Prediction of Maximum Scour Around Circular Bridge Piers Using Semi-Empirical and Machine Learning Models

Abstract

Local scour around bridge piers is one of the primary causes of structural failure in bridges. Therefore, this study focuses on addressing the estimation of maximum scour depth (dsm), which is essential for safe and resilient bridge design. Many studies in the last eight decades have included metadata collection and developed around 80 empirical formulas using various scour-affecting parameters of different ranges. To date, a total of 33 formulas have been comparatively analyzed and ranked based on their predictive accuracy. In this study, novel formulas using semi-empirical methods and gene expression programming (GEP) have been developed alongside an artificial neural network (ANN) model to accurately estimate dsm using 768 observed data points collected from published work, along with eight newly conducted experimental data points in the laboratory. These new formulas/models are systematically compared with 74 empirical literature formulas for their predictive capability. The influential parameters for predicting dsm are flow intensity, flow shallowness, sediment gradation, sediment coarseness, time, constriction ratio, and Froude number. Performances of the formulas are compared using different statistical metrics such as the coefficient of determination, Nash–Sutcliffe efficiency, mean bias error, and root-mean-squared error. The Gauss–Newton method is employed to solve the nonlinear least-squares problem to develop the semi-empirical formula that outperforms the literature formulas, except the formula from GEP, in terms of statistical performance metrics. However, the feed-forward ANN model outperformed the semi-empirical model during testing and validation phases, respectively, with higher CD (0.790 vs. 0.756), NSE (0.783 vs. 0.750), lower RMSE (0.289 vs. 0.301), and greater prediction accuracy (64.655% vs. 61.935%), providing approximately 15–18% greater accuracy with minimal errors and narrower uncertainty bands. Using user-friendly tools and a strong semi-empirical model, which requires no coding skills, can assist designers and engineers in making accurate predictions in practical bridge design and safety planning.