustrated in detail in Section 3 is applied to a viaduct built in Northern Italy in the 1970s in the Massa-Carrara province. The fundamental seismic hazard parameters of the site where the viaduct is located are the following: soil type C and a PGA equal to 0.156 g.  
The viaduct is made by two adjacent carriageways, which are independent due to the presence of a continuous longitudinal joint, and it is characterized by the presence of four simply supported spans, measuring 40.40 m in length. The planimetric and altimetric layout is rectilinear, as shown in Figure 8. The roadway presents an overall width equal to 9.86 m, and the spans are made of a precast concrete girder, composed of three longitudinal pre-stressed I beams with five transverse beams. The structure of the deck is a concrete slab with a thickness equal to 20 cm. The span is characterized by the presence of 3 \(\times\) 2 elastomeric bearings placed in the pier cap. The deck is supported by three hexagonal hollow RC piers, whose main characteristics are reported in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \(f_{ck}\) & \(k\) & \(\varepsilon_{u,0}\) & \(w/c\) & \(t_{i}\) \\ \hline
[MPa] & [-] & [\%] & [-] & [year] \\
28 & 0.0116 & 9 & 0.6 & 13.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Constant parameters. Figure 8: The FEM of the viaduct. Table 3 reports the most important characteristics of the viaduct. The first three fundamental natural periods which characterize the dynamic behavior of the viaduct are: T\({}_{1}\) = 2.73 s, T\({}_{2}\) = 2.56 s, and T\({}_{3}\) = 2.41 s. Figure 9 reports the vibration mode shapes related to the above-mentioned first three natural periods. In Tables 4 and 5, the results of the corrosion effects are expressed in terms of longitudinal rebars, and the stirrups' diameters and area variations are reported, considering the \(i_{corr,20}\) values calculated using the assumptions presented in [53; 54], for the different time steps mentioned in Section 3. The variation in the steel ultimate deformation (\(\varepsilon_{u,0}\)) is calculated by means of the relation proposed by [68]. Considering the results reported in Tables 4 and 5, it is important to recall that the corrosion effects begin to develop 13.5 years after the bridge is built and, consequently, before this point, no steel reinforcement reduction diameter is present. Taking into account the results obtained using the assumptions reported in [53] related to the evaluation of \(i_{corr}\) values, the variation of the steel reinforcement diameter leads to the values of area reduction always being less than 9%, even considering the time step of 100 years after the building of the viaduct. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Piers** & **Cross-Section** & **Height** & **Longitudinal Steel Rebar** & **Stirrups** \\ \hline
[n\({}^{\circ}\)] & [m] & [m] & [-] & [-] \\
1 & \(4.0\times 2.5\) & 5.06 & 148\(\Updownarrow\)14 & \(\Updownarrow\)10/20 \\
2 & \(4.0\times 2.5\) & 10.84 & 148\(\Updownarrow\)14 & \(\Updownarrow\)10/20 \\
3 & \(4.0\times 2.5\) & 15.51 & 148\(\Updownarrow\)14 & \(\Updownarrow\)10/20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Pier properties. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Span** & **Length** & **Bearings** & **Pier** & **Pier Shape** & **Pier Thickness** \\ \hline
[n\({}^{\circ}\)] & [m] & [-] & [n\({}^{\circ}\)] & [-] & [m] \\
4 & 200 & \(2\times 3\) & 3 & Hexagonal hollow & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Viaduct main properties. Figure 9: Vibration mode shapes of the first three natural periods of the viaduct. Instead, considering the results obtained for the \(i_{corr}\) values suggested by [54] for the three analyzed corrosion scenarios, a significant reduction in steel reinforcement area occurs 50 years after the construction of the viaduct, in the high corrosion scenario.