Maximum scour depth estimation around side-by-side piers due to spacing effects for sustainable hydraulic infrastructure design

A lot of research has been done on single bridge piers using experimental, numerical or database-driven models. However, there have not been many studies on groups of piers placed next to each other in the cross-flow direction. This is important for bridge design, especially with increased traffic and new bridge structures being built. Closely spaced piers often have to be placed side by side to meet the growing traffic demand. This paper reviews past research on how water flows around side-by-side piers, focusing on its impact on scouring around the piers under clear water conditions. This paper thoroughly examines how various hydraulic factors, as discussed in previous studies, influence the maximum depth of scour ( d m ) including flow intensity, flow shallowness, sediment coarseness, constriction ratio, time, and side-by-side pier spacing . A new formula using Multiple Non-Linear Regression (MNLR) and Partial Least Squares Regression (PLSR) has been developed to determine d m around side-by-side piers and compared with the existing literature formulas. The formulas are evaluated using statistical parameters like correlation coefficient (R), Nash Sutcliffe Efficiency (NSE), Normalised Root Mean Squared Error (NRMSE), and Index Agreement (IA). Notably, the newly developed formula for side-by-side pier using MNLR shows the best performance with R= 0.93, NSE= 0.86, NRMSE= 0.09, IA= 0.96, and 96 % of values within ± 80 % accuracy. This study investigates flow structure interaction, based on how the pier spacing influences d m . The goal is to enhance the understanding of scour around side-by-side bridge piers, contributing to the development of resilient and sustainable infrastructure.