Mohammad Vaghefi

This paper explores the impact of an apron in mitigating scour downstream of a trapezoidal PK weir through an experimental study. Three apron lengths were tested with two sediment types under varying hydraulic conditions to address local scouring. Results show that longer aprons reduce scouring, especially at lower densimetric Froude numbers, affecting the location of the maximum scour depth and its volume. On average, apron lengths of 1 P, 1.5 P, and 2 P (P is weir height) decrease the scour hole areas and volumes by approximately 69–77 %. Scour indices decrease by 73–90 % for corresponding apron lengths. New empirical equations have been proposed to aid in apron design, and the estimation of various scour hole geometries. Bayesian Optimized Neural Network (BONN), Extreme Gradient Boosting model tuned by Optuna algorithm (XGBoost-Optuna), and Random Forest were also developed for forecasting scour hole characteristics in the presence of apron. Various regression tests, including residual plots and uncertainty quantification, were imposed to compare the models. The results demonstrated that the XGBoost-Optuna model outperformed the other models, achieving a correlation coefficient ranging from 0.924 to 0.985, a root mean squared error between 0.055 and 5.072, and a mean relative percentage error of 7.14–11.71 %. Most forecasts generated by the XGBoost-Optuna model fell within ±20 % error margins, highlighting its superiority in predicting scour hole characteristics in the presence of the apron for PK weirs.