Prediction of Maximum Scour around Circular Bridge Piers using Semi-Empirical and Machine Learning Models

Local scour around bridge piers is a leading cause of structural failure. Therefore, the estimation of maximal scour depth (dsm) is essential. 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 maximum 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 metadata points collected from 40 literatures, along with eight newly conducted experimental data in the laboratory. These new formulas/model are systematically compared with 74 empirical literature formulas for their predictive capability. The influential parameters for predicting dsm, in this study, are flow intensity, flow shallowness, sediment gradation, sediment coarseness, time, constriction ratio, and Froude number. Performances of the formulas/models 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 was found to be the best model among all, 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.