## 1 Introduction  
Carbonation is among the primary reasons for the initiation of corrosion of steel rebar in reinforced concrete structures. Due to carbonation, the pH value of the pore solution of concrete decreases to values around 9, the protective oxide layer of steel rebar is destroyed, therefore, the corrosion of steel rebar initiates. Additionally, given load effects and environmental actions, inevitable cracks have frequently occurred for concrete structures since the early ages. Cracks can aggravate the ingression of CO\({}_{2}\) and considerably lessen the service existence of concrete structures. Carbonation of concrete is happening faster due to global warming, leading to increases in CO2 concentration and environmental temperature. Hence, for the carbonation durability style of reinforced concrete (RC) structures, the influence of cracking and global warming should be taken into consideration [1]. Abundant studies have been carried out on the carbonation behavior of concrete. [PERSON] [2] proposed a carbonation model that considered the influences of concrete mixing proportions and environmental conditions on CO\({}_{2}\) diffusivity and concrete carbonation resistance. [PERSON] et al. [3] evaluated the service life of concrete using the safety factor method and Monte Carlo simulation. They found that the analysis results from the two methods were similar. [PERSON] and [PERSON] [4] analyzed the service life of concrete structures considering both the corrosion initiation period and corrosion propagation period. Performance-based methodology was used to achieve the target service life of concrete structures. However, the studies of [PERSON] [2], [PERSON] et al. [3] and [PERSON] and [PERSON] [4] focused on sound concrete and the effect of cracking on carbonation was not considered. Regarding the carbonation of cracked concrete, [PERSON] et al. [5] proposed an analytical technique for predicting the carbonation depth of cracked concrete. Diffusion of CO\({}_{2}\) in sound concrete and cracked concrete was simulated. [PERSON] et al. [6] evaluated the carbonation process of cracked concrete by using the two-dimensional finite element method. The influences of crack width and depth on carbonation were analyzed. However, the studies of [PERSON] et al. [5] and [PERSON] et al. [6] did not consider the uncertainties involved in predicting carbonation depth. [PERSON] and [PERSON] [7] proposed a probabilistic approach for the carbonation durability design of cracked concrete to consider the uncertainties of carbonation prediction. Nevertheless, it should be noticed that [PERSON] and [PERSON] [7]'s study did not consider the effect of curing periods on the carbonation of concrete. With increasing curing periods, the carbonation resistance of concrete is improved [8; 9]. Moreover, the effect of climate change on carbonation was not considered by [PERSON] et al. [5], [PERSON] et al. [6] and [PERSON] and [PERSON] [7]. Regarding the effects of climate change on the carbonation of concrete, [PERSON] et al. [10] proposed a mathematical model to consider the effect of CO\({}_{2}\) concentration increase on the carbonation of concrete; however, the effect of the increase in environmental temperature on carbonation was not considered in their study. [PERSON] et al. [11] proposed a model that considered climate change impact on the corrosion of concrete where the effects of increases in CO\({}_{2}\) concentration and environmental temperature on the corrosion initiation stage, crack initiation stage and crack propagation stage were highlighted. Furthermore, [PERSON] et al. [12] proposed engineering strategies for the corrosion control of concrete considering climate change. However, the studies conducted by [PERSON] et al. [10] and [PERSON] et al. [11; 12] did not consider the effect of pre-corrosion cracks on the service life of concrete. To summarize, the current models only consider a single effect such as the either crack effect or climate change effect on the service life of concrete.