# VoI-Based Optimization of Structural Assessment for Spatially Degrading RC Structures
## 4 Case Study: A Simply Supported RC Girder Bridge
### Costs  
For the calculation of the life-cycle costs, different cost values are required: costs of maintenance/repair actions, costs of the monitoring strategy itself, and costs of failure. Although the importance of life-cycle cost analysis is generally acknowledged [40,41], data on these costs might be difficult to obtain. Even though some information on the costs can be available, some of them might still be hard to estimate.  
As a first estimate for the monitoring costs, cost values for the three considered monitoring strategies are summarized in Table 2. The number of sensors for strategy 1 refers to the number of uniaxial accelerometers used. The corresponding costs are the costs for a modal analysis, which include the costs for instrumentation of the bridge and the data processing. The number of sensors for strategy 2 refers to the number of elements (in the discretization of the random fields) equipped with a sensor of an optic fiber, both at lower and upper fiber of the girder. The optic fibers used have a length equal to the length of the girder and are applied each time to the top fiber and bottom fiber of the girder. Each of these fibers has 10 sensors along its length, measuring the strains. These 10 sensors correspond to the 10 elements in which the girders are discretized. For strategy 3, the number of sensors refers to the number of discrete strain sensors applied on the bridge.  
To estimate the costs of failure and repair, in [42], it is stated that these costs could be monotized and presented as a percentage of the total bridge value \(C_{BV}\), which is given by \(C_{BV}=f_{B}\cdot C_{0}\), with \(C_{0}\) the structural/construction costs defined as the initial bridge value per square meter of bridge deck, and \(f_{B}\) a factor for multiplication of the bridge value due to its importance in the network. The basic structural costs \(C_{0}\) can be based on [43], where  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Monitoring Data** & **Number of Sensors** & **Costs** \\ \hline Frequencies and mode shapes & 20 & 69000 \\ (strategy 1) & 35 & 610,000 \\  & 50 & 611,000 \\ \hline Frequencies and strain mode shapes & 10 & 610,000 \\ (strategy 2) & 20 & 615,000 \\  & 30 & 620,000 \\  & 40 & 625,000 \\  & 50 & 630,000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Assumed monitoring costs for the example bridge.  
a value of 1200 euro per square meter of bridge deck is suggested. The importance of the bridge in the road network \(f_{B}\) is evaluated based on:  
* Road category (\(G_{RC}\));
* Average annual daily traffic (\(G_{AADT}\));
* Detour distance (\(G_{DD}\));
* Largest span (\(G_{LS}\));
* Total length of the bridge (\(G_{TL}\)).  
Each of these variables have grade 1 to 5 and \(f_{B}=1+1/5[0.25(G_{RC}+G_{AADT}+G_{DD})+0.125(G_{LS}+G_{TL})]\). Values for these variables can be found in [44]. For the bridge under consideration, a structural/construction cost of \(C_{0}=\ell 126,672\) is estimated and a factor \(f_{B}\) equal to \(1/5[0.25(2+2+5)+0.125(2+2)]=1.55\). This construction cost \(C_{0}\) only relates to the superstructure of the bridge and is also in line with global cost estimates provided by the local road authorities in Flanders [45].  
According to [46], a cost of failure of the bridge equal to 5 times the total bridge value is assumed, resulting in a cost of failure of \(\ell 981,708\).  
The influence of different assumptions on the repair costs is investigated in Section 5.2.1. The considered cost models are also summarized there.