Design of Riprap Stone Around Bridge Piers Using Empirical and Neural Network Method

Document Type : Research Papers


1 Ph.D. of Water Engineering, Civil and Environmental Department, Amirkabir University of Technology, P.O. Box 15915, Tehran, Iran

2 Professor, Civil and Environmental Department, Amirkabir University of Technology, P.O. Box 15915, Tehran, Iran


An attempt was made to develop a method for sizing stable riprap around bridge piers based on a huge amount of experimental data, which is available in the literature. All available experimental data for circular as well as round-nose-and-tail rectangular piers were collected. The data for rectangular piers, with different aspect ratios, aligned with the flow or skewed at different angles to the flow, were used in this analysis. In addition, new experiments were also conducted for larger pier width to riprap size ratio, which was not available in the literature. Based on at least 190 experimental data, the effect of important parameters on riprap stability were studied which showed that the effective pier width is the most effective parameter on riprap stability. In addition, an empirical equation was developed by multiple regression analysis to estimate the stable riprap stone size around bridge piers. The ratio of predicted to experiment riprap size value for all experimental data is larger than one with an average value of 1.75, which is less than many other empirical equations. Finally, in order to achieve a higher accuracy for riprap design, the artificial neural network (ANN) method based on utilizing non-dimensional parameters was deployed. The results showed that the ANN model provides around a 7% improved prediction for riprap size compared to the conventional regression formula.


Main Subjects

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  • Receive Date: 17 February 2014
  • Revise Date: 23 September 2014
  • Accept Date: 26 October 2014
  • First Publish Date: 01 June 2015