Estimating Pier Scour Depth: Comparison of Empirical Formulations with ANNs, GMDH, MARS, and Kriging

Scouring, occurring when the water flow erodes the bed materials around the bridge pier structure, is a serious safety assessment problem for which there are many equations and models available in the literature in order to estimate the approximate scour depth. This research work is aimed to study how the surrogate models estimate the scour depth around circular piers, and compare the results with those of the empirical formulations. To this end, the pier scour depth is estimated in non-cohesive soils based on a sub-critical flow and live bed conditions using the artificial neural networks (ANNs), group method of data handling (GMDH), multivariate adaptive regression splines (MARS), and Gaussian process models (Kriging). A database containing 246 lab data gathered from various studies is formed, and the data is divided into three random parts: 1) training, 2) validation, and 3) testing in order to build the surrogate models. The statistical error criteria such as the coefficient of determination (R2), root mean squared error (RMSE), mean absolute percentage error (MAPE), and absolute maximum percentage error (MPE) of the surrogate models are then found and compared with those of the popular empirical formulations. The results obtained reveal that the surrogate models‘ test data estimations are more accurate than those of the empirical equations; Kriging has better estimations than the other models. In addition, the sensitivity analyses of all the surrogate models show that the pier width‘s dimensionless expression (b/y) has a greater effect on estimating the normalized scour depth (Ds/y).