## 3 Carbonation-Induced Corrosion
### Initiation Phase  
The initiation phase of the process of carbonation-induced corrosion is marked by carbonation penetration, and it finishes roughly with the depassivation of reinforcement. Comprehensive descriptions of numerous analytical models of concrete carbonation and their development can be found in [40]. The analytical model that defines the limit state of carbonation-induced depassivation presented and applied in this article is supported by the _fib_[7; 8; 9]. The model was initially developed in the research projects DuraCrete [41] and DARTS [42]. In later development of the model, [PERSON] and [PERSON] [43] excluded the inverse carbonation resistance parameter \(R_{NAC}-1\) and introduced an additional parameter--carbonation rate \(k_{NAC}\). The limit state equation of carbonation-induced depassivation, where the carbonation depth is compared with concrete cover, is given by Equation (11):  
\[g(t)\ =\ c-x_{c}(t), \tag{11}\]  
where:  
\(c\) is the concrete cover (mm), and  
\(x_{c}(t)\) is the carbonation depth at time \(t\) (mm). Furthermore, carbonation depth can be expressed as:  
\[x_{c}(t)\ =\ k_{NAC}\cdot\sqrt{k_{e}\cdot k_{c}\cdot k_{a}}\cdot\sqrt{t}\cdot W(t), \tag{12}\]  
where:  
\(k_{NAC}\) is the carbonation rate for standard test conditions (mm/years\({}^{0.5}\)),  
\(k_{e}\) is the function describing the environmental effect of relative humidity,  
\(k_{c}\) is the function describing the effect of curing/execution,  
\(k_{a}\) is the function describing the effect of CO\({}_{2}\) concentration in the ambient air,  
\(t\) is time (year), i.e., the age of structure, and  
\(W(t)\) is the function describing the effect of wetting events. The carbonation rate \(k_{NAC}\) in Equation (12) represents the resistance of the concrete mixture to carbonation, where the rate of the particular mixture is derived under constant (standard) test conditions. Tested values of carbonation rates of different concrete mixtures under standard test conditions can be found in [43; 44; 45]. The mean values of such tested carbonation rates are expressed as dependent on cement types, as shown in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Exposure Class** & **Description of Environment** & **Informative Example of Where This Exposure Class** \\ \hline XC1 & Dry or permanently wet & Parts of the bridges permanently submerged in water. \\ XC2 & Wet, rarely dry & Parts of the bridges subject to long-term water contact; \\  & & Many bridge foundations. \\ XC3 & Moderate humidity & Bridge elements sheltered from rain. \\ XC4 & Cyclic wet and dry & Bridge surfaces subject to water contact, not within \\  & & exposure class XC2. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of exposure classes for the corrosion induced by carbonation according to EN 206-1 [38], with informative examples given for bridges. The shaded elements in Table 2 were obtained through linear extrapolation of measured values. Furthermore, [PERSON] and [PERSON] [43; 44; 45] consider that carbonation rate is normally distributed with the unique standard deviation \(s\), which is unrelated to concrete mixture and is equal to 1.1 mm/years\({}^{0.5}\). The environmental coefficient \(k_{e}\) introduces the effect of relative humidity on carbonation, and is described as:  
\[k_{e}\ =\ \left(\frac{1-\left(\frac{RH_{a}}{100}\right)^{f_{e}}}{1-\left( \frac{RH_{l}}{100}\right)^{f_{e}}}\right)^{g_{e}}, \tag{13}\]  
where:  
\(RH_{a}\) is the relative humidity of ambient air (%),  
\(RH_{l}\) is the reference (laboratory) humidity (%),  
\(f_{e}\) is the exponent (-), and  
\(g_{e}\) is the exponent (-). As an input for the relative humidity \(RH_{a}\), data from the nearest weather station may be used. Since relative humidity varies in a range from 0 to 100%, restricted distributions with an upper limit may be used to describe \(RH_{a}\), such as beta or Weibull (max) distribution.