Document Type: Original/Review Paper


1 Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran.

2 Department of Architecture Engineering, University of Sistan and Baluchestan, Zahedan, Iran.

3 Department of Civil Engineering, Bozorgmehr University of Qaenat, Qaen, Iran.



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 in the literature to estimate the approximate scour depth. This research is aimed to study how 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 was estimated in non-cohesive soils based on a subcritical flow and live bed conditions using the artificial neural networks (ANN), 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 was formed and the data were divided into three random parts: 1) training, 2) validation and 3) testing 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 were then found and compared with those of the popular empirical formulations. Results revealed that the surrogate models’ test data estimations were more accurate than those of the empirical equations; Kriging has had better estimations than other models. In addition, sensitivity analyses of all surrogate models showed that the pier width’s dimensionless expression (b/y) had a greater effect on estimating the normalized scour depth (Ds/y).