Prediction of scour depth around bridge abutments with different shapes using machine learning models

Accurate assessment of scour depth around bridge abutments is crucial for the reasonable design of abutment structures. Due to the complexity of the scour process, it is difficult to utilize the traditional empirical equations to achieve the precise estimation. This study implements Machine Learning (ML) models including M5' Model Tree (M5'MT), Multivariate Adaptive Regression Spline (MARS), Locally Weighted Polynomial Regression (LWPR) and Multigene Genetic Programming (MGGP) to predict the scour depth around bridge abutments with shapes of the vertical-wall, 45? wing-wall and semicircular. Literature experimental data is adopted with four input parameters including excess abutment Froude number (F-e), relative sediment size (d(50)/l), relative submergence (d(50)/h) and relative flow depth (h/l) considered for the prediction of relative scour depth (d(s)/l) with l defined as the transverse abutment length. The optimal input combination for each model is firstly determined using the correlation analysis and sensitivity analysis, based on which the results from MGGP presents the best agreement with the experimental data for the vertical-wall and semicircular abutments, while LWPR outperforms the other models for the 45? wing-wall abutment. Besides, comparing with the empirical equations and ML models employed in the literature, the accuracy of scour depth prediction is significantly improved with the ML models implemented in this study. Finally, the uncertainty analysis is conducted and further validates the superiority of the implemented ML models. Considering the comprehensive performance for all types of abutments in terms of accuracy, reliability and interpretability, MGGP is recommended as the representative of the implemented ML models with its MAPE of 2.40% for vertical-wall abutment, 3.95% for 45? wing-wall abutment, and 3.85% for semicircular abutment.