# Climate Change Impact on Corrosion of Reinforced Concrete Bridges and Their Seismic Performance
## 4 Case Study
Focusing on the stirrups, these appear to be completely corroded after 100 years of the viaduct's service life, with a high corrosion level. Moreover, the presence of corrosion effects influences the dynamic behavior of the viaduct, due to the reduction in the pier stiffness as a function of the age of the viaduct. In fact, considering the \(i_{corr}\) values proposed by [54], it is possible to observe a slight increase in the first fundamental natural periods, which characterize the dynamic behavior of the viaduct. On the contrary, due to the limited values of steel reinforcement diameter obtained for each corrosion scenario analyzed 100 years after the viaduct was built, this fact does not occur when using the \(i_{corr}\) values proposed by [53]. As mentioned in Section 3, to investigate the seismic performance of the viaduct, several multi-modal analyses were carried out, through an iterative process based on an increasing demand spectrum until the required limit state is reached, to evaluate the peak ground acceleration, which leads to the failure of the first monitored structural element (\(PGA_{C}\)) and its related return period (\(RP_{C}\)). Starting from these values, the assessment of the seismic performance of the viaduct is defined by means of appropriate indicators, called risk indices, calculated as the ratio between \(PGA_{C}\) and the design peak ground acceleration (\(PGA_{D}\)), which is obtained as reported in [16], and as the ratio between the associated return periods:  
\[RI_{PGA}=\frac{PGA_{C}}{PGA_{D}}, \tag{6}\]  
\[RI_{RP}=\frac{RP_{C}}{RP_{D}}, \tag{7}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{10}{c}{**Corrosion Scenario**} \\ \cline{2-13} \(t\) & & \multicolumn{4}{c}{**Slight**} & \multicolumn{4}{c}{**Moderate**} & \multicolumn{4}{c}{**High**} \\  & & \(i_{corr}\) = 0.172 [\(\mu\)A/cm\({}^{2}\)] & & \multicolumn{4}{c}{\(i_{corr}\) = 0.345 [\(\mu\)A/cm\({}^{2}\)]} & \multicolumn{4}{c}{\(i_{corr}\) = 0.431 [\(\mu\)A/cm\({}^{2}\)]} \\  & \(d_{0}\) & \(d\) & \(\Delta A_{s}\) & \(\varepsilon_{u}\) & \(d_{0}\) & \(d\) & \(\Delta A_{s}\) & \(\varepsilon_{u}\) & \(d_{0}\) & \(d\) & \(\Delta A_{s}\) & \(\varepsilon_{u}\) \\
**[Years]** & **[mm]** & **[mm]** & **[mm]** & **[\%]** & **[\%]** & **[mm]** & **[mm]** & **[\%]** & **[\%]** & **[mm]** & **[mm]** & **[\%]** & **[\%]** \\ \hline \multirow{3}{*}{0-13.5} & 10.00 & 10.00 & 0.00 & 9.00 & 10.00 & 10.00 & 0.00 & 9.00 & 10.00 & 10.00 & 0.00 & 9.00 \\  & 14.00 & 14.00 & 0.00 & 9.00 & 14.00 & 14.00 & 0.00 & 9.00 & 14.00 & 14.00 & 0.00 & 9.00 \\  & 10.00 & 9.85 & 1.46 & 8.79 & 10.00 & 9.71 & 2.92 & 8.59 & 10.00 & 9.64 & 3.65 & 8.36 \\  & 14.00 & 13.85 & 1.04 & 8.85 & 14.00 & 13.71 & 2.09 & 8.70 & 14.00 & 13.64 & 2.61 & 8.54 \\  & 10.00 & 9.75 & 2.45 & 8.57 & 10.00 & 9.51 & 4.92 & 8.14 & 10.00 & 9.39 & 6.15 & 7.92 \\  & 14.00 & 13.75 & 1.75 & 8.69 & 14.00 & 13.51 & 3.52 & 8.38 & 14.00 & 13.39 & 4.39 & 8.23 \\  & 100 & 10.00 & 9.65 & 3.45 & 8.39 & 10.00 & 9.31 & 6.92 & 7.78 & 10.00 & 9.14 & 8.65 & 7.48 \\  & 14.00 & 13.65 & 2.47 & 8.57 & 14.00 & 13.31 & 4.95 & 8.13 & 14.00 & 13.14 & 6.18 & 7.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Steel reinforcement diameter and area variation calculated considering the assumptions reported in [53].