Developing new equations for maximum scour depth near tandem, side-by-side, and eccentric piers

There is a significant gap in the study of interference effects on side-by-side, tandem, and eccentric piers, which is critical for bridge design. This study investigates how hydraulic parameters affect the maximum scour depth ( d m ). These are pier spacings, flow intensity, flow shallowness, flow skew angle, sediment coarseness, sediment gradation, and time. Three different sets of equations are proposed to determine the d m around side-by-side, tandem, and eccentric piers, considering multiple factors and comparing them with existing literature. The accuracy of the equations is evaluated using statistical parameters such as correlation coefficient ( R), Nash-Sutcliffe efficiency (NSE), normalized root-mean-square-error (NRMSE), and index agreement (IA). The tandem front pier equation shows the highest accuracy with R = 0.91, NSE = 0.83, NRMSE = 0.23, and IA = 0.95. Likewise, the tandem rear pier equation excels in the highest accuracy with R = 0.83, NSE = 0.69, NRMSE = 0.31, and IA = 0.90. This research improves the robustness of scour prediction equations for two-piers by studying influential parameters.