## 5 Case Study
### Carbonation Propagation  
To determine the duration of the initiation phase \(t_{ini}\), first the parameters in Equation (17) have to be determined. Some of these parameters are constants, and others can be obtained from design documents, performed inspections, meteorological data, literature survey, etc. Moreover, results of measured carbonation depth can serve for the crosschecking of such determined parameters. Alternatively, when substantial information related to the measured carbonation depth is known, a Bayesian updating procedure can be used to directly update the initially assumed carbonation depth. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Values** & **Horizontal Reinforcement** & **Vertical Reinforcement** \\ \hline concrete cover [mm] & circa 30 & circa 40 \\ raster [cm] & 15 & 20 \\ diameter [\(\varphi\)] & 14 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Properties of reinforcement in bridge wings, grasped from design documents and performed tests. Figure 5: Properties of measured carbonation depths and reinforcement in bridge wings, obtained from the design documents and the performed tests. Time of wetness _ToW_ was determined based on historical measurements obtained from the weather stations in Ganserndorf, located 1.45 km from the bridge [59]. Precipitation data were available for each day from 1971 to 2014. From the data, the average number of rainy days for each year was calculated, and expressed as a percentage. Rainy days were divided into days with more than 2.5 mm of rainfall and those with more than 0 mm of rainfall, as presented in Figure 6.  
Furthermore, the mean value of precipitation > 2.5 mm for all average yearly values in the period 1971-2014 was calculated and depicted. This value is equal to 0.145, and it was used as the _ToW_ of the Weikendorf Bridge. On the other hand, relative humidity \(RH_{a}\) of the ambient air could not be determined as precisely as the time of wetness, since the closest weather station available is located 20 km from the bridge. For this reason, all available weather stations in the state of Lower Austria were analyzed based on the measurements of the Central Institute for Meteorology and Geodynamics [60], as depicted in Figure 7. Data were available in the form of average humidity for the whole period 1981-2010, measured at 7:00 AM and 2:00 PM. When different stations are analyzed, considering an average value between 7:00 AM and 2:00 PM, the data exhibit a mean value of 72.37% and a standard deviation of 2.23%. As stated in the previous chapters, the 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 the wind, the orientation of the structural element, etc. From the available meteorological data, it was not possible to compare exact precipitation and wind directions. However, being mostly sheltered by the embankment, the wings are considered to have a low probability of driving rain. Hence, a probability of driving rain of \(p_{dr}\) = 0.1 was used for the analysis. No concrete cover \(c\) was found to be assigned in the design documents, while the tested concrete cover in the test report was only assigned approximately, as shown in Table 13. In _fib_ Bulletin 34 [7], it is stated that that the observed standard deviations of concrete cover obtained from field measurements range from 2 mm \(\leq s\leq\) 15 mm. Moreover, deviation in concrete cover can be associated with level of quality control, e.g., the coefficient of variation can be assumed to be 15% in structures with high quality control, 20% in structures with medium, and 30% in those with low quality control. Since the wings of the Weikendorf bridge are considered to be constructed with medium quality control, the concrete cover was assumed to be normally distributed with the mean value of 30 mm, coefficient of variation of 20%, and standard deviation of 6 mm.