Bridge pier scour depth modelling using experimental and machine learning approaches

This study compares three machine learning (ML) models: adaptive neuro-based fuzzy inference system (ANFIS), extra tree regression (ETR), and particle swarm optimisation with eXtreme gradient boosting (PSO-XGBoost). A dataset of 604 cases was used, including 589 from literature and 15 from experiments performed on circular bridge piers (4.0–8.0 cm) under clear water scouring conditions in fine sand. A gamma test identified the best input combination: pier width to flow depth (b/y), approach velocity to incipient velocity (V/Vc), Froude number (Fr), pier width to median sediment size (b/d50), and geometric standard deviation (σg). Among the tested models, PSO-XGBoost performed best, achieving R2 > 0.95, MAPE < 2.0%, and RMSE < 0.07. The study confirms that scour depth increases with pier diameter and is strongly influenced by flow conditions such as water depth and discharge. It also highlights the superiority of ML models over empirical methods, offering valuable support to bridge engineers in predicting scour depth and ensuring infrastructure safety.