# Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data
## 4 Discussion  
In the present study, large, alluvial, and sand-bed rivers were taken into account with the intention of evaluating the significance of several influential variables in estimating maximum scour depth. Comparing four different categories, i.e., pier geometry (\(b_{\textit{of}}\)), hydraulic (\(y\), \(v\), \(\tau\), and \(Fr\)), sediment (\(\tau_{c}\), and \(Re_{p}\)), and compound hydraulic-sediment variables (\(v_{c}\), \(Fr_{c}\), and \(Fr_{d}\)), it was elucidated that pier geometry variables are the most influential ones. Rating pier geometry variables above hydraulic variables was expected because more than 70% of the data used in this study exceeds the threshold value of \(y/b_{\textit{of}}\) = 2.6, over which the flow depth is no longer significant for the pier scour process (52). The approach velocity and the flow depth have the next largest impact on scour depth, while local shear stress and Froude number remain the least important variables. The latter confirms the traditional approach assumptions that the equilibrium state of scour depth primarily depends on both the pier width and approach flow velocity, while flow depth is just an indirect effect of the downflow magnitude (38). The introduction of new hydraulic variables such as \(\tau\) and \(Fr\) is supposed not to significantly contribute to the variance of scour depth due to their unreliable estimation and small ranges of values. A similar conclusion can be drawn regarding the sediment variables. In this study, \(d_{50}\) was excluded from analysis, suspecting that it has a negligible effect, so two new sediment variables (\(\tau_{c}\), \(Re_{p}\)) were included in the scour depth equation. Even though it was expected that \(Re_{p}\) would play a more significant role owing to a larger standard deviation than \(d_{50}\), both sediment variables \(\tau_{c}\) and \(Re_{p}\) yielded the lowest Pearson correlation coefficients, which shed light on sediment properties in general (\(d_{50}\), \(\tau_{c}\), and \(Re_{p}\)) as being insignificant on scour depth variance. In order to consider the effect of sediment properties, it was recommended to use compound hydraulic-sediment variables such as \(v_{c}\), \(Fr_{c}\), and \(Fr_{d}\) that consist of both the acting forces of the flow and sediment properties. In this study, the compounded hydraulic-sediment variables and hydraulic variables had a similar impact on the scour prediction because the average values of their Pearson correlation coefficients were 0.408 and 0.340, respectively. A comparable observation was made by [PERSON] et al. (2019), who deem that shear Reynolds number, a function of grain size and shear velocity, is a more  
Figure 6: Pearson correlation coefficients (\(r\)) for selected influential variables that are classified into four variable categories. The selected variables are taken from the filtered dataset. adequate variable for evaluating sediment transport than \(Re_{p}\), \(d_{50}\), or other variables whose evaluation is based only on sediment properties. Furthermore, at the beginning of this paper, there was a doubt concerning which variable should be used to assess the incipient motion of sediment, \(v_{c}\) or \(\tau_{c}\). The doubt originates from the fact that \(v_{c}\) is a function of \(y\) and \(d_{50}\), while \(\tau_{c}\) is a function of \(d_{50}\). The assumption that the compound hydraulic-sediment variable would be more significant was verified by Pearson correlation coefficients of \(v_{c}\) and \(\tau_{c}\) with values of 0.474 and \(-\)0.006, respectively. After \(v_{c}\), which proved to be the most influential variable in the category of compound hydraulic-sediment variables, \(Fr_{d}\) and \(Fr_{c}\) are next in the sequence. It was expected that \(Fr_{d}\) would show a stronger association with scour depth since it has been previously determined as the most influencing variable in the group of variables that describe sediment properties [55; 56; 57]. The introduction of sediment variables into the scour depth equation showed negligible effects.