**OFFICE OF BRIDGE DEVELOPMENT**

**MANUAL FOR HYDROLOGIC AND HYDRAULIC DESIGN**

**CHAPTER 11, EVALUATING SCOUR AT BRIDGES**

**APPENDIX C**

**ESTIMATING SCOUR IN**

**BOTTOMLESS ARCH CULVERTS**

![](media/image1.png)

**SEPTEMBER 2005**

**APPENDIX C**

**ESTIMATING SCOUR IN BOTTOMLESS CULVERTS**

TABLE OF CONTENTS

1\.
INTRODUCTION.....................................................................\.....3

2\.
POLICY......................................................................................4

A.
GENERAL...........................................................................\...
4

B. FOOTINGSON ROCK OR
PILES...................................................4

C. FOOTINGS ON ERODIBLE
SOIL...................................................4

3\. DESIGN
GUIDELINES..................................................................
5

A.
INTRODUCTION......................................................................5

B. DESIGN
CONCEPT....................................................................5

C. DESIGN
PROCEDURE.........................................................\......10

D. SPECIAL DESIGN
PROCEDURES................................................12

4\.
REFERENCES.............................................................................13

ATTACHMENT 1: EXAMPLE PROBLEM USE OF NOMOGRAPH FOR PRELIMINARY CULVERT
SELECTION

ATTACHMENT 2: EXAMPLE PROBLEM USING THE BOTTOMLESS CULVERT MODULE

ATTACHMENT 3: CLEAR WATER SCOUR EQUATIONS

**CHAPTER 11 -- EVALUATING SCOUR AT BRIDGES**

**APPENDIX C**

**ESTIMATING SCOUR IN BOTTOMLESS CULVERTS**

**1. INTRODUCTION**

The SHA\'s Office of Bridge Development (OBD) does not have a formal
policy regarding the use of bottomless arch culverts on SHA projects.
Bottomless arch culverts are considered one of many structural options
available to a designer when developing solutions to a stream crossing
of a highway. As with any option, there are a number of technical and
practical factors which must be considered when implementing a structure
design. Among these are geotechnical and foundation conditions,
hydraulic and scour considerations, stream geomorphology, geometric and
structural features, constructability, cost, etc. All of these factors
are investigated in determining the most appropriate structure. There
are times when a bottomless arch culvert may be feasible, but another
structure type is selected for other overriding reasons. OBD does not
predetermine the use of any specific type of structure, but determines
the most appropriate structure type on a case-by-case basis. County and
local bridge owners are encouraged to perform the same type of
investigation for their structure projects, including consideration of
bottomless arch culverts, if deemed appropriate and if the structures
satisfactorily meet all needs of the particular project. Guidance
regarding hydrologic, hydraulic, geomorphic and scour considerations are
presented in Chapters 8, 9, 10 and 11 and 13 of the Office of Bridge
Development Interim Manual of Hydrologic and Hydraulic Design (8).
Structural, geotechnical and other considerations are presented in
various other directives of the SHA.

Safety to the traveling public is the primary concern in the selection
of a structure. When Federal or State funds are used in the construction
of bottomless culverts, the SHA requires that a scour report be prepared
to demonstrate that the structure is stable for worst-case scour (8).

The purpose of this Appendix C of Chapter 11 is to present SHA policy
regarding the objective of the scour evaluation (a stable structure for
worst-case scour conditions) and to provide guidance on the
considerations to be evaluated in reaching the design objective for
bottomless arch culverts. It replaces the SHA policy directive issued by
Mr. Freedman, Director, Office of Bridge Development, in September 1997.

SHA policy and guidance regarding the design of bottomless culverts is
presented below. The ABSCOUR Program is the method selected by the SHA
Office of Bridge Development for evaluating scour in bottomless culverts
(12). Further discussion of the procedures used in developing the design
equations for the ABSCOUR Program is contained in Appendix A of Chapter
11 of the H&H Manual (8). Results from recent cooperative studies by the
FHWA (Federal Highway Administration), Maryland SHA, Contech and Conspan
(9) are used in the development of the design approach presented below.

At this time, SHA and FHWA are still evaluating various aspects of scour
in bottomless culverts through a cooperative research study. Chapter 11,
Appendix C will be updated and finalized at the completion of this
study.

**[2. POLICY]{.underline}**

[A. GENERAL]{.underline}

-   Analyze bottomless arch culverts supported on footings for worst
    case scour conditions in accordance with SHA policy for bridges
    (10). The scour report and other appropriate design studies shall
    document that the structure is stable for worst-case scour
    conditions, and shall be submitted to the SHA for approval.

-   Evaluate the 100-year, 500-year and overtopping floods to determine
    the worst-case scour conditions.

-   Prepare scour evaluations and reports in accordance with the
    provisions of Chapter 11 of the H&H Interim Manual and the
    Bottomless Culvert module in the Maryland SHA Bridge Scour (ABSCOUR)
    Program (12).

-   Unstable channel conditions below the crossing site, such as
    headcutting, degradation, and channel migration, if not addressed at
    the design stage, are likely to have a future adverse effect on the
    stability of the structure to be provided. Do not apply the design
    procedure presented in this guideline to crossing locations
    experiencing downstream headcutting and degradation unless other
    measures to control the channel instability are provided.

[B. FOOTINGS ON ROCK OR PILES]{.underline}

-   Wherever practicable, place footings on scour resistant rock or on
    piles.

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-   Standard SHA geotechnical procedures are to be followed for taking
    and analyzing rock cores, and for designing foundations on rock or
    on piles.

-   It is standard practice to consult with representatives of the SHA
    Office of Materials and Technology when evaluating the erodibility
    of rock.

[C. FOOTINGS ON ERODIBLE SOIL]{.underline}

-   Place the bottom of the spread footing at an elevation at least one
    foot below the elevation of (worst case) contraction scour plus long
    term degradation.

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-   Protect footings with riprap or other scour countermeasure to
    minimize the potential for damage from scour. Riprap installations
    are to conform to the minimum D50 sizes and blanket thicknesses
    presented in Chapter 11 and in the ABSCOUR Program.

Site conditions can be expected to vary widely in Maryland, and there
may be locations where judgment is needed in the interpretation and
application of the above policy. Questions concerning the interpretation
and application of SHA policy and guidance should be directed to Messrs
Andrzej Kosicki (410 545-8340) or Len Podell (410 545-8362) of the
Office of Bridge Development.

**[3. DESIGN GUIDELINES]{.underline}**

[A. INTRODUCTION]{.underline}

The design guidance in this section applies to typical stream crossings
with low to moderate flow velocities in the culvert. Additional design
features and analyses may be warranted to assure the stability of a
culvert founded in erodible soil when one or more of the following
conditions are present:

-   High velocity flow

-   Unstable channel conditions

These additional design considerations may include one or more of the
following features:

-   Redesign of the culvert to increase the waterway area and reduce the
    velocity of flow in the culvert,

```{=html}
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```
-   Use of Class 3 riprap instead of Class 2 riprap for the riprap pad
    depicted in Figure 1,

-   Use of a lining such as riprap, concrete, etc. to protect the entire
    channel bottom within the culvert,

-   Placement of the culvert on piles,

-   Channel stabilization features upstream and/or downstream of the
    culvert, or

-   Evaluation of alternative designs.

In some cases, bottomless culverts are used at sites where there is
little flow and low velocities; consequently scour depths may be
insignificant. Foundation elevations and the need for scour protection
should be based on the particular site conditions for such culverts.

[B. DESIGN CONCEPT]{.underline}

Computing scour in a bottomless culvert is similar to computing scour at
a bridge abutment. The flow distribution in the channel and on the flood
plain approaching the inlet of a bottomless box culvert is similar to
that in a channel contracted by vertical-wall abutments at a bridge. The
upstream cross-section of the channel and flood plain is generally wider
than the culvert width and the flow velocity is lower than the velocity
in the culvert. Discussion of the scour computation procedure is
explained in Attachment 3 and also in the ABSCOUR User's Manual, Chapter
11, Appendix A (8). Figure 1 depicts a schematic typical section for a
bottomless culvert installation. [Please note also the comments in
Section C, Design Procedure.]{.underline}

The deepest scour typically occurs at the culvert entrance in the area
of the contracting flow; and at the exit in the area of expanding flow
(See Figure 2). In the culvert barrel, the flow lines are generally
parallel to the culvert walls and the deepest scour, contraction scour,
will often occur at the thalweg near the center of the channel. However,
it is not unusual for the thalweg to oscillate over time between the
culvert walls.

Figure 2 represents the actual scour measurements taken of a model of a
bottomless culvert in the FHWA Hydraulic Laboratory at the Turner
Fairbanks Highway Research Center (9). The scour pattern here is very
clear with the darkest areas representing the deepest scour at the
culvert entrance and exit. The contraction scour within the culvert
barrel is not as deep, occurring near the center of the channel. In view
of this scour pattern, the typical pattern for placement of the riprap
is depicted in Figure 3.

![](media/image2.png){width="5.997916666666667in"
height="7.047916666666667in"}

![](media/image3.jpeg){width="5.726388888888889in"
height="3.0868055555555554in"}

**Figure 2**

**Scour Pattern at a Bottomless Culvert**

![](media/image4.png){width="4.219444444444444in"
height="4.281944444444444in"}

**Figure 3**

**Plan View of Riprap Scour Protection for a Bottomless Culvert**

Small streams in Maryland generally have well vegetated overbank areas.
For worst case scour conditions, a significant portion of the flood flow
conveyed to the culvert may come from these overbank areas. Because of
the vegetative cover and the low velocities in the upstream reach, the
bed load delivered to the culvert from overbank flow may be small. For
such cases, it may be reasonable to assume a clear-water scour condition
for the analysis. Estimated scour depths are typically on the
conservative side as compared with live bed scour.

For clear water scour, the bed material in the bottomless culvert will
be scoured by the higher flow velocity. As the scour progresses, the
cross sectional area of the flow increases and the flow velocity
correspondingly decreases. This process continues until the flow
velocity is reduced to the critical (or competent) velocity where the
particles on the bed cease to move.

The Bottomless Culvert Module in ABSCOUR (12) can be used to evaluate
either clear water or live bed scour. The user is encouraged to consider
both conditions and then decide which type of scour is most appropriate
for a given site condition.

*There are three important considerations for the user to keep in mind
when using the clear water scour equations in the ABSCOUR program:*

-   *It is important that the user select the particle size that will be
    typical of the material in the [bottom]{.underline} of the scour
    hole.*

-   *There is very little information available regarding the critical
    velocity of particles with a D50 size smaller than 0.001 ft. or
    0.3 mm. Use of the clear water equations for this material must be
    tempered with the user's judgment.*

-   *Special studies and engineering judgment will be needed to
    determine the critical shear stress and/or critical velocity of
    cohesive soils.*

When rock is present, an evaluation needs to be made as to whether it is
erodible or scour resistant. FHWA guidelines advise that rock with an
RQD of less than 50% is considered as erodible. Generally, the SHA
follows the criteria of considering the threshold for scour resistant
rock as an RQD value of 75% or greater. There is considerable variation
in the erodiblity of different types of rock and rock formations in this
threshold range between 50 to 75 percent RQD values. For this reason, it
is standard practice to consult with representatives of the SHA Office
of Materials and Technology when evaluating the erodibility of rock. SHA
is also using the Erodibility Index Method (See the Utilities Module in
the ABSCOUR Program) as a guide in evaluating scour in erodible rock.

The need for a full scour evaluation for footings on rock will be
determined on a case by case basis.

Conditions at the culvert outlet and downstream channel should be
assessed. If the downstream channel is unstable and degrading, or if a
headcut is migrating upstream towards the culvert, the foundations may
be vulnerable to undermining. The ABSCOUR analysis is not appropriate
for the analysis of this condition.

Placement of stream bed controls (cross vanes, etc,) or other means of
channel stabilization may serve to mitigate potential problems with
scour and degradation (11).

[C. DESIGN PROCEDURE]{.underline}

*C.1 Select the typical channel cross-section at the culvert location.*

Select a representative cross-section of the channel and overbank area
within the limits of the proposed culvert. For preliminary design of
shallow channels, select an average elevation as representative of the
channel and overbank sections

*C.2 Select a Preliminary Culvert Size*

Figure 4 presents a nomograph which can be used as a preliminary design
aid in selecting a size of culvert that will limit the contraction scour
to tolerable depths. (See Example problem on page 9). A trial and error
approach is suggested in arriving at a preliminary culvert size. Once a
reasonable culvert size is determined, the design computations can be
made as outlined below:

![](media/image5.png)**Figure 4**

**Plot for Preliminary Selection of Culvert Type and Size**

An illustrative example of the use of Figure 4 is presented in
Attachment 1.

*C.3 Use the HEC-RAS Program (13) to compute water surface profiles.*

Evaluate the 100-year, 500-year and Overtopping floods as appropriate.

*C.4 Compute Contraction Scour and Culvert Wall (Abutment) Scour using
the Bottomless Culvert Module in the ABSCOUR Program.*

Detailed guidance on the use of the ABSCOUR Program is contained in the
Users Manual (Appendix A of Chapter 11) as well as in the Help Screens
in the ABSCOUR Program.

*C.5 Evaluate the potential for long term degradation, headcutting and
channel migration*

Refer to the procedures in the OBD Manual of Hydrologic and Hydraulic
Design, including Chapter 14, Stream Morphology, for assessing concerns
with channel instability.

*C.6 Design the Culvert Footing*

Place the bottom of the footing at least one foot below the combined
depth of channel contraction scour and any estimated long term
degradation. As a minimum, the footings on the upstream headwall and
downstream endwall should be designed to the same elevation as the
culvert footings and protected in a similar manner with riprap. As
depicted in Figure 2, the deepest scour can be expected near the culvert
headwall. In some cases where the abutment scour is severe, it may be
prudent to increase the depth of the footings for the headwall.

Please note that for some installations, it may be cost effective to
place the structural footing on a non-erodible base that extends to a
depth of one-foot below channel contraction scour plus long term
degradation. This type of design should be approved by the structural
engineer.

*C.7 Select the Scour Countermeasure.*

Procedures for selecting the appropriate size of riprap are contained in
the Utility Module of the ABSCOUR Program. These procedures are based on
the guidance contained in the FHWA HEC-23, [Bridge Scour and Stream
Instability Countermeasures.]{.underline} (14) Design the width and
thickness of the riprap wall protection to keep the contraction scour
away from the wall footings, keeping in mind the [minimum blanket
dimensions]{.underline} indicated in Figure 1. Deeper and wider riprap
blankets should be considered where the contraction scour exceeds the
depth of the riprap. Prior approval should be obtained from the SHA for
use of scour countermeasures other than riprap.

*C.8 Evaluate the Trial Design*

The objective here is to select the appropriate combination of (1) the
culvert cross-sectional area and (2) the footing design so as to achieve
a cost effective structure that is compatible with the stream
morphology. Where moderate flow velocities are present, achieving a
cost-effective design should not be a problem. As culvert velocities
increase, however, scour can be expected to increase. Culvert foundation
costs will also increase to accommodate the need for deeper footing
depths, increased excavation quantities, more extensive riprap
installations and more complex stream diversion measures. These factors
may also create more disturbance to the stream during and after
construction.

For very long culverts, the wall or abutment scour component decreases
and the risk of undermining the wall also decreases. For these long
culverts, it may be reasonable to reduce the size of the riprap blanket
at a point well beyond the culvert entrance. However, such design
modifications should be made on a case by case basis, subject to SHA
approval.

If the selected culvert size results in deep scour depths, the engineer
should consider increasing the culvert size to reduce culvert velocities
and scour. If increasing the culvert size is not feasible, there are
various countermeasures that can be used to protect the culvert from
scour:

-   Use of a larger D50 riprap size and a wider, deeper riprap
    installation,

-   Lining the entire channel bottom with riprap, concrete, etc. or

-   Placement of the culvert foundation on piles.

In some cases where scour is severe, consideration should also be given
to use of an alternative design.

[D. SPECIAL DESIGN CONSIDERATIONS.]{.underline}

*D.1 Pier Scour*

It is advantageous to use a single cell bottomless arch culvert,
whenever practical, to span the stream. This approach can often serve to
minimize obstructions to bankfull flow, thereby minimizing changes to
sediment transport and stream morphology. In the event that a multiple
cell structure is to be designed, the following guidance is offered with
respect to computing scour for the embankment section located between
adjacent culvert cells. This guidance applies when the spacing between
the adjacent culvert walls is small, being on the order of the
dimensions of a pier.

-   Treat the area between adjacent culvert walls as a pier

-   Calculate local pier scour using the Pier Scour Module in the
    ABSCOUR Program. Use the depth of flow, y2 (the total flow depth
    after contraction scour has taken place). Determine the
    corresponding values for the velocity of flow and the Froude Number
    at the entrance to the culvert. Measure the local pier scour from
    the contracted scour depth as determined by the value of y2.

This approach is reasonable for designs where the culvert cell walls of
adjacent culverts are close together. It becomes less valid as the
intervening space between the culvert cells increases. Judgment is
needed in applying this concept to a particular site installation.

*D.2 Unstable Channels*

For unstable streams, the engineer is encouraged to consider the use of
cross-vanes or other stream controls to establish a stable stream
channel in the reach of the highway crossing. Reference is made to
Chapter 14, Stream Morphology, for a discussion on conducting stream
stability studies.

**4. REFERENCES**

1.  FHWA, "Evaluating Scour at Bridges," HEC No. 18, Fourth Edition, May
    2001.

2.  Vanoni, Vito A., Manual on Sedimentation, Sedimentation Engineering,
    ASCE Hydraulic Division, 1975.

3.  Kirchhoff, Robert H., Potential Flows, Computer Graphic Solutions,
    Marcel Dekker, Inc. New York, 1985.

4.  Milne-Thomson, L. M., Theoretical Aerodynamics, Fourth Edition,
    Macmillan, London, 1968.

5.  Palaviccini, M., "Scour Predictor Model at Bridge Abutments," Doctor
    of Engineering Dissertation, The Catholic University of America,
    Washington, D.C., 1993.

6.  Chang, Fred, "Analysis of Pressure Scour," Unpublished Research
    Report, 1995.

7.  Maynord, Steven T., Toe Scour Estimation in Stabilized Bendways,
    Technical Note, ASCE Journal of Hydraulic Engineering, August 1996.

8.  Maryland State Highway Administration, Office of Bridge Development,
    H&H Interim Manual for Hydrologic and Hydraulic Design.

9.  Maryland State Highway Administration and Federal Highway
    Administration, "Scour in Bottomless Culverts", Hydraulic Laboratory
    Studies, 1999 and 2002.

10. Letter from Earle S. Freedman, Deputy Chief Engineer, Office of
    Bridge Development, SHA to All County Engineers on the subject of
    scour in bottomless culverts dated September 17, 1997.

11. Rosgen, Dave, Applied River Morphology, Wildland Hydrology, Pagosa
    Springs, CO. 1996

12. Maryland SHA Bridge Scour Program (ABSCOUR), May 2003

13. HEC-RAS River Analysis System, U.S. Army Corps of Engineers,
    Hydrologic Engineering Center, Version 3.11 dated May 2003.

14. FHWA HEC-23, Bridge Scour and Stream Instability Countermeasures,
    March 2001

15. C.R. Neill, Guide to Bridge Hydraulics, Transportation Association
    of Canada, June 2001.

ATTACHMENT 1

EXAMPLE PROBLEM TO ILLUSTRATE USE OF THE NOMOGRAPH FOR PRELIMINARY
CULVERT SELECTION

Given: An arch culvert with a shape similar to the middle or dotted line
in the nomograph in Figure 2. From a hydraulic analysis, the average
flow depth is 9 feet and the average flow velocity is 8 feet per second.
The channel bed is composed of gravel with a D50 of 1.8 mm.

Trial run no. 1

For a flow depth of 9 feet and a D50 gravel size of 1.8 mm, the
competent or critical velocity (determined from Neill's competent
velocity curves (15)) is 3.6 ft/sec. ( Please note that critical
velocity using Neill's method can be computed by using the procedure in
the Utility Module of ABSCOUR)

Vdesign/Vc = 8/3.6 = 2.2.

From the nomograph, ys/y1 is approximately 0.90

The contraction scour depth is 0.9 times the flow depth of 9 feet or 8.1
feet. This contraction scour is considered to be too great for the given
site conditions.

Trial run no. 2

A larger culvert is selected. The flow depth is reduced to 7.0 feet and
the average velocity reduced to 6 ft/sec.

The competent or critical velocity for this condition is decreased to
3.5 fps

Vdesign/Vc = 6/3.5 = 1.7. From the nomograph, ys/y1 is approximately 0.5

The contraction scour depth is 0.5 times the flow depth of 7.0 feet or
3.5 feet. A contraction scour depth of 3.5 feet is considered acceptable
for this site.

The culvert dimensions for trial run No. 2 can be used as a starting
point for the scour evaluation.

ATTACHMENT 2

EXAMPLE PROBLEM USING THE BOTTOMLESS CULVERT MODULE

IN ABSCOUR

**[INPUT DATA]{.underline}**

(Refer to the input menus for the bottomless culvert module in ABSCOUR)

[1. PROJECT INFORMATION]{.underline}

Example Problem, Arch Culvert Alternative, Q-100 discharge = 590 cfs

[2. APPROACH SECTION DATA FROM HEC-RAS]{.underline}

  ----------------- ----------------- ----------------- -------------------
                    LEFT OVERBANK     CHANNEL           RIGHT OVERBANK

                                                        

  DISCHARGE cfs     130               300               160

  FLOW TOP WIDTH ft 20                8                 30

  AVE. FLOW DEPTH   6                 8                 6
  ft                                                    

  MED. BED D~50~ ft 0.0059            0.0059            0.0059

                                                        

  AVE BANK SLOPE Z  2                                   2

                                                        

  AVE ENERGY SLOPE                    .002              
  ----------------- ----------------- ----------------- -------------------

3\. [CULVERT DATA]{.underline}

+----------------+----------------+----------------+------------------+
|                | LEFT OVERBANK  | CHANNEL        | RIGHT OVERBANK   |
+----------------+----------------+----------------+------------------+
| WATER SURFACE  |                | 100            |                  |
| ELEV INSIDE    |                |                |                  |
| CULVERT        |                |                |                  |
+----------------+----------------+----------------+------------------+
| WATERWAY AREA  | 30.4           | 64             | 30.4             |
| A              |                |                |                  |
|                |                |                |                  |
| (MEASURED FROM |                |                |                  |
| CULVERT        |                |                |                  |
| X-SECTION)     |                |                |                  |
| Ft^2^          |                |                |                  |
+----------------+----------------+----------------+------------------+
| CULVERT FLOW   | 8              | 8              | 8                |
| WIDTH (W) ft   |                |                |                  |
+----------------+----------------+----------------+------------------+
| ELEV CULVERT   | 98.04          | 101            | 98.04            |
| CROWN          |                |                |                  |
+----------------+----------------+----------------+------------------+
| CULVERT TYPE   |                | ARCHED         |                  |
+----------------+----------------+----------------+------------------+
| SETBACK FROM   | 8              |                | 8                |
| EDGE OF        |                |                |                  |
| CHANNEL ft     |                |                |                  |
+----------------+----------------+----------------+------------------+
| MED. BED D~50~ | 0.0059         | 0.0059         | 0.0059           |
| ft             |                |                |                  |
+----------------+----------------+----------------+------------------+
| LONG TERM      | 0              | 0              | 0                |
| AGGRADATION OR |                |                |                  |
| DEGRADATION    |                |                |                  |
+----------------+----------------+----------------+------------------+
| SAFETY FACTOR  |                | 1.2            |                  |
+----------------+----------------+----------------+------------------+

[4. UPSTREAM CULVERT DATA]{.underline}

  ----------------- ----------------- ----------------- -------------------
                    LEFT OVERBANK     CHANNEL           RIGHT OVERBANK

  WATER SURFACE                       100.8             
  ELEV. UPSTREAM OF                                     
  CULVERT                                               

  DISCHARGE THAT    0                 0                 0
  OVERTOPS OR                                           
  BY-PASSES ROADWAY                                     

  ELEV CULVERT      99.4              102               99.4
  CROWN AT UPSTREAM                                     
  SIDE                                                  

  EMBANKMENT SKEW   90                                  90
  ANGLE                                                 

  IS FUTURE LATERAL NO                NO                NO
  MIGRATION APT TO                                      
  OCCUR?                                                
  ----------------- ----------------- ----------------- -------------------

**[OUTPUT RESULTS]{.underline}**

1:
\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*

2: \* Maryland State Highway Administration \*

3: \* Bottomless Culvert Scour Program \*

4: \* Version 6 Build 1.15e, May 5, 2003 \*

5:
\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*

6:

7: Time stamp: 07/14/2003 2:17:50 PM

8:

9: Input Data:

10:

11: Project information:

12:
\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

13: Project name: bc2 Example problem

14: Project number:

15: Description: higher discharge

16:

17:

18: Project options:

19: Program calculates critical and boundary shear stresses at approach
section

20: Program decides the scour type as either live bed or clear water
scour

21: Program calculates the unit width discharge at the bridge section

22: Program calculates critical velocity at bridge section

23: Program calculates sediment transport parameter k2

24: Clear-water scour uses Neill\'s method

25: English Units

26:

27: Approach Section Data:

28:
\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

29: Left Channel Right

30: \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

31: Approach section discharge (cfs): 130 300 160

32: Approach section top width (ft): 20 8 30

33: Approach flow depth (hydraulic depth) (y1) (ft): 6 8 6

34: Approach median particle size, D50(ft): .0059 .0059 .0059

35: Bank slope (Z) in the vicinity of the bridge (Z H: 1 V): 2 2

36: Energy slope (S) at approach section: .002

37:

38: ABSCOUR Overrides

39:

40: Reserved for override

41: Reserved for override

42: Reserved for override

43: Reserved for override

44: Reserved for override

45: Reserved for override

46: Reserved for override

47:

48: Downstream Culvert Data:

49:
\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

50: Downstream water surface elevation under culvert: 100 ft

51:

52: Left Channel Right

53: \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

54: Waterway area (A) measured normal to flow (sf): 30.4 64 30.4

55: Culvert flow width (W) measured normal to flow (ft): 8 8 8

56: Hydraulic depth (A/W) (ft): 3.80 8.00 3.80

57: ABSCOUR X-Section elevation (#50-#56) (ft): 96.20 92.00 96.20

58: Culvert type: arched

59: Setback (- for an abutment in channel) (ft): 8 8

60: Low chord elevation downstream side of culvert (ft): 98.04 101 98.04

61: Correction factor for low chord submergence (#50-#60\>0)(ft): 0.00
0.00 0.00

62: Median particle size under culvert, D50(ft): .0059 .0059 .0059

63: Estimated long-term aggradation(+) or degradation(-) (ft): 0 0 0

64: Safety factor (typical ranges 1.2 to 1.4): 1.2

65:

66: Upstream Culvert Data

67:
\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

68: Water surface elevation upstream side of culvert: 100.8 ft

69:

70: Left Channel Right

71: \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

72: Overtopping flow/Flow redistribution (cfs): 0 0 0

73: Water depth at upstream side of culvert (#68-#57) (ft): 4.60 8.80
4.60

74: Low chord elevation upstream side of culvert (ft): 99.04 102 99.04

75: Low chord height (#74-#57) (ft): 2.84 10.00 2.84

76: Pressure flow, Yes or NO: (Yes if #73\>#75 at channel) No No No

77: Embankment skew angle (degrees): 90 90

78: Is future lateral migration of channel likely to occur?: no

79:

80: Output Computation And Results

81:

82: Approach Section:

83:

84: Total discharge (cfs): 590

85:

86: Left Channel Right

87: \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

88: Approach average flow velocity (fps): 1.083 4.688 0.889

89: Approach unit width discharge (cfs/ft): 6.5 37.5 5.333

90: Approach section depth (ft): 6 8 6

91: Approach section Froude Number: 0.0779 0.2921 0.064

92: Approach section critical shear stress(psf): 0.0236 0.0236 0.0236

93: Approach boundary shear stress(psf): 0.7488 0.9984 0.7488

94: Approach sediment transport parameter (k2): 0.64 0.64 0.64

95: Scour type: Live Bed Live Bed Live Bed

96: Approach unit width discharge for computing Kv(cfs/ft): 11.667 9.118

97:

98: Downstream Culvert Computations:

99:

100: Left Channel Right

101: \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

102: Method of computing flow velocity adjustment: Short Setback Short
Setback

103: Flow velocity (fps): 4.728 4.728 4.728

104: Adjustment to hydraulic depth (y0)adj (ft): 4 8 4

105: Unit width discharge (#104\*#103)(cfs/ft): 18.91 37.821 18.91

106: Unit width discharge for computing Kv (cfs/ft): 23.333 25.833

107: Critical velocity (fps): N/A N/A N/A

108:

109: Downstream Contraction Scour Computations:

110:

111: Left Channel Right

112: \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

113: Clear water scour flow depth (y2)(ft): 5.517 9.252 5.517

114: Live bed scour flow depth (y2)(ft): 11.888 8.044 13.494

**115: Interpolated scour flow depth (y2)(ft): 9.687 8.044 10.374**

116: Pressure flow coefficient (Kp): 1 1 1

117: Adjusted scour flow depth (y2)adj (#116\*#115(ft): 9.687 8.044
10.374

**118: Contraction scour depth (ys) (#117-#104\>0)(ft): 5.687 0.044
6.374**

119: Final contraction scour depth (#118\*#64)(ft): 6.825 0.052 7.649

120: Contraction scour elevation(#50-#104-#119-#61+#63)(ft): 89.175
91.948 88.351

121:

122: Total Culvert Scour At Side wall:

123:

124: Left Channel Right

125: \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

126: Side wall local velocity factor (Kv): 1.283 1.168

127: Side wall spiral flow factor (Kf): 1 1

128: Pressure flow coefficient (Kp): 1 1

**129: Scour depth at side wall (y2a)adj
(#115\*#127\*#126\^94\*#128)(ft) 11.363 11.457**

130: Initial side wall scour depth (ysa)(#129-#104\>0)(ft): 7.363 7.457

131: Coefficient for side wall shape factor (Kt): 1 1

132: Coefficient for embankment angle (Ke): 1 1

133:

**134: Final side wall scour depth (ysa)adj(#130\*#131\*#132\*#64)(ft):
8.835 8.948**

135: Side wall scour elevation(#50-#104-#134-#61+#63)(ft): 87.165 87.052

**[ATTACHMENT 3 CLEAR WATER SCOUR EQUATIONS]{.underline}**

The ABSCOUR Program computes contraction and abutment scour as described
in the Users Manual (Appendix A) of Chapter 11. This procedure is
modified slightly for culverts to account for the difference in the
shapes between bridges and culverts. The logic of the ABSCOUR program is
outlined below.

Obtain the following information for the culvert (See Figure 1):

Q = discharge per culvert barrel, cfs

W = nominal width of culvert (at the spring line), ft

q = discharge per unit width = Q/W, ft2/s

y1 = average depth of flow inside the culvert (not at the culvert inlet
or outlet) ft.

> V = average flow velocity inside the culvert (not at the culvert inlet
> or outlet) ft/sec.
>
> D50 = average soil particle sizes for the channel and overbank areas
> inside the culvert. For live bed scour, the D50 size can be obtained
> from pebble counts or other sampling techniques. For clear water
> scour, the D50 particle size should be representative of the soils [at
> the estimated depth of contraction scour, ft]{.underline}.
>
> H = rise of the arch from the stream bed to the crown of the arch
> (ft.). For pressure flow conditions, assume that the flow depth y1 is
> equal to H, the crown of the culvert

CLEAR WATER CONTRACTION SCOUR IN RECTANGULAR CULVERTS

The equations below are based on the competent velocity curves contained
in Neill's Guide to Bridge Hydraulics, Reference 7:

y2 = y1 + ys **(1)**

Where

y2 = average depth of flow inside the culvert after scour has taken
place.

y1 = average depth of flow inside the culvert before scour has taken
place.

ys = depth of scour

The following equations are used to solve for y2.

[For D~50~ ≤ 0.001 ft.]{.underline}

y~2~ = (q/ (2.84 (D~50~)^0.15^))^0.67^ **(2)**

[For 0.1\> D~50~\> 0.001 ft.]{.underline}

y~2~=\[q/(11.5D~50~^.35^)\]^x^ **(3)**

Where x = 1/\[1+(0.123/D~50~^0.20^)\]

[For D~50~ ≥ 0.1 ft.]{.underline}

y~2~ = \[q/(11.5D~50~^0.33^)\]^0.86^ **(4)**

CLEAR WATER CONTRACTION SCOUR IN SIMPLE ARCHED CULVERTS

Most bottomless culverts have the shape of an arch and therefore have
less capacity than a structure with vertical walls for the same height
and width. The following equations apply for computing contraction scour
in arched culverts. Solution of the equations requires either a trial
and error approach or plotting of the q Vs y2 relationship. A trial and
error approach is used for the ABSCOUR program.

[For D~50~ ≤ 0.001 ft.]{.underline}

q = 2.84 y~2~^0.5^ D~50~^.0.15^ (y~2~ -- 1/3 (y~1~/H)^2^ y~1~ ). **(5)**

[For 0.1\> D~50~\> 0.001 ft.]{.underline}

q = 11.5 y~2~^x^ D~50~^0.35^ (y~2~ -- 1/3 (y~1~/H)^2^ y~1~ ) **(6)**

Where x = 0.123/ D~50~^0.2^

[For D~50~ ≥ 0.1 ft.]{.underline}

q = 11.5 y~2~^0.167^ D~50~^0.333^ (y~2~ -- 1/3 (y~1~/H)^2^ y~1~) **(7)**

COMPUTATION OF WALL OR ABUTMENT SCOUR AT THE CULVERT ENTRANCE

The ABSCOUR Program computes abutment or wall scour. In the manner
presented below.

The scour depth y2 in equations 1-4 above is defined as the uniform
contraction scour depth across the width of the channel inside the
culvert. It is measured from the water surface to the channel bottom,
taking into account that contraction scour has taken place.

At the entrance to the culvert, however, there will be additional
turbulence and resulting scour at the culvert footings as the flow
transitions from the flood plain into the culvert.

For a single barrel bottomless culvert, the footings should be treated
in the same manner as bridge abutments for purposes of estimating scour.
The wall area at the culvert inlet is a region of higher velocity flow
due to the rapidly contracting flow and the resulting vortex action.
This is similar to the flow at a vertical wall abutment, resulting in
localized scour that is deeper than the contraction scour in the
channel. The SHA abutment scour equations can be used to estimate the
scour depth at the culvert wall near the culvert entrance. This is
accomplished as follows: the contraction scour depth y2 computed above
is multiplied by the correction factors, Kv and Kf to account for higher
velocity and vortex flow, respectively, near the culvert wall. These
correction factors are computed by Equations 8 and 9 (See also the Users
Manual, App. A of Chapter 11):

K~v~ = 0.8(q~1'\ ave~/q~2'\ ave~) ^1.5^ + 1 **(8)**

K~f~ = 0.1 + 4.5F for clear water scour **(9)**

Where

q~1'\ ave~ = average unit flow in the approach channel, ft

q~2'\ ave~ = average unit flow in the culvert ft

F = Froude Number of approach flow: F= V/ (gy) ^0.5^

V = Velocity of Flow, ft/s

y = flow depth, ft

g = 32.2 ft/sec^2^

The term Kv is related to the effect of the higher flow velocity which
occurs near the culvert wall.

The term Kf is related to the effect of vortex flow on scour at the
corner of the culvert. The limits of the Kf value range from 1.0 to 3.2.
If the value computed by Equation 9 is less than 1.0, use a value of
1.0. If the value computed by Equation 9 is greater than 3.2, use a
value of 3.2.

The scour depth at the culvert walls, y~w~ can be written as:

Scour depth, y~w~ = K~f~ \* (K~v~ ^0.857^ ) \* y~2~ **(10)**

Where

y~w~ = total water depth at the culvert wall measured from water surface
to the channel bed after scour has taken place.

y~2~ = total water depth at the center of the culvert measured from
water surface to the channel bed after scour has taken place. If the
culvert is operating under pressure flow conditions, the program will
compute a pressure scour coefficient, k~p~, to apply to the contraction
scour as explained in the Users Manual, Appendix A.

For multiple barrel culverts, typically two cell culverts, the center
footings should be treated as a pier for purposes of estimating local
pier scour. The local pier scour should be added to the contraction
scour to obtain the total scour for the middle footing.