## 3 Carbonation-Induced Corrosion
### Initiation Phase
The reference humidity \(RH_{l}\) has to be chosen in accordance with the test conditions to determine the carbonation resistance of the concrete. Since the carbonation rates presented in Table 2 were tested under standard test conditions, which imply relative humidity of 65 \(\pm\) 5%, the reference humidity \(RH_{l}\) should be chosen within the range 60-70%. The parameters \(g_{e}\) and \(f_{e}\) have to be determined by means of a curve-fitting procedure with the actual test data. According to project DARTS [42], the best results are gained with \(f_{e}\) being equal to 5 and \(g_{e}\) being equal to 2.5. Curing of newly built structures is performed to prevent the drying of fresh concrete, and as such, it affects the hydration, and subsequently the carbonation, of the concrete. This has a prevailing effect on carbonation, and it can be taken into account through the curing/execution coefficient \(k_{c}\), expressed in Equation (14):  
\[k_{c}\ =\ \left(\frac{t_{c}}{7}\right)^{h_{c}}, \tag{14}\]  
where:  
\(t_{c}\) is the curing time (days), and  
\(b_{c}\) is the exponent (-). The curing time \(t_{c}\) is considered a constant, the value of which should be derived from execution documents or valid standards at the time of construction. The value of the variable \(b_{c}\) was quantified in DARTS [42] as being normally distributed with a mean value \(m=-0.567\) and standard deviation \(s=0.024\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cement Type**} & \multicolumn{8}{c}{**w/c Ratio**} \\ \cline{2-10}  & **0.40** & **0.45** & **0.50** & **0.55** & **0.60** & **0.65** & **0.70** & **0.75** & **0.80** \\ \hline CEM I & **1** & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ CEM II/A & **1** & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ CEM II/B & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ CEM III/A & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ CEM III/B & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean values \(m\) of carbonation rate \(k_{NAC}\) (mm/years\({}^{0.5}\)) for different combination of cement types and w/c ratios [46]. Coefficient \(k_{a}\), shown in Equation (15), describes the relation of the ambient air CO\({}_{2}\) content \(C_{a}\) and the laboratory content \(C_{l}\) used for standard test purposes:  
\[k_{a}\ =\ \frac{c_{a}}{c_{l}}, \tag{15}\]  
where:  
\(C_{a}\) is the CO\({}_{2}\) concentration of ambient air (kg/m\({}^{3}\)) or (vol. %), and  
\(C_{l}\) is the CO\({}_{2}\) concentration during concrete testing in laboratory (kg/m\({}^{3}\)) or (vol. %). The ambient air CO\({}_{2}\) concentration depends on parameters such as traffic volume, CO\({}_{2}\) emission of local industry, atmospheric stability, wind speed, etc. [47]. [PERSON] and [PERSON] [44] included assumed maximum and minimum CO\({}_{2}\) concentrations obtained from literature review, and divided these values between rural and urban locations, as shown in Table 3.  
In wetting periods, concrete surface absorbs water and thus inhibits carbonation. To take into account the meso-climatic conditions due to wetting events, the time-dependent function was introduced [42], called the environmental or wetting function \(W(t)\):  
\[W(t)\ =\ \left(\frac{t_{0}}{t}\right)^{\frac{(p_{dr}\cdot T_{0}W)^{bw}}{2}}, \tag{16}\]  
where:  
\(t_{0}\) is the reference time (year),  
\(p_{dr}\) is the probability of driving rain (-),  
\(ToW\) is the time of wetness (-), i.e., days with daily rainfall \(\geq\) 2.5 mm, and  
\(b_{w}\) is the regression exponent (-). Parameters \(ToW\) and \(p_{dr}\) are introduced in order to take into account the wetness of concrete surfaces that are not horizontal. Time of wetness \(ToW\) represents a percentage of rainy days per year, where a rainy day is considered to be a day with a minimum amount of precipitation water of 2.5 mm. Probability of driving rain \(p_{dr}\) represents an average distribution of the wind direction during rain events, and it depends on the strength and direction of wind, the orientation of the structural element, etc.