## 3 Verification of Proposed Model
### Service Life of Cracked Concrete Considering Climate Change  
Climate models project the responses of numerous climate variables such as in global environmental temperature and sea level to different scenarios of greenhouse gas emissions and other human-related emissions. Of these different scenarios, the IPCC-AR5 scenario, which was proposed by the Intergovernmental Panel on Climate Change (IPCC), is considered as one of the best models for climate change [15]. Figure 6 shows the CO\({}_{2}\) concentration increase. Representative Concentration Pathways (RCP) 8.5, RCP 4.5 and RCP 2.6 scenarios were considered in this study. RCP 8.5 projected higher CO\({}_{2}\) concentration increases than RCP 4.5 and RCP 2.6. Figure 7 shows the temperature increase for different climate change scenarios. Both mean temperature rises and the upper and lower 90% confidence intervals of each scenarios are included in Figure 7.  
In this section, parameter analysis was carried out to calculate the carbonation depth, probability of corrosion initiation and service life of cracked concrete. Two W/C (0.45 and 0.65), two concrete cover depths (25 mm and 35 mm) and three crack widths (0.05 mm, 0.10 mm and 0.15 mm) were used in the parameter analysis. In this study, W/C = 0.45, cover depth = 35 mm, crack width = 0.05 mm represents the upper limit of service life and W/C = 0.65, cover depth = 25 mm, crack width = 0.25 mm represents the lower limit of service life. Figure 6: Global averaged CO\({}_{2}\) concentration rise. RCP: Representative Concentration Pathways. Figure 7: Global averaged temperature rise. Table 2 shows statistical parameters. In this study, we considered the uncertainties of the \(CV\) and \(CR\). The concrete cover depth was assumed to have a normal distribution [11] and the coefficient of variance of cover depth was assumed to be 0.2 [3]. The carbonation rate parameter at the initial time was assumed to have a normal distribution [11] and the coefficient of variance of the carbonation rate parameter was 0.15 [3]. For CO\({}_{2}\) concentration and global temperature, the coefficient of variance increased with time [11]. At the initial time, the coefficient of variance equaled zero and at the 100-year mark, the coefficient of variance was taken to be 0.06 [11]. In addition, in this parameter study, the relative humidity was set as 65%, the initial environmental temperature was set as 25 \({}^{\circ}\)C, the curing period before carbonation testing was 28 days and the interspace of the concrete crack was 100 mm. Table 3 shows the summary of the analyzed cases. Six cases were analyzed: the RCP 2.6, RCP 4.5, RCP 8.5, RCP 8.5 upper 90% confidence interval, RCP 8.5 at the time slice 2050 and RCP 8.5 upper 90% confidence interval at the time slice 2050. To some extent, the different analysis cases such as RCP 2.6, RCP 4.5, RCP 8.5, RCP 8.5 upper 90% confidence interval, RCP 8.5 at the time slice 2050 and RCP 8.5 upper 90% confidence interval at the 2050-time slice, can represent specific cities [14; 16; 17]. Based on the concrete hydration-carbonation integrated model, the carbonation depth of concrete could be calculated. Furthermore, by using the Monte Carlo method, the probability of corrosion initiation was determined. The probability of corrosion initiation for the analysis cases is shown in Figures 8-13. With the increase in cover depth (seen in a comparison between Figure 8a,b and between Figure 8c,d), the probability of corrosion initiation decreased. With the decrease in water-to-cement ratio (based on a comparison between Figure 8a,c and between Figure 8b,d, the probability of corrosion initiation also decreased. Higher W/C with a lower crack width may present a lower probability of corrosion than a lower W/C with a higher crack width. In this study, we treated the water-to-cement ratio and crack width separately and did not consider the effect of water content on the chance of cracking.