## 3 Carbonation-Induced Corrosion
### Propagation Phase
This implies that reliable findings are lacking, which would connect critical values of performance indicators (\(P_{x}(t)\), \(w(t)\), \(\Delta A_{\delta}(t)\), \(\Delta\varphi(t)\),... ) at which the states of cracking, spalling and collapse are triggered. Hence, it is hard to accurately express the duration of different propagation periods. To overcome this problem, a questionnaire was organized by _fib_'s Task Group 5.6, in which experts all over the world gave their opinion on expected penetration depths and propagation periods in carbonation environment. The estimations were given within the exposure class XC4, for a reference temperature of \(T_{\textit{ref}}\) = 293 K, assuming that depassivation had already occurred. Collected data were statistically elaborated and presented in [7], where the propagation periods were described by lognormal distribution, as shown in Table 5.  
In cases where the average yearly temperature \(T_{\textit{real}}\) of the object being investigated differs from 293 K, the values in Table 5 need to be adapted using the formula for the temperature dependence of reaction rates (Arrhenius equation) [50], as presented in Equation (23):  
\[t_{\textit{prop}}(T_{\textit{real}})\ =\ \frac{t_{\textit{prop}}(T_{\textit{ref}})}{ e^{b\cdot(\frac{1}{T_{\textit{ref}}}-\frac{1}{T_{\textit{real}}})}}, \tag{23}\]  
where:  
\(t_{\textit{prop}}(T_{\textit{real}})\) is the duration of propagation period based on real temperature \(T_{\textit{real}}\) (year),  
\(t_{\textit{prop}}(T_{\textit{ref}})\) is the duration of propagation period based on reference temperature \(T_{\textit{ref}}\) (year),  
\(b\) is the regression parameter (\(b\) = 4900 K),  
\(T_{\textit{ref}}\) is the reference temperature (\(T_{\textit{ref}}\) = 293 K), and  
\(T_{\textit{real}}\) is the average yearly ambient temperature of the object considered (K). Furthermore, in addition to the duration of propagation periods, critical corrosion depths \(P_{\textit{crit}}\) causing the events of cracking and spalling can also be extracted from [7], as presented in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Critical Corrosion Depth \(P_{\textit{crit}}\)** & **Mean \(m\)** & **Standard Deviation \(s\)** & **Location Parameter \(\mu\)** & **Scale Parameter \(\sigma\)** \\ \hline \(P_{\textit{crit},\textit{rot}}\) [um] & 171.0 & 57.00 & 5.09 & 0.32 \\ \(P_{\textit{crit},\textit{rot}}\) [um] & 342.0 & 95.00 & 5.80 & 0.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Critical corrosion depths \(P_{\textit{crit}}\) linked to the events of cracking and spalling, according to data presented in [7]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Event**} & \multicolumn{2}{c}{**Duration of**} & \multirow{2}{*}{**Mean Value \(m\)**} & **Standard** & **Location** & **Scale** \\  & & & **Deviation \(s\)** & **Parameter \(\mu\)** & **Parameter \(\sigma\)** \\ \hline cracking & \(t_{\textit{prop},\textit{rot}}\) [year] & 4.5 & 1.5 & 1.45 & 0.32 \\ spalling & \(t_{\textit{prop},\textit{rot}}\) [year] & 9.0 & 2.5 & 2.16 & 0.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Duration of propagation periods \(t_{\textit{prop}}\) linked to the events of cracking and spalling according to data presented in [7].