U.S. Department of the Interior—U.S. Geological Survey

A method was developed for 

rapid estimation of scour depths at 

highway bridges based on limited site 

data that could be obtained at a site in 

a matter of hours rather than the 

several days or longer that is required 

by more detailed methods. A faster 

method is needed to estimate scour 

depths because scour assessments are 

required for a large number of bridges 

as part of a national program to 

inventory scour-susceptible bridges 

throughout the United States. Data 

from detailed scour analyses 

performed by the U.S. Geological 

Survey in Colorado, Indiana, Iowa, 

Mississippi, Missouri, Montana, New 

Mexico, South Carolina, Texas, and 

Vermont and the Montana 

Department of Transportation were 

used to develop relations between 

scour depth and hydraulic variables 

that can be rapidly measured or 

estimated in the field.

BACKGROUND

Scour at highway bridges 

involves sediment-transport and 

erosion processes that cause 

streambed material to be removed 

from the bridge vicinity and generally 

is separated into components of pier 

scour, abutment scour, and 

contraction scour. Pier scour occurs 

when flow impinges against the 

upstream side of the pier, forcing the 

flow in a downward direction and 

causing scour of the streambed 

adjacent to the pier. Abutment scour 

happens when flow impinges against 

the abutment, causing the flow to 

change direction and mix with 

adjacent main-channel flow, resulting 

in scouring forces near the abutment 

toe. Contraction scour occurs when 

flood-plain flow is forced back 

through a narrower opening at the 

bridge, where an increase in velocity 

can produce scour. Total scour for a 

particular site is the combined effects 

of each component. While different 

materials scour at different rates, the 

ultimate scour attained for different 

materials is similar and depends 

mainly on the duration of peak 

streamflow acting on the material 

(Lagasse and others, 1991, p. 90). 

Scour can occur within the main 

channel, on the flood plain, or both.

The most commonly used 

detailed method for analysis of scour 

(Level 2 analysis) uses hydrologic, 

hydraulic, and sediment-transport 

related engineering concepts to make 

quantitative scour-depth estimates. 

Estimation of scour depth using the 

Level 2 analysis requires substantial 

personnel and computer resources and 

several days or more to complete for 

each site. Given that almost 485,000 

bridges in the United States are over 

waterways and may be susceptible to 

scour to some degree, a detailed scour 

analysis at all sites may not be 

feasible. Accordingly, the U.S. 

Geological Survey began a study to 

develop a method for rapid estimation 

of scour depths that would (1) require 

only limited, easily measured onsite 

data, (2) provide estimates of scour 

depth that would compare reasonably 

to estimates from detailed methods 

and would tend to not underestimate 

scour depth, and (3) provide estimates 

of scour depth at a given site in a few 

hours or less, so that scour 

assessments at bridges of interest 

might be completed in a timely 

fashion.

DESCRIPTION OF METHOD

Calculated scour-depth and 

hydraulic data from Level 2 scour 

analyses were used to develop a 

method for the rapid estimation of 

scour depths based on limited data 

that can be easily measured or 

estimated from a site visit. To ensure 

Rapid-Estimation Method For 

Assessing Scour at Highway 

Bridges Based on Limited Site Data

Bridge scour on Rio Puerco River, New Mexico. Photo courtesy of Steven D. Craigg, U.S. Geological Survey. 
that the rapid-estimation method 

would be applicable to a wide range 

of geographic and hydrologic 

conditions, data from ten States were 

used to develop the method.

Although scour depths can be 

explicitly calculated using the Level 2 

equations, complex hydraulic 

variables in some equations cannot be 

easily measured or estimated in the 

field. Surrogate variables that could 

be easily measured or estimated were 

substituted for the more complex 

variables in the Level 2 scour 

equations to arrive at simpler forms of 

the scour equations. These simpler 

equations were used to develop 

relations between scour depths and 

the surrogate variables. To ensure that 

the rapid-estimation method would 

tend to overestimate rather than 

underestimate scour depths compared 

to detailed methods, relations between 

scour depths and the selected 

surrogate variables were based on 

envelope curves rather than best-fit 

curves.

For example, important 

variables for estimation of pier scour 

(fig. 1) using the rapid-estimation 

method include pier width and length, 

flow angle of attack, and the average 

Froude number of flow in the bridge 

section. Froude number is a hydraulic 

term related to flow depth and 

velocity. Of these variables, pier 

width was the most significant. The 

other variables were combined with 

pier-scour depth to form a term called 

the pier scour function (ξ) that could 

be plotted against pier width. Data 

from Level 2 analyses were thus 

plotted and an envelope curve was 

used to encompass the data. The 

envelope curve is used to determine a 

value for the pier scour function (fig. 

2), which is then used to calculate 

pier-scour depth.

In a similar manner, envelope 

curves for abutment scour and 

contraction scour were also 

developed. Hydraulic variables 

needed to apply the envelope curves 

range from as few as two for abutment 

scour to ten or more for typical 

conditions of contraction scour. 

0 12 2 4 6 8 10

PIER WIDTH, IN FEET

0

24

2

4

6

8

10

12

14

16

18

20

22

PIER-SCOUR FUNCTION (ξ), IN FEET

Figure 2. Envelope curve for estimation of

pier scour function.

To apply the rapid-estimation 

method, a peak discharge having a 

100-year recurrence interval is 

estimated using existing USGS 

methods such as those described by 

Jennings and others (1994). The 100-

year discharge is divided by estimated 

width of flow at the bridge section to 

yield a term called unit discharge at 

the bridge. A graph developed from 

Level 2 data (fig. 3) is used to 

estimate velocity at the bridge from 

unit discharge, and a second graph 

(fig. 4) is used to estimate bridge 

backwater from velocity at the bridge. 

Backwater, the increase in flow depth 

upstream from a bridge (fig. 5), is 

used to estimate upstream flow depth 

and other variables required for 

application of the envelope curves. 

Figures 3 and 4 were developed from 

data from Montana and Colorado and 

may need to be modified for use in 

other States. Because determination 

of variables on the basis of figures 3 

and 4 is an intermediate step in the 

method, best-fit relations were used so 

that moderate estimates of velocity 

and backwater result, which are then 

used in further steps to actually apply 

the envelope curves. Estimated scour 

depths from the envelope curves are 

entered on a standardized scour 

analysis reporting form together with 

various qualitative observations about 

hydraulic and geomorphic conditions 

that may affect scour. Scour prisms, 

based on scour depths and angles of 

repose for typical streambed 

materials, can be plotted on the design 

drawings as described by Richardson 

and others (1993, p. 46-47) to 

determine whether scour holes are a 

threat to pier or abutment foundations 

(fig. 6). The total scour depth used for 

plotting purposes on design drawings 

and for assessment of scoursusceptibility is contraction scour plus 

pier scour for piers and contraction 

scour plus abutment scour for 

abutments.

FLOW ANGLE

AND VELOCITY

LENGTH

TOP VIEW OF PIER

WIDTH

DEPTH

SECTION VIEW OF

BRIDGE CROSSING

BRIDGE

PIER

Figure 1. Variables used for estimation of

pier scour.
EVALUATION AND 

LIMITATIONS OF METHOD

Two approaches were used to 

field test the rapid-estimation 

method. In the first approach, several 

individuals experienced in bridge 

scour-related fields independently 

applied the method to the same 

selected sites, and the averages of 

individual results were compared to 

results from detailed methods at the 

sites. In the second approach, the 

mean and standard deviation 

determined from results obtained by 

each individual for each site were 

used to obtain an indication of 

variability among individuals. 

Results showed generally good 

agreement in both approaches.

In addition to the two 

comparison approaches used, it was 

also determined that for contraction 

scour, 28 of 33 scour-depth estimates 

by the rapid-estimation method 

equaled or exceeded corresponding 

0 180 20 40 60 80 100 120 140 160

VELOCITY SQUARED, IN FEET SQUARED 

PER SECOND SQUARED

0

6

1

2

3

4

5

BACKWATER, IN FEET

Figure 4. Graph for estimation of backwater at

bridge.

Figure 3. Graph for estimation of velocity at 

bridge.

1 1,000 10 100

UNIT DISCHARGE AT BRIDGE, IN CUBIC

FEET PER SECOND PER FOOT

1

50

2

3

4

5

7

10

20

30

40

VELOCITY AT BRIDGE, IN FEET PER SECOND

Figure 6. Sketch of scour prism showing possible threat to left abutment and pier 

foundations.

Figure 5. Side view of stream showing backwater and hydraulic variables at and 

upstream from bridge.
Fact Sheet FS- –96

depths calculated by the Level 2 

method; for pier scour, 17 of 24 

estimates by the method exceeded 

corresponding Level 2 depths; and for 

abutment scour, 55 of 66 estimates by 

the method equaled or exceeded 

corresponding Level 2 depths. On the 

basis of 123 separate scour 

components investigated by five 

different individuals, it was found that 

no more than about two hours was 

required to conduct and report scourdepth estimates for each bridge site. 

The evaluation effort described above 

demonstrates that the method can be 

successfully used to rapidly estimate 

scour depths at bridge sites.

Because considerable 

engineering judgment may be 

involved in applying the rapidestimation method to site-specific 

conditions, reasonable estimates of 

scour depth are possible only if the 

method is applied by a qualified 

individual possessing knowledge and 

experience in the fields of bridge 

scour, hydraulics, and flood 

hydrology. Although the rapidestimation method is useful for 

estimating scour depths to identify 

potentially scour-critical bridges, it 

does not replace more detailed 

methods commonly used for design 

purposes in the rehabilitation or 

replacement of bridges. The rapidestimation method is also subject to 

the same limitations as the more 

detailed methods for the estimation of 

scour. The development, application, 

and evaluation of the rapidestimation method is described in 

detail in the recent report by 

Holnbeck and Parrett (1997). This 

report, as well as reports describing 

the Level 2 method in detail (Lagasse 

and others, 1991, and Richardson and 

others, 1993) need to be read and 

understood before undertaking any 

scour assessments.

REFERENCES CITED

Holnbeck, S.R., and Parrett, Charles, 

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.

Jennings, M.E., Thomas, W.O., and 

Riggs, H.C., 1994, Nationwide summary of U.S. Geological Survey 

regional regression equations for 

estimating magnitude and frequency 

of floods for ungaged sites, 1993: 

U.S. Geological Survey WaterResources Investigations Report

94-4002, 196 p.

Lagasse, P.F., Schall, J.D., Johnson, F., 

Richardson, E.V., Richardson, J.R., 

Chang, F., 1991, Stream stability at 

highway structures: U.S. Department of Transportation No. FHWAIP-90-014 Hydraulic Engineering 

Circular 20, 195 p.

Richardson, E.V., Harrison, L.J., Richardson, J.R., and Davis, S.R., 1993, 

Evaluating scour at bridges (2d 

ed.): U.S. Department of Transportation Hydraulic Engineering Circular 18, 132 p.

FOR MORE INFORMATION

USGS State representative

301 South Park Avenue

Federal Building, Room 428

Helena, MT 59626-0076

(406) 441-1319

Email: dc_mt@usgs.gov

Additional earth science

information can be found by

accessing the USGS Home Page

on the World Wide Web at

http://www.usgs.gov/

For more information on

all USGS reports and products

(including maps, images,

and computerized data), call

1-800-USA-MAPS

The USGS provides maps,

reports, and information to

help others meet their needs

to manage, develop, and protect

America’s water, energy, mineral,

biological, and land resources.

We help find the natural resources

needed to build tomorrow, and

supply the scientific understanding

needed to help minimize or mitigate

the effects of natural hazards and

environmental damage caused by

natural and human activities. The

results of our efforts touch the

daily life of almost every American.

May 1997 244-96

By Stephen R. Holnbeck

 and Charles Parrett