## 5 Conclusions  
The present study proposed an efficient framework for the fragility assessment of in-plane MAB subject to flood-induced scour by integrating metamodeling techniques with limit state analysis. The significance of this research is that it allows us to expand the knowledge regarding MAB behavior under flooding events and ease the computational process related to performing fragility analyses. This latter advancement enables infrastruc  
Figure 11: Fragility curves based on the geotechnical uncertainties of: (**a**) soil beneath the foundation; (**b**) backfill. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**ID** & **Description** & **Element** & **Type** & **Nominal Values** & **Units** & **CV (\%)** & **Type** & **Reference** \\ \hline \(FA_{S}\) & Friction angle & Soil & Dense & 37.42 & \({}^{\circ}\) & 10 & Lognormal & [45] \\ \(SD_{S}\) & Saturated density & Soil & Dense & 21.50 & kN/m\({}^{3}\) & 5 & Lognormal & [45] \\ \(DDs_{S}\) & Dry density & Soil & Dense & 18.50 & kN/m\({}^{3}\) & 5 & Lognormal & [45] \\ \(FA_{S}\) & Friction angle & Soil & Loose & 31.59 & \({}^{\circ}\) & 10 & Lognormal & [45] \\ \(SD_{S}\) & Saturated density & Soil & Loose & 19.50 & kN/m\({}^{3}\) & 5 & Lognormal & [45] \\ \(DD_{S}\) & Dry density & Soil & Loose & 15.50 & kN/m\({}^{3}\) & 5 & Lognormal & [45] \\ \(SD_{B}\) & Saturated density & Backfill & Dense & 20.00 & kN/m\({}^{3}\) & 5 & Lognormal & [45] \\ \(C_{B}\) & Cohesion & Backfill & Dense & 20.00 & kPa & 10 & Lognormal & [45] \\ \(FA_{B}\) & Friction angle & Backfill & Dense & 22.78 & \({}^{\circ}\) & 10 & Lognormal & [45] \\ \(DD_{B}\) & Dry density & Backfill & Dense & 18.00 & kN/m\({}^{3}\) & 5 & Lognormal & [45] \\ \(SD_{B}\) & Saturated density & Backfill & Loose & 18.00 & kN/m\({}^{3}\) & 5 & Lognormal & [45] \\ \(C_{B}\) & Cohesion & Backfill & Loose & 5.00 & kPa & 10 & Lognormal & [45] \\ \(FA_{B}\) & Friction angle & Backfill & Loose & 19.29 & \({}^{\circ}\) & 10 & Lognormal & [45] \\ \(DD_{B}\) & Dry density & Backfill & Loose & 16.00 & kN/m\({}^{3}\) & 5 & Lognormal & [45] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Random variables for the parametric analysis. ture managers to assess the safety of a large stock of MAB more efficiently and therefore enhance the decision-making process by supporting the prioritization of maintenance and replacement strategies within the transportation network. The proposed methodology was applied to a case study, the \"Vala do Carregado\" bridge located in Portugal, and flood fragility curves were derived for different scour scenarios. Furthermore, a fragility surface was obtained for different flow discharge and angle of attack values, which may affect bridge reliability. Based on the obtained results, the following conclusions can be made:  
* The sensitivity analysis allowed identification of the strong influence of geotechnical parameter uncertainty on the bridge response. The most relevant variables when assessing the bridge in-plane capacity were the backfill mechanical properties, which were validated by the literature [18, 52]. * The bridge reliability decreased with each increment of the flow discharge. However, the loss of bearing capacity for values of discharge where most of the scour depth values were lower than the \(F_{t}\) was slight when compared with higher discharge values. Safety levels are met if the reliability of the structure is higher than the target reliability (i.e., \(\beta_{\text{target}}=4.3\) corresponding to a failure probability bellow \(10^{-5}\)) for structures with consequences involving high human and economic losses, according to NP 1990 [54]. A decrease of the reliability index below the safety levels was identified for cases in which most of the values obtained for scour depth were below the foundation thickness. * In all scenarios, failure probability increased with the flow discharge due to its significance on the estimation of the scour depth.