**OFFICE OF BRIDGE DEVELOPMENT**

**BRIDGE SCOUR PROGRAM**

**CHAPTER 11 APPENDIX A**

**PART 1: DERIVATION OF METHODOLOGY**

**ABSCOUR**

**USERS MANUAL**

![](media/image1.jpeg){width="6.35in" height="3.25in"}

**OCTOBER 2005**

Preface

ABSCOUR 7, Build 1.01 dated August 25, 2005 replaces ABSCOUR 6, Build
1.15e dated September 30, 2004. This program is being updated on a
regular basis. Before using any version of the program, the user is
advised to check the web site below for the most up-to-date version:

[http://www.wtbco.com/scour/scour.html]{.underline}

The material presented in this ABSCOUR Users Manual has been carefully
researched and evaluated. It is being continually updated and improved
to incorporate the results of new research and technology. However, no
warranty expressed or implied is made on the contents of this manual.
The distribution of this information does not constitute responsibility
by the Maryland State Highway Administration or any contributors for
omissions, errors or possible misinterpretations that may result from
the use or interpretation of the materials contained herein.

The 2005 ABSCOUR 7 Build 1.01 version makes several significant changes
to the September 2004 Build 1.22 version including:

1.  Capability for plotting existing cross-sections from HEC-RAS at the
    Approach Section and the Bridge Section and for overlaying these
    plots on the ABSCOUR cross-sections for easy comparison and
    evaluation.

2.  Detailed guidance on use of safety factors

3.  Modification of the k~f~ factor for spiral flow at abutments

4.  Guidance on selection of critical velocities for cohesive soils

5.  Override Option for the use of 2-D velocity computations.

6.  Revised text and figures to clarify input parameters for the
    program.

Questions regarding the use of the ABSCOUR Program should be directed to
the Office of Bridge Development, Structure Hydrology and Hydraulics
Unit

**OBD BRIDGE SCOUR PROGRAM (ABSCOUR)**

**APPENDIX A - USERS MANUAL, PART 1**

**CAPABILITIES AND LIMITATIONS**

ABSCOUR is a computer program developed by the Office of Bridge
Development for estimating and evaluating scour at bridges and
bottomless arch culverts. The program serves as an analytical tool to
assist the user in identifying and utilizing the appropriate bridge
geometry, hydraulic factors and soils/rock characteristics to estimate
scour at structure foundations.

The program is not an expert system. The accuracy of the answers
obtained (scour depths) depends on the accuracy of the input
information, the selection of the most appropriate analytical methods
available in the program and the user's judgment. However, careful
attention to the guidance in the manual should result in reasonable
estimates of scour. Design considerations for scour should include other
factors than scour depths as discussed in this Appendix and in Chapter
11.

PROGRAM CAPABILITIES

1.  Estimate contraction scour under a bridge for left overbank, channel
    and right overbank using Laursen's live bed scour equation, and/or
    the option of either Laursen's clear water scour equations or
    Neill's competent velocity equations for clear water scour,

2.  Estimate abutment scour,

3.  Estimate pier scour using the FHWA HEC-18 equations,

4.  Print input and output information for the scour report,

5.  Plot the scour cross-section for the scour report,

6.  Estimate scour for open channel and pressure flow conditions,

7.  Estimate scour in cohesive soils and rock,

8.  Estimate scour in bottomless arch culverts,

9.  Estimate minimum D~50~ rock riprap sizes for design, based on the
    FHWA HEC 23 equations for abutments and piers,

10. Permit easy changes to hydraulic and soil parameter inputs in order
    to conduct sensitivity analyses of the estimated scour depths.

USER ASSISTANCE

1.  Users Manual

2.  Help screens and text files in the ABSCOUR Program to define,
    illustrate and explain each input parameter, using the F-1 key or
    the Help File.

3.  Background on the concepts used to develop the ABSCOUR methodology,

4.  Over-ride features to allow the user to modify the program logic,

5.  Simple and fast procedures to conduct sensitivity analyses of input
    parameters.

6.  The Structure Hydraulics and Hydrology Unit in the Office of Bridge
    Development is available to provide user assistance, upon request.

OUTPUT FILES

7.  A detailed report summarizing the factors considered in the scour
    computations.

8.  Plots of the Approach Section, Bridge Section and Scour
    Cross-Section under the bridge to a user defined scale for a plotter
    or to a dxf file for use in Microstation. This includes a scour
    cross-section for combinations of abutments and piers, and a
    comparison of the ABSCOUR cross-section with the corresponding
    HEC-RAS cross-section

LIMITATIONS

1.  The accuracy of the scour computations is dependent upon the
    experience and judgment of the user in the selection of input data
    and appropriate analytical methods. The methods selected for
    analysis need to be consistent with the field conditions as
    reflected in the input data and with appropriate hydraulic and
    sediment transport concepts.

2.  Ideally, a 3-D model should be used to determine hydraulic flow
    conditions and to estimate scour, whereas the hydraulic data used to
    provide the input data (HEC-RAS) is typically a 1-D model. ABSCOUR
    contains subroutines that permit the user to modify the HEC-RAS
    hydraulic data (which are based on conveyance) to consider a more
    conservative flow (worst case) distribution under the bridge for
    purposes of estimating scour. [The user needs to verify that the
    hydraulic model (HEC-RAS, WSPRO) provides for a reasonable flow
    distribution upstream, through and downstream of the
    bridge.]{.underline}

3.  Available methods for estimating clear water scour, particularly for
    very fine-grained sands and cohesive materials, should be assumed to
    provide for rough estimates of competent or critical velocities, and
    need to be applied with judgment. More accurate methods are
    available through use of the EFA (Erosion Function Apparatus) to
    actually calculate the critical velocity of Shelby tube samples
    through a laboratory procedure.

4.  Available methods for estimating scour in rock have had limited
    verification and need to be applied with judgment.

5.  There are an infinite number of possibilities to consider in
    developing a universal model for evaluating scour at a bridge.
    ABSCOUR will address a limited number of these conditions. The user
    is provided with flexibility through overrides and other mechanisms
    to expand the range of conditions which can be analyzed by ABSCOUR.
    Nonetheless, the user is encouraged to make a critical review of the
    estimated scour depths to verify that the numbers look reasonable.
    If the analysis is not reasonable, and there is no obvious error in
    the computations, the user is encouraged to get in touch with the
    Office of Bridge Development.

It is the SHA's experience that the ABSCOUR Program, when applied with
appropriate consideration of the site conditions and scour parameters,
gives reasonable results for bridges over the small and medium-sized
channels typical of Maryland streams. We have had limited experience in
applying ABSCOUR to crossings with wide flood plains, particularly for
site conditions consisting of swamps and wetlands on wide flood plains
where the one-dimensional assumption about flow may not be valid.

**USERS MANUAL**

**FOR THE SHA BRIDGE SCOUR PROGRAM (ABSCOUR)**

######## TABLE OF CONTENTS

Preface..................................................................................................2

Capabilities and
Limitations...........................................................................................\...3

PART 1: DEFINITIONS AND DERIVATION OF THE ABSCOUR METHODOLOGY

I. OVERVIEW 8

> A. LIVE BED SCOUR 8
>
> B. CLEAR WATER SCOUR 8
>
> **II. CONTRACTION SCOUR 8**
>
> A. LAURSEN'S LIVE BED CONTRACTION SCOUR EQUATION 8
>
> B. MODIFICATION FOR PRESSURE FLOW 10
>
> C. DEVELOPMENT OF THE ABUTMENT SCOUR EQUATIONS 10
>
> C.1 Upstream Approach Section, Section 1 10
>
> C.2 Bridge (Contracted) Section 11
>
> C.3. Computation of Velocity for Contraction Scour Computations 12
>
> C.4 Contraction Scour Computationsfor Abutment with a Short Setback
>
> (Method A) 16
>
> C.5. Determination of or k~2~: 18
>
> C.6 Critical Shear Stress and Boundary Shear Stress 18
>
> **III. ABUTMENT SCOUR 19**
>
> A. ADJUSTMENT FACTOR FOR VELOCITY : 1-D AND 2-D MODELS 19
>
> B. ADJUSTMENT FACTOR: SPIRAL FLOW AT ABUTMENT TOE... ...\...\...21
>
> C. LOCAL ABUTMENT SCOUR EQUATION FOR VERTICAL WALL ABUTMENTS 21
>
> D. ADJUSTMENT OF ABUTMENT SCOUR FOR PRESSURE FLOW. ..22
>
> E. COMPUTATION OF ABUTMENT SCOUR DEPTH (ABSCOUR
> PROGRAM)........................................................................22
>
> F. OTHER ADJUSTMENTS TO THE ABUTMENT SCOUR DEPTH, y~sa~ ... .23
>
> F.1 Adjustment Factor, Kt, for Abutments with Wingwall and
>
> Spillthrough Slopes
> ......................................................
> ................23
>
> F.2 Adjustment Factor K~e~ for Embankment Skew
> Angle...........................24
>
> F.3 Adjustment Factor, FS, for Factor of
> Safety......................................25
>
> G. FINAL SCOUR
> ELEVATION........................................................25
>
> **IV. CLEAR WATER SCOUR EQUATIONS 25**
>
> A. CONTRACTION SCOUR 25
>
> B. ABUTMENT SCOUR 26
>
> **V. COMPUTATIONAL PROCEDURES 26**

VI
REFERENCES..............................................................................27

PART 2: GUIDELINES FOR APPLYING THE ABSCOUR PROGRAM 30

> **I. Introduction 29**
>
> **II. Development of the Input Data for the ABSCOUR (Abutment Scour)
> Model 30**
>
> A. STEP ONE - HYDRAULIC MODEL 31
>
> A.1 Water Surface Profile 31
>
> A.2 Development of Abscour Model Cross-sections 31
>
> B. STEP TWO -PROJECT INFORMATION MENU 31
>
> B.1 Project Name and Description 32
>
> B.2 Over-Rides 32
>
> C. STEP THREE - APPROACH SECTION 33
>
> C.1 Enter Approach Section Data 35
>
> D. STEP FOUR - DOWNSTREAM BRIDGE DATA 38
>
> D.1 Enter the Downstream Bridge Data 38
>
> E. STEP FIVE - UPSTREAM BRIDGE DATA 42
>
> E.1 Enter the Upstream Bridge Data 42

F STEP 6 PIER
DATA...................................................\....................45

G. STEP 7 ACTUAL SECTIONS
......................................................\...46

> **III. COMPUTATIONS AND PROGRAM OUTPUT INFORMATION 48**
>
> A. ABSCOUR Output 48
>
> B. ABSCOUR Program Logic 58
>
> C. EVALUATION OF THE PROGRAM OUTPUT 58
>
> C.1 Overrides 58
>
> C.2 Bridge Section Data 59
>
> C.3 Contraction Scour Table 59
>
> C.4 Abutment Scour Table 59
>
> C.5 Scour Depth Elevation 60
>
> C.6 Scour
> Cross-Section...............................................................\...60
>
> C.7 Evaluation of the Computed Scour Values 60
>
> **IV QUESTIONS TO CONSIDER-REVIEW OF THE ABSCOUR OUTPUT 62**
>
> **VI. COMPUTATION OF PIER SCOUR 64**
>
> A. Pier Local Scour Introduction 64
>
> B Option 1 64
>
> C Option 2 66
>
> E Option 3 . 66
>
> **VI. UTILITY MODULE 67**
>
> A. RIPRAP 67
>
> B. CRITICAL VELOCITY 68
>
> C. SCOUR IN ROCK 69
>
> C.1 Application of the Erodibility Index Method 69
>
> D. STREAM POWER CALCULATIONS 70
>
> E. ERODIBILITY INDEX CALCULATIONS 71
>
> E.1 COMPUTING THE ERODIBILITY INDEX FOR ROCK 71
>
> E.2 DESIGN PROCEDURE 71

ATTACHMENT 1: COMPUTATION OF THE VELOCITY OF FLOW USED IN THE ABUTMENT
SCOUR COMPUTATIONS. 73

> I. COMPUTATION OF VELOCITY AND SCOUR 73
>
> II\. EXAMPLE PROBLEM 1 76
>
> III\. COMPUTATION OF CONTRACTION SCOUR: 77
>
> A. Short Setback - CASE A in Figure A1-1 77
>
> B. Intermediate Setback of 70 Feet -Wide Overbank Section - CASE B in
> Figure A1-1 78
>
> C. Long Setback CASE C in Figure A1-1 79
>
> D. Special Case Intermediate Setback-Narrower Overbank -
>
> CASE D in Figure A1-1 79

ATTACHMENT 2: COMPLEX APPROACH FLOW CONDITIONS.....................82

> I. EXAMPLE 1 - TYPICAL FLOW DISTRIBUTION 83
>
> II\. EXAMPLE 2 - UNBALANCED FLOW ONDITION........................
> \...79
>
> III\. EXAMPLE 3 - BEND IN THE
> RIVER......................................... ...\...80
>
> IV\. EXAMPLE 4 - CONFLUENCE UPSTREAM OF BRIDGE................... .80

ATTACHMENT 3: SAFETY
FACTORS.......................................................86

ATTACHMENT 4: CRITICAL VELOCITIES IN COHESIVE
SOILS....................88

> **PART 1: DERIVATION OF THE ABSCOUR METHODOLOGY**

# [I. OVERVIEW]{.underline}

## [A. LIVE BED SCOUR]{.underline}

The method presented in this guideline for estimating abutment scour is
based on Laursen's contraction scour equation as presented in the FHWA
Publication HEC No. 18, Fourth Edition. (1). This equation was
originally derived by Straub (2) considering that the shear stresses
(and thus the rates of sediment transport) in an uncontracted section
and a contracted section are the same. It assumes a long contracted
channel where the flow is considered to be uniform and the scour depth
is constant across the channel section.

The contracting flow at the entrance corner of a channel constriction
differs significantly from the conditions described above. The flow
velocity across the channel is not uniform. The velocity near the edge
of the constriction is faster than that in the midstream. Because of
this higher velocity and its associated turbulence, the scour depth near
the edge or corner of the constriction is usually deeper than in the
center of the channel. The flow pattern at the upstream corner of an
abutment will be similar to the flow at the entrance corner of a
contracted channel, when the bridge approach roads obstruct overbank
flow or the abutment constricts the channel. Local abutment scour can be
expected to be deeper than the contraction scour in the center of the
channel. Laursen's contraction scour equation is used as the basis for
developing equations for estimating local abutment scour. Velocity
variations caused by the flow contraction and spiral flow at the toe of
the abutment are considered in developing the equations.

## [B. CLEAR WATER SCOUR]{.underline}

The contraction and abutment scour equations developed for live bed
scour have been modified for the computation of clear water scour. The
User has the options of selecting Laursen's clear water scour equation
or Neill's competent velocity procedure.

# [II. CONTRACTION SCOUR]{.underline}

## [A. LAURSEN'S LIVE BED CONTRACTION SCOUR EQUATION]{.underline} 

Laursen's equation for estimating scour in a contracted section in a
simple rectangular channel can be expressed in the following form:

**y~2~/y~1~ = (W~1~/W~2~) ^k2^ (1-1)**

where:

y~1~ = flow depth in the approach section

> y~2~ = total flow depth in the contracted section (y~2~ = y~1~ + y~s~,
> where y~s~. is the scour depth)
>
> W~1~ = channel width of the approach section
>
> W~2~ = channel width of the contracted section
>
> k~2~ = experimental constant related to sediment transport (originally
> identified as θ by Laursen).

These dimensions are illustrated in Figure 1-1

![](media/image2.wmf)

**Figure 1-1**

**Plan View of Approach and Bridge Sections**

Please note that this equation is a simplified form of Equation 1-1 in
HEC-18 for a contraction of a constant flow in a rectangular channel
with a uniform bed-material.

The ratio of q~2~/ q~1~ may be substituted for W~1~/ W~2~, and Equation
1-1 may be rewritten as:

**y~2~/y~1~ = (q~2~/q~1~)^k2^ (1-2)**

where:

q~1~ = unit discharge in the approach section

q~2~ = unit discharge in the contracted (bridge) section

y~1~ = total flow depth in the approach section

y~2~ = total flow depth in the contracted (bridge) section

k~2~ = experimental constant related to sediment transport

Equation 1-2 is a comparative equation, equating the rates of sediment
transport at the uncontracted and contracted sections. The equation
applies to the live-bed condition to the extent that the shear stresses
in the two sections are considered equal. The application of this
equation can be extended to clear water scour for the special case where
the shear stresses in the two sections are both equal to the critical
shear stress. The contracted section, Section 2, is best represented for
most cases as the downstream end of the bridge where the flow is
contracted and uniform. The upstream uncontracted section, Section 1,
should be selected at a point upstream where the flow is uniform and not
influenced by the bridge contraction. The directions in the HEC-RAS
program regarding ineffective flow areas can be used as a guide in
selecting the approach section.

## [B. MODIFICATION FOR PRESSURE FLOW]{.underline}

If the bridge is subject to pressure flow, Equation 1-2 needs to be
modified to account for the additional contraction scour caused by the
pressure flow:

**y~2~/y~1~ = (q~2~/q~1~)^k2^ \* k~p~ (1-2a)**

where:

k~p~ is the pressure flow coefficient ( See Eq.1-25, Section III.D of
Part 1.

> All other values are the same as in Equation 1-2.

## [C. DEVELOPMENT OF THE ABUTMENT SCOUR EQUATIONS]{.underline}

The following guidance is offered in developing the abutment scour
equations and in explaining the information needed for application of
the abutment scour (ABSCOUR) method to compute contraction and abutment
scour.

### *C.1 Upstream Approach Section, Section 1*

Section 1 is the upstream approach section. Convert the actual
cross-sections from the water surface profile model program to ABSCOUR
model cross-sections for the subareas of the left overbank, main channel
and right overbank. Represent each subarea as a rectangle having a width
and average depth. Obtain the top width (T) and flow area (A) of each
subarea from the output tables of the water surface profile model.
Compute the hydraulic depth of flow for each subarea as y = A/T. The
computation of hydraulic depth and top width from the HEC-RAS model is
acceptable for Section 1, but is not appropriate for Section 2, as
explained below. Figure 1-2 shows an example of an approach section.

![](media/image3.wmf)

**Figure 1-2: Definition sketch for the Approach Section (Looking
Downstream)**

*(Please note that W and T may be used interchangeably in figures and
equations to designate a channel or floodplain width)*

The ABSCOUR estimating procedure is based on the consideration that the
cross-section at the approach section remains constant in the reach
between the approach section and the upstream bridge section. Select the
upstream model cross-section with this consideration in mind. Guidance
on modeling complex approach flow conditions is presented in Attachment
2 of this Users Manual. For bridges located on bends, the distribution
of contraction scour needs to be assessed with regard to the effect of
bendway scour (7).

Verify that values used for y (depth), V (velocity), T (width), q
(discharge per foot of width) and Q (discharge) are consistent to assure
that Q = VA (where A = area = T\*y) and q = V\*y for each cross-section
subarea.

### *C.2 Bridge (Contracted) Section*

All measurements relative to bridge widths, abutment setbacks, etc,
should be made perpendicular to the flow in the channel and on the flood
plains. This consideration is most important for bridges skewed at an
angle to the channel.

As indicated in Figure 1-3, the actual cross-section under the bridge
needs to be converted into the ABSCOUR Cross-section. A detailed
step-by-step procedure is used to do this as explained in Part 2, Step
Four of this manual.

![](media/image4.wmf)

**Figure 1-3**

**Definition Sketch for Bridge Section (Looking Downstream)**

*(Please note that W and T may be used interchangeably in figures and
equations to designate a channel or floodplain width)*

A basic limitation of the HEC-RAS program is that it distributes flow
under the bridge by conveyance calculations. This approach does not take
into account the three dimensional flow patterns observed in the field
at bridge contractions. For scour calculations, it is important to
account for the high local flow velocities and turbulence near the
abutments caused by the contracting flow in the overbank areas upstream
of the bridge. Findings from recent field surveys and laboratory studies
of compound channels indicate that, for bridges with abutments near the
channel banks, the overbank flow converges into the channel with rapid
acceleration and high turbulence.

Converging flows under bridges with abutments near the channel banks
tend to mix and distribute uniformly, with higher local velocities
observed at abutments. On the other hand, if the abutment is set well
back from the channel bank near the edge of the flood plain, the
overbank flow and the main channel flow tend to remain separated from
each other and do not mix as the flow passes under the bridge. This
concept is applied in the ABSCOUR model for purposes of computing
velocities of flow.

### *C.3. Computation of Velocity for Contraction Scour Computations*

This section explains how the velocity of flow is computed for the
various conditions that occur at Section 2, the Bridge Section Figure
1-4 illustrates the various scour parameters addressed in this section.

![](media/image5.wmf)

**Figure 1-4**

####### **Definition Sketch for Contraction Scour Computations at Section 2, Bridge Section**

Please recall from Equation 1-2 (or Equation1-2a for pressure flow) as
depicted below, that the unit discharge (q~2~) must be determined in
order to compute the live bed total flow depth (**y~2~**) under the
bridge and that (q~2~) = V\*y~o~ .

**y~2~/y~1~ = (q~2~/q~1~)^k2^ (1-2)**

**y~2~/y~1~ = (q~2~/q~1~)^k2^ \* k~p~ (1-2a)**

Referring to Figure 1-4 above, once the total flow depth y~2~ is
calculated, the contraction scour depth can be computed as the total
scour depth (**y~2~**) minus the original flow depth (**y~o~**) or:

**y~s~ = y~2~ - y~o~ (1-2b)**

The final contraction scour depth is computed as:

**Final y~s~ = y~s~ \* FS (1-2c)**

where FS = Factor of safety.

The discussion below describes the various methods for computing the
velocity of flow under the bridge for various site conditions so that
the contraction scour can be determined.

-   **Method A Short Setback:** When an abutment is set back a distance
    from the channel bank no greater than five times the depth of flow
    in the channel, it is defined as a "short setback." For short
    setbacks, uniform mixing of flow is assumed so that the velocity of
    flow is the same throughout the waterway area at the downstream end
    of the bridge (Section 2). The average velocity of flow (V~ave~)
    under the bridge is computed as:

**V~ave~ = Q / A (1-3)**

where:

Q = total flow under the bridge, and

> A = sum of the channel and flood plain flow areas under the bridge as
> measured from bridges plans.
>
> The unit discharge per foot (q) is computed as:

**q~2~ = V ~ave~ \* y~o~ (1-4)**

where:

> y~o~ = hydraulic depth of flow on the flood plain or in the channel =
> A/T, where T is the top width of the subarea.
>
> Note that the value of y~o~ will be different for the left overbank,
> channel and right overbank areas (Refer to Figure 1-3). It is computed
> as waterway area (A) of the subarea divided by the top width (T) of
> the subarea. The downstream water surface elevation input by the user
> serves as the datum for measuring the hydraulic depth and for all
> other vertical measurements at Section 2.
>
> The flow depth of scour, y~2,~ is defined as the distance from the
> water surface to the scoured channel bed elevation and the actual
> scour depth (y~s~) is defined as y~s~= y~2\ -~ y~o~ (Refer to Figure
> 1-4). In the immediate area of the channel banks, there is a
> transition in the flow depth y~o~ between the channel and the flood
> plain. The User selects the bank slope 'Z' (1 vertical to Z
> horizontal) in the vicinity of the bridge in order to approximate the
> actual ground elevation more closely in the bank area. The flow depth
> in the bank area is designated as (y~o~)~adj~, and is computed by
> ABSCOUR using Equation 1-5:

**(y~o~)~adj~ = y~o~ (setback)/Z (1-5)**

where

(y~o~)~adj~ = adjusted Section 2 overbank flow depth before scour.

y~o..~ = downstream section average channel flow depth before scour

> setback = the distance from the edge of channel to the face of the
> abutment for vertical and wingwall types or toe of the slope for a
> spillthrough slope
>
> Z = bankfull slope where Z is the horizontal dimension and 1 is the
> vertical dimension

-   **Method B Intermediate Setback:** This method for computing
    velocity applies where the Abutment Setback is greater than 5 times
    hydraulic depth of the channel, but less than 75% of the flood plain
    width. For this method, the program makes an interpolation to
    compute the velocity of flow on the overbank between Method A
    (Equation 1-3), the short setback, and Method C, the long setback
    (Equation1-7). The average velocity at the overbank area is adjusted
    by the following equations:

> **V~mix~ = Q/A (short setback) at a setback distance of 5 y~o~
> (1-6a)**
>
> **V~o~ = Q~o~/A~o~ (long setback) (1-6c)**
>
> **(V~a~)~o~ = V~mix~- (V~mix~-V~o~) \*(Setback-5\*y~o~)
> /(0.75\*W~o~-5\*y~o~) (1-6d)**

where:

y~o~ = flow depth in channel

W~o~ = width of overbank flood plain under bridge (W~2~)

> V~mix~ = the velocity of the totally mixed flow condition., i.e.,
> average total flow under bridge for the short setback case where
> setback = 5\*y~o~
>
> V~o~ = the overbank flow velocity assuming a separate flow condition
> (i.e. long setback condition)
>
> (V~a~)~o~ = the average overbank velocity for this medium setback case
>
> This method provides for a smooth transition between the short and
> long setback cases. There are a few special methods that are
> considered in the program to cover all possible combinations of flow
> depths, velocities and setbacks. These special methods are discussed
> in Attachment 1.

-   **Method C Long Setback:** This method for computing velocity
    applies where the setback distance of the abutment from the channel
    bank is greater than seventy five percent of the flood plain width.
    For this case, the assumption is made that the flow on the flood
    plain at the approach section remains on the flood plain as it flows
    under the bridge. Similarly, the flow in the main channel at the
    approach section remains in the channel under the bridge.
    Accordingly, the following relationship will hold true for flows on
    either the right or left flood plain subsections for the approach
    section (1) and the bridge section (2):

**Q~1~ = Q~2~**

**q~1~ W~1~ = q ~2~ W~2~**

**q ~2~ = q~1~ \*W~1~ /W~2~ (1-7)**

> The discharge, Q~1~, in any cross-section subarea of Section 1
> (channel, overbank area) is obtained from the HEC-RAS program, and the
> unit discharge, q~1~, is computed as Q~1~ /W~1~. W~1~ and W~2~ are
> obtained from the HEC-RAS program or from bridge plans.
>
> The flow velocity under the bridge for any subarea is computed as:
>
> **V~2~= q ~2~ / y~o2~ (1-8)**
>
> where y~o2~ is the flow depth under the bridge
>
> • **Modeling Flow Conditions for Different Setbacks of the Left and
> Right Abutments:** It is likely that situations will occur where one
> abutment will meet the criteria for analysis by Method A, Short
> Setback, and the other abutment for analysis by Method C Long Setback
> or Method B, Intermediate Setback. For such cases, computations for
> the left and right abutments are treated separately. As an example,
> assume that the left flood plain is set back from the channel a
> distance of more than 75 % of the width of the flood plain, (Method C
> analysis) and the right abutment is set back from the channel a
> distance less than five channel flow depths (Method A analysis). The
> ABSCOUR program will compute scour for the left abutment using unit
> discharges computed only for the left overbank (V = Q~overbank~/A
> ~overbank~). The ABSCOUR program will compute scour for the right
> abutment using unit discharges computed for mixed flow where:

**V~mix~= (Q~channel~ +Q~right\ overbank~)/(A~channel~ +A
~right\ overbank~). (1-9)**

> There are actually 16 different combinations of channel
> characteristics and of the abutment setbacks considered in the ABSCOUR
> calculations. These are presented in Attachment 1 of this manual.

### *C.4 Contraction Scour Computations for Abutment with a Short Setback (Method A)*

When the abutment has no setback (is at the channel bank), the scour at
the overbank will be equal to that for channel. When the setback is
small, the scour at the overbank will be very close to the scour in the
channel. However, due to the idealization of channel and overbank flow
into the rectangular shapes for the ABSCOUR cross-section, the
calculated overbank scour may be based on clear water scour (as
determined from the Approach Section calculations) when it is actually
subject to live bed scour conditions from the main channel. There is
obviously a transition zone between the no setback case and the case
where the abutment is set well back on the flood plain.

The limit of the transition zone is defined as five times the flow depth
in the downstream channel. When there is no setback, the channel scour
flow depth (y~2~) is used for the contraction scour.

When the abutment setback on the flood plain exceeds the limit of the
transition zone, separate flow is assumed between the channel and the
flood plain, and contraction scour is computed directly using the
procedure described for the medium setback or the long setback.

When the setback is within this transition zone of from zero to 5y~o~,
the following scheme is used to compute contraction scour:

> 1\. ABSCOUR separately calculates both clear water scour flow depth
> and live bed scour flow depth for (1) the channel section and (2) the
> overbank section at a distance of 5 y~o~.
>
> 2\. The channel contraction scour flow depth (y~2~) is the scour when
> the setback is equal to or less than zero - that is no setback case.
>
> 3\. The overbank contraction scour flow depth (y~2~) is the overbank
> scour when the setback is located on the flood plain beyond the
> channel banks a distance equal to 5 times the flow depth in the
> downstream channel (SB = 5y~o~)

There are four combination of overbank scour which may occur in the
transition zone:

> 1\. Clear water scour with no setback
>
> 2\. Clear water scour with setback = 5y~o~
>
> 3\. Live bed scour with no setback
>
> 4\. Live bed scour with setback = 5y~o~

The computed overbank contraction scour will be interpolated between
these four cases, depending on the setback distance and the scour type
(live-bed or clear water at overbank and channel).

For example, when the channel is live bed and the overbank is clear
water, then the overbank contraction scour for the actual setback
(between 0 and 5 times channel flow depth) will be interpolated between
case 3 ( live bed scour with no setback) and case 2 (clear water scour
with setback = 5y~o~). The interpolation depends on the distance that
the abutment is set back from the channel bank and the scour type at the
overbank and channel sections.

A parabolic interpolation is used for the contraction scour flow depth
calculation (y~2~) since this method provides for a smooth transition
that approximates the scour depths computed through the application of
Laursen's contraction scour equations. The contraction scour flow depth
is modified as necessary to take into account the effect of any pressure
scour and to apply a safety factor to the design (See Attachment 1).

Next, the abutment scour flow depth (y~2a~) is computed directly from
the interpolated contraction scour value as indicated by Equation 1-10.
A detailed discussion of Equations 1-10 through 1-12 and the derivation
of k~f~ and k~v~ are presented in Section III, Abutment Scour. *The
abutment scour equations are introduced here primarily to present the
complete process for computing scour for the short setback method.*

**y~2a~ = ( k~f~ \* (k~v~)^k2^ ) \* (total contraction flow depth)
(1-10)**

As described earlier, modifications to the total contraction scour to
account for pressure flow are applied to the total contracted flow depth
prior to making the computation of Equation 1-10. The unadjusted
abutment scour depth (y~sa~) is computed as:

**(y~sa~) = y~2a~ - (y~o~)~adj~ (1-11)**

where:

(y~o~)~adj~ = flow depth before scour occurs.

The final or adjusted abutment scour depth (y~sa~)~adj~ is computed as:

**(y~sa~)~adj~ = K~t~ \* K~e~ \*FS \* y~sa~ (1-12)**

where:

K~t~ = modification for abutment shape

> K~e~ = modification for embankment skew
>
> FS = factor of safety

y~sa~ = initial abutment scour estimate noted above (y~sa~ = y~2a~ -
(y~o~) ~adj~)

### *C.5. Determination of k~2~ or θ:*

The value of *k~2~* (θ) in Equation 1-2 varies from 0.637 to 0.857
depending on the critical shear stress of bed material to the boundary
shear stress in the normal channel section. For clear-water flow it is
0.857 and for live-bed flows it is less depending on the ratio of shear
stress to the critical shear stress of the bed material. Laursen (2)
established the variation of θ-value as a function of τ~c~/τ~1~ as shown
in Figure 2.24 in ASCE Manual on Sedimentation (2). This curve may be
approximated by the following equation:

**k~2~ or θ = 0.11(τ~c~/τ~1~ + 0.4)^2.2^ + 0.623 (1-13)**

Where τ~c~ is the critical shear stress and τ~1~ is the boundary shear
stress in the upstream or normal channel section. If τ~c~ is equal to or
greater than τ~1,~ then clear water scour can be expected to take place
at the bridge, and the value of k~2~ (θ) should be selected as 0.857.

### *C.6 Critical Shear Stress and Boundary Shear Stress*

Critical shear stress, τ~c~, may be calculated by several methods. For
non-cohesive materials and for fully developed clear-water scour,
Laursen (1) used the following simple empirical equation developed for
practical use:

**τ~c~ = 4D~50~ (1-14)**

where:

> D~50~ is the median particle size in the section (channel bed or
> overbank area) under consideration. On overbank areas, estimating the
> critical shear stress may also involve consideration of the flood
> plain vegetation.

The boundary shear stress, τ~1~, in the approach channel or overbank
subarea may be calculated as:

**τ~1~ = γ  y~1~S ~ave~ (1-15)**

where:

γ    =  62.4  lbs/ft^3^, in the English system

y~1~ = flow depth or hydraulic depth of the reach approximated by the

depth at the approach section, and

> S~ave~ = the average energy slope between the approach section and the
> downstream section. (Refer to Part 2, Section C.1).

# 

# [III. ABUTMENT SCOUR]{.underline}

Figure 1-5 illustrates the various factors used in the evaluation of
abutment scour.

![](media/image6.wmf)

**Figure 1-5: Definition Sketch for Abutment Scour Computations at
Section 2,**

**Bridge Section (Looking Downstream)**

## [A. ADJUSTMENT FACTOR FOR VELOCITY]{.underline}

The simple model depicted in Figure 1-1 and the accompanying analysis
applies only to a long contraction where the flow velocity is considered
uniform. For flow constricted by an abutment, the velocity across the
section is not uniform, and the velocity at the face of the abutment is
higher. To compute abutment scour, the contraction scour equations need
to be modified to account for the higher velocity and resulting deeper
scour which occurs at the abutment.

The two-dimensional potential flow pattern around a rectangular abutment
was used for evaluating the velocity distribution across the contracted
section. A study of the velocity distribution in this constricted
section (3, 4) applying the principles of potential flow revealed that
the ratio of the velocity at the toe of the abutment to the mean
velocity of the flow in the contracted section of a simple rectangular
channel can be approximated by the following equation:

**k~v~ = 0.8(q~1~/q~2~)^1.5^ + 1 (1-16a)**

where:

> k~v~ = ratio of velocity at the abutment toe to the mean velocity in
> the contracted section.
>
> q~1~ = average unit discharge in the approach section, and
>
> q~2~ = average unit discharge in the bridge section.

Equation 1-16 applies to a simple contraction, where the unit discharge
of the approach section is less than that in the contraction,
q~1~\<q~2~. The values of k~v~ should be limited to the range of values
between 1.0 and 1.8*.* If the computed value is less than 1.0, use a
value of 1.0; if the computed value is greater than 1.8, use a value of
1.8.

[Computation of k~v~ for 2-D flow models]{.underline}

If the ABSCOUR user selects a 2-D model instead of a 1-D model such as
HEC-RAS for the hydraulic analysis, k~v~ should be computed by a
different procedure. The 2-D model can be used to measure directly the
velocity of flow at the face or toe of the abutment (V~face~). Referring
back to equation 1-16a, k~v~ is defined as the ratio of velocity at the
abutment face or toe to the mean velocity (V~ave~) in the adjacent
contracted section. Both of these parameters are calculated by the 2-D
model. The procedure to calculate k~v~ is described below:

1\. Select the override option for 2-D flow on the Project Information
Card

2\. Step 1 above will open two cells on the Downstream Bridge Data Card:

1.  Enter the calculated/measured flow velocity at the abutment face/toe
    in the cell designated V~face~

2.  Enter the calculated/measured average flow velocity in the adjacent
    contracted section in the cell designated V~ave~

3\. The ABSCOUR program will then calculate k~v~ using Equation 1-16b:

k~v~ = V~face~/V~ave~ **1-16b**

[B. ADJUSTMENT FACTOR FOR SPIRAL FLOW AT ABUTMENT TOE]{.underline}

The above discussion with respect to the velocity coefficient reflects
the limited analysis available using two-dimensional flow concepts. The
flow at an abutment toe is in spiral motion, which is three-dimensional.
Accordingly, a factor for adjusting two-dimensional flow to
three-dimensional flow needs to be added to Equation 1-2. Available
scour data for vertical-wall abutments were analyzed (5). The analyses
resulted in the following two envelop equations for determining the
value of the spiral flow adjustment factor, k~f\ .~

For clear-water scour:

**k~f~ = 0.13 + 5.85F (1-20)**

For live-bed scour:

**k~f~ = 0.46 + 4.16F (1-21)**

where:

> k~f~ = experimental coefficient for spiral flow at the abutment toe.
> *(The values of k~f~ should range from 1.0 to 4.0.* If the computed
> value is less than 1.0, use a value of 1.0; if the computed value is
> greater than 4.0, use a value of 4.0.)
>
> F = Froude number of the flow in the approach channel or overbank
> subarea, depending on the location of the abutment.
>
> **F = V~1~/ (gy~1~)^0.5^ (1-22)**
>
> where:
>
> V~1~ is the average velocity
>
> y~1~ is the average depth in the approach subarea
>
> g is the gravitational constant.

## [C. LOCAL ABUTMENT SCOUR EQUATION - VERTICAL WALL ABUTMENTS]{.underline} 

The adjustment factors presented above are combined with Laursen's
contraction scour equation to develop the equation for abutment scour
for a vertical wall abutment:

**y~2~/y~1~ = k~f~(k~v~q~2~/q~1~)^k2^ (1-23)**

where:

> y~1~ = total flow depth in the approach section,
>
> y~2~ = total flow depth of scour in the contracted section (y~2~ =
> yo + y~s~, where y~o~ = the initial flow depth and y~s~ = the scour
> depth )
>
> q~1~ = unit discharge in the approach section

q~2~ = unit discharge in the contracted section

> k~2~ = experimental constant related to sediment transport (identified
> as θ by Laursen).

## [D. ADJUSTMENT OF ABUTMENT SCOUR DEPTH FOR PRESSURE FLOW]{.underline}

For conditions of pressure flow, Equation 1-23 needs to be adjusted to
account for the effect of pressure flow by multiplying by the pressure
coefficient, k~p~:

**y~2~/y~1~ = (k~f~ \*(k~v~\*q~2~/q~1~)^k2^ )\* k~p~ (1-24)**

The pressure coefficient, k~p~, has been determined experimentally (6).
Preliminary conclusions suggest that k~p~ be applied within the
following limits:

**k~p~ = 0.66F~1~ ^-0.45^ (1-25)**

where:

F~1~ = Froude Number in the main channel at the approach section.

The values of k~p~ should range from 1.0 to 1.15. If the computed value
is less than 1.0, use a value of 1.0. Cases of severe submergence are
defined where the depth of flow above the low chord is greater than 40%
of the flow depth as measured from the channel bottom to the low chord
(h/d~1~\> 0.4), See Figure 1-6. For this case, the value of k~p~ should
be multiplied by a factor of 1.15. If the computed value of k~p~ exceeds
1.15, use a value of 1.15.

![](media/image7.wmf)

**Figure 1-6**

**Definition Sketch for Pressure Scour**

These preliminary findings are still being verified. The ABSCOUR program
uses a value of k~p~ of 1.1 for pressure scour when the upstream water
surface is equal to or greater than 1.2 of the distance of the height of
the low chord above the streambed. The k~p~ value varies linearly
between 1.0 and 1.1 for submergences of the low chord between 1.0 and
1.2

## [E. COMPUTATION OF ABUTMENT SCOUR DEPTH (ABSCOUR PROGRAM)]{.underline}

The ABSCOUR program computes abutment scour as:

**y~2a~ = k~f~\*(k~v~ )^k2^ \* (contraction scour flow depth) (1-26)**

where:

> the contraction scour flow depth is defined by either Equation 1-2 (no
> pressure flow) or 1-2a (pressure flow) as appropriate.

For conditions of open channel flow or pressure flow at a bridge, using
the depths determined from Equation 1-11, the unadjusted abutment scour
depth is:

**y~sa~ = y~2a~ - (y~o~) ~adj~ (1-27)**

where:

y~sa~ = unadjusted abutment scour depth,

y~2a~ = depth of flow at the bridge abutment after scour has occurred

> (y~o)adj~ = initial depth of flow at the bridge abutment, prior to the
> occurrence of scour. As noted earlier, the adjustment factor is
> applied to modify flow depths affected by the bank slope.

## [F. OTHER ADJUSTMENTS TO THE ABUTMENT SCOUR DEPTH, y~sa~]{.underline}

The final abutment scour depth, (y~sa~) ~adj~ is determined from the
following adjustments:

**(y~sa~)~adj~ = Kt \* Ke \*FS \* y~sa~ (1-28)**

where:

Kt = modification for abutment shape

> Ke = modification for embankment skew

FS = factor of safety.

y~sa~ = initial scour estimate from Equations 27 = y~2a~ - (y~o~) ~adj~

**Please note that these adjustment factors are applied to the initial
abutment scour depth to arrive at a final abutment scour depth and
elevation.**

The adjustment factors are described below:

### *F.1 Adjustment Factor, Kt, for Abutments with Wingwall and Spillthrough Slopes*

The scour depth estimated from Equation 1-23 for vertical wall abutments
is adjusted by the program for spillthrough slopes and wing-wall
abutments by multiplying by the adjustment factor K~t~. The factor is
computed on the basis of the ratio of the horizontal offset provided by
the spillthrough slope or wingwall to the total length of the abutment
and approach embankment in the flood plain. This factor serves to
account for the more streamlined flow condition provided by the wingwall
or spillthrough slope.

The abutment shape factors in HEC-18 Table 8.1 (0.55 for spillthrough
abutment and 0.82 for wingwall abutment) apply to short abutments. As
the length of the abutment and approach road in the flood plain
increase, the effect of a spillthrough slope in reducing scour is
decreased. For long approach road sections on the flood plain, this
coefficient will approach a value of 1.0. Similarly, scour for vertical
wall abutments with wingwalls on short abutment sections is reduced to
82 percent of the scour of vertical wall abutments without wingwalls. As
the length of this abutment and approach road in the flood plain
increase, the effect of the wingwall in reducing scour is also
decreased. For long approach road sections in the flood plain, K~t~ will
approach a value of 1.0. Refer to Part II of this report for a
definition sketch of the ABSCOUR Shape Factor as SF = X~1~/X~2~

For a spillthrough slope abutment:

**Kt = 0.55 +0.05 (( 1/SF) - 1) (1-29)**

For abutments with wingwalls:

**Kt = 0.82 + 0.02((1/SF) - 1) (1-30)**

If SF \< 0.1, then Kt = 1.0

Detailed information on the selection of the Shape Factor, SF, is
provided in Part 2, Section E, Upstream Bridge Data.

### *F.2 Adjustment Factor K~e~ for Embankment Skew Angle*

For highways embankments skewed to flood plain flow, a correction
factor, Ke, is computed to account for the effect of the embankment skew
on abutment scour. Detailed information on the selection of the Shape
Factor, SF, is provided in Part 2, Section E, Upstream Bridge Data, and
in the FHWA publication HEC-18). The embankment skew angle, α , is the
angle between the direction of flow and the centerline of the roadway
(bridge) at the left or right abutment:

**Ke = (α/90)\^0.13 (1-31)**

This value will be usually different for each abutment. Note that the
embankment skew may not be the same as the skew angle of the abutment.
The effect of the abutment skew angle is taken into account by using the
flow width that is normal to the flow.

### *F.3 Adjustment Factor, FS, for Factor of Safety*

In developing the ABSCOUR equations for estimating abutment scour,
available information from laboratory studies collected by the
consultant firm of GKY and Associates was used as a means of calibrating
the model. These laboratory tests were conducted in simple rectangular
straight channels (laboratory flumes) with uniform flow. A total of 126
data points were used to develop the envelop equation describing the
average value of the coefficient for the spiral flow adjustment factor,
k~f~ . Use of the envelope curve provides for a limited factor of safety
in the calculations. However, natural rivers are not accurately
represented by the simple flow conditions modeled in a laboratory flume.
For practical design, use of a safety factor is recommended to take into
account the effect of the complex flow patterns which can be expected to
occur at bridges Selection of a safety factor is described in Attachment
3.

## [G. FINAL SCOUR ELEVATION]{.underline}

**Elev. of Bottom of Scour Hole = Water surface elevation - (yo)~adj~ -
(y~sa~)~adj~ (1-32)**

Please note that Equation 1-32 takes into account all factors in
Equations 1-5, and 1-28. The user must modify these values where
aggradation or degradation is a consideration.

# [IV. CLEAR WATER SCOUR EQUATIONS]{.underline}

## [A. CONTRACTION SCOUR]{.underline}

Laursen's contraction scour equation in the form of Equation 1-2 assumes
the bed materials and the shear stresses in the approach and the
contracted sections are the same. Where the bed material of the approach
section is not the same as the contracted section, Equation 1-2 should
not be used. Where the upstream section is covered with vegetation and
no sediment is transported (clear water scour), Neill's concept may be
used in determining contraction scour. The bed material in the
contracted section will be eroded until (1) the bed shear is reduced to
its critical value, or (2) the flow depth increases until it reaches the
depth where the shear stress is reduced to the value of the critical
shear stress. Equation 1-2 for contraction scour, then, may be reduced
to the following form:

**y~2~ = y~c~ (1-33)**

where:

y~c~ = flow depth in contracted channel when bed shear is at the
critical value.

Clear water scour occurs at a structure when the upstream channel bed is
armored or the flood plain is covered with vegetation and no sediment is
transported to the bridge. For such cases, the following clear water
scour equations are used in the ABSCOUR program to solve for y~2~. These
equations are developed from Neill's competent velocity curves,
Reference 11.

> [For D~50~ ≤ 0.001 ft.]{.underline}
>
> **y~2\ ~**= \[q/(2.84 D~50~^.15^)\]^0.67^ **(1-34)**
>
> [For 0.1\> D~50~\> 0.001 ft.]{.underline}
>
> y~2~=\[q/(11.5D~50~^.35^)\]^x^ **(1-35)**

where:

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

> [For D~50~ ≥ 0.1 ft.]{.underline}
>
> y~2~ = \[q/(11.5D~50~^.33^)\]^0.86^ **(1-36)**

The following relationship applies to the above equations:

**y~2~ = y~1~ + y~s~ (1-37)**

where:

y~1~ = flow depth before scour

y~2~ = flow depth after scour

y~s~ = contraction scour depth below stream bed.

If pressure flow conditions exist, the value of y~2~ is increased as:

**y~2~ ~(modified)~ = k~p~ \* y~2~ . (1-38)**

The value of k~p~ is explained in Section III D.

## [B. ABUTMENT SCOUR]{.underline} 

Once the clear water contraction scour value is determined, clear water
abutment scour (y~2a~) can be calculated as:

**y~2~a = ( k~f~ (k~v~)^0.857^) y~2~ (1-39)**

where:

> y~2~ = clear water contraction scour depth determined from Equations
> 1-34 to 1-36.
>
> k~f~ is dependent on the intensity of the spiral flow in the approach
> flow, and is calculated as explained in Part I, Section III B.
>
> k~v~ is related to the contraction ratio of the approach flow and is
> calculated as explained in Part I, Section III A.

# [V. COMPUTATIONAL PROCEDURES]{.underline}

# 

The computational procedures in the ABSCOUR program described above have
been developed on the basis of straight channels with rectangular cross
sections. Actual stream channels and flood plains are likely to vary
significantly from these geometric shapes. The Engineer needs to apply
judgment when using the ABSCOUR methodology to evaluate scour at an
actual bridge crossing. The ABSCOUR User's Guide presented in Part 2 of
this paper discusses ways to input data and interpret output data so as
to achieve a reasonable estimate of contraction, pier and abutment scour
for cases where the channel is not straight or where there is a complex
flow distribution in the approach channel.

VI\. 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,
Interim Manual for Hydrologic and Hydraulic Design, 2003

9\. Peggy A. Johnson, Pier Scour at Wide Piers, ASCE North American
Water and Environment Congress, June 1996.

10\. FHWA, "Bridge Scour and Stream Instability Countermeasures," HEC
No. 23, Fourth Edition, May 2001

11\. "Guide to Bridge Hydraulics", Second Edition, Transportation
Association of Canada, 2001.

#####