## 3 Verification of Proposed Model
### Service Life of Cracked Concrete Considering Climate Change
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Mean** & **Coefficient of Variance** & **Distribution** \\ \hline \multirow{2}{*}{Cover depth} & 25 mm & \multirow{2}{*}{0.2 [3]} & \multirow{2}{*}{Normal [11]} \\ \cline{2-3} \cline{5-5}  & 35 mm & & \\ \hline \multirow{2}{*}{Carbonation rate parameter} & \multirow{2}{*}{\(CR=\sqrt{\frac{2[CO_{2}(t)]_{\text{o}},D_{\text{op}}(t)}{[CH]+3[CSH]}}\)} & \multirow{2}{*}{0.15 [3]} & \multirow{2}{*}{Normal [11]} \\ \hline CO2 concentration & \([CO_{2}(t)]\) & & \\ \hline Temperature & 25+\(\Delta T\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Climate Scenarios** & **Time Slices** \\ \hline RCP 8.5 & 2000 \\ RCP 4.5 & 2000 \\ RCP 2.6 & 2000 \\ RCP 8.5-upper 90\% confidence interval & 2000 \\ RCP 8.5 & 2050 \\ RCP 8.5-upper 90\% confidence interval & 2050 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of analysis cases. Figure 8: Probability of corrosion initiation-RCP 8.5, time slice 2000. (**a**) W/C: 0.65, Cover depth: 25 mm; (**b**) W/C: 0.65, Cover depth: 35 mm; (**c**) W/C: 0.45, Cover depth: 25 mm; (**d**) W/C: 0.45, Cover depth: 35 mm. Figure 9: Probability of corrosion initiation-RCP 4.5, time slice 2000. (**a**) W/C: 0.65, Cover depth: 25 mm; (**b**) W/C: 0.65, Cover depth: 35 mm; (**c**) W/C: 0.45, Cover depth: 25 mm; (**d**) W/C: 0.45, Cover depth: 35 mm. Figure 11: Probability of corrosion initiation-RCP 8.5 upper 90% confidence interval, time slice 2000. (**a**) W/C: 0.65, Cover depth: 25 mm; (**b**) W/C: 0.65, Cover depth: 35 mm; (**c**) W/C: 0.45, Cover depth: 35 mm. Figure 10: Probability of corrosion initiation-RCP 2.6, time slice 2000. (**a**) W/C: 0.65, Cover depth: 25 mm; (**b**) W/C: 0.65, Cover depth: 35 mm; (**c**) W/C: 0.45, Cover depth: 25 mm; (**d**) W/C: 0.45, Cover depth: 35 mm. Figure 12: Probability of corrosion initiation-RCP 8.5, time slice 2050. (**a**) W/C: 0.65, Cover depth: 25 mm; (**b**) W/C: 0.65, Cover depth: 35 mm; (**c**) W/C: 0.45, Cover depth: 25 mm; (**d**) W/C: 0.45, Cover depth: 35 mm. Figure 13: Probability of corrosion initiation-RCP 8.5 upper 90% confidence interval, time slice 2050. (**a**) W/C: 0.65, Cover depth: 25 mm; (**b**) W/C: 0.65, Cover depth: 35 mm; (**c**) W/C: 0.45, Cover depth: 25 mm; (**d**) W/C: 0.45, Cover depth: 35 mm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**W/C**} & \multirow{2}{*}{**Cover Depth (mm)**} & \multirow{2}{*}{**Crack Width (mm)**} & \multicolumn{3}{c}{**Service Life (Years)**} \\ \cline{5-6}  & & & **No Climate Change** & **With Climate Change** & **Relative Ratio** \\ \hline \multirow{4}{*}{0.65} & \multirow{4}{*}{25} & 0.05 & 16.045 & 15.356 & 0.957 \\  & & 0.15 & 5.877 & 5.785 & 0.984 \\  & & 0.25 & 3.526 & 3.492 & 0.990 \\ \cline{2-6}  & \multirow{4}{*}{35} & 0.05 & 31.372 & 28.563 & 0.910 \\  & & 0.15 & 11.481 & 11.168 & 0.973 \\  & & 0.25 & 7.033 & 6.923 & 0.984 \\ \hline \multirow{4}{*}{0.45} & \multirow{4}{*}{25} & 0.05 & 43.739 & 38.748 & 0.886 \\  & & 0.15 & 15.150 & 14.554 & 0.961 \\  & & 0.25 & 9.163 & 8.983 & 0.980 \\ \cline{2-6}  & \multirow{4}{*}{35} & 0.05 & 85.228 & 71.684 & 0.841 \\  & & 0.15 & 29.570 & 27.054 & 0.915 \\ \cline{2-6}  & & 0.25 & 17.865 & 16.994 & 0.951 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Service life of cracked concrete-RCP 2.6, time slice 2000.