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Publication Number:  FHWA-HRT-16-045    Date:  October 2016
Publication Number: FHWA-HRT-16-045
Date: October 2016


Updating HEC-18 Pier Scour Equations for Noncohesive Soils

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Balancing safety and cost is critical to smart investment when estimating scour at bridge piers in noncohesive soils. This report summarizes a study to improve techniques for estimating scour under a broad range of conditions using quantitative measures of reliability and accuracy. Attention is focused on situations with higher uncertainty including sites with coarse bed materials and bridge designs with pier groups. This study will provide improved guidance to bridge engineers involved with foundation design. The study described in this report was conducted at the Federal Highway Administration Turner-Fairbank Highway Research Center J. Sterling Jones Hydraulics Laboratory.

Mayela Sosa
Acting Director, Office of Infrastructure
Research and Development


This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation.

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers’ names appear in this report only because they are considered essential to the objective of the document.

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The Federal Highway Administration (FHWA) provides high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.


Technical Report Documentation Page

1. Report No.


2. Government Accession No. 3 Recipient's Catalog No.
4. Title and Subtitle

Updating HEC-18 Pier Scour Equations for Noncohesive Soils

5. Report Date

October 2016

6. Performing Organization Code
7. Author(s)

Haoyin Shan, Roger Kilgore, Jerry Shen, and Kornel Kerenyi

8. Performing Organization Report No.


9. Performing Organization Name and Address

2 Eaton Street, Suite 603
Hampton, VA 23669

10. Work Unit No. (TRAIS)

11. Contract or Grant No.
12. Sponsoring Agency Name and Address

Office of Infrastructure Research and Development
Federal Highway Administration
6300 Georgetown Pike
McLean, VA 22101-2296

13. Type of Report and Period Covered

Laboratory Report
January 2014–November 2015

14. Sponsoring Agency Code


15. Supplementary Notes

The Contracting Officer’s Technical Representative (COR) was Kornel Kerenyi (HRDI-50).

16. Abstract

A dataset of 594 bridge pier scour observations from two laboratory and three field studies was compiled. The dataset served as the testing ground for evaluating potential enhancements to the pier scour tools for noncohesive soils in Hydraulic Engineering Circular 18 (HEC-18). In the current (fifth) edition of HEC-18, there are two primary equations for pier scour in noncohesive soils. One is the general equation applicable to most situations, including clear water and live bed conditions. The second is a coarse bed material equation recommended only for use under clear water conditions with coarse bed materials. The objective of this research was to determine if the coarse bed materials equation could be used for conditions beyond those under which it is currently limited. A framework for evaluating the two equations was developed using qualitative and quantitative tools.

The coarse bed equation is referred to as the Hager number/gradation coefficient (HN/GC) equation because it references the use of both in the equation formulation. After adjusting the HN/GC equation to a target reliability index of 2.0, it was evaluated on its ability to predict scour for a wide range of conditions in noncohesive soils. Partitioned subsets of the data based on key conditions—including the HEC-18 coarse bed criteria, clear water versus live bed transport conditions, gradation, and median grain size—were used for the evaluation. The equation performed reasonably consistently in all partitioned datasets, leading to the conclusion that it may be used for a broader range of conditions. A subgroup of pier group scour observations was assessed to determine if the equation could also be used for pier groups. The equation performed better for single piers but offered a basis for predicting local scour at pier groups..

Considering these findings, the modified HN/GC equation is recommended for use on a broader range of noncohesive soil conditions for pier scour. Recommended limits for application of the equation are as follows: (1) clear water or live bed conditions (V1/Vc,50 < 5.2), (2) sands, gravels, and cobbles (0.0079 inches (0.2 mm) < D50 < 5 inches (127 mm)), (3) gradation coefficients ( σ ) less than 7.5, (4) Froude number less than 1.7, and (5) single piers.

17. Key Words

Bridge scour, local scour, pier scour, sediment gradation, nonuniform bed material, coarse bed material, reliability index, pier groups, Hager number.

18. Distribution Statement

No restrictions. This document is available to the public through the National Technical Information Service, Springfield, VA 22161.

19. Security Classification
(of this report)


20. Security Classification
(of this page)


21. No. of Pages


22. Price
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized

SI* (Modern Metric) Conversion Factors

Table of Contents

Chapter 1. Introduction

Chapter 2. Data Characteristics

Chapter 3. Analysis of Pier Scour

Chapter 4. Conclusions and Recommendations


List of Figures

Figure 1. Equation. Pier scour in coarse bed materials (HEC-18)

Figure 2. Equation. Hager number

Figure 3. Equation. General pier scour equation in HEC-18

Figure 4. Graph. Distribution of grain size classification

Figure 5. Equation. Laursen’s critical velocity equation

Figure 6. Equation. RI

Figure 7. Equation. Ratio of measured to predicted scour depth

Figure 8. Equation. RE

Figure 9. Equation. RRMSE

Figure 10. Equation. Dimensionless scour depth

Figure 11. Graph. Predicted versus measured scour: HEC-18 general pier scour equation

Figure 12. Graph. Predicted versus measured scour: HEC-18 coarse bed pier scour equation

Figure 13. Graph. Error versus bed load transport: general equation

Figure 14. Graph. Error versus bed load transport: coarse bed equation

Figure 15. Graph. Error versus y1/D50: general equation

Figure 16. Graph. Error versus y1/D50: coarse bed equation

Figure 17. Graph. Error versus gradation coefficient: general equation

Figure 18. Graph. Error versus gradation coefficient: coarse bed equation

Figure 19. Equation. HN/GC equation for pier scour with RI = 2.0

Figure 20. Graph. Predicted versus measured scour: HN/GC equation with RI = 2.0

List of Tables

Table 1. Data sources

Table 2. Noncohesive grain size classification for 594 pier scour observations

Table 3. Ratio of velocity to critical velocity

Table 4. Performance of HEC-18 general pier scour equation

Table 5. Performance of HEC-18 coarse bed equation

Table 6. Performance of the HN/GC equation with RI = 2.0

Table 7. Performance of the HN/GC equation on pier type with RI = 2.0

List of Symbols

a Pier diameter or width, ft (m)
D50 Median grain size of the sediment, ft (m)
D84 Grain size for which 84 percent (by weight) is smaller, ft (m)
Fr1 Froude number for approach flow, dimensionless
g Gravitational acceleration, ft/s2 (m/s2)
H Hager number (densimetric particle Froude number), dimensionless
K1 Correction factor for pier nose shape
K2 Correction factor for angle of attack of flow
K3 Correction factor for bed condition
Kw Correction factor for wide piers in shallow flow
Sg Specific gravity of the sediment, dimensionless
V1 Approach flow velocity, ft/s (m/s)
Vc,50 Critical velocity based on D50, ft/s (m/s)
y1 Approach flow depth, ft (m)
ys Scour depth, ft (m)
ys,m Measured scour depth, ft (m)
ys,p Predicted scour depth, ft (m)
σ Sediment gradation coefficient (D84/D50), dimensionless



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