# Near-Nature Ecological Technique for Pier Scour Countermeasure in a Submerged Overfall
## 2 Concept of Artificial Water Weeds and Its Protective Effect against Pier Scouring
Strips made with four different diameters of the circular cross-section and materials, listed in Table 1, were tested. The relationship between the ratio of bent width \(L_{w}\) and the length of strip \(L_{a}\), (\(L_{w}/L_{a}\)) and \(L_{a}/\sqrt{A}\) is shown in Table 1 and plotted in Figure 4. \(L_{w}/L_{a}\) and \(L_{a}/\sqrt{A}\) show an exponential relationship in Equation (2), and the correlation coefficient is more than 0.9. This equation represents the degree of the bent arc along with the change in length while the strip is made of a certain material. \[\frac{L_{w}}{L_{a}}\ =\ \alpha\exp\left(\beta\frac{L_{a}}{\sqrt{A}}\right), \tag{2}\]  
Figure 3: Schematic of bent arc test on the strip. Figure 4 shows that when \(L_{w}/L_{a}=0.1\), an obvious change of \(L_{a}/\sqrt{A}\) occurs. Therefore, we define the flexibility index as \(L_{a}/\sqrt{A}\) at \(L_{w}/L_{a}=0.1\), as shown in Equation (3). \[F_{i}\ =\ \frac{L_{a}}{\sqrt{A}}\ \left(if\ \frac{L_{w}}{L_{a}}\ =\ 0.1\right), \tag{3}\]  
This index is a characteristic of material property. When \(F_{i}\) is smaller, it represents that the strip is softer; for a perfect rigid rod, as \(L_{w}/L_{a}=0.1\) is required, a very large \(L_{a}\) is needed, and \(F_{i}\) is defined as infinite at this moment. For flexibility of a flow arranging strip with length \(L\) in real, \(F_{p}\) represents the flexibility parameter of arranging strips placed on site. \(F_{p}\) denotes the ratio of \(L/\sqrt{A}\) to \(F_{i}\) defined in Equation (4). When the value of \(F_{p}\) is large, then it means the arranging strips are soft. The perfect rigid strips have a value of \(F_{p}=0\). \[F_{p}\ =\ \left(L/\sqrt{A}\right)/F_{i}. \tag{4}\]  
The hydraulic characteristic of CKAW's protective effect is explained in Figure 5. When flow passes through a submerged overall, the velocity can be divided into horizontal and vertical components. \(V_{x}\) and \(V_{z}\) represent the flow velocity in the original condition, and \(V_{yx}\) and \(V_{yz}\) represent the flow velocity in a riverbed sheltered by CKAW. Assuming that the resultant velocity in the front fringe of horizontal platform in the protected and unprotected conditions is the same, the only change in the flow velocity is the direction of the component. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material Composition** & **Diameter \(D_{a}\)** & \(\alpha\) & \(\beta\) & **Correlation Coefficient \(R^{2}\)** & **Flexibility Index** \\
**and Application** & **(mm)** & & & & & \(F_{i}\) \\ \hline Cotton dressmaking & 0.1 & 2.5276 & \(-\)0.01305 & 0.9226 & 248 \\ Cotton dressmaking & 1.0 & 1.4780 & \(-\)0.05840 & 0.9212 & 46 \\ Nylon craft use & 1.5 & 3.2063 & \(-\)0.01618 & 0.9950 & 211 \\ Silk and satin & 2.0 & 1.7109 & \(-\)0.02562 & 0.9789 & 110 \\ Chinese knots & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Flexibility index of strips made of different materials and sizes. Figure 4: Relationship between \(L_{w}/L_{a}\) and \(L_{a}/\sqrt{A}\) of strips made of different materials and sizes. After passing through the strips, the flow tends to transfer to x component and shows \(V_{px}\) > \(V_{x}\) and \(V_{px}\) < \(V_{z}\). The flume bed is sheltered from scour because the scouring energy is diminished, thus reducing the scour depth. In restraining overall-induced scour, the main factor is to control the downward flow velocity \(V_{y}\) and restrain pier-induced scour. Thus, controlling \(V_{x}\) is a main factor. A greater contraction effect of pier induces, a larger \(V_{x}\) and local scour at the pier will occur. In this paper, the topography of the flume bed was measured after the local scour reached an equilibrium state. The interaction between scour depth (\(d_{s}\)) and CKAW is discussed in detail in the following sections.