## 3 Verification of Proposed Model
### Service Life of Cracked Concrete Considering Climate Change
\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 & 15.912 & 14.944 & 0.939 \\  & & 0.15 & 5.826 & 5.665 & 0.972 \\  & & 0.25 & 3.511 & 3.444 & 0.981 \\ \cline{2-6}  & \multirow{4}{*}{35} & 0.05 & 31.203 & 27.732 & 0.889 \\  & & 0.15 & 11.443 & 10.897 & 0.952 \\  & & 0.25 & 7.010 & 6.780 & 0.967 \\ \hline \multirow{4}{*}{0.45} & \multirow{4}{*}{25} & 0.05 & 43.978 & 37.326 & 0.849 \\  & & 0.15 & 15.244 & 14.327 & 0.940 \\  & & 0.25 & 9.223 & 8.856 & 0.960 \\ \cline{2-6}  & \multirow{4}{*}{35} & 0.05 & 85.578 & 63.018 & 0.736 \\  & & 0.15 & 29.628 & 26.507 & 0.895 \\  & & 0.25 & 17.933 & 16.715 & 0.932 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Service life of cracked concrete-RCP 8.5 upper 90% confidence interval, time slice 2000. \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 & 10.969 & 10.257 & 0.935 \\  & & 0.15 & 4.022 & 3.928 & 0.977 \\  & & 0.25 & 2.379 & 2.350 & 0.988 \\ \cline{2-6}  & \multirow{4}{*}{35} & 0.05 & 21.317 & 18.779 & 0.881 \\  & & 0.15 & 7.830 & 7.468 & 0.954 \\  & & 0.25 & 4.788 & 4.631 & 0.967 \\ \hline \multirow{4}{*}{0.45} & \multirow{4}{*}{25} & 0.05 & 30.192 & 25.386 & 0.841 \\  & & 0.15 & 10.456 & 9.798 & 0.937 \\ \cline{1-1}  & & 0.25 & 6.298 & 6.088 & 0.967 \\ \cline{1-1} \cline{2-6}  & \multirow{4}{*}{35} & 0.05 & 59.710 & 44.026 & 0.737 \\ \cline{1-1}  & & 0.15 & 20.709 & 18.264 & 0.882 \\ \cline{1-1}  & & 0.25 & 12.517 & 11.583 & 0.925 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Service life of cracked concrete-RCP 8.5, time slice 2050. Figure 16: Relative service life of cracked concrete-RCP 2.6, time slice 2000. Figure 17: Relative service life of cracked concrete-RCP 8.5 upper 90% confidence interval, time slice 2000. Figure 18: Relative service life of cracked concrete-RCP 8.5, time slice 2050. The summary of the analysis results for various cases is shown as follows. First, in the RCP 8.5, RCP 4.5 and RCP 2.6 climate change scenarios for concrete structures with a time slice 2000 and a 50-year service life, after considering climate change, service life will reduce by 16%, 14.5% and 11%, respectively. The reduction trend of service life was similar to the increase trends of CO\({}_{2}\) concentration and global temperature. Second, with a time slice 2000, as the climate change scenario changed from RCP 8.5 to RCP 8.5 upper 90% confidence interval, service life loss slightly increased from 16% to 16.5%. This was due to the increase in global temperature. While with a time slice 2050, as the climate change scenario changed from RCP 8.5 to RCP 8.5 upper 90% confidence interval, service life loss slightly increased from 24% to 25%. The service life loss may have more uncertainty in the near future than in the present. Third, in the case of the RCP 8.5 climate change scenario, for concrete structures with a 50-year service life, when the time slice changed from 2000 to 2050, service life loss increased from 16% to 24%. This was because the increase of CO\({}_{2}\) concentration and temperature were much higher in the 2050-2100 range than the 2000-2050 range of RCP 8.5. In addition, as shown in Tables 4 and 8, when the time slice changed from 2000 to 2050, the service life was reduced because of the increase in CO\({}_{2}\) concentration and temperature.