## 5 Case Study
### Visual Inspection  
The condition states (ratings) introduced in Table 9 are assigned based on the results of visual inspections, which are commonly carried out by teams of trained technicians. During visual inspection, they try to detect defects and damage, and, depending on their extent, assign the aforementioned condition state. Furthermore, visual inspection comprises the use of only simple tools such as hammers to remove cracked parts of concrete, rebound hammers to detect areas with lower compressive strength, etc. During the inspections, the following is therefore recorded: (i) the identified defects and damages, such as cracks, concrete spalling, steel corrosion, etc., (ii) the required immediate intervention measures, (iii) the reparability of the observed defects and damage, and (iv) the comparison of the existing condition of the structure with the previously recorded one. Accordingly, in 2005, the Weikendorf Bridge was assigned the condition state CS3, due to several damage zones with spalled parts of concrete, primarily in the abutments and wings. The same condition state was assigned in subsequent inspections, until 2014, when the bridge was repaired. Before 2005, inspection records contained only a description of the condition, without a condition state being assigned. Following the inspection in 2013, it was decided that additional testing should be performed, such as determining  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Element**} & \multirow{2}{*}{**Label**} & \multicolumn{2}{c}{**Concrete Class**} & \multirow{2}{*}{**w/c Ratio Range [58]**} & \multicolumn{2}{c}{**Concrete Class**} \\  & & \multicolumn{2}{c}{**ONORM B 3302 [57]**} & & \multicolumn{2}{c}{**ONORM B 4710-1 [59]**} \\ \hline Wings & W & B160 & 0.74–1.03 & C12/15 \\ Abutments & A & B160 & 0.74–1.03 & C12/15 \\ Edge beams & EB & B225 & 0.61–0.88 & C16/20 \\ Girder & G & B400 & 0.32–0.64 & C30/37 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Prescribed w/c ratios in connection to concrete classes and cement strength classes [58].  
Figure 3: Cross-section of the Weikendorf Bridge with assigned concrete classes according to [57].  
compressive strength, measuring reinforcement properties, measuring carbonation depth, etc. From the performed tests, it was found that the abutments exhibited high levels of chloride and carbonation, and the wings exhibited high levels of carbonation.  
Taking into account the condition state grading system of five states, the state of the process at time \(t\) = 38 years (in 2005) can be denoted by an \(n\)-dimensional vector \(p\)(38). Thus, Equation (1) takes the form:  
\[p\)(38) = [p_{1}(38)p_{2}(38)p_{3}(38)p_{4}(38)p_{5}(38)]. \tag{24}\]  
Furthermore, if the fact that the structure is graded to be in CS3 at the age of 38 years is taken with certainty, the probability vector denoting the state of the process becomes:  
\[p\)(38) = (0 0 1 0 0). \tag{25}\]  
However, such representation implies that no uncertainty is connected with the result of visual inspection. This is presumed, since a condition rating is usually assigned as a deterministic value, making it hard to allocate a level of uncertainty to such a condition state. If, for example, an indication were to exist that the visual inspection was performed with \(\pm 15\%\) of accuracy, the probability vector denoting the state in Equation (25) could be formed as \(p\)(38) = (0 0 0.15 0.70 0.15).