Estimation of Clear-Water Local Scour at Pile Groups Using Genetic Expression Programming and Multivariate Adaptive Regression Splines

Abstract

The physical process of scour around pile groups is complex. Due to economical and geotechnical considerations, multiple pile bridge piers have become more common in bridge designs. Various empirical models have been developed to estimate scour depth at pile groups. However, these models are mostly based on the conventional statistical regression approaches and are not able to adequately capture the highly nonlinear and complex relationship between scour depth and its influential factors. In this study, genetic expression programming (GEP) and multivariate adaptive regression splines (MARS) were utilized to estimate clear-water local scour depth at pile groups using the flow, sediment, and pile characteristics. Two combinations of data were used to train the GEP and MARS models. The first combination included dimensional variables (e.g., mean flow velocity and depth, mean grain diameter, pile diameter). The second combination contained nondimensional parameters. Results indicated that GEP and MARS can accurately estimate scour depth. Both models yielded better results when the dimensional data were used. In addition, the MARS model with a root mean square error (RMSE) of 0.0220 m and correlation coefficient (R2) of 0.902 outperformed the GEP model with an RMSE of 0.0285 m and R2 of 0.834. Performance of the GEP and MARS models was compared with that of the existing equations. The comparison showed that both models perform better than the regression-based empirical equations. Finally, a sensitivity analysis showed that pile diameter has the most significant impact on equilibrium scour depth.