## 3 Carbonation-Induced Corrosion
### Propagation Phase  
During the propagation phase, the process of reinforcement corrosion takes place, the rate of which is governed by the availability of water and oxygen on the steel surface [40]. The consequences of reinforcement corrosion are the cracking of the cover, loss of steel concrete bond, decrease of steel cross-section, and loss of steel ductility [48]. In _fib_ Bulletin 34 [7], these consequences are contained in the limit states of crack formation, spalling of the concrete cover, and collapse. These limit states are divided into serviceability limit states (SLS), which include the events of crack formation and spalling, and the ultimate limit state (ULS), which includes the event of collapse in different modes. To differentiate among collapse modes, different robustness classes (ROC) are described in [7]. These classes are given in connection with a rough estimate on the percentage of cross-section loss \(\Delta A_{s}\) that causes particular collapse modes, as presented in Table 4. In other words, sufficient reliability regarding the ULS could be achieved by adding the needed extra reinforcement (sacrificial cross-section) in the amount presented in Table 4. However, it should be noted that these values are a rough estimate and need to be confirmed by further research. Propagation of corrosion can be observed through several performance indicators, including the corrosion depth \(P_{x}\), rate of corrosion \(v_{corr}\), loss of cross-section area \(\Delta A_{s}\), loss of bar diameter \(\Delta\varphi\), concrete crack width \(w\), and so on. The simplified model for determining the corrosion depth \(P_{x}(t)\) can be expressed as in Equation (19):  
\[P_{x}(t)\ =\ t\cdot v_{corr}, \tag{19}\]  
where:  
\(t\) is the time of propagation (year), and  
\(v_{corr}\) is the corrosion rate (mm/year). The value of bar diameter \(\varphi(t)\) as function of time and corrosion depth can be calculated according to Equation (20):  
\[\varphi(t)\ =\ \varphi_{0}-\alpha\cdot P_{x}(t), \tag{20}\]  
where:  
\(\varphi_{0}\) is the initial bar diameter (mm), and  
\(\alpha\) is the factor accounting the type of corrosion (pitting or homogeneous) (-). Corrosion types can be divided into homogeneous (uniform) corrosion and pitting (localized) corrosion, which result from carbonation-induced depassivation and chloride-induced depassivation, respectively. For homogeneous corrosion, it is assumed that the factor accounting for the type of corrosion \(\alpha\) ranges between 0 and 2. On the contrary, for chloride-induced corrosion, it can be as high as 10 [49]. Furthermore, the loss of bar diameter expressed in percentages \(\Delta\varphi(t)\) is given by Equation (21):  
\[\Delta\varphi(t)\ =\ 100.\frac{\phi_{0}-\phi(t)}{\phi_{0}}. \tag{21}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Robustness Class (ROC)** & **Characteristics** & **Loss of Cross-Section \(\Delta A_{s}\) (\%)** \\ \hline ROC 3 & \
\begin{tabular}{c} bending reinforcement outside of \\ anchorage and laps \\ shear reinforcement, anchorage zones \\ with confinement \\ ROC 1 \\ \end{tabular} &
\begin{tabular}{c} 25 \\ 15 \\ anchorage zones without confinement \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Robustness classes (ROC) in relation to cross-section loss [7]. According to [41], the concrete crack width \(w(t)\) can be expressed in connection to corrosion depth \(P_{x}(t)\), as shown in Equation (22):  
\[w(t)\ =\ w_{0}+\beta\cdot(P_{x}(t)\cdot P_{0}), \tag{22}\]  
where:  
\(w_{0}\) is the crack width when it is visible (\(\approx\)0.05) (mm),  
\(\beta\) is the parameter that controls the propagation (-), and  
\(P_{0}\) is the loss of reinforcement bar diameter when crack width is visible (mm). It should be noted that the correlation between concrete quality, corrosion rates and microenvironment has not yet been quantified in detail.