# Bridge Assessment under Earthquake and Flood-Induced Scour
## 2 Methodology
### Intensity Measures (IM) and Flood and Earthquake Hazards  
The expected strong and ground motion characteristics are delineated to generate fragility curves derived from real accelerograms and spectrum-matching techniques. A group of real earthquake accelerograms matched to the target response spectrum employing the wavelets algorithm introduced by [PERSON] and [PERSON] [17] are generated and reflect seismic properties specific to the area of the bridge ensuring alignment with the soil conditions prevalent in the locality. Spectral matching adjusts the selected time history record to align with the target response spectrum. The spectrum functions as a reference point as the produced accelerograms will undergo refinement to align with its response spectrum. Eurocode 8 target response spectrum will be defined to produce the necessary adjusted records for each seismic level (\(a_{\text{gR}}\) = 0.05 g, 0.10 g, 0.20 g, and up to 0.5 g).  
The impact of scouring on the bridge will be assessed based on the depths of the scour. Various equations have been proposed to forecast local scour depth under different riverbed conditions. Drawing from model-scale experiments, two commonly utilized equations are tailored for sand and clay bed streams. Since sand is the most susceptible to erosion, this study will concentrate on a bridge in a sand-bed stream.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Component** & **EDP** & **Slight** & **Moderate** & **Extensive** & **Complete** \\ \hline \multirow{2}{*}{Bents} & \multirow{2}{*}{Curvature ductility, \(\mu_{\phi}\)} & \(\geq\)1.0 and & \(\geq\)4.0 and & \(\geq\)8.0 and & \multirow{2}{*}{\(\geq\)12.0} \\  & & \(<\)4.0 & \(<\)8.0 & \(<\)12.0 & \\ \hline \multirow{2}{*}{Abutment} & \multirow{2}{*}{Longitudinal deformation, \(\Delta_{\text{a,long}}\)} & \(\geq\)35 and & \(\geq\)55 and & \(\geq\)79 and & \multirow{2}{*}{\(\geq\)276} \\  & [mm] & \(<\)55 & \(<\)79 & \(<\)276 & \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Elastomeric bearings \\ \end{tabular} } & \multirow{2}{*}{Longitudinal deformation, \(\Delta_{\text{bearing}}\) [mm]} & \(\geq\)30 and & \(\geq\)60 and & \(\geq\)90 and & \multirow{2}{*}{\(\geq\)120} \\  & & \(<\)60 & \(<\)90 & \(<\)120 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Damage threshold limits.  
This study addresses scour, which arises from the erosive impact of the river, by assessing the maximum depth of local scour induced by floods at the bent and abutment foundations. Scour can manifest in three forms: long-term riverbed degradation, local scour at bents and abutments foundations, and contraction scour at the bridge [3]. This study primarily examines the scouring of bents and abutment foundations caused by flowing water. The scour depths (\(y_{\text{s}}\)) at bents and abutments are determined with the expression of HEC-18 [3]:  
\[\frac{y_{\text{s}}}{a}=2.0\cdot K_{1}\cdot K_{2}\cdot K_{3}\cdot\left(\frac{y_ {1}}{a}\right)^{0.35}\cdot F_{1}^{0.43} \tag{1}\]  
Correction factor \(K_{1}\) accounts for the nose shape of the bents, \(K_{2}\) accounts for the angle of the flow direction, and \(K_{3}\) accounts for the riverbed condition, \(y_{1}\) is the flow depth, \(a\) is the width of the bent, and \(Fr_{1}\) is the number of Froude. The equation provided is suitable for assessing local bent scour for a live bed and clear water. However, for this particular case study, the focus is on evaluating live-bed bent scour. Bridge scour depths calculated from Expression (1) will be incorporated into finite element analyses.