Riprap Design for Bridge Piers Using Nonparametric Models

In this study, bridge pier riprap sizing has been derived using new data mining techniques. Classification and regression tree (CART) and multivariate adaptive regression splines (MARS) were used to design a stable riprap size around bridge piers. The dimensionless parameters of pier shape factor (Ks), Froude number (Fr), pier width to flow depth ratio (b/y), specific gravity (1-Sg), riprap layers (n) and placement of riprap mattress to original sediment bed level (1-d/y) as input data and the riprap diameter to flow depth ratio (DR/y) as output one, were employed for training and testing the models. The applied models had similar performances in the training phase, while the results of testing phase showed better performance for the CART model. Some of the riprap stability equations and statistical criteria were used to investigate the performance of the applied models. The statistical analysis showed that the CART model had a better performance than the other equations, so that its sum of squares error value reduced to one-third, with respect to the Hec18 equation. In addition, the accuracy of the CART model was 88% which was 15% more than that of the Hec-18 equation. Sensitivity analysis on the CART model indicated that the Froude number and pier width to flow depth ratio had the highest effects on riprap stability.