An Examination of the Dependency between Maximum Equilibrium Local Scour Depth and the Grain Size/Structure Size Ratio

Raphael Crowley,William Cottrell,Alexander Singleton

doi:10.3390/w12113117

Abstract

This paper begins by demonstrating how the Florida Department of Transportation (FDOT) local scour equations take the ratio between grain size and structure size into account when computing equilibrium local scour depth and contrasts this with the well-known Colorado State University (CSU) equation that does not take sediment information into account. Then, a relatively recent empirical formulation from the J-L. Briaud research group for computing local equilibrium scour depth is presented that appears to take the structure size/grain size ratio into account indirectly. Next, a possible explanation for the dependency between local equilibrium scour depth and the structure/grain size ratio is presented that was originally developed by D. Max Sheppard in 2004. This explanation shows that superimposing the pressure gradient around a particle with the pressure gradient around a pile leads to the dependency between equilibrium scour depth and the grain size/structure size ratio. Finally, a new formulation for local equilibrium scour depth based upon turbulent energy spectrum decay is presented. This new formulation reduces the local scour problem to a problem whereby turbulent diffusivity must be better understood. However, this new formulation also appears to show a dependency between equilibrium scour depth and the grain size/structure size ratio. Overall, the analysis presented herein provides several reasons, explanations, and pieces of evidence to suggest that the grain/structure size ratio is an important parameter to consider when computing local equilibrium scour depth.

Highlights

Introduction and Background InformationThe current set of design guidelines for scour, Hydraulic Engineering Circular No 18 Arneson, et al [1], presents two methods for predicting equilibrium local depths scour for steady flow around bridge foundations
This paper presented a review of steady flow local scour dependency on the ratio between structure size and grain size
As noted in this manuscript, the current state-of-the-art empirical formulations for steady flow equilibrium scour depth appear to take this ratio into account to some extent

Summary

Introduction

Introduction and Background InformationThe current set of design guidelines for scour, Hydraulic Engineering Circular No 18 Arneson, et al [1], presents two methods for predicting equilibrium local depths scour for steady flow around bridge foundations. Where ys is the scour depth; b is the pier width; yo is the upstream water depth; V is the upstream current; g is the acceleration due to gravity; and K1 , K2 , and K3 are correction factors for pier nose shape, current attack angle, and bed condition, respectively. This formulation assumes that local scour depth is y a function of local Froude Number (i.e., the √Vgy term) and bo only. As Mueller [8] noted, it frequently overpredicted observed scour

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