Riprap incipient motion for overtopping flows with machine learning models

Riprap stones are frequently applied to protect rivers and channels against erosion processes. Many empirical equations have been proposed in the past to estimate the unit discharge at the failure circumstance of riprap layers. However, these equations lack general impact due to the limited range of experimental variables. To overcome these shortcomings, support vector machine (SVM), multivariate adaptive regression splines (MARS), and random forest (RF) techniques have been applied in this study to estimate the approach densimetric Froude number at the incipient motion of riprap stones. Riprap stone size, streambank slope, uniformity coefficient of riprap layer stone, specific density of stones, and thickness of riprap layer have been considered as controlling variables. Quantitative performances of the artificial intelligence (AI) models have been assessed by many statistical measures including: coefficient of correlation (R), root mean square error (RMSE), mean absolute error (MAE), and scatter index (SI). Statistical performance of AI models indicated that SVM model with radial basis function (RBF) kernel had better performance (SI = 0.37) than MARS (SI = 0.75) and RF (SI = 0.63) techniques. The proposed AI models performed better than existing empirical equations. From a parametric study the results demonstrated that the erosion-critical stone-referred Froude number (Fs,c) is mainly controlled by the streambank slope.