Potential-Scour Assessments and 

Estimates of Scour Depth Using Different 

Techniques at Selected Bridge Sites in 

Missouri

By Richard J. Huizinga and Paul H. Rydlund, Jr.

U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the Missouri Department of Transportation

Scientific Investigations Report 2004–5213
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2004

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

For more information about the USGS and its products:

Telephone: 1-888-ASK-USGS

World Wide Web: http://www.usgs.gov/

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to reproduce any copyrighted materials contained within this report.

Suggested citation: 

Huizinga, R.J., and Rydlund, P.H., Jr., 2004, Potential-scour assessments and estimates of scour depth using different

techniques at selected bridge sites in Missouri: U.S. Geological Survey Scientific Investigations Report 2004–5213, 42 p.
iii

Contents

Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

History of Scour Studies in Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Purpose and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Study Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Potential-Scour Assessments (Level 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Estimates of Scour Depth Using Different Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Rapid Estimation Method (Level 1+) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Special Variables Needed for Application in Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Determination of Average Bed Location for Referencing Average Depth. . . . . . . . . . . . . . . . . . . . . . . . 10

Modification of Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Road Overflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Presence of Additional Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Sites Located in the Mississippi Alluvial Plain Region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

General Procedure of Level 1+ Assessments in Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Scour Predictor Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Final Qualitative Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Detailed Hydraulic Assessments (Level 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Hydraulic Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Contraction Scour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Pier Scour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Abutment Scour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Reports. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Comparison of Level 1+ Results to Level 2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Contraction Scour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Main Channel Contraction Scour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Overbank Contraction Scour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Discussion of Contraction Scour Depth Estimate Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Pier Scour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Abutment Scour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Validation of Level 1+ Procedures Using Level 2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Average Main Channel Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Difference in Water-Surface Elevation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Determination of Road Overflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

General Limitations of Scour Depth Estimation Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Verification of Scour Depth Estimates Using Field Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Scour Depth as a Function of Flood Duration in Cohesive Soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Assumption of Soil Homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Accuracy and Consistency of Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
iv

Figures

1–3. Maps showing—

1. Highway districts and major physiographic regions of Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

2. Distribution of potential-scour assessment (Level 1) sites in Missouri. . . . . . . . . . . . . . . . . . . . . . . . . .8

3. Distribution of rapid estimation method (Level 1+) sites in Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . .9

4. Definition sketch of average flow area, average bed, and average flow depth as used in

rapid estimation assessment (Level 1+) in Missouri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5. Map showing distribution of detailed hydraulic assessment (Level 2) sites in Missouri . . . . . . . . . . . . 18

6–15. Graphs showing—

6. Contraction and local pier scour depths for simulated maximum discharge of 1,000,000

cubic feet per second through Horse Island Chute bridge near Chester, Illinois. . . . . . . . . . . . . . 22

7. Total scour depths for three discharge simulations through Horse Island Chute bridge

near Chester, Illinois . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

8. Comparison of discharge through bridge used in rapid estimation assessment (Level 1+) 

with that used in detailed hydraulic assessment (Level 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

9. Comparison of average main channel contraction scour depths determined by rapid

estimation assessment (Level 1+) with those determined by detailed hydraulic 

assessment (Level 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

10. Comparison of average overbank contraction scour depths determined by rapid

estimation assessment (Level 1+) with those determined by detailed hydraulic 

assessment ( Level 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

11. Comparison of average pier scour depths determined by rapid estimation assessment 

(Level 1+) with those determined by detailed hydraulic assessment (Level 2) . . . . . . . . . . . . . . . . 30

12. Comparison of average abutment scour depths determined by rapid estimation

assessment (Level 1+) with those determined by detailed hydraulic assessment (Level 2) . . . 32

13. Relation between unit discharge (q2) and average main channel velocity at bridge (V2) 

for selected sites in Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

14. Relation between average main channel velocity at bridge squared (V2

2

) and difference in 

water-surface elevation between bridge and approach sections (∆h) for selected sites 

in Missouri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

15. Comparison of 100-year peak discharge through bridge estimated using rapid estimation 

assessment (Level 1+) equation with that determined in detailed hydraulic assessment 

(Level 2) for bridges with impendent road-overtopping discharge less than 100-year 

peak discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

16. Relation between scour depth estimated using the Colorado State University equation and 

the residual (measured scour minus the estimated scour depth) at selected sites in 

Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Tables

1. Number of bridges that received potential-scour (Level 1), rapid estimation (Level 1+), 

and detailed hydraulic (Level 2) assessments, grouped by Missouri Department of 

Transportation (MoDOT) district . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

2. Bridge site information, potential and observed scour index values, scour susceptibility,

and subsequent rapid estimation (Level 1+) or detailed hydraulic (Level 2) assessments

of bridges that received a potential-scour assessment (Level 1) in Missouri . . . . . . . . . . . . . . . . . . . . . . .CD

3. Bridge site information and estimated scour depths from rapid estimation assessments 

(Level 1+ ) in Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CD
v

4. Summary of rapid estimation assessments (Level 1+) and resultant detailed hydraulic 

assessment (Level 2) candidates by Missouri Department of Transportation (MoDOT) district. . . . . 17

5. Bridge site information and computed scour depths from detailed hydraulic assessments 

(Level 2) in Missouri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CD

6. Summary of detailed hydraulic assessments (Level 2) by Missouri Department of

Transportation (MoDOT) district . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

7. Summary of discharge data, measured scour depths, and scour depths estimated using various 

methods at selected sites in Missouri. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
vi

Conversion Factors and Datum

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

Area

square foot (ft2

) 929.0 square centimeter (cm2)

square foot (ft2

) 0.09290 square meter (m2)

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2)

Flow rate

foot per second (ft/s) 0.3048 meter per second (m/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Hydraulic gradient

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

Unit discharge*

cubic foot per second per foot [(ft3

/s)/

ft] 0.09290

cubic meter per second per meter 

[(m3/s)/m]

Acceleration

foot per second squared (ft/s2) 0.3048 meter per second squared (m/s2)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F = (1.8 x °C) + 32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C = (°F - 32) / 1.8

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

*Unit discharge: The standard unit for unit discharge is cubic foot per second per foot [(ft3/s)/ft]. 

In this report, the mathematically reduced form, foot squared per second (ft2/s), is used for convenience.
Potential-Scour Assessments and Estimates of Scour 

Depth Using Different Techniques at Selected Bridge 

Sites in Missouri

By Richard J. Huizinga and Paul H. Rydlund, Jr.

Abstract

The evaluation of scour at bridges throughout the state of 

Missouri has been ongoing since 1991 in a cooperative effort by 

the U.S. Geological Survey and Missouri Department of Transportation. A variety of assessment methods have been used to 

identify bridges susceptible to scour and to estimate scour 

depths. A potential-scour assessment (Level 1) was used at 

3,082 bridges to identify bridges that might be susceptible to 

scour. A rapid estimation method (Level 1+) was used to estimate contraction, pier, and abutment scour depths at 1,396 

bridge sites to identify bridges that might be scour critical. A 

detailed hydraulic assessment (Level 2) was used to compute 

contraction, pier, and abutment scour depths at 398 bridges to 

determine which bridges are scour critical and would require 

further monitoring or application of scour countermeasures.

The rapid estimation method (Level 1+) was designed to 

be a conservative estimator of scour depths compared to depths 

computed by a detailed hydraulic assessment (Level 2). 

Detailed hydraulic assessments were performed at 316 bridges 

that also had received a rapid estimation assessment, providing 

a broad data base to compare the two scour assessment methods. The scour depths computed by each of the two methods 

were compared for bridges that had similar discharges. For Missouri, the rapid estimation method (Level 1+) did not provide a 

reasonable conservative estimate of the detailed hydraulic 

assessment (Level 2) scour depths for contraction scour, but the 

discrepancy was the result of using different values for variables that were common to both of the assessment methods. The 

rapid estimation method (Level 1+) was a reasonable conservative estimator of the detailed hydraulic assessment (Level 2) 

scour depths for pier scour if the pier width is used for piers 

without footing exposure and the footing width is used for piers 

with footing exposure. Detailed hydraulic assessment (Level 2) 

scour depths were conservatively estimated by the rapid estimation method (Level 1+) for abutment scour, but there was substantial variability in the estimates and several substantial 

underestimations.

Introduction

Scour is the removal of the channel bed and bank material 

by flowing water, and is the leading cause of bridge failures in 

the United States (Richardson and Davis, 2001). Total scour is 

divided into three primary components: general scour, which 

refers to long-term geomorphicological processes that cause 

degradation (lowering), aggradation (filling), or lateral shifting 

of the natural channel; contraction scour, which refers to the 

erosion of material that occurs when the cross-sectional flow 

area of the stream is reduced or contracted; and local scour, 

which refers to the localized erosion of material caused by flow 

vortex action that forms near bridge piers and abutments (Richardson and others, 1991, 1993; Richardson and Davis, 1995, 

2001; Holnbeck and Parrett, 1997). Although scour processes 

continually are at work, the processes are accelerated during 

high-flow conditions, and the potential for scour-related problems at a bridge tend to increase during such events.

History of Scour Studies in Missouri

In 1988, the Federal Highway Administration (FHWA) 

recommended that “every bridge over a scourable stream, 

whether existing or under design, should be evaluated as to its 

vulnerability to floods in order to determine the prudent measures to be taken for its protection” (U.S. Federal Highway 

Administration, 1988). In 1991, the U.S. Geological Survey 

(USGS) and the Missouri Department of Transportation 

(MoDOT) began a cooperative study to accomplish two goals: 

(1) to develop and use a suitable screening process to identify 

“scour-susceptible” bridges, and (2) for bridges identified as 

“scour-susceptible,” perform a detailed hydraulic evaluation 

and estimate values of scour using accepted hydraulic techniques. The hydraulic information can be used by MoDOT for 

possible implementation of countermeasures. The term “scoursusceptible” describes a bridge that is deemed potentially unstable because abutment and/or pier foundations have the potential 

to be undermined by erosion of the channel bed or banks (U.S. 

Federal Highway Administration, 1988).

The FHWA categorizes scour assessments into three levels, depending on complexity (Lagasse and others, 1991):
2 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

• Level 1: A qualitative analysis of stream characteristics, simple geomorphic concepts, and other qualitative 

indicators to assess the scour potential of a bridge.

• Level 2: An application of hydrologic, hydraulic, and 

sediment transport concepts to determine quantitative 

scour-depth estimates.

• Level 3: An application of mathematical or physical 

modeling studies (used only for investigation of highly 

complex situations, because of the additional expense 

and time required).

All three of these levels were used in the study in Missouri: 

Level 1-type potential-scour assessments (hereinafter referred 

to as “Level 1”) were used to meet the first goal of the study, and 

Level 2-type detailed hydraulic assessments (hereinafter 

referred to as “Level 2”) were used to meet the second goal of 

the study, with a quasi-Level 3 analysis used at one hydraulically complex site described in Huizinga and Rydlund (2001). 

The Level 1 assessments identified 1,327 bridges as scoursusceptible. As a way to reach the second goal of the study and 

to meet time-frame requirements established by the FHWA, a 

rapid estimation method (hereinafter referred to as “Level 1+”) 

developed by the USGS in Montana (Holnbeck and Parrett, 

1997) was used to evaluate bridges deemed scour-susceptible 

by the Level 1 assessment to identify bridges that might be 

scour critical. In 2002, 104 bridges were identified that had not 

been assessed for scour-susceptibility; these bridges received a 

Level 1+ assessment without a Level 1 assessment. In all, Level 

1 assessments were performed at 3,082 bridges, Level 1+ 

assessments were performed at 1,396 bridges, and Level 2 

assessments were performed at 398 bridges (of which 316 also 

received a Level 1+ assessment). The number of bridges that 

received each type of assessment, grouped by MoDOT district 

and county in Missouri, are shown in table 1.

Table 1. Number of bridges that received potential-scour (Level 1), rapid estimation (Level 1+), and detailed hydraulic 

(Level 2) assessments, grouped by Missouri Department of Transportation (MoDOT) district.

[--, no bridges]

County

(fig. 1)

Bridges that received 

Level 1 assessment

Bridges that received 

Level 1+ assessment

Bridges that received 

Level 2 assessment

MoDOT District 01

Andrew 27 14 7

Atchison 51 14 7

Buchanan 45 4 1

Caldwell 23 11 4

Clinton 11 1 1

Daviess 37 21 11

De Kalb 32 16 7

Gentry -- 29 18

Harrison 53 19 8

Holt 47 9 7

Nodaway 58 24 13

Worth 13 8 3

Total 397 170 87

MoDOT District 02

Adair 32 11 4

Carroll 58 30 17

Chariton 48 11 11

Grundy 27 19 7

Howard 28 4 1

Linn 53 15 8

Livingston 40 17 11

Macon 33 8 5

Mercer 23 14 9

Putnam 28 14 6

Randolph 17 3 2

Saline 39 1 2

Schuyler 28 6 3

Sullivan 31 18 10

Total 485 171 96
Introduction 3

MoDOT District 03

Audrain 24 9 6

Clark 18 5 5

Knox 22 8 3

Lewis 19 4 3

Lincoln 32 9 2

Marion 15 7 --

Monroe 16 9 1

Montgomery 18 9 4

Pike 16 7 4

Ralls 14 6 --

Scotland 28 8 7

Shelby 18 6 3

Warren 19 8 4

Total 259 95 42

MoDOT District 04

Cass 26 2 --

Clay 49 19 5

Henry 27 10 3

Jackson 57 15 9

Johnson 42 5 1

Lafayette 53 3 --

Platte 47 18 7

Ray 36 11 6

Total 337 83 31

MoDOT District 05

Benton 3 4 --

Boone 35 16 1

Callaway 32 19 6

Camden 12 2 --

Cole 19 12 11

Cooper 26 10 5

Gasconade 17 7 3

Maries 10 7 2

Miller 13 8 5

Moniteau 5 2 2

Morgan 3 2 1

Osage 16 12 2

Pettis 17 13 6

Total 208 114 44

MoDOT District 06

Franklin 37 11 2

Jefferson 45 21 2

St. Charles 25 13 4

St. Louis 60 49 12

St. Louis City 4 2 --

Total 171 96 20

Table 1. Number of bridges that received potential-scour (Level 1), rapid estimation (Level 1+), and detailed hydraulic 

(Level 2) assessments, grouped by Missouri Department of Transportation (MoDOT) district.—Continued

[--, no bridges]

County

(fig. 1)

Bridges that received 

Level 1 assessment

Bridges that received 

Level 1+ assessment

Bridges that received 

Level 2 assessment
4 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

MoDOT District 07

Barry 5 4 --

Barton 10 1 --

Bates 30 9 1

Cedar 8 2 --

Dade 5 3 --

Jasper 34 14 --

Lawrence 27 17 2

McDonald 19 17 1

Newton 19 10 --

St. Clair 8 8 --

Vernon 33 8 --

Total 198 93 4

MoDOT District 08

Christian 10 4 --

Dallas 5 7 1

Douglas 1 1 --

Greene 18 13 --

Hickory 2 1 --

Laclede 12 3 1

Ozark 7 5 1

Polk 7 3 --

Stone 6 3 --

Taney 7 6 --

Webster 6 3 1

Wright 6 3 1

Total 87 52 5

MoDOT District 09

Carter 8 3 1

Crawford 10 3 --

Dent 17 1 1

Howell 17 7 --

Iron 10 7 1

Oregon 15 12 3

Phelps 13 4 --

Pulaski 11 1 --

Reynolds 18 5 --

Ripley 23 16 5

Shannon 11 6 --

Texas 11 4 --

Washington 9 9 --

Total 173 78 11

MoDOT District 10

Bollinger 26 16 2

Butler 77 33 2

Cape Girardeau 59 32 6

Dunklin 83 67 8

Madison 11 3 --

Mississippi 45 1 --

Table 1. Number of bridges that received potential-scour (Level 1), rapid estimation (Level 1+), and detailed hydraulic 

(Level 2) assessments, grouped by Missouri Department of Transportation (MoDOT) district.—Continued

[--, no bridges]

County

(fig. 1)

Bridges that received 

Level 1 assessment

Bridges that received 

Level 1+ assessment

Bridges that received 

Level 2 assessment
Potential-Scour Assessments (Level 1) 5

Purpose and Scope

The purpose of this report is to describe potential-scour 

assessments and estimates of scour depth at selected bridge sites 

in Missouri. Results of the Level 1, Level 1+, and Level 2 

assessments performed during a 13-year study in Missouri are 

presented. This report describes the methods used to obtain 

Level 1+ and Level 2 scour depth estimates, and compares the 

results of the two methods at 316 bridges.

In the comparison, scour depths determined by the Level 

1+ method are compared against depths determined by the 

Level 2 method (the reference base). Depths determined by the 

Level 1+ method that are less than depths determined by the 

Level 2 method are therefore referred to as “underestimates” in 

this report, whereas depths greater than the Level 2 estimates 

are referred to as “overestimates.”

Study Area

The study area includes the state of Missouri, which contains 114 counties and the city of St. Louis. MoDOT has divided 

the State into 10 highway districts (fig. 1). Missouri has a total 

area of 69,674 square miles, and consists of parts of three major 

physiographic regions: the Central Lowlands, the Ozark Plateaus, 

and the Mississippi Alluvial Plain (Fenneman, 1938) (fig. 1).

Approximately 45 percent of the study area is in the Central Lowlands region, predominantly in the northwestern part of 

the State, north of the Missouri River (fig. 1). Elevations in this 

region range from 600 to 1,200 feet above the North American 

Vertical Datum of 1988 (NAVD 88), and the area has numerous 

wide, flat valleys incised by rivers (Alexander and Wilson, 

1995; Hauck and Nagel, 2003). This region is made up of loess 

or clayey glacial till soils overlying sedimentary shales, limestones, and dolomites. Streambeds in this region primarily are 

made up of very fine gravels, sands, and cohesive soils.

Approximately 45 percent of the study area is in the Ozark 

Plateaus region in the south-central part of the State (fig. 1). 

This region typically is wooded, rugged, and has deep narrow 

valleys separated by sharp ridges. Elevations in this region 

range from about 800 to 1,700 feet above NAVD 88 (Alexander 

and Wilson, 1995; Fenneman, 1938; Hauck and Nagel, 2003). 

It primarily is composed of limestone and dolomite layers interspersed with sandstone and shale layers, overlying igneous 

rocks that in one location protrude through the layers to form 

the St. Francois Mountains in the southeastern part of the state. 

The limestone and dolomite layers contain cherty material that 

often is present in the streambeds in this region. 

In the extreme southeast part of the State is the Mississippi 

Alluvial Plain region (fig. 1). About 10 percent of the State’s 

area is in this region, which consists of well-drained alluvial 

deposits that are relatively flat, with elevations ranging from 

200 to 300 feet above NAVD 88 (Alexander and Wilson, 1995; 

Hauck and Nagel, 2003). Streams in this region are very low 

gradient, and are incised in alluvial deposits from the Mississippi River. Numerous dredged ditches drain this area, and 

many of the natural channels have been straightened and leveed. 

Within the Mississippi Alluvial Plain region is Crowley’s 

Ridge, which has the streamflow characteristics of the Ozark 

Plateaus physiographic region.

Potential-Scour Assessments (Level 1)

A potential-scour assessment (Level 1) is a methodology 

by which specific characteristics of a bridge site are documented and the potential for damaging scour to occur is qualitatively determined. The bridge site is examined for evidence of 

past scour, such as existing scour holes around the bridge piers 

or abutments, mass wasting of the banks at or near the bridge, 

or slumped riprap on the abutments or on the banks near the 

bridge. The evidence of past scour is a key indicator that the site 

experiences scour and would warrant a more detailed evaluaMoDOT District 10—Continued

New Madrid 118 88 16

Pemiscot 83 33 --

Perry 15 13 6

St. Francois 15 11 2

Ste. Genevieve 22 19 1

Scott 57 16 3

Stoddard 113 85 7

Wayne 43 27 5

Total 767 444 58

Grand Total 3,082 1,396 398

Table 1. Number of bridges that received potential-scour (Level 1), rapid estimation (Level 1+), and detailed hydraulic 

(Level 2) assessments, grouped by Missouri Department of Transportation (MoDOT) district.—Continued

[--, no bridges]

County

(fig. 1)

Bridges that received 

Level 1 assessment

Bridges that received 

Level 1+ assessment

Bridges that received 

Level 2 assessment
6 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri
Estimates of Scour Depth Using Different Techniques 7

tion. The site also is examined for characteristics that might 

increase the potential for scour to occur, such as the flow angle 

of attack, the percentage of channel and flood-plain constriction 

caused by the bridge and road approach embankments, the presence of piers in the main channel, or the presence of debris rafts 

at piers. The various characteristics are assigned a value that 

pertains to the propensity of the characteristic to exacerbate or 

minimize scour at the site. Forms used to collect bridge site 

data, the characteristics examined with regards to observed 

scour and potential scour, and the values assigned to these characteristics in Missouri are documented in Huizinga and Waite 

(1994). Level 1 assessments were made at 3,082 bridges in Missouri, as shown in figure 2.

The values assigned to the evidence of past scour are combined into a total observed-scour index. Similarly, the values 

assigned to the characteristics that affect the scour potential are 

combined into a total potential-scour index. These two indices 

were used to qualitatively determine whether or not a bridge 

was susceptible to scour. Computed index values for potential 

and observed scour for each bridge evaluated in the Level 1 

assessment are provided in table 2, on the compact disk at the 

back of this report. If a bridge had an observed-scour index of 3 

or higher, or a potential-scour index of 40 or higher, it became 

a candidate for further evaluation; otherwise, it was classified as 

not susceptible to scour. Occasionally a bridge that was classified as not susceptible to scour received further evaluation, as 

noted in the remarks column of table 2.

Estimates of Scour Depth Using Different 

Techniques

The Level 1 assessment indicated that 1,327 bridges would 

require a more detailed evaluation for scour, based on the computed potential- and observed-scour index values. Upon completion of the Level 1 work, detailed hydraulic assessments 

(Level 2’s) had been completed at 35 bridges that the Level 1 

assessment indicated were most susceptible to scour, as well as 

2 overflow bridges that the Level 1 assessment indicated were 

not susceptible to scour, but were in proximity to 1 of the 35 

bridges. A rapid estimation method (Level 1+) developed by 

Holnbeck and Parrett (1997) was utilized to further evaluate the 

remaining 1,292 bridges deemed scour-susceptible based on the 

Level 1 assessment, and approximate scour depths were calculated. Sites that had scour depths greater than defined values 

were then assessed with a detailed hydraulic assessment (Level 

2) using the guidelines set forth in Hydraulic Engineering Circular No. 18 (HEC-18) (Richardson and Davis, 1995, 2001).

Rapid Estimation Method (Level 1+)

The rapid estimation method (Level 1+) is a method by 

which pertinent data can be collected about a bridge site during 

a brief visit, from which scour depths can be estimated. It is not 

intended to replace the more detailed Level 2 method, but it is 

considered useful for limited-detail bridge scour assessments. 

This method was chosen to assess the 1,292 bridges that 

required a more detailed evaluation of scour as determined by 

the Level 1 potential- and observed-scour index values that had 

not yet received a Level 2 assessment (fig. 3). In 2002, MoDOT 

identified 104 bridges that had not been previously assessed for 

scour-susceptibility, and these bridges also received a Level 1+ 

assessment (fig. 3).

The Level 1+ method uses calculated scour-depth and 

hydraulic data from Level 2 assessments from 10 states, including Missouri. Relations between significant hydraulic or physical variables and calculated scour depths were developed from 

the Level 2 assessments. Surrogate variables that could easily 

be measured or estimated in the field were substituted for more 

complex hydraulic variables required in the Level 2 analyses, 

and the scour equations were simplified to utilize the surrogate 

variables to estimate scour depths. The Level 1+ method is 

designed to overestimate scour depths, compared to the Level 2 

method, by using envelope curves to define the relation rather 

than best-fit curves. An exhaustive explanation of the development, implementation, and limitations of the Level 1+ method 

is contained in Holnbeck and Parrett (1997), but two special 

variables and additional computation requirements needed to 

apply the method, as well as the general procedure of the 

method as applied in Missouri, are discussed in the following 

sections.

Special Variables Needed for Application in Missouri

Two variables discussed in Holnbeck and Parrett (1997) 

that are presumed to vary regionally are the average main channel velocity at the bridge, V2, and the difference in water-surface elevation from the approach section to the downstream 

face of the bridge, ∆h. The first regional variable, the average 

main-channel velocity, V2, is critical in the determination of 

scour, and is determined by taking the total discharge through 

the bridge opening, Q2, divided by the total flow area at the 

bridge, A2. However, to enable comparison of widely varying 

ranges of bridge span and discharge, Holnbeck and Parrett 

advocate converting the total discharge to a unit discharge, q2, 

by dividing the total discharge, Q2, by the estimated top width 

of flow at the downstream face of the bridge opening (adjusted 

for any skewness to flow and for effective pier width), W2. The 

average velocity is determined using an equation that defines 

the relation between the unit discharge, q2, and the average 

velocity, V2. Holnbeck and Parrett (1997) developed this relation for Montana using data from Level 2 analyses done in 

Montana and Colorado, which share similar physiography. 

In Missouri, Level 2 analyses had been completed at only 

35 sites before the Level 1+ assessment, and all of these sites 

were in the Central Lowlands region. To avoid any physiographic regional bias in the Level 1+ assessments, gage information was used to develop the relation for V2. However, discharge measurements at gages typically are not of sufficient
8 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri
Estimates of Scour Depth Using Different Techniques 9
10 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

magnitude to be comparable to the flows used in the Level 1+ 

assessment. Therefore, the slope and area for 23 gages in the 

Central Lowlands region and 29 gages in the Ozark Plateaus 

region found in Alexander and Wilson (1995) were used to estimate the 100- and 500-year peak discharges at the gages using 

the regional regression equations. Discharge measurements at 

each gage were used to approximate the average velocity at the 

100-year and 500-year discharges, and this information was 

used to develop a relation that estimates the average main-channel velocity from the unit discharge at the gage for the Central 

Lowlands and Ozark Plateaus physiographic regions:

V2 = 0.931 q2

0.395 for the Central Lowlands, and (1)

V2 = 0.950 q2

0.399 for the Ozark Plateaus (2)

where

V2 is the average main channel velocity, in feet per 

second (ft/s);

q2 is the unit discharge per foot of width, in cubic feet 

per second per foot (ft3/s/ft) or square feet per 

second (ft2/s), computed as Q2/W2;

Q2 is the total discharge through the bridge, in cubic feet

per second (ft3/s); and

W2 is the estimated adjusted top width of flow, in feet.

Equations 1 and 2 have coefficients of determination (R2) of 

0.36 and 0.49, respectively. An average main-channel velocity 

equation was not determined for the Mississippi Alluvial Plain 

region because of sparse gage data in this region. Equation 1 for 

the Central Lowlands was used for sites in the Mississippi Alluvial Plain region.

The second regional variable, the difference in water-surface elevation from the approach section to the downstream 

face of the bridge, ∆h, requires information about the water-surface elevation at the approach section, typically one bridge 

length upstream from the bridge. Information on approach conditions typically is not available from discharge measurements 

at gages; therefore, the Level 2 assessments performed at 35 

sites in Missouri before the Level 1+ assessments were used to 

develop a relation between the average velocity at the bridge, 

V2, and ∆h, which was determined to be:

∆h = 0.030 V2

2 + 0.03 (3)

where

∆h is the change in water-surface elevation from the

approach section to the downstream face of the

bridge, in feet; and

V2 is the average main channel velocity determined

from equation 1 or 2, in feet per second (ft/s).

Equation 3 has a coefficient of determination (R2) of 0.52. 

Although all of the 35 Level 2 assessments were in the Central 

Lowlands physiographic region, equation 3 was used to determine ∆h in all three physiographic regions, because the Level 2 

assessments were the only source for these data in Missouri 

before the Level 1+ assessments. However, as will be shown 

later, equation 3 provides a reasonable estimation of ∆h

throughout Missouri.

Determination of Average Bed Location for 

Referencing Average Depth

The flow area at the bridge is controlled by the geometry 

of the bridge opening, and the average velocity, V2, would be 

represented by the “average” flow area, A2, for a given discharge. For a rectangular bridge opening, the average flow area

A2 = badj * y2 (4)

where

A2 is the average area of flow, in square feet (ft2

);

badj is the clear span of the bridge, b, adjusted for skew,

computed as b * cos θ, in feet;

θ is the flow angle of approach of the bridge, or skew, 

in degrees; and 

y2 is the depth of flow at the downstream bridge face, 

in feet.

In the case of a rectangular bridge opening, equation 1 or 2 can 

be used to directly determine the depth of flow, because

Q2 = V2 A2

and, therefore

q2 = V2 y2. (5)

However, as noted in Holnbeck and Parrett (1997), when a 

bridge has spill-through abutments, the bridge opening can be 

approximated by a trapezoidal shape and an iterative procedure 

must be followed to determine the actual flow width. This process is further complicated when the abutments are set back 

from the channel so that flow is conveyed in both the mainchannel and setback areas of the bridge opening, as is the case 

at a majority of the bridges assessed in Missouri.

Therefore, when each site was visited, the “average bed”, 

of the channel at the bridge had to be determined. As shown in 

figure 4, the average bed of the bridge opening was chosen so 

that the average flow area would approximate a rectangle; 

therefore, equation 1 or 2 could be used to determine the depth 

of flow at the bridge, y2. Although the location of the average 

bed is dependent upon the depth of flow, it typically was chosen 

such that the area below the average bed in the channel approximately equaled the area above the average bed on the setback 

areas of the bridge (fig. 4). In this way, the average flow area is 

approximated as a rectangle, and equation 5 could be used. The 

water-surface elevation was determined using the average depth 

of flow (from equation 5) above this “average bed”, and depths 

of flow on the setbacks and on the approach flood plains were 

determined relative to the water surface.

Results obtained using the average flow approximation 

technique indicated depths determined by this method were rea-
Estimates of Scour Depth Using Different Techniques 11

sonable for most of the sites assessed by the Level 1+ method. 

However, as will be shown later, at sites that had substantial setback areas relative to the channel area, the approximation technique resulted in an “average” channel flow depth that was substantially less than the depth of flow in the channel used in the 

Level 2 assessments, which resulted in lower main channel contraction scour depths in the Level 1+ assessments compared to 

the Level 2 assessments. Similarly, bridges with substantial setback areas tended to have lower average velocities in Level 1+ 

assessments than bridges with small setback areas, which 

resulted in lower pier scour depth estimates in the Level 1+ 

assessments compared to the Level 2 assessments.

Modification of Discharge

MoDOT requested that scour depth estimates be made for 

two discharges: the 100-year peak discharge, Q100, (the discharge that has a 100-year recurrence interval, or a 1 percent 

chance of occurring in any given year), and a second discharge 

equal to the lesser of the 500-year peak discharge, Q500, or the 

discharge that causes impending overtopping of the road 

embankments adjacent to the bridge, Qimp, (impendent discharge). The two flood discharges were generically labeled Qa

and Qb, and the scour depth estimates were associated with the 

part of the total flood discharge that passed through the bridge 

opening, labeled Q2a and Q2b. The bridges being assessed were 

plotted on a map, and the contributing drainage basin was determined for each. The area and slope of each basin were obtained, 

and the 100-year and 500-year peak discharges were determined for each site based on the regression equations described 

in Alexander and Wilson (1995). Generally, the calculated 100-

year discharge was used as the first flood discharge, Qa; the calculated 500-year discharge was used as the second discharge, 

Qb; and the discharges through the bridge, Q2a and Q2b, were 

equal to the total discharges, Qa and Qb. Occasionally, however, 

modifications to the calculated 100-year and 500-year discharges were required to find the discharge through the bridge. 

Characteristics of the site that would warrant modification of 

the discharges were: adjacent road embankments that would 

experience road overflow; the presence of additional bridges 

(for example, bridges designed for flood-plain overflow, or 

bridges over secondary channels that were not hydraulically 

isolated from the bridge in question); or, bridges located in the 

Mississippi Alluvial Plain physiographic region.

Road Overflow

When the potential for road overtopping existed at a site, 

the following procedure was followed:

1. The depth of flow relative to the average bed of the channel at the bridge associated with impendent road overtopping, y2imp, was determined at the highest point of the 

road cross section (typically the center line or the high 

side of a tilted curve) at the lowest section of road 

embankment.

2. The top width of flow under the bridge associated with 
12 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

that depth, bimp, was determined and adjusted for skew as

(bimp)adj = bimp * cos θ. (6)

3. The unit discharge associated with the impendent 

discharge was calculated using equation 5

q2 = V2 y2

or,

y2 = q2 / V2. (7)

Replacing V2 using equation 1 for the Central Lowlands,

y2 = q2 / (0.931 q2

0.395)

and simplifying yields

q2imp = (0.888 y2imp

1.653) for the Central Lowlands. (8)

Similarly, replacing V2 using equation 2 for the Ozark 

Plateaus and simplifying yields

q2imp = (0.918 y2imp

1.664) for the Ozark Plateaus. (9)

4. Using the unit discharge from equation 8 or 9 and the 

adjusted top width of flow from equation 6, the 

impendent discharge was determined as

Qimp = q2imp * (bimp)adj. (10)

It was assumed that the total impendent discharge also 

passed through the bridge, or Q2imp = Qimp.

5. The two discharges used to estimate scour depths at the 

site were assigned using the following logic:

a. if Qimp is less than Q100, Qa was assumed to be Q100, 

and

Q2a = Q100 - 1

/2(Q100 - Qimp); (11)

Qb and Q2b were assumed to be Qimp.

b. if Qimp was between Q100 and Q500, Qa and Q2a were 

assumed to be Q100, and Qb and Q2b were assumed to 

be Qimp.

c. if Qimp was greater than Q500, Qa and Q2a were 

assumed to be Q100, and Qb and Q2b were assumed to 

be Q500.

Presence of Additional Bridges

When an additional bridge was present, separate assessments were performed for the primary bridge in question and 

the additional bridge(s). To determine the part of the flood discharges to assign to each bridge, the approximate conveyance of 

each bridge was determined. Conveyance is a component of the 

Manning’s uniform-flow equation (Chow, 1959), and is defined 

as

(12)

where

K is the conveyance of the section, in cubic feet per 

second (ft3

/s);

n is the Manning’s roughness coefficient for the section

(Chow, 1959; Barnes, 1967; Arcement and

Schneider, 1989);

A is the cross-sectional area of the section, in square 

feet (ft2

); and

R is the hydraulic radius of the section, in feet.

The approximate conveyance of each bridge opening was determined using the average flow area of the bridge opening, 

assuming the depth and hydraulic radius were both approximated by the distance from the average bed to the low steel of 

the bridge deck, or

or, simplifying

(13)

where

Ki is the approximate conveyance of the individual bridge

i, in cubic feet per second (ft3/s);

n is the Manning’s roughness coefficient averaged for

the total bridge opening;

b is the total bridge length (skew is ignored), in feet; and

yls is the distance from the average bed to the low steel of

the bridge deck, in feet.

A conveyance ratio for each bridge was established, using

γi = Ki

 / Ktot (14)

where

γi is the conveyance ratio of the individual bridge i;

Ki is the approximate conveyance of the individual bridge

i, in cubic feet per second (ft3/s); and

Ktot is the sum of the approximate conveyances of all the

individual bridges, in cubic feet per second (ft3/s).

The two flood discharges, Qa and Qb, and the discharges passing through the bridge, Q2a and Q2b, were modified by the conveyance ratio of each bridge to get the flood discharges and 

bridge discharges for each bridge. The upstream flood plain was 

divided into sections to be associated with each bridge, and each 

bridge was examined separately.

K 1.49

n

----------AR2 3⁄ =

Ki

1.49

n

---------- b yls ( ) ⋅ yls

2 3⁄ =

Ki

1.49

n

----------b yls

5 3⁄ = ⋅
Estimates of Scour Depth Using Different Techniques 13

When a combination of road overflow and additional 

bridges existed at a site, the discharge modification for road 

overflow was performed first, and the resulting Qa, Qb, Q2a, and 

Q2b were then distributed to the various bridges using the calculated conveyance ratios.

Sites Located in the Mississippi Alluvial Plain Region

Because of the low gradients and general lack of substantial relief in the Mississippi Alluvial Plain region of the state, 

the region is drained by a complex system of interconnected 

dredged ditches. The main ditches often are leveed, but many of 

the tributary ditches are not. During floods, the smaller tributary 

ditches will overtop their banks and spread over wide areas, 

with minimal flow velocities (except near bridges). Furthermore, roadways in this area often are raised slightly above the 

level of the surrounding land, and will cross several ditches that, 

while separated physically by substantial distance, are hydraulically connected to one another during floods. The regional 

regression equations in Alexander and Wilson (1995) use drainage area as the only variable for determination of discharge in 

the Mississippi Alluvial Plain. However, the equations for this 

region were derived from gaging stations on the main ditches, 

whereas determination of the contributing drainage area of a 

particular bridge on the tributary ditches is difficult because of 

the hydraulic connectivity of these ditches in floods.

Therefore, only the discharge that caused impending road 

overtopping, Qimp, was used to compute the scour depths for a 

majority of the sites located in the Mississippi Alluvial Plain 

region. The impendent discharge was determined using the 

techniques described in the Road Overflow section and the Central Lowlands equation (eq. 8) was used to determine the depth 

of flow. For bridges located at or near a gaging station on one 

of the principal rivers or main ditches, two discharges were used 

as in the other regions. Bridges located in the Crowley’s Ridge 

area of the Mississippi Alluvial Plain region (fig. 1) were considered to be in the Ozark Plateaus region, and scour depths 

were computed for two discharges.

General Procedure of Level 1+ Assessments in 

Missouri

The following general procedure was followed to assess 

bridges using the Level 1+ method in Missouri:

1. In the office, the location of the site is established, the area 

and slope of the contributing drainage are determined, and 

the physiographic province in which it lies is determined. 

From this information, the 100-year and 500-year peak 

discharges, Q100 and Q500, are calculated using the 

regression equations in Alexander and Wilson (1995).

2. The site is visited, and the presence of potential road 

overflow sections or additional bridges is established. If 

present, the peak discharges are modified, and the 

discharges through the bridge, Q2a and Q2b, are 

determined.

3. The flow angle of attack, or skew of the bridge to flow, θ, 

is determined.

4. The clear span of the bridge (length of the bridge from 

abutment face to abutment face), b, is adjusted by the 

skew angle, as

badj = b * cos θ. (15)

5. The average bed is calculated at the location where the 

area below the average bed in the channel approximately 

equals the area above the average bed on the setback 

areas of the bridge (fig. 4). The base of a survey rod is set 

at this location.

6. The preliminary unit discharge, q2, is determined by 

dividing the discharge through the bridge by the adjusted 

span length as the top width of flow,

q2 = Q2 / badj. (16)

7. The average velocity is determined from equation 1 or 2, 

and the average depth of flow above the average bed is 

determined from equation 7.

8. Using the survey rod set at the average bed, the depth of 

flow is measured and the top width of flow is adjusted to 

account for spill-through abutments (if necessary), and 

then adjusted for skew, b*

adj.

9. Repeat steps 6 through 8 until the depth of flow, y2, from 

one iteration to the next changes by less than 0.5 feet.

10. Determine the difference in water-surface elevation from 

the approach to the downstream bridge face, ∆h, by 

squaring the average velocity from step 7 and using 

equation 3.

11. Determine the average main channel depth of flow at the 

approach as:

y1 = y2 + ∆h. (17)

12. Repeat steps 6 through 11 for the second discharge, either 

the impendent road overtopping discharge, Qimp, or the 

500-year peak discharge, Q500.

13. Determine the width of flow, W, an average Manning’s 

roughness coefficient, n, and the elevation relative to the 

average bed of the left and right setbacks at the bridge, 

the left and right flood plains at the approach, and the 

channel at the bridge and at the approach.

14. Approximate the median particle size of the material in 

the channel, D50mc, and on the overbank immediately 

upstream from the bridge, D50ob, using visual 

identification of the material as cobbles, gravel, sand 

(coarse, medium, or fine), or silt/clay.

15. Determine the average width, total length, and flow angle 

of attack (if different than the bridge skew) for the bents 

or piers. If there is a difference between bents and/or 
14 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

piers on the overbank and those in the main channel, 

obtain information for each type.

16. Determine the abutment shape coefficient (Richardson 

and others, 1993).

17. Take the parameters collected at each site and process 

them using a spreadsheet that calculates the estimated 

depth of scour using the envelope curves and scour 

predictor equations developed by Holnbeck and Parrett 

(1997).

Scour Predictor Equations

The scour predictor equations as applied in Missouri are 

reproduced below. A full explanation of the development, 

implementation, and limitations of these equations, as well as 

the envelope curves associated with the scour predictor equations, can be found in Holnbeck and Parrett (1997).

In the following equations for contraction scour, the depth, 

y, width of flow, W, and an average Manning’s roughness coefficient, n, collected during step 13 in the previous section are 

used. These three variables were collected for the left and right 

setbacks at the bridge, the left and right flood plains at the 

approach, and the main channel at the bridge and approach. For 

simplicity in the following equations, the three variables are:

yx is the average depth in the section, in feet;

Wx is the width of the section, in feet; and

nx is the average Manning’s roughness coefficient of the

section (Chow, 1959; Barnes, 1967; Arcement and

Schneider, 1989).

The subscript x of the variables follows the convention:

1 is the main channel at the approach;

2 is the main channel at the bridge;

lob is the left overbank or flood plain at the approach;

rob is the right overbank or flood plain at the approach;

lsb is the left setback at the bridge; and

rsb is the right setback at the bridge.

Additionally, discharge for each section was apportioned using 

the conveyance ratio of each section, γx, determined by

γx = Kx / Ktot (18)

where

γx is the conveyance ratio of the section;

Kx is the conveyance of the section, in cubic feet per 

second (ft3

/s); and

Ktot is the total conveyance of the whole section, in cubic

feet per second (ft3/s).

Equation 18 is the same as equation 14, except that the conveyance ratio is for a portion of the flow area at the bridge or 

approach rather than for one bridge of a multiple bridge site. 

Then, using equation 18 and the form of equation 13, the conveyance ratio for the main channel at the approach, γ1, is

(19)

where the width of the section, Wx, is used in place of the bridge length, b, from equation 13. Simplifying and 

rearranging yields

. (20)

γ1

K1

Ktot

-------- K1

K1 + + Klob Krob ( )

--------------------------------------------

1.49

n1

----------W1y1

5 3⁄

⎝ ⎠ ⎛ ⎞

1.49

n1

----------W1y1

5 3⁄

⎝ ⎠ ⎛ ⎞ 1.49

nlob

----------Wlobylob

5 3⁄

⎝ ⎠ ⎛ ⎞ 1.49

nrob

----------Wrobyrob

5 3⁄

⎝ ⎠ ⎛ ⎞ + +

== = ---------------------------------------------------------------------------------------------------------------------------

γ1

1

1 n1

W1y1

5 3⁄ -----------------

⎝ ⎠ ⎜ ⎟ ⎛ ⎞ Wlobylob

5 3⁄

nlob

--------------------- Wrobyrob

5 3⁄

nrob

+ --------------------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞

+

---------------------------------------------------------------------------------------- 1 n1

W1y1

5 3⁄ -----------------

⎝ ⎠ ⎜ ⎟ ⎛ ⎞ Wlobylob

5 3⁄

nlob

--------------------- Wrobyrob

5 3⁄

nrob

+ --------------------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞

+

–1

= =
Estimates of Scour Depth Using Different Techniques 15

Similarly, the conveyance ratios for the main channel at the 

bridge is

, (21)

for the left setback at the bridge is

, (22)

and for the right setback at the bridge is

. (23)

These are the conveyance ratios by which the discharge in the 

approach section, Q1, or through the bridge, Q2, can be 

weighted to represent flow in the appropriate section in the following equations.

For main channel contraction scour, it was necessary to 

determine which scour scenario (whether live bed or clear 

water) would occur. In Missouri, the main channel typically 

was assumed to experience live-bed contraction scour, except 

when the average velocity in the channel, V2, was less than the 

critical velocity of incipient motion, calculated as

Vc = 11.17 y1

1/6 D1/3 (24)

where

Vc is the critical velocity above which bed material of

size D and smaller will be transported, in feet per

second (ft/s);

y1 is the average depth of flow in the upstream channel,

in feet; and

D is the particle size for Vc, in feet, typically assumed to

be the approximate median particle size of material

in the main channel, D50mc.

The presence of vegetation on the flood plains upstream from 

relief bridges or the overbank areas upstream from the main 

bridge would prevent transport of material to the contracted 

section; therefore, these areas were assumed to experience 

clear-water scour.

For live-bed conditions, the contraction scour predictor 

variable for main channel contraction scour is

. (25)

where

Q2 is the total discharge through the bridge, in cubic feet

per second (ft3

/s); and

Q1 is the total discharge in the approach, in cubic feet per

second (ft3

/s); all other variables are defined previously.

When there is no flow over adjacent road embankments or 

through additional bridges such that Q1 = Q2, equation 25 is the 

same as equation 22 in Holnbeck and Parrett (1997) when the 

appropriate conveyance terms (eqs. 20 and 21) are used. The 

discharge terms are included in equation 25 because road overflow and the presence of additional bridges occur regularly in 

Missouri. For clear-water conditions, the contraction scour predictor variable for main channel contraction scour is

. (26)

Equations 25 and 26 can be used at a bridge without setbacks. 

The conveyance ratio term, γ2, in the numerator of both equations weights the total discharge through the bridge, Q2, for 

flow on the setbacks. This term becomes 1 in equations 25 and 

26 when no setbacks are present, and the total discharge through 

the bridge is used to determine the scour predictor variable.

For contraction scour in the left and right setback areas at 

the bridge,

(27)

and

(28)

where

χlsb is the contraction scour predictor variable for clearwater contraction scour on the left setback, in feet;

χrsb is the contraction scour predictor variable for clearwater contraction scour on the right setback, in feet; 

and

D50ob is the approximate median particle size of the material

on the overbanks immediately upstream from the

bridge, in feet; all other variables are defined previously.

The contraction scour predictor variable, χ, determined from 

one of the above equations is entered on the abscissa of the 

appropriate envelope curve found in Holnbeck and Parrett 

(1997) to determine the estimated main channel or overbank 

contraction scour depth.

For pier scour, the average pier width, a, is entered on the 

abscissa of the pier scour envelope curve found in Holnbeck and 

Parrett (1997) to obtain the value for the pier scour function, ξ, 

defined as

(29)

γ2 1 n2

W2y2

5 3⁄ -----------------

⎝ ⎠ ⎜ ⎟ ⎛ ⎞ Wlsbylsb

5 3⁄

nlsb

-------------------- Wrsbyrsb

5 3⁄

nrsb

+ --------------------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞

+

–1

=

γlsb 1 nlsb

Wlsbylsb

5 3⁄ --------------------

⎝ ⎠ ⎜ ⎟ ⎛ ⎞ W2y2

5 3⁄

n2

----------------- Wrsbyrsb

5 3⁄

nrsb

+ --------------------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞

+

–1

=

γrsb 1 nrsb

Wrsbyrsb

5 3⁄ ---------------------

⎝ ⎠ ⎜ ⎟ ⎛ ⎞ W2y2

5 3⁄

n2

----------------- Wlsbylsb

5 3⁄

nlsb

+ -------------------- ⎝ ⎠ ⎜ ⎟ ⎛ ⎞

+

–1

=

χmc,lb y1

γ2Q2

γ1Q1

----------- ⎝ ⎠ ⎛ ⎞ W1

W2

------ ⎝ ⎠ ⎛ ⎞ y1 = –

χmc,cw 0.122y1

γ2Q2

D50mc

1

3

--

y1

7

6

--

W1

---------------------------

6

7

--

y1 = –

χlsb 0.122ylsb

γlsbQ2

D50ob

1

3

--

ylsb

7

6

--

Wlsb

---------------------------------

6

7

--

ylsb = –

χrsb 0.122yrsb

γrsbQ2

D50ob

1

3

--

yrsb

7

6

--

Wrsb

----------------------------------

6

7

--

yrsb = –

ξ yps

Kp2Fr2

0.15 = ---------------------
16 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

where

ξ is the pier scour function, in feet;

yps is the pier scour depth determined by the rapidestimation method, in feet;

Kp2 is the correction factor for flow angle of attack on 

the pier, computed as [cos θp + (Lp/a) sin

θp]

0.65;

Lp is the length of the pier, in feet;

a is the average pier width, in feet;

θp is the flow angle of attack on the pier (which may or

may not be the same as the skew of the bridge), in

degrees;

Fr2 is the Froude number of the average flow at the 

downstream face of the bridge, computed as 

V2/(g y2)

1/2;

V2 is the average velocity in the main channel at the

bridge determined by equation 1 or 2, in feet 

per second (ft/s);

g is the acceleration of gravity, 32.2 feet per second

squared (ft/s2); and

y2 is the average depth of flow at the downstream face 

of the bridge, in feet.

The average pier width was used to determine a value of the pier 

scour function, ξ, for a typical pier or bent in the main channel 

and a typical pier or bent on the setback, and equation 29 was 

solved for the pier scour depth, yps.

For abutment scour, the flow depth at the abutment, ya, is 

entered on the abscissa of the abutment scour envelope curve 

found in Holnbeck and Parrett (1997) to obtain the value for the 

abutment scour function, Ψ, defined as

(30)

where

Ψ is the abutment scour function, in feet;

Ka1 is the coefficient for abutment shape (Richardson 

and others, 1993); and

yas is the abutment scour depth determined by the 

rapid estimation method, in feet.

The average flow depth at the abutment was taken as ylob for 

the left abutment and yrob for the right abutment. These depths 

were used to determine the value of the abutment scour function, Ψ, and equation 30 was solved for the abutment scour 

depth, yas.

Final Qualitative Assessment

The scour depths estimated at each bridge were compared 

to limiting depth criteria set by MoDOT; sites with one or more 

scour depths larger than the set limits became candidates for a 

detailed hydraulic assessment (Level 2). Limiting criteria were 

set at 5.0 feet of contraction or abutment scour and 10.0 feet of 

pier scour; bridges with depths greater than one or more of these 

values were examined using the Level 1 site assessment forms, 

photos, and bridge plans. The qualitative criteria used in the 

examination, based on MoDOT recommendations, were as follows:

1. If only main channel contraction scour existed and the 

main channel piers were set on bedrock, the site was no 

longer a Level 2 candidate.

2. If only abutment scour existed, and the abutments were 

protected, the site was no longer a Level 2 candidate. 

Abutment scour depths were viewed with 

skepticism—particularly when any sort of protection 

existed—with the realization that abutment scour depths 

were overestimated by the HEC-18 equations.

3. If the contributing drainage area was 25 square miles or 

less, such that the flood wave would be short and the 

substructural elements would be visible upon flood 

recession, the bridge was no longer a Level 2 candidate. 

In the Mississippi Alluvial Plain physiographic province, 

if the impendent discharge was less than 5,000 cubic feet 

per second or the bridge was shorter than 100 feet, it was 

considered a “small drainage area” site (< 25 square 

miles).

4. If road overflow sections existed on both flood plains, 

such that the public would not be able to access the 

bridge during floods of a magnitude greater than the 

impendent road overtopping discharge, the site was no 

longer a candidate (provided criteria 5 was not met for 

the scour values at the impendent road overtopping 

discharge).

5. If the estimated scour depths were 5 feet greater than the 

initial limiting criteria, especially in the case of pilingtype substructures, items 1 through 4 were ignored and 

the site remained a Level 2 candidate.

6. In the Mississippi Alluvial Plain physiographic region, 

the presence of levees on both upstream banks or flood 

plains would cause little to no constriction of flow at the 

bridge, and the site was no longer a Level 2 candidate. 

The primary cause of channel change at these bridge sites 

will be channel degradation because of dredging. This 

criterion was used to remove the candidacy of bridges 

that had large clear-water overbank scour values; 

however, it is intuitive that if there is little to no 

constriction at the bridge because of levees on the 

upstream banks, there will be no substantial contraction 

scour.

Estimated scour depths for all of the bridges assessed using 

the Level 1+ method are provided in table 3, on the compact 

disk at the back of this report. A summary of the Level 1+ 

assessment by MoDOT district in Missouri is shown in table 4.

Ψ 0.55

Ka1

----------y = as
Estimates of Scour Depth Using Different Techniques 17

Detailed Hydraulic Assessments (Level 2)

Detailed hydraulic assessments (Level 2), were conducted 

at 398 bridges at 350 unique sites throughout Missouri (fig. 5). 

Not all of these bridges were Level 2 candidates based on the 

results of the Level 1 or Level 1+ assessments. Twenty-two 

bridges that were not Level 2 candidates based on the Level 1 

and Level 1+ assessments were assessed because they were in 

proximity (or hydraulically connected) to a Level 2 candidate, 

such as a bridge on the flood plain designed to carry overflow, 

or a pair of bridges upstream from a confluence. Twenty-nine 

bridges over major rivers and two bridges on smaller streams 

were evaluated without a Level 1 or Level 1+ assessment. However, eight Level 2 candidates from the Level 1+ assessment 

were dropped because of bridge replacements, improvements, 

or other changes at the bridge that mitigated scour.

The procedure of a Level 2 assessment is fully described in 

the four editions of the FHWA Hydraulic Engineering Circular 

No. 18 (HEC-18) (Richardson and others, 1991, 1993; and 

Richardson and Davis, 1995, 2001); the analysis procedure and 

scour-depth equations were applied in Missouri with only slight 

modification. However, HEC-18 underwent changes with each 

edition; the general form of the various equations for contraction, pier, and abutment scour did not change substantially, but 

coefficients and terms were added or removed, and the methods 

used to determine certain variables evolved with time. A discussion of the hydraulic analysis and each scour depth equation follows, along with variations in each edition of HEC-18 and any 

modifications when used in Missouri.

Hydraulic Analysis

Application of the HEC-18 scour depth equations required 

estimates of flood discharges, hydraulic properties, and watersurface profiles. Flood discharge estimates for the 100-year and 

500-year peak discharges (Q100 and Q500) were determined for 

each site based on the regression equations described in Alexander and Wilson (1995). The Water-Surface PROfile Computation (WSPRO) step-backwater model (Shearman, 1990; 

Shearman and others, 1986) was used to determine hydraulic 

properties and water-surface profiles at each site, using the field 

data collected at the site such as cross sections, bridge geometry, and Manning’s roughness coefficient estimates.

In addition to the 100-year and 500-year peak discharges, 

scour computations often were made for the discharge that caused 

either impending road overtopping or impending levee overtopping (impendent discharge, or Qimp). If the site experienced road 

overtopping by either the 100-year or 500-year discharge, the 

impendent discharge typically was included as a potential worstcase scour scenario (for example, maximum flow pressure at the 

bridge, without relief from road overflow). Similarly, if levees 

were present on the upstream or downstream flood plains that 

were overtopped by either the 100-year or 500-year discharge, the 

discharge that caused impendent levee overtopping usually was 

included as a check to see if it created a worst-case scour scenario. 

The impendent discharge (whether road or levee) was determined 

by trial and error in the WSPRO model of the site.

The results of the hydraulic analysis were used as input to 

a series of spreadsheets and FORTRAN programs that calculated the contraction, pier, and abutment scour depths using the 

HEC-18 equations for each discharge. The spreadsheets and 

programs were modified and updated with the release of each 

edition of HEC-18.

Table 4. Summary of rapid estimation assessments (Level 1+) and resultant detailed hydraulic assessment (Level 2) candidates by 

Missouri Department of Transportation (MoDOT) district.

MoDOT 

district

Bridges that 

received Level 1+ 

assessment

Level 1+ bridges 

deemed not 

susceptible to 

scour by limiting 

criteria

Level 1+ bridges 

with depths greater 

than limiting criteria 

(preliminary Level 2 

candidates)

Bridges removed 

from preliminary 

Level 2 candidate 

list by qualitative 

assessment

Level 2 candidates 

from Level 1+ 

assessment1

01 170 28 142 71 71

02 171 22 149 74 75

03 95 25 70 34 36

04 83 23 60 35 25

05 114 28 86 54 32

06 96 61 35 22 13

07 93 70 23 19 4

08 52 28 24 19 5

09 78 48 30 19 11

10 444 256 188 136 52

Grand Total 1,396 589 807 483 324

1Values in this column do not equal MoDOT district totals in table 1 or table 6 because Level 2 assessments were performed at bridges in addition to those from the Level 1+ assessment.
18 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri
Estimates of Scour Depth Using Different Techniques 19

Contraction Scour

Contraction scour is evaluated for two basic scenarios: 

live-bed scour, which occurs when the approach flow is transporting bed material; and clear-water scour, which occurs when 

the approach flow is not transporting bed material (Richardson 

and Davis, 2001). In Missouri, live-bed scour typically occurs 

in the main channel, and clear-water scour occurs at the main 

bridge setbacks or at relief bridges.

The fundamental equation for both types of contraction 

scour is

ycs = yc2 - yc0 (31)

where

ycs is the average contraction scour depth, in feet;

yc2 is the average depth in the contracted section after

scour (for example, at the bridge), in feet; and

yc0 is the existing depth in the contracted section before

scour, in feet.

The existing depth in the contracted section before scour, yc0, 

was introduced with the third edition of HEC-18 (Richardson 

and Davis, 1995). Before this, equation 31 was

ycs = yc2 - yc1

where

yc1 is the average depth in the upstream main channel, 

in feet.

The third and fourth editions of HEC-18 indicated that yc1 could 

be used to estimate yc0, particularly if the contraction scour hole 

fills in during the falling stage. For this reason, yc1 consistently 

was used in place of yc0 for assessments in Missouri.

For live-bed contraction scour, yc2 is determined as

(32)

where

Q1 is the discharge in the upstream channel transporting

sediment, in cubic feet per second (ft3

/s);

Q2 is the discharge in the contracted channel, in cubic feet

per second (ft3/s);

W1 is the width of the upstream main channel that is

transporting bed material, in feet;

W2 is the width of the main channel in the contracted 

section less pier width(s), in feet; and

kc1 is a coefficient that depends on whether the material

transported is mostly contact bed material (kc1 =

0.59), contains some suspended material (kc1 =

0.64), or is mostly suspended bed material (kc1 =

0.69).

An additional term came and went from equation 32 with 

the various editions of HEC-18, which modified the contraction 

scour based upon a ratio of the Manning’s roughness coefficients between the approach and the contracted section. However, when the roughness essentially was the same between the 

sections, the term dropped out of the equation. Therefore, this 

term was ignored in all of the assessments in Missouri. Nevertheless, the Manning’s roughness coefficient is implicitly 

included in the equation, because it is included in the determination of the two discharge terms, Q1 and Q2. 

For clear-water contraction scour, yc2 is determined as

(33)

where

Ku is a coefficient equal to 0.0077 (English units);

Qo is the discharge through the bridge or on the setback

area at the bridge associated with the width, Wo, 

in cubic feet per second (ft3

/s);

Wo is the width of the contracted section less pier

width(s), in feet;

Dm is the diameter of the smallest non-transportable 

particle in the bed material in the contracted section,

typically assumed to be 1.25 D50, in feet; and

D50 is the median diameter of bed material, or the particle

size in a mixture of which 50 percent are smaller, in

feet.

For clear-water scour applications of equations 31 and 33 in 

Missouri, yc0 was assumed to be the average depth of flow 

through the relief bridge or on the setback area at the main 

bridge, which essentially equalled the depth of flow of the 

unscoured bed.

Equation 33 has undergone only minor changes since the 

first edition of HEC-18. In the first edition (Richardson and others, 1991), Ku was equal to 1/120, and Dm was assumed to be 

D50, rather than 1.25 D50. The second edition (Richardson and 

others, 1993), introduced Dm as 1.25 D50, and the third edition 

changed Ku to approximately 1/130 (which comes from Ku = 

1/40 in SI units).

As in the Level 1+ assessments, the main channel typically 

was assumed to experience live-bed contraction scour, except 

when the average velocity in the approach channel, V2, was less 

than the critical velocity of incipient motion, calculated by 

equation 24 and shown here for clarity;

Vc = 11.17 yc1

1/6 D1/3

where

Vc is the critical velocity above which bed material of

size D and smaller will be transported, in feet per

second (ft/s);

yc1 is the average depth of flow in the upstream channel,

in feet; and

D is the particle size for Vc, in feet, typically assumed

to be D50.

When the average approach velocity was nearly equal to the 

critical velocity, both live-bed and clear-water scour were computed for the main channel, and the values were compared. The 

presence of vegetation on the flood plains upstream from relief 

bridges or the overbank areas immediately upstream from the 

yc2

Q2

Q1

------ ⎝ ⎠ ⎛ ⎞ 6 7⁄ W1

W2

------ ⎝ ⎠ ⎛ ⎞ kc1

y = c1

yc2

KuQo

2

Dm

2 3⁄ Wo2 ------------------

3 7⁄

=
20 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

main bridge would prevent transport of material to the contracted section; therefore, these areas were assumed to experience clear-water scour.

Pier Scour

The equation for pier scour is

(34)

where

yps is the pier scour depth, in feet;

yp is the depth of flow just upstream from the pier, 

in feet;

Kp1 is the correction factor for pier nose shape, ranging

from 0.9 to 1.1;

Kp2 is the correction factor for flow angle of attack, 

computed as [cos θp + (Lp/a) sin θp]

0.65;

Lp is the length of the pier, in feet;

a is the pier width, in feet;

θp is the flow angle of attack on the pier (which may or

may not be the same as the skew of the bridge), in

degrees;

Kp3 is the correction factor for bed condition, ranging from

1.1 to 1.3, assumed to be 1.1 in Missouri;

Kp4 is the correction factor for armoring by bed material,

assumed to be 1.0 in Missouri;

Frp is the Froude number just upstream from the pier,

computed as Vp/ (g yp)

1/2; 

g is the acceleration of gravity, 32.2 feet per second

squared (ft/s2

); and

Vp is the velocity of flow upstream from the pier, in 

feet per second (ft/s).

For round-nosed piers aligned with the flow, HEC-18 puts 

a limit on the total depth of scour that can be anticipated. For Frp

< 0.8, the maximum scour depth is 2.4 times the pier width, a; 

for Frp > 0.8, the maximum scour depth is 3.0 times the pier 

width, a.

Equation 34 has undergone only minor changes since the 

first edition of HEC-18. In the first edition (Richardson and others, 1991), Kp3 and Kp4 were not in the equation; Kp3 was added 

in the second edition (Richardson and others, 1993), and Kp4

was added in the third edition (Richardson and Davis, 1995). 

However, neither of these additional factors substantially 

changed the results of pier scour in Missouri. The bed condition 

factor, Kp3, varies from 1.1 to 1.3 depending on the dune heights 

in the channel, but is 1.1 for dunes as much as 10 feet high (typically not seen in channels in Missouri, with the exception of the 

large rivers). Furthermore, the dune height was not measured at 

sites in Missouri. Similarly, the armoring factor, Kp4, is 1.0 for 

situations when D50 < 2 mm (millimeters) or D95 < 20 mm, 

which typically is the case in Missouri.

When equation 34 was applied to Level 2 assessments in 

Missouri for piers or bents located in the channel or on the channel banks, the depth of flow upstream from the pier, yp, and the 

velocity upstream from the pier, Vp, were assumed to be the 

maximum values in the channel area. This was to account for 

possible shifts in the channel thalweg during a flood event. 

However, for piers or bents located on the setback areas, the 

depth of flow upstream from the pier or bent was used for yp, 

and the maximum velocity on the setback area was used for Vp

for all piers or bents on a particular setback.

With the fourth edition of HEC-18 (Richardson and Davis, 

2001), a comprehensive procedure for determining pier scour at 

complex pier foundations was introduced. Complex pier foundations are present extensively in Missouri, and consist of a column with a pile group, pile cap, or spread footer. Most pier 

scour research has focused on solid piers, with little research on 

pile groups, pile caps, and solid piers in any combination being 

exposed to flow (Richardson and Davis, 2001). Until the fourth 

edition of HEC-18, pier scour caused by exposed footings, pile 

caps, or pile groups were estimated using equation 34 with a 

modified approach velocity and depth. However, the fourth edition provided equations for pier scour at complex foundations 

that separated the foundation into its various components, and 

computed scour for each component relative to its position to 

the channel bed. The total complex foundation pier scour depth 

was a sum of the scour components. The complex foundations 

procedure was used in Missouri for Level 2 assessments performed after 2001. Before this time, pier scour depths for 

exposed footings were calculated using equation 34 with and 

without footing exposure; the deeper of the two computed 

depths was reported as a worst case.

Abutment Scour

Two equations are used to determine abutment scour 

depth; Froehlich’s live-bed scour equation, and the HIRE equation. The Froehlich equation is

(35)

where

yas is the abutment scour depth, in feet;

ya is the average depth of flow on the flood plain (computed as Ae/Le in HEC-18, but assumed to be the

depth of flow at the abutment toe in Missouri), 

in feet;

Ae is the flow area of the approach section obstructed 

by the embankment, in square feet (ft2

);

Le is the length of the embankment projected normal 

to flow (computed as Le adj = Ae/ya in Missouri), 

in feet;

Ka1 is the coefficient for abutment shape, ranging from

0.55 to 1.0;

Ka2 is the coefficient for angle of the embankment to flow,

computed as ;

θe is the angle of the embankment to the flow, in degrees;

with θe less than 90 degrees if embankment points

downstream and θe greater than 90 degrees if 

yps yp 2.0Kp1Kp2Kp3Kp4

a

yp

---- ⎝ ⎠ ⎛ ⎞ 0.65

Frp

0.43 =

yas ya 2.27Ka1Ka2

Le′

ya

------ ⎝ ⎠ ⎛ ⎞ 0.43

Fra1

0.61 = + 1

θe

90° -------- ⎝ ⎠ ⎛ ⎞ 0.13
Estimates of Scour Depth Using Different Techniques 21

embankment points upstream;

Le’ is the length of active flow obstructed by the embankment (determined by engineering judgement), in

feet;

Fra1 is the average Froude number of approach flow

upstream from the abutment toe, computed as 

Ve/ (g ya)

1/2;

Ve is the average velocity of approach flow, computed 

as Qe/Ae, in feet per second (ft/s); and

Qe is the approach flow obstructed by the abutment and

approach embankment, in cubic feet per second 

(ft3

/s).

The HIRE equation is

(36)

where

Fra2 is the Froude number based on the velocity and depth

adjacent to and upstream from the abutment toe,

computed asVa/ (g ya)

1/2; and

Va is the flow velocity at the abutment toe, in feet per 

second (ft/s), and all other variables are defined 

previously.

The HIRE equation did not change in the four editions of HEC18. In Missouri, the Froehlich equation primarily was used, and 

the HIRE equation was used when the embankment length was 

greater than 25 times the depth of flow at the abutment toe.

The Froehlich equation had a tendency to overestimate 

abutment scour—noted in every edition, but especially in the 

fourth edition (Richardson and Davis, 2001)—and a modification to address this issue occurred in the fourth edition. The 

length of the embankment projected normal to flow, Le, was 

changed to the length of active approach flow obstructed by the 

embankment, Le’, which removed the effect of areas on the 

flood plain that convey shallow or low-velocity flow. However, 

before the fourth edition of HEC-18 was released, it was recognized in Missouri that the abutment scour equation likely overestimated abutment scour, so the abutment scour equation variables were modified. Rather than determining the average

depth of flow on the flood plain using the area of blocked flow 

and the embankment length normal to flow (as designated in 

HEC-18), the depth of flow at the abutment toe was used as ya

and the effective length of the embankment, Le adj, was determined by dividing the area of blocked flow by this depth. This 

resulted in less extreme values being calculated for abutment 

scour by shortening the embankment length normal to flow. 

When the fourth edition of HEC-18 was released, the new 

active flow length term, Le’, was used in place of Le adj.

Reports

After the various scour depth values were determined 

using the HEC-18 equations, the scour depths were plotted on a 

profile of the bridge to create a scour prism (fig. 6). Plots for 

each discharge used in the WSPRO and scour analyses were 

created (fig. 6), as well as a plot that shows the scour prisms for 

all of the various discharges (fig. 7).

A report was created that provided the details of the 

hydraulic analysis and the scour depth computations for each 

site. The report contains a brief discussion of the site, which 

included characteristics of the site, a description of the 

bridge(s), trends of channel change with time, and the amount 

of exposure the bridge foundations experience as a result of the 

computed scour depths. An aerial photograph of the site from 

USGS Digital Orthophoto Quadrangles (DOQs) with the location of sections used in the WSPRO model was included with 

sites completed after 1998; before this time, a topographic map 

of the site with the location of the sections used in the WSPRO 

model was included. Photographs of the site taken during the 

site visit, tables of computed scour depths, and the various scour 

prisms also were included. An appendix to each report contained a detailed description of the site and associated drainage 

basin, Manning’s roughness coefficients assigned to the channel and flood plains, the assumptions used in the WSPRO analysis and in the scour computations, the input and output files 

from WSPRO, and the output files from the scour depth computation program.

The reports include a rough classification of each bridge as 

having substantial, moderate, or minimal exposure. Substantial 

exposure was defined as when more than two-thirds of the total 

foundation depth was exposed or the foundation was undermined; moderate exposure was defined as when one-quarter to 

two-thirds of the total foundation depth was exposed; minimal 

exposure was defined as when less than one-quarter of the total 

foundation depth was exposed. Computed scour depths for all 

of the bridges assessed using the Level 2 method are given in 

table 5, on the compact disk at the back of this report. A summary of the Level 2 assessment by MoDOT district in Missouri 

are shown in table 6.

Comparison of Level 1+ Results to Level 2 Results

The Level 1+ method was designed such that estimates of 

scour depths should nearly equal or exceed the values computed 

by the Level 2 method to provide conservative estimates of 

scour depth (Holnbeck and Parrett, 1997). Level 2’s were completed at 82 bridges that were not assessed as Level 1+’s; however, Level 2’s were completed at 316 bridges for which Level 

1+’s had been done, which provides a wide data base with 

which to compare the results of the two assessment procedures.

To provide a reasonable comparison between the results of 

the two assessments, it was necessary to identify a variable that 

was common between the two assessments for a given bridge. 

As mentioned in the previous sections, computed scour depths 

are associated with the discharge through the bridge opening 

(flow in the main channel and setbacks under the bridge, as 

opposed to the total discharge, which might include road overflow or flow through an adjacent bridge). For a majority of the 

bridges, scour depths were computed for two discharges in the 

yas ya 4Fra2

0.33 Ka1

0.55 = ----------Ka2
22 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri
Estimates of Scour Depth Using Different Techniques 23
24 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

Level 1+’s (Q100 and either Q500 or Qimp), and for as many as 

three discharges in the Level 2’s (at least Q100 and Q500, as well 

as Qimp if road overflow occurred in the Q100 or Q500 discharges). The two discharges for a given bridge in the Level 1+, 

Q2a and Q2b, were compared to the discharges used in the Level 

2 for the same bridge to find a match. For example, the discharge through the bridge opening for the 100-year peak discharge of the Level 1+ was compared to the discharge through 

the bridge opening for the 100-year peak discharge of the Level 

2 for the same bridge; the same was done with the 500-year 

peak discharge or the impendent discharge. If the discharge 

through the bridge for the Level 1+ matched the Level 2 discharge within 10 percent, it was considered a good match and 

the scour depths were considered comparable.

Because of the coarse nature of the methods to determine the 

impendent discharge or modify the discharge for an adjacent 

bridge in the Level 1+’s, it often was difficult to find a match 

between the impendent discharge of the Level 1+ and the impendent discharge of the Level 2 at a given bridge. Furthermore, if 

the impendent discharge in the Level 1+ was substantially different from the Level 2 impendent discharge (for example, the Level 

1+ Qimp was greater than the Q100, whereas the Level 2 Qimp was

less than the Q100), finding a match between any of the Level 1+ 

and Level 2 discharges for a given bridge also was compromised. 

If a match could not be made between the discharges at a specific 

recurrence interval (for example, the 100-year peak discharge), 

the two Level 1+ discharges through the bridge were compared to 

any and all of the Level 2 to find a match.

Consequently, of the 316 bridges common to both assessment methods (with 595 individual discharges by Level 1+, and 

1,019 individual discharges by Level 2), 327 discharges at 212 

bridges matched within 10 percent (fig. 8). Five bridges had no 

scour depths computed in the Level 1+ assessment; three were 

relief structures with no observable scour, and two were well 

protected bridges over a large river with no observable scour. 

An additional 22 bridges had no match between the various discharge types of the Level 1+ and the Level 2 (for example, the 

Level 2 had a Q100 and Q500, but the Level 1+ had Qimp only, 

as frequently occurred in the Mississippi Alluvial Plain region). 

The remaining bridges had one or more discharges through the 

bridge opening that did not match within 10 percent (fig. 8).

The 327 discharges that matched within 10 percent were 

examined for comparable values of main channel contraction 

scour, overbank contraction scour (both left and right), pier scour 

(main channel and overbank), and abutment scour (left and right). 

Occasionally, a bridge had a scour depth determined by the Level 

1+ but not the Level 2, or vice versa; these values are not included 

in the comparisons of Level 1+ and Level 2 depths. For each type 

of scour, the number of comparable values are stated as 

“matches.” For example, there were main channel contraction 

values determined by both the Level 1+ and the Level 2 assessments at all 212 bridges for the 327 matching discharges, so there 

are 327 “matches” of main channel contraction scour. However, 

there were only 137 of the matching discharges that had values 

for the left overbank in both the Level 1+ and Level 2 assessments; these were combined with 133 such “matches” for the 

right overbank, for a total of 270 “matches” of overbank contraction scour. Similarly, there were 313 main channel pier scour 

“matches,” and 83 overbank pier scour “matches,” for a total of 

396 “matches” of pier scour. There were 296 left abutment scour 

“matches,” and 297 right abutment scour “matches,” for a total of 

593 “matches” of abutment scour.

In all of the comparisons, the scour depth computed in the 

Level 1+ is compared to the value obtained in the Level 2. An

Table 6. Summary of detailed hydraulic assessments (Level 2) by Missouri Department of Transportation (MoDOT) district.

[--, no bridges]

MoDOT 

district

Bridges that 

received Level 

2 assessment

Level 2 bridges 

with 

substantial 

exposure

Level 2 bridges 

with either 

substantial or 

moderate 

exposure1

Level 2 bridges 

with moderate 

exposure

Level 2 bridges 

with either 

moderate or 

minimal 

exposure1

Level 2 bridges 

with minimal 

exposure

Level 2 bridges 

with 

foundations 

set on 

bedrock2

01 87 61 4 17 -- 5 5

02 96 62 2 23 2 7 5

03 42 27 -- 11 2 2 1

04 31 18 -- 5 1 7 5

05 44 32 -- 8 -- 4 10

06 20 12 -- 8 -- -- 3

07 4 2 -- 1 -- 1 1

08 5 5 -- -- -- -- 3

09 11 4 -- 6 -- 1 4

10 58 35 -- 11 1 11 4

Grand Total 398 258 6 90 6 38 41

1

Occasionally, a range of possible pile penetration lengths is given for a bridge pier or bent; these bridges could be classified as one or the other, depending on the true pile penetration in the field.

2

Sites with foundations set on bedrock are a non-exclusive subset of the total number.
Estimates of Scour Depth Using Different Techniques 25
26 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

equal-value line is shown in all comparison plots. When a point 

plots above the equal-value line, the Level 1+ value is a conservative (larger) estimate of the Level 2 scour depth; the closer to 

the equal-value line, the more closely the Level 1+ estimates the 

Level 2 value.

Contraction Scour

Contraction scour was separated into its two types, live bed 

and clear water. In the Level 1+ assessments, contraction scour 

in the main channel generally was considered to be live bed, 

because the velocity in the approach channel, V1, was assumed 

to be equal to the average velocity in the channel, V2. However, 

in the Level 2 assessments, 41 of the 327 comparisons were 

computed as clear-water scour, typically because the computed 

velocity in the approach channel, V1, was insufficient to transport material in the Level 2 assessment. The main channel contraction scour depths computed by both the live bed and the 

clear-water equations in the Level 2’s are shown in figure 9. The 

contraction scour on the overbanks (fig. 10) was considered to 

be clear water without exception in both assessments.

Main Channel Contraction Scour

Generally, the Level 1+ method did not provide either a 

markedly conservative or a close estimate of the Level 2 main 

channel contraction scour depth in Missouri (fig. 9A). There is 

a substantial amount of variability in the Level 1+ depths, and 

the Level 1+ depths appear to underestimate the Level 2 scour 

as much as overestimate. When the 41 Level 1+ estimates that 

were computed as clear-water scour in the Level 2 are removed 

(fig. 9A), the range of variability is not improved, and more than 

one-half of the matches (154 of 286 live-bed matches) plot 

below the equal-value line.

The variability does not appear to be dependent upon the 

physiographic region (figs. 9B, 9C, and 9D). When the main 

channel contraction scour values are examined by physiographic region, the Level 1+ method does not provide any better 

estimate of the Level 2 main channel scour depth in the Central 

Lowlands (region I, fig. 9B) than in the Ozark Plateaus (region 

II, fig. 9C). A majority of the Central Lowlands data plot below 

the equal-value line (104 out of 222 live-bed matches were 

above, fig. 9B), as do a majority of the Ozark Plateaus data (28 

out of 63 live-bed matches were above, fig. 9C). There were 

only two sites in the Mississippi Alluvial Plain for which the 

discharge through the bridge provided a match (region III, fig. 

9D), and the Level 1+ estimate underestimated the Level 2 

depth (the single live-bed match was below the equal-value line, 

fig. 9D).

The range of variability below the equal-value line is more 

substantial than above the equal-value line in all three regions. 

A best-fit trend line from the origin through the data in each 

region falls well below the equal-value line (figs. 9A, 9B, 9C, 

and 9D), which confirms that the magnitude of the Level 1+ 

underestimations is larger than the magnitude of the overestimations. However, it should be noted that no matter which 

region is examined, there were several cases where the extremes 

of variability were seen (that is, the Level 1+ estimated a zero 

depth of scour when the Level 2 resulted in some finite depth, 

and vice versa).

Overbank Contraction Scour

Generally, the Level 1+ method provides a more conservative estimate of the Level 2 overbank channel contraction scour 

depth than for main channel contraction scour in Missouri (161 

of 270 matches fall above the equal-value line, fig. 10A). However, as is the case for the main channel contraction scour, there 

is a substantial amount of variability in the estimates. There 

appears to be a slight difference in the variability when the overbank contraction scour values are examined by physiographic 

region (figs. 10B, 10C, and 10D). A larger majority of the Central Lowlands data plot above the equal-value line (105 of 169 

matches, fig. 10B), and the estimates are clustered more closely 

together around the equal-value line, which implies a better estimate of the Level 2 depths. A slight majority also plot above the 

equal-value line for the Ozark Plateaus data (55 of 100 matches, 

fig. 10C), but the data exhibit more variability than the Central 

Lowlands data. The single Mississippi Alluvial Plain data point 

plots above the equal-value line (fig. 10D). A best-fit trend line 

from the origin through the data in the Central Lowlands and the 

Ozark Plateaus regions falls below the equal-value line (figs. 

10B and 10C), as does the best-fit trend of all of the data (fig. 

10A), which implies that the magnitude of the Level 1+ underestimations is larger than the magnitude of the overestimations.

Discussion of Contraction Scour Depth Estimate Comparisons

As stated earlier, the Level 1+ method was developed to 

provide conservatively high estimates of scour depth relative to 

more-detailed procedures like the Level 2 method. However, 

discrepancies between scour depths determined by the Level 1+ 

method and scour depths determined by the Level 2 method for 

a number of sites in Missouri lead to the conclusion that the 

Level 1+ method may have underestimated contraction scour in 

some instances. Likely factors that account for many of the discrepancies in estimating scour depth by the two methods are, 

therefore, offered and discussed further here.

First, the Level 1+ method uses surrogate variables for 

flow depth and width based on simplified hydraulic procedures. 

These variables are then used to derive other hydraulic variables, and all variables are then used in the scour depth calculations. Application of these methods to the complex bridge openings and channels typically encountered in the Missouri study 

resulted in flow depths and widths that differed somewhat from 

those determined by the Level 2 method, and these differences 

account for some of the discrepancy in calculated contraction 

scour depths. Flow depths and widths determined by the Level 

2 method, however, are equally subject to interpretation and can 

vary based on an individual's judgment and the data collected in 

the field, thus scour depths produced by a particular method can 

vary.
Estimates of Scour Depth Using Different Techniques 27
28 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri
Estimates of Scour Depth Using Different Techniques 29

Secondly, in addition to being sensitive to flow-depth and 

width variables, calculated contraction scour depths also are 

sensitive to certain equation variables that are common to both 

methods. For live-bed scour calculations, the important common variable is the Manning's roughness coefficient and for 

clear-water scour calculations, the important common variable 

is the median particle size, or D50. Because these equation-sensitive variables are common to both methods and should ideally 

be determined based on similar levels of effort, critical comparisons between the two methods should, strictly speaking, be 

based on use of identical values of roughness coefficient and 

median particle size. For many bridge sites in this study, values 

of roughness coefficient used in the Level 1+ method did not 

equal values used in the Level 2 method, mainly because many 

Level 2 analyses were conducted by a different individual than 

conducted the corresponding Level 1+ assessment. Furthermore, the median particle size often was visually estimated in 

the Level 1+ assessment, whereas more specific values based 

upon lab analysis or more thorough evaluation were used in the 

Level 2 assessments. Differences in calculated scour depth 

between methods are thus an outcome to be expected for sites 

where variables common to both methods differed in the values 

used between methods.

In an attempt to address these considerations, a subset of 

the bridges for which the Level 1+ underestimated the Level 2 

contraction scour depths was randomly chosen, and the Level 

1+ contraction scour depths were recomputed using values for 

width, Manning's roughness, and median particle size from the 

Level 2 assessment (flow depths were not altered, because 

depths in the Level 1+ were interdependent and based on the 

location of the “average bed” and not a true bed elevation). Contraction scour depths for 24 bridges in the Central Lowlands and 

13 bridges in the Ozark Plateaus were recomputed using the values from the Level 2 assessments. The 24 bridges in the Central 

Lowlands represented 39 of 118 underestimated values of livebed main channel contraction scour and 47 of 64 underestimated values of overbank contraction scour, and the 13 bridges 

in the Ozark Plateaus represented 19 of 35 underestimated values of live-bed main channel contraction scour and 27 of 45 

underestimated values of overbank contraction scour. A substantial decrease in the number of underestimations was 

observed when the values of width, roughness, and median particle size from the Level 2 assessments were used in the Level 

1+ equations. Proportionally extending the results from the random subset to the entire set of underestimations in the Central 

Lowlands, a substantial majority of the main channel contraction scour results (approximately 163 out of 222 live bed) and 

the overbank contraction scour results (approximately 152 out 

of 169 matches) presumably would overestimate the Level 2 

results. Similarly in the Ozark Plateaus, a substantial majority 

of the main channel contraction scour results (approximately 51 

out of 63 live-bed matches) and the overbank contraction scour 

results (approximately 87 out of 100 matches) presumably 

would overestimate the Level 2 results. This would imply that 

approximately 18.4 percent of the Level 2 contraction scour 

depths would be underestimated by Level the 1+ method. By 

way of comparison, Holnbeck and Parrett (1997) experienced 

approximately 15.2 percent underestimation of Level 2 contraction scour depths in their study.

A majority of the remaining underestimates of contraction 

scour likely can be attributed to the location of the average bed 

in the Level 1+, or a difference in the depth of flow in the channel used in the Level 1+ compared to the Level 2. As described 

in the Determination of Average Bed Location section earlier in 

this report, the average bed of the bridge was chosen so that the 

average flow area would approximate a rectangle in the Level 

1+ assessments. Therefore, the “average bed” actually was the 

average bed of the whole bridge opening—including any setback areas of the bridge—and not the average bed of the channel alone. The water-surface elevation at the bridge was taken 

as the “average bed” plus the average depth computed by equation 5. In both the Level 1+ and the Level 2 assessments, the 

depths of flow on the setbacks and on the approach flood plains 

were measured relative to the water-surface elevation. However, the depth of flow in the channel was taken as the average 

depth in the Level 1+ assessments, whereas in the Level 2 

assessments, the depth of flow in the channel was determined 

utilizing the average ground elevation of the channel bed relative to the water-surface elevation. For many bridges in Missouri, this difference in the channel depth of flow did not create 

a substantial difference in the contraction scour, because the setback areas were small relative to the overall bridge opening, and 

therefore, the average depth nearly equalled the channel depth 

of flow used in the Level 2 assessment. However, bridges with 

substantial setback areas often had a depth of flow in the channel in the Level 2 assessment that was much greater than the 

average depth used in the Level 1+, which would lead to substantially different results for main channel contraction scour. 

Furthermore, if the average bed was located incorrectly at a 

bridge with substantial setback areas, the resultant water-surface elevation used to determine flow depths on the setbacks 

and flood plains in the Level 1+ also would be incorrect, which 

subsequently could lead to incorrect values of width on the 

flood plains.

Pier Scour

The pier scour depth computed in the Level 1+ assessments compared to the Level 2 for all bridges with matching 

discharges is shown in figure 11A. In general, the points form a 

cluster around the equal-value line, which implies that the Level 

1+ method provides a reasonable close estimate of the Level 2 

pier scour depth in Missouri (but typically not a conservative 

estimate). However, computations were made for piers with 

exposed footings or complex foundations exposed to flow in the 

Level 2 assessments, but not in the Level 1+ assessments. When 

the results for piers without exposed foundations are considered 

alone (fig. 11A), the Level 1+ method generally provides a conservative estimate of the Level 2 scour depth, as a majority of 

the values plot above the equal-value line in figure 11A (150 of 

248 matches). There are no substantial differences between
30 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri
Estimates of Scour Depth Using Different Techniques 31

regions when the pier scour data are examined by physiographic 

region (figs. 11B, 11C, and 11D). 

However, if the piers with footing exposure are reassessed 

using the footing width instead of the pier width in the Level 1+ 

pier scour estimation equation, a large majority of the piers with 

footing exposure plot above the equal-value line (131 of 148 

matches with footing exposure). In the field, however, it is difficult to predict if footing exposure will occur without a copy of 

the bridge plans. For this reason, it would be helpful to have 

some sort of indication of the depth of the pier footings in future 

assessments, and use the footing width as the pier width in the 

Level 1+ assessment if the potential for footing exposure exists.

A majority of the Level 1+ values that plot below the 

equal-value line likely arise from the difference between the 

velocities used in the Level 1+ and Level 2 assessments. The 

Level 1+ uses a Froude number based on the average velocity 

calculated by equation 1 or 2, whereas the Level 2 uses a Froude 

number based on the maximum velocity in the main channel 

and the maximum overbank velocity on the overbanks. A substantial difference existed between the average velocity used in 

the Level 1+ assessment and the maximum channel velocity for 

most of the bridges that were underestimated by the Level 1+ 

assessment. This difference was most noticeable at bridges that 

had substantial setbacks, which would reduce the average 

velocity compared to a bridge with smaller setbacks. The other 

variable in the Level 1+ pier scour estimation equation is the 

flow angle of attack, or skew, and differences in this variable 

between the Level 1+ and Level 2 assessments accounts for several underestimations, as well as a few substantial overestimations. However, 99 of 114 Level 1+ underestimations (for piers 

with and without footing exposure) are less than 2.5 feet different from the Level 2 pier scour depth, and 112 of 114 are less 

than 5 feet different. Holnbeck and Parrett (1997) also observed 

occasional underestimations, with 7 out of 24 Level 2 pier scour 

depths (approximately 29.2 percent) being underestimated by 

the Level 1+. A best-fit trend line from the origin through the 

pier data (with and without footing exposure) falls above the 

equal-value line in each region (figs. 11A, 11B, 11C, and 11D).

The distinct horizontal linear bands of values in the Level 

1+ pier scour depths for piers without footing exposure in figure 

11 are a function of the simplification of the Level 1+ pier scour 

estimation equation (eq. 29) as compared to the full pier scour 

equation used in Level 2 assessments (eq. 34). The principal 

variables in the Level 1+ equation are pier width, alignment to 

flow, and average Froude number. MoDOT typically uses standardized pier shapes throughout the state, and regularly aligns 

the piers to flow; furthermore, the average Froude number is 

determined by the average depth and average velocity, which 

are related to each other by equations 1, 2, and 3. This results in 

a narrow band of possible scour depths for a given pier geometry for piers aligned with the flow. The lowest distinct band 

(with Level 1+ pier scour depths approximately 3.2 feet) corresponds to bents with 10-inch wide steel H-piles. The second 

band (with Level 1+ depth approximately 3.9 feet) corresponds 

to bents with 1-foot diameter timber piles. The next distinct 

band (with Level 1+ values approximately 7.7 feet) corresponds 

to piers or bents with 2.5-feet wide columns. Similar bands are 

seen in the results modified for footing exposure, and correspond to standard footing widths of 6 feet and 9 feet. Level 1+ 

pier scour depth values between these distinct linear bands typically are those with some other column or footing geometry, or 

with a skewed flow angle of attack (measured in 5 degree increments, which creates other less distinct bands on the plot). In 

contrast, the full pier scour equation used in Level 2 assessments (eq. 34) is affected by several variables, and yields a 

wider range of pier scour depths for a given pier geometry.

Abutment Scour

The abutment scour depth computed in the Level 1+ 

assessments compared to the Level 2 for all bridges with matching discharges is shown in figure 12. The Level 1+ method generally provides a conservative estimate of the Level 2 scour 

depth in Missouri, as a majority of the values (502 of 593 

matches) plot above the equal-value line in figure 12A. However, like the contraction scour comparison, the Level 1+ 

method does not provide a close estimate, as there is a substantial amount of scatter around the equal-value line.

Also like the overbank contraction scour comparison, the 

Central Lowlands data cluster together above the equal-value 

line (fig. 12B), which implies a conservative estimate of the 

Level 2 depths. There is more variability in the Ozark Plateaus 

data (fig. 12C). Only the Mississippi Alluvial Plain data plot 

entirely above the equal-value line (fig. 12D), but the amount of 

available data is sparse. A best-fit trend line from the origin 

through the data in each region falls above the equal-value line 

(figs. 12A, 12B, 12C, and 12D). 

For 63 of the 91 abutment scour depths underestimated by 

the Level 1+, the difference between the Level 1+ and the Level 

2 abutment scour depth was less than 5 feet. Holnbeck and Parrett (1997) also observed occasional underestimations, with 11 

out of 66 Level 2 abutment scour depths (approximately 16.6 

percent) being underestimated by the Level 1+. However, for 

Missouri, 6 of the Level 1+ depth underestimates were 10 feet 

or more different from the Level 2 abutment scour depth.

The only variables in the Level 1+ abutment scour estimation equation (eq. 30) are the depth of flow on the approach 

flood plain and the abutment type (vertical, vertical with wing 

walls, or spill through). Therefore, for a given abutment type, 

the abutment scour depth is dependent entirely upon the depth 

of flow on the approach flood plain. If this depth is underestimated, the abutment scour also would be underestimated. As 

was noted in the contraction scour depth estimate comparison 

discussion, an incorrectly located average bed at the bridge 

could lead to an incorrect flood-plain flow depth, and it was 

observed that 49 of the 91 underestimations of abutment scour 

depth also had an underestimation of main channel contraction 

scour. The larger underestimations of abutment scour are 

almost entirely the result of an underestimation of the depth of 

flow on the flood plain in the Level 1+ assessment.
32 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri
Estimates of Scour Depth Using Different Techniques 33

Validation of Level 1+ Procedures Using Level 2 

Results

The two region-specific variables described in the Rapid 

Estimation Method (Level 1+) section are the average main 

channel velocity at the bridge, V2, and the difference in watersurface elevation from the approach section to the downstream 

face of the bridge, ∆h, and are defined by equations 1 through 

3. Holnbeck and Parrett (1997) developed these relations for 

Montana using Level 2 data from Montana and Colorado. However, Level 2 data for all three physiographic regions of Missouri were not available before the Level 1+, so gage information was used to develop the relation for V2, and Level 2 data for 

the Central Lowlands region was used to develop the relation 

for ∆h throughout Missouri. Now that Level 2 data exists for all 

three regions, a validation of the data used to develop the relations can be made.

Average Main Channel Velocity

The average main channel velocity at the bridge, V2, was 

determined from a relation with the unit discharge through the 

bridge, q2. Unit discharge and average channel velocity data 

from the original 35 sites in the Central Lowlands are shown 

with the gage data used to develop equation 1 in figure 13A. 

Similarly, unit discharge and velocity data for bridges in the 

Ozark Plateaus are shown with the gage data used to develop 

equation 2 in figure 13B. The lines represented by equations 1 

and 2 also are shown. It appears that equations 1 and 2 are both 

somewhat low compared to the Level 2 data for these regions, 

and that a more appropriate best fit might be represented by the 

dashed lines in figure 13A and 13B.

Using the dashed lines instead of equations 1 and 2 would 

result in a higher average velocity in the channel for a given unit 

discharge. Based on the discussion in the comparison of pier 

scour results earlier in this report, an increase in velocity would 

yield higher estimations of pier scour depth for a given pier 

geometry and skew. On the other hand, equation 7 shows that 

an increase in velocity would result in a corresponding decrease 

in flow depth in the main channel. Based on the discussion in 

the comparison of abutment scour results earlier in this report, 

a decrease in depth would yield lower estimations of abutment 

scour depth for a given abutment type. Presumably, a similar 

decrease in main channel and overbank contraction scour 

depths also would occur. However, because equations 1 and 2 

are logarithmic, the depth decreases exponentially with 

increases in velocity. For this reason, the abutment scour depth 

estimates (and presumably the main channel and overbank contraction scour depth estimates) are more sensitive to a decrease 

in depth than the pier scour depth estimates are to the corresponding increase in velocity. Therefore, the relations defined 

by equations 1 and 2 yield more conservative results than would 

relations defined by the Level 2 data.

Difference in Water-Surface Elevation

The difference in water-surface elevation from the 

approach section to the downstream face of the bridge, ∆h, was 

determined from a relation with the square of the average main 

channel velocity, V2. The Level 2 data for the original 35 sites 

in the Central Lowlands used to develop equation 3 are shown 

in figure 14, as is the line represented by equation 3. Only the 

Central Lowlands data were available before the Level 1+, and 

it was assumed that this relation could be applied throughout 

Missouri. Upon completion of the Level 2’s, similar data for 72 

bridges in the Ozark Plateaus were obtained (fig. 14). A best-fit 

regression equation for the Ozark Plateaus data yields the following relation:

∆hOP = 0.030 V2OP

2 + 0.05 (37)

where

∆hOP is the change in water-surface elevation from the

approach section to the downstream face of the

bridge in the Ozark Plateaus, in feet; and

V2OP is the average main channel velocity for bridges in 

the Ozark Plateaus, in feet per second (ft/s).

In comparison, equation 3 (using only Central Lowlands data) 

is:

∆h = 0.030 V2

2 + 0.03

which means for a given V2, equation 37 and equation 3 yield a 

∆h that differs by only 0.02 feet. Furthermore, when Level 2 

data for 22 bridges in the Mississippi Alluvial Plain region are 

plotted, the trend of the data also is along the line defined by 

equation 3 (fig. 14). Therefore, using equation 3 throughout 

Missouri was a valid assumption.

Determination of Road Overflow

In the Level 1+ assessments, when the impendent road 

overtopping discharge, Qimp, was less than the 100-year peak 

discharge, Q100, the flow through the bridge opening, Q2a, had 

to be adjusted for the amount of flow over the road. However, 

at the time of the Level 1+ assessment, there were insufficient 

data to quantitatively determine the amount of flow that would 

pass through the bridge opening when flow overtopped an adjacent low road embankment. When Qimp was less than Q100, it 

was assumed that one-half of the difference between Q100 and 

Qimp would pass over the road, and the flow through the bridge 

opening was assumed to be

Q2a = Q100 - 1

/2(Q100 - Qimp)

as defined earlier in equation 11, or

Q2a = Qimp + 1

/2(Q100 - Qimp). (38)
34 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri
Estimates of Scour Depth Using Different Techniques 35

It was presumed that equation 11 or equation 38 overestimated 

the part of the total flow that would pass through the bridge 

opening by underestimating the flow over the road embankment, particularly for bridges with wide flood plains and low 

road embankments, but no quantitative data existed to prove 

otherwise.

Using the data from the Level 2 assessments, the flow 

through the bridge opening as estimated by equation 38 was 

compared to the flow through the bridge opening as determined 

by the hydraulic analysis using WSPRO in the Level 2 assessments for sites where Qimp was less than Q100. Generally, equation 38 resulted in a flow through the bridge opening, Q2a, that 

was within a range of 85 percent to 150 percent of the value 

determined by WSPRO analysis, except for sites with very low 

road embankments and wide flood plains (fig. 15). The range 

was considered acceptable for most bridges with road overflow 

because it overestimates flow through the bridge opening as 

compared to the WSPRO analyses, resulting in reasonable, conservative scour estimates.

However, for sites with very low road embankments and 

wide flood plains, where Qimp is less than approximately 25 

percent of Q100, equation 38 resulted in a Q2a that was substantially greater than (as much as 470 percent) the value determined by WSPRO analysis, which would result in unreasonable 

overestimations of scour depth. For these sites, it was determined that limiting the flow through the bridge to 150 percent 

of the impendent discharge, or
36 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

Q2a = 1.5 Qimp (39)

brought the value of Q2a back into the range of 85 percent to 150 

percent of the value determined by WSPRO analysis (fig. 15). 

In future work with the Level 1+ method at sites where Qimp

< 0.25 Q100, therefore, the use of equation 39 is encouraged to 

determine Q2a to maintain a reasonable estimate of flow 

through the bridge opening as scour depth.

General Limitations of Scour Depth Estimation 

Methods

Estimates of scour depths using either the rapid estimation 

method (Level 1+) or the detailed hydraulic assessment (Level 

2) are designed to be conservative in terms of risk. In the latest 

edition of HEC-18, Richardson and Davis (2001) state:

“The equations and methodologies presented in [the 

HEC-18] manual, which predict the maximum scour 

depth in non-cohesive soil, may, in some circumstances be too conservative. The pier scour equation 

represents an envelope curve of the deepest scour 

observed during the various laboratory studies and 

field data.”

The conservative approach usually is reasonable and cost-effective from the standpoint of bridge design. When evaluating 

existing structures, however, the conservative approach could 

indicate that a structure will be undermined by a peak discharge 

that historically had been observed at a bridge without the 

bridge failing. Factors determining the vulnerability of an existing structure are complex, but several considerations that apply 

to both scour depth estimation methods, as applied in Missouri, 

are discussed below.

Verification of Scour Depth Estimates Using Field Data

The equations and methodologies provided in HEC-18 

generally were formulated using laboratory research with noncohesive soils with limited verification using field data. In the 

latest edition of HEC-18, Richardson and Davis (2001) state:

“The current equations and methods for estimating 

scour at bridges are based primarily on laboratory 

research. Very little field data have been collected to 

verify the applicability and accuracy of the various 

design procedures for the range of soil conditions, 

stream flow conditions, and bridge designs encountered throughout the United States. In particular, 

DOTs are encouraged to initiate studies for the purpose of obtaining field measurements of scour and 

related hydraulic conditions at bridges for evaluating, 

verifying, and improving existing scour prediction 

methods.”

This limitation of the equations and methods has always been 

recognized, as a similar statement is found in each edition of 

HEC-18 (Richardson and others, 1991, 1993; Richardson and 

Davis, 1995). Given that the HEC-18 equations and methods 

represent an “envelope curve approach,” it is reasonable to 

assume that the scour depths estimated by the Level 1+ and 

Level 2 assessments for sites in Missouri may overestimate the 

actual scour that would occur.

For pier scour, HEC-18 uses a modified form of an equation developed at Colorado State University (CSU) because it 

was good for design as it rarely under-predicted measured scour 

depth when compared to measured scour depths (Richardson 

and Davis, 2001). However, it is acknowledged that the HEC18 pier scour equation also frequently over-predicts observed 

scour. In a study of scour in Missouri by Becker (1994), pier 

scour depths observed at several sites throughout Missouri were 

compared to depths computed using seven pier scour estimation 

equations. Becker’s study included the original CSU equation 

with a 10-percent increase, which makes it equivalent to the 

HEC-18 pier scour equation used in the Level 2 assessments in 

Missouri (eq. 34) with coefficients Kp3 and Kp4 set to 1.1 and 

1.0, respectively. Becker indicates that the modified CSU equation overestimated the observed scour depth for all the sites 

examined in Missouri (fig. 16). An approximate best-fit trend 

line through the data indicates that as the estimated scour depth 

increases, the magnitude of the overestimation increases.

The scour depths estimated by the Level 1+ and Level 2 

assessments at sites in Missouri for this report generally were 

not verified with field measurements, and Becker’s (1994) 

study predominantly includes floods with recurrence intervals 

less than 5 years, which are substantially less than those used in 

the Level 2 assessments. However, three of the sites in Becker’s 

study subsequently received a Level 2 assessment and had scour 

depth measurements obtained during the 1993 floods that had 

recurrence intervals estimated to be between 50 and 500 years 

(Parrett and others, 1993), which is comparable to those used in 

the Level 2 assessments. A comparison of the pier scour depths 

measured and estimated by Becker are shown in table 7.

The contraction scour and abutment scour equations in 

HEC-18 primarily were developed through laboratory experimentation, also with limited field verification (Richardson and 

Davis, 2001). The only exception is the HIRE abutment scour 

equation (eq. 36), which was based on field measurements of 

scour at the end of spurs in the Mississippi River obtained by the 

U.S. Army Corps of Engineers, a field situation that closely 

resembles the laboratory experiments for abutment scour. Nevertheless, both abutment scour equations are acknowledged to 

have a tendency to overpredict the magnitude of scour that may 

develop. Only the contraction scour equations specifically are 

not acknowledged to be conservative in HEC-18. As was stated 

earlier in the Comparison of Level 2 Results to Level 1+ Results 

section, the Level 1+ method was designed such that estimates 

of scour depths should nearly equal or exceed the values computed by the Level 2 method to provide a conservative estimate. 

Therefore, if the Level 2 results tend to overestimate observed 

scour depths, the Level 1+ also will tend to overestimate 

observed scour depths.
Estimates of Scour Depth Using Different Techniques 37
38 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

Scour Depth as a Function of Flood Duration in 

Cohesive Soils

Scour depths estimated by the rapid estimation method 

(Level 1+) and the detailed hydraulic assessment (Level 2) 

shown in tables 3 and 5 are the maximum scour depths for a 

non-cohesive soil. The maximum scour depth often is assumed 

to occur at a given bridge during a single flood event. However, 

this may not be the case for cohesive soils (silts and clays) such 

as are found in various locations throughout Missouri. In the latest edition of HEC-18, Richardson and Davis (2001) state:

“The maximum depth of local scour at piers in cohesive soils is the same as in non-cohesive soils. Time is 

the difference. Maximum scour depth is reached in 

hours or one runoff event in non-cohesive sand, but 

may take days and many runoff events in cohesive 

clays. Local pier scour in cohesive clays may be 

1,000 times slower than non-cohesive sand. In addition, by inference, contraction scour and local scour 

at abutments in cohesive soils do not reach maximum 

depth as rapidly, but the ultimate scour depth will be 

the same as for non-cohesive soil.” (emphasis added)

“Because cohesive soils can scour much slower than 

non-cohesive soils, it is reasonable to include the 

scour rate in the calculations. Indeed, while one 

flood may be sufficient to create the maximum scour 

depth in cohesionless soils, the scour depth after 

many years of flood history at a bridge in an erosion 

resistant cohesive soil may only be a fraction of [the 

maximum scour depth].”
Estimates of Scour Depth Using Different Techniques 39

Little research has been done on the time rate of scour for 

cohesive soils. Therefore, HEC-18 provides no specific guidance on calculating scour depths in cohesive soils. From the 

standpoint of bridge design, using the conservative approach is 

reasonable, as it is assumed that the maximum scour will be 

reached sometime within the service life of a typical bridge subjected to multiple flood events. However, the time rate of scour 

can have a profound effect on the stability of an existing structure. Based on the comments in HEC-18, it appears to be possible that a structure in a cohesive soil could experience a single 

flood event of sufficient magnitude that would cause it to be 

undermined based on the results of the Level 2 assessment, and 

yet not be undermined because the flood event was not of sufficient duration to cause the maximum scour depth to be reached.

Assumption of Soil Homogeneity

The contraction scour estimation equations in both the 

Level 1+ and Level 2 methods are dependent upon the median 

particle size, D50, of the soils present in the channel or on the 

overbanks. As described in the General Procedure of Level 1+ 

Assessments section earlier in this report, the median particle 

sizes of the main channel and overbank materials in the Level 

1+ assessments were estimated by visually identifying the 

material as cobbles, gravel, sand (coarse, medium, or fine), or 

silt/clay. In the Level 2 assessments, the median particle sizes 

of the main channel and overbank materials were determined by 

laboratory analysis of a representative sample of the material 

obtained from the channel or overbank. Both assessment methods used a representative sample to account for surface variations in soil composition in the channel or on the overbank. The 

difference in the level of effort used to obtain the median particle sizes was observed to lead to a difference in contraction 

scour results between the two assessment methods.

However, in addition to the level of effort difference 

between the assessment methods, the representative surface 

sample did not account for variations in soil composition with 

depth, such as stratified layers of gravel, sand, silt, clay, or rock. 

Both assessment methods assume that the surface sample also 

is representative of a homogeneous soil that does not change 

with depth, which will allow the maximum scour depth to be 

reached. This limitation was acknowledged in every Level 2 

assessment. Changes in the subsurface strata will result in different scour depths at a given site because of the time rate of 

scour difference between non-cohesive to cohesive soils as discussed earlier, or because of the presence of scour-resistant 

rock, both of which might limit scour. Information from soil 

borings would be helpful to determine the presence of subsurface strata that would be resistant to scour and would, therefore, 

limit the maximum scour depth.

Accuracy and Consistency of Variables

As stated in the contraction scour depth estimate comparison, discrepancies in the calculated contraction scour depths 

arose from differences in the flow depths and widths between 

the Level 1+ and Level 2 methods. Furthermore, calculated contraction scour depths also were sensitive to certain equation 

variables that are common to both methods, most notably the 

Manning's roughness coefficient for live-bed contraction scour, 

and the median particle size for clear-water contraction scour. 

Therefore, equation-sensitive variables that are common to both 

Table 7. Summary of discharge data, measured scour depths, and scour depths estimated using various methods at selected sites 

in Missouri (modified from Becker, 1994).

[MoDOT, Missouri Department of Transportation; USGS, U.S. Geological Survey; ft3/s, cubic feet per second; --, no data; >, greater than]

MoDOT 

structure 

number

USGS 

station 

number

Date of 

measurement Time

Scour 

measurement 

discharge 

(ft3

/s)

Flood peak 

discharge 

(ft3/s)

Recurrence 

interval range

(years)

Measured 

scour 

depth

(feet)

Estimated 

scour 

depth

(feet)1

Chariton River on State Route 6 in Adair County

L 534 06904500 07/13/1993 0030 -- 20,900 10-502 -- --

1445 17,400 -- -- 1.9 7.0

Chariton River on State Route 129 in Chariton County

L 344 06905500 07/08/1993 0915 27,200 -- -- 4.7 8.2

07/13/1993 1945 -- 31,300 >1002 -- --

Gasconade River on State Route 89 in Osage County

A 1411 06934000 09/28/1993 1000 -- 106,000 54 -- --

1328 101,000 -- -- 4.1 11.1

1Calculated using modified Colorado State University equation (Becker, 1994), which essentially is the same equation as was used in detailed 

hydraulic assessment (Level 2). Becker’s scour measurement discharge and the associated field parameters were used in the equation to provide a 

direct comparison with the measured scour depth. 2From Parrett and others (1993).
40 Potential-Scour Assessments and Estimates of Scour Depth Using Different Techniques at Selected Bridge Sites in Missouri

methods should ideally be determined by similar methods, and 

critical comparisons between the two methods should be based 

on use of similar or identical values of flow depth, flow width, 

roughness coefficient, and median particle size. Obviously, this 

logic extends to the calculation of the pier scour and abutment 

scour depth. Differences in calculated scour depth between 

methods should be expected for sites where inconsistent values 

are assigned to variables common to both methods.

Finally, whether a scour analysis is conducted by the Level 

1+ or the Level 2 method, unreliable scour-depth estimates can 

result for either method if important equation variables are 

determined based on an insufficient level of effort or where 

variables are not appropriate for the hydraulic conditions being 

analyzed. Furthermore, interpretations involved in the application of either method can produce results for estimated scour 

depth that vary within a particular method as well as between 

methods. Holnbeck and Parrett (1997) acknowledge these limitations in the Level 1+ assessment method, and state that field 

parameters should be obtained by individuals with “considerable field experience and sound judgment regarding bridge 

scour, flood hydrology, and hydraulics. Even for highly experienced individuals, the results of field testing of the 

method...indicated that some experience with the rapid estimation method itself is required to produce reliable and generally 

reproducible results.”

Summary

A potential-scour assessment (Level 1) was used by the 

U.S. Geological Survey, in cooperation with the Missouri 

Department of Transportation, at 3,082 bridges in Missouri to 

identify bridges that might be susceptible to scour. Values 

assigned to characteristics of the site, such as the presence of 

existing scour and evidence of past scour, were combined into 

an observed scour index. Other site characteristics that might 

exacerbate or mitigate scour were combined into a potentialscour index. These indices were used to rank the 3,082 bridges 

for their susceptibility to scour. Nearly 1,300 bridges were identified as scour-susceptible, requiring additional analysis.

A rapid estimation method (Level 1+) was used to estimate 

contraction, pier, and abutment scour depths at 1,396 bridge 

sites throughout Missouri. The results were used in conjunction 

with a qualitative assessment recommended by the Missouri 

Department of Transportation (MoDOT) to determine which 

sites were potentially scour critical and would require additional analysis. 

A detailed hydraulic assessment method (Level 2) was 

used to compute estimates of contraction, pier, and abutment 

scour depths at 398 bridges throughout Missouri. MoDOT uses 

the scour results to determine if the bridge sites are scour critical 

and will need further monitoring or application of scour countermeasures. Thirty-five Level 2 assessments were completed 

before implementation of the Level 1+ method. Twenty-nine 

additional assessments were completed at bridges over major 

rivers without either a Level 1 or Level 1+ assessment, and 22 

assessments were completed at bridges that had been deemed 

not susceptible to scour but were in proximity and hydraulically 

connected to a Level 2 bridge.

A Level 2 assessment was performed at 316 bridges that 

had received a Level 1+ assessment, which provided a broad 

data base to compare the two scour assessment methods. The 

scour depths computed by each of the two methods were compared for bridges that had similar discharges through the bridge 

opening. For Missouri, the Level 1+ assessment was a reasonable conservative estimator of Level 2 pier scour depths if the 

pier width is used for piers without footing exposure and the 

footing width is used for piers with footing exposure. The Level 

2 abutment scour depths were conservatively estimated by the 

Level 1+ assessment, but there was substantial variability in the 

estimates and several substantial underestimates. The Level 1+ 

assessment did not provide a reasonable conservative estimate 

of the Level 2 contraction scour depths in Missouri, but the discrepancy primarily was the result of using different values for 

variables that were common to both of the assessment methods 

and, therefore, should have been similar or identical in the two 

methods.

References

Alexander, T.W., and Wilson, G.L., 1995, Technique for estimating the 2- to 500-year flood discharges on unregulated 

streams in rural Missouri: U.S. Geological Survey WaterResources Investigations Report 95–4231, 33 p.

Arcement, G.J., Jr., and Schneider, V.R., 1989, Guide for 

selecting Manning’s roughness coefficients for natural channels and flood plains: U.S. Geological Survey Water-Supply 

Paper 2339, 38 p.

Barnes, H.H., Jr., 1967, Roughness characteristics of natural 

channels: U.S. Geological Survey Water-Supply Paper 1849, 

213 p.

Becker, L.R., 1994, Investigation of bridge scour at selected 

sites on Missouri streams: U.S. Geological Survey WaterResources Investigations Report 94–4200, 40 p.

Chow, V.T., 1959, Open-channel hydraulics: New York, 

McGraw-Hill Book Company, 680 p.

Fenneman, N.M., 1938, Physiography of Eastern United States: 

New York, McGraw-Hill Book Company, 723 p.

Hauck, H.S., and Nagel, C.D., 2004, Water Resources Data for 

Missouri, Water Year 2003, U.S. Geological Survey WaterData Report MO–03–1, 776 p.

Holnbeck, S.R., and Parrett, C., 1997, Method for rapid estimation of scour at highway bridges based on limited site data: 

U.S. Geological Survey Water-Resources Investigations 

Report 96–4310, 79 p.

Huizinga, R.J., and Rydlund, P.H., Jr., 2001, Simulation of flow 

and evaluation of bridge scour at Horse Island Chute bridge 

near Chester, Illinois: U.S. Geological Survey WaterResources Investigations Report 01–4176, 28 p.
References 41

Huizinga, R.J., and Waite, L.A., 1994, Methodology for the 

assessment of scour at bridge sites in Missouri: U.S. Geological Survey Open-File Report 94–544, 23 p.

Lagasse, P.F., Shall, J.D., Johnson, F., Richardson, E.V., Richardson, J.R., and Chang, F., 1991, Stream stability at highway structures: U.S. Federal Highway Administration Publication FHWA-IP-90-014 Hydraulic Engineering Circular 

No. 20, 195 p.

Parrett, Charles, Melcher, N.B., and James, R.W., Jr., 1993, 

Flood discharges in the Upper Mississippi River Basin, 1993, 

in Floods in the Upper Mississippi River Basin, 1993: U.S. 

Geological Survey Circular 1120–A, 14 p.

Richardson, E.V., and Davis, S.R., 1995, Evaluating scour at 

bridges (3d ed.): U.S. Federal Highway Administration Publication FHWA-IP-90-017 Hydraulic Engineering Circular 

No. 18, 204 p.

Richardson, E.V., and Davis, S.R., 2001, Evaluating scour at 

bridges (4th ed.): U.S. Federal Highway Administration Publication FHWA NHI 01-001 Hydraulic Engineering Circular 

No. 18, 378 p.

Richardson, E.V., Harrison, L.J., and Davis, S.R., 1991, Evaluating scour at bridges: U.S. Federal Highway Administration 

Publication FHWA-IP-90-017 Hydraulic Engineering Circular No. 18, 105 p.

Richardson, E.V., Harrison, L.J., Richardson, J.R., and Davis, 

S.R., 1993, Evaluating scour at bridges (2d ed.): U.S. Federal 

Highway Administration Publication FHWA-IP-90-017 

Hydraulic Engineering Circular No. 18, 132 p.

Shearman, J.O., 1990, User’s manual for WSPRO—A computer model for water surface profile computations: U.S. 

Federal Highway Administration Publication FHWA-IP-89-

027 Hydraulic Computer Program HY-7, 177 p.

Shearman, J.O., Kirby, W.H., Schneider, V.R., and Flippo, 

H.N., 1986, Bridge waterways analysis model-research 

report: U.S. Federal Highway Administration Research 

Report FHWA-RD-86-108, 122 p.

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Washington, D.C., Federal Highway Administration Technical Advisory 5140.20, 4 p.
For additional information contact:

U.S. Geological Survey

Missouri Water Science Center

1400 Independence Road

Mail Stop 100

Rolla, MO 65401

(573) 308-3664 or

http://mo.water.usgs.gov