# Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data
## 2 Methodology
### Variable Reduction
Based on the PCA results, 5 variables were discarded from further analyses, and all remaining variables can be classified into the following categories: pier geometry (_b_, \(l\), and _b_eff), hydraulic (_y_, \(v\), _\(\tau\)_, and _Fr_), compounded hydraulic-sediment variables (_v_, _Fr_, and _Fr_d), sediment properties (_d_50, \(r\), and _Re_p), and channel properties (_B_ and _S_). Previous studies have concluded that \(d\)50 can be eliminated from the development of the scour equation since its range of values is small when compared to the other variables, which consequently leads to biased results [19]. Since only field data are used in this study, \(d\)50 is expected to be negligible due to reaching large values of the ratio _b_/_d_50 [45,46]. In order to obtain information on sediment properties, only \(\tau\)c and Rep were retained for developing the equation, while \(d\)50 was discarded. Figure 2: Results of PCA analysis: (**a**) Loading plot that presents a total of 21 variables in the coordinate system with the first two principal components on the axes; (**b**) Contribution of each variable to the retained first three principal components throughout the squared cosines of the variables. Values in bold correspond for each variable to the principal component for which the squared cosine is the largest. Similarly, the variables describing pier geometry (\(\theta\), \(b\), \(l\) and \(b_{\mathit{ef}}\)) are also close together. The angle of flow attack (\(\theta\)) is not a reliable variable for scour prediction because flow direction depends on the water level and changes over time. This makes the measurement of \(\theta\) arbitrary and should be used only when it can be reliably estimated [24]. The former debate was supported by the PCA results, which suggested that \(\theta\) and \(l\) should not be used in scour prediction, leaving \(b\) and \(b_{\mathit{ef}}\) as the only descriptors of pier geometry. Taking into consideration the difficult approximation of complex pier geometry (in the case of a group of piers, pile caps, etc. ), this study uses \(b_{\mathit{ef}}\) as the pier geometry variable, which is reduced to b when no other data is known but can be adjusted for pier alignment when necessary. Both variables from the channel properties category (\(B\) and \(S\)) can be excluded. Although river width was an important variable for validating the filter applied to obtain a database corresponding to the large rivers, it is not necessary to include it in the development of the equation since this paper focuses on local scour. Stream slope is a local variable, originally measured in PSDB-2014 near the bridge. Since \(S\) was only used for estimating shear stress, a variable that estimates the drag force of flowing water, it can be eliminated from scour equation development. The remaining variables are a combination of commonly used variables in scour prediction as well as variables that are rarely used in scour research on field conditions (\(\tau\), \(\tau_{c}\), \(Re_{p}\)). Although \(\tau\) has been previously recognized as an influential variable for scour prediction [47], it is usually omitted from conventional scour equations due to difficulties in obtaining direct measurements in a complex flow environment [19]. However, \(\tau\) and \(v\) are both variables that reflect drag forces in front of the pier. Since it is challenging to measure \(v\) in situ during the flood, perhaps it can be replaced by \(\tau\). Locally measured variables (\(y\) and \(S\)) in the original PSDB-2014 database allow \(\tau\) to be estimated for each pier. Since it is not sufficiently investigated how much local value of \(\tau\) contributes to \(d_{s}\) compared to \(v\), its importance for the local scour process will be evaluated in this study. The incipient motion of sediment starts when \(\tau\) exceeds the critical shear stress (\(\tau_{c}\)). Instead, in equations for estimating scour depth, \(v_{c}\) is mainly used because it is easier to measure and is proportional to \(\tau_{c}\).