# Experimental Study of Scour Hole Depth around Bridge Pile Using Efficient Cross-Section
## 3 Methodology
### Bridge Pier Piles Models Selection  
The experimental model is the scaled archetype of Pakhtoon Gari bridge (Figure 2a) situated across the river Kabul (34.021 N, 71.832 S Google Earth). This bridge is a multiple-span bridge composed of prestressed concrete I beam and a concrete deck supported on concrete stub abutments. The total span length between the bridge's abutments is 420 m with 14 equal spans of 30 m center to center between the piers. The bridge is supported by a piled foundation with 104 piles in the piers and 20 piles in the abutments. The pier piles are arranged in a group of 8, laid out in a rectangular grid pattern of 2 \(\times\) 4 piles. The individual pile is 750 mm in diameter, where the embedment is 28 m in piers and 18 m in abutments. Because of the important effect of pile geometry on scour depth, an experimental investigation has been carried out using three different pile cross-sections: circular, square and lenticular. An experimental pile group model is prepared to employ a reasonable geometric scaling factor derived after several mathematical trials. To study the scour characteristic of this model, a scaled ratio of 1:30 is selected based on the limitations due to the flume size, water pump capacity and environmental constraints. Considering the ratio of prototype length (L\({}_{\text{p}}\)) to model length (L\({}_{\text{m}}\)), the geometric scale factor (L\({}_{\text{r}}\)) is  
\[\text{L}_{\text{r}}=\frac{\text{L}_{\text{p}}}{\text{L}_{\text{m}}} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sieve No** & **Sieve Size** & **Material** & **Percent** & **Percent** & **Percent** \\
**(mm)** & **Retained** & **Percent** & **Retained** & **Cumulative** & **Cumulative** \\ \hline \multicolumn{6}{c}{**Total Amount of Sample = 500 gm**} \\ \hline \#16 & 1.00 & 13.20 & 2.64 & 4.24 & 95.76 \\ \hline \#30 & 0.50 & 104.00 & 20.80 & 25.04 & 74.96 \\ \hline \#50 & 0.30 & 279.40 & 55.88 & 80.92 & 19.08 \\ \hline \#100 & 0.15 & 72.80 & 14.56 & 95.48 & 4.52 \\ \hline \#200 & 0.08 & 12.80 & 2.56 & 98.04 & 1.96 \\ \hline Pan & 0.00 & 9.80 & 1.96 & 100.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 3: Sieve analysis. Given the system involving open channel flow, it is necessary to consider the Froude number. Thus  
\[\text{F}_{\text{r}}=\frac{\text{V}}{\sqrt{\text{g}\times\text{y}}} \tag{2}\]  
where V defines the velocity of the flow, y and g represents the flow depth and acceleration due to gravity. In order to remain consistent, the Froude number of the experimental model and its prototype structure is taken the same:  
\[\frac{\text{V}_{\text{p}}}{\sqrt{\text{y}_{\text{p}}}}=\frac{\text{V}_{\text{m }}}{\sqrt{\text{y}_{\text{m}}}} \tag{3}\]  
\[\text{V}_{\text{p}}=\frac{\text{V}_{\text{m}}\ \sqrt{\text{y}_{\text{p}}}}{ \sqrt{\text{y}_{\text{m}}}} \tag{4}\]  
\[\text{V}_{\text{p}}^{2}=\frac{\text{V}_{\text{m}}^{2}\ y_{\text{p}}}{\text{y}_ {\text{m}}} \tag{5}\]  
Since,  
\[\frac{\text{y}_{\text{p}}}{\text{y}_{\text{m}}}=30 \tag{6}\]  
\[\text{V}_{\text{p}}^{2}\ =30\text{V}_{\text{m}}^{2} \tag{7}\]  
Moreover, the discharge in the testing flume can be calculated as:  
\[\frac{\text{Q}_{\text{p}}}{\text{A}_{\text{p}}}=5.48\frac{\text{Q}_{\text{m}} }{\text{A}_{\text{m}}} \tag{8}\]  
\[\text{Q}_{\text{p}}=5.48\frac{\text{B}_{\text{p}}\ y_{\text{p}}}{\text{B}_{ \text{m}}\ y_{\text{m}}}\ Q_{\text{m}} \tag{9}\]  
Figure 3:0  
where the width of the prototype and model are 400 m and 0.3 m, respectively. Incorporating these values in Equation (10), the resultant discharge of the prototype. Figure 3:1  
Figure 3:2  
Now, it turns out, when using Equation (12), that the model flow rate \(\text{Q}_{\text{m}}=4.8\ \text{Ls}^{-1}\) gives geometric similarity to the actual flow rate of 1061 m\({}^{3}\) s\({}^{-1}\), based on the average peak flood flow in the last fifty years in the Kabul river. Similarly, using the scale factor of 1:30, the model dimensions are determined, as shown in Table 2, Figures 4 and 5.