New Semiempirical Formula for Evaluating the Equilibrium Scour Depth at Bridge Piers

Estimating the equilibrium scour depth (yse) at bridge piers is essential for both bridge foundation design and flood risk assessment. Traditional methods typically rely on empirical formulas derived from data-fitting procedures, which often result in significant overestimations of the local scour phenomenon. While such conservative predictions may be acceptable for design purposes, they are less suitable for accurate risk evaluation. In this paper, we propose a new formula for predicting yse, grounded in a theoretical framework previously developed by one of the authors. This foundation is enhanced with empirically derived functions, obtained from laboratory data, to account for complex phenomena that remain difficult to capture theoretically, such as sediment nonuniformity. We demonstrate that the resulting semiempirical formula consistently outperforms five of the most widely used local scour methods in the literature. Predictive accuracy is evaluated through four different performance metrics, using more than 600 laboratory data and some selected field data whereby the formula could be confidently applied. The proposed approach provides unbiased estimates and avoids the systematic overestimations that characterize the reference methods, thus making it particularly suitable for risk assessment applications. Furthermore, the potential extension of the model to bridge design is discussed, proposing the introduction of an appropriate safety factor. Finally, we discuss the limitations of the proposed model and outline potential directions for future improvements.