Throughout the lifespan of a bridge, morphological changes in the riverbed affect the variable action-imposed loads on the structure. This emphasizes the need for accurate and reliable data that can be used in model-based projections targeted for the identification of risk associated with bridge failure induced by scour. The aim of this paper is to provide an analysis of scour depth estimation on large sand-bed rivers under the clear water regime, detect the most influential (i.e., explanatory) variables, and examine the relationship between them and scour depth as a response variable. A dataset used for the analysis was obtained from the United States Geological Survey’s extensive field database of local scour at bridge piers, i.e., the Pier-Scour Database (PSDB-2014). The original database was filtered to exclude the data that did not reflect large sand-bed rivers, and several influential variables were omitted by using the principal component analysis. This reduction process resulted in 10 influential variables that were used in multiple non-linear regression scour modeling (MNLR). Two MNLR models (i.e., non- dimensional and dimensional models) were prepared for scour estimation ; however, the dimensional model slightly overperformed the other one. According to the Pearson correlation coefficients (r), the most influential variables for estimating scour depth were as follows: Effective pier width (r = 0.625), flow depth (r = 0.492), and critical and local velocity (r = 0.474 and r = 0.436), respectively. In the compounded hydraulic-sediment category, critical velocity had the greatest impact (i.e., the highest correlation coefficient) on scour depth in comparison to densimetric Froude and critical Froude numbers that were characterized by correlation coefficients of r = 0.427 and r = 0.323, respectively. The remaining four variables (local and critical bed shear stress, Froude number, and particle Reynolds number) exhibited a very weak correlation with scour depth, with r < 0.3.