Local scour around bridge abutments in vegetated beds under ice-covered flow conditions – An experimental study and mathematical assessment using machine learning methods

• The first investigation of local scour at bridge abutments under ice-covered flow in vegetated channel bed. • The cover roughness, abutment shape and vegetation density are critical factors affecting the scour depth. • Using various machine learning techniques, two formulas have been created to accurately predict the maximum scour depth. Local scour around bridge abutments is a critical process that can cause bridge failures, posing substantial environmental risks. Accurate estimation of the maximum scour depth around bridge abutments is crucial for bridge design. In the current study, extensive experiments have been conducted in a large-scale outdoor flume to investigate local scour around the bridge in the presence of vegetation in the channel bed and ice cover on the water surface. Different layout vegetation patterns and densities, water surface cover conditions, abutment shapes, and particle size of bed material are considered. Based on data collected from laboratory experiments, this study employs machine learning methods, including Artificial Neural Networks (ANN), Support Vector Machines (SVM), Multiple Linear Regression (MLR), and Gene Expression Programming (GEP), to predict the maximum scour depth around the abutments, with the GEP model showing the highest accuracy. Results revealed deeper scour with higher Froude numbers, rectangular abutments, and increased ice roughness, while coarser sediments and dense, staggered vegetation reduced scour. Sensitivity analysis using the Partial Mutual Information (PMI) and SHAP (SHapley Additive exPlanations) captured the effects of key variables affecting the maximum scour depth around abutments, including flow Froude number (Fr), the ratio of median grain size of bed material to flow depth (d 50 /H), the standard deviation of sediments (σ g ), the ratio of ice cover roughness coefficient to that of channel bed (n I /n B ), abutment shape factor (K s ), and vegetation roughness density (λ). Two predictive formulas were developed for use in vegetated, ice-covered channels.