Comparison of the HEC-18, Melville, and Sheppard Pier Scour Equations

Abstract

Three frequently cited pier scour equations are the HEC-18 (also known as the CSU equation), Melville and Sheppard equations. Direct comparisons of these three equations were conducted for a wide range of realistic hydraulic, pier size and sediment size conditions. Each equation was applied following the procedure prescribed in the applicable manuals. The range of conditions was intended to cover the vast majority of pier scour calculations that would be encountered during scour evaluations. More than 2500 scour calculations were performed for each equation. This exercise was not meant to determine which equation is right, wrong, better, or worse. It was meant to give insight into the similarities and differences between the results of the equations and to address the topic of the perceived degree of conservativeness in pier scour calculations. Each of the equations predicts much greater or less scour than the other two depending on the specific input data. The Melville equation tends to produce the greatest scour and the Sheppard equation tends to produce the least. On average, the Melville equation computes scour over 30 percent more than the Sheppard equation and the HEC-18 equation computes scour approximately 15 percent more than the Sheppard equation. The majority of results were within +/- 30 percent for HEC-18 compared with Sheppard. One difference between the equations is that Sheppard includes a threshold velocity condition for pier scour, so it can predict zero scour for some conditions. Neither the HEC-18 nor Melville equations include this threshold velocity, so some amount of pier scour is always computed for these equations.