Effect of compound channel hydraulics on bridge abutment scour [Apr. 1998]

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DEPARTMENTAL RESEARCH GDOT RESEARCH PROJECT NO. 9411
FINAL REPORT
GEORGIA DEPARTMENT OF TRANSPORTATION

EFFECT OF COMPOUND

"l

CHANNEL HYDRAULICS ON

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BRIDGE ABUTMENT SCOUR

OFFICE OF MATERIALS & RESEARCH
RESEARCH AND DEVELOPMENT BRANCH

Georgia Department of Transportation Office of Materials and Research
GDOT Research Project No. 9411 Final Report
EFFECT OF COMPOUND CHANNEL HYDRAULICS ON BRIDGE ABUTMENT SCOUR
by
Terry W. Sturm, Ph.D., P.E. Associate Professor
School of Civil & Environmental Engineering Georgia Institute of Technology Atlanta, GA 30332 April, 1998
The contents of this report reflect the views of the author, who is responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Georgia Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.

TECHNICAL REPORT STANDARD TITLE PAGE

I. Report No. FHWA-GA-98-9411

2. Government Accession No.

4. Title and Subtitle

Effect of Compound Channel Hydraulics on Bridge Abutment Scour

7. Author Dr. Terry W. Sturm Associate Professor, School of Civil and Environmental Engineering Georgia Institute of Technology
9. Performing Organization Name and Address Georgia Institute of Technology School of Civil and Environmental Engineering Atlanta, GA 30332-0355

3. Recipient's Catalog No. 5. Report Date
Aprill998 6. Performing Organization Code 8. Performing Organiz. Report No.
9411
10. Work Unit No.
11. Contract or Grant No.

12. Sponsoring Agency Name and Address Georgia Department of Transportation No.2 Capitol Square Atlanta, Georgia 30334

13. Type of Report & Period Covered Final 1995-1997
14. Sponsoring Agency Code

15. Supplementary Notes Prepared in cooperation with the U.S. Department of Transportation Federal Highway Administration.
16. Abstract This study examines the effects of compound channel hydraulics on bridge abutment scour where the abutments terminate in
wide, roughened floodplains. Water discharge, abutment length, and sediment size were varied to determine their effects on he time development and equilibrium depth of local clear-water scour around abutments that terminate in such floodplains. It is shown that the discharge distribution in the bridge approach channel and its redistribution in the contracted section are important determinants of scour depth. The effects of sediment size are accounted for by the critical velocity at incipient motion. It is demonstrated that scour depth can be related to local values of velocity and depth near the abutment face as well as to approach hydraulic conditions.
Based on the experimental results, a dimensionless relationship is proposed for taking into account the effects of time development of scour. A methodology for assessing the expected magnitude of bridge abutment scour is suggested for the purpose of identifying bridges subject to excessive abutment scour in order that remedial action may be taken. Finally, the comparisons of WSPRO results, experimental results, and results from a 2-D numerical turbulence model have shown that WSPRO is adequate for estimating the independent parameters needed for abutment scour prediction, as long as bridge approach hydraulic conditions are utilized as predictor variables.

17. Key Words Compound channel hydraulics, bridge abutment, scour, floodplain

18. Distribution Statement No Restrictions

19. Security Classif. (ofthis report) Unclassified
Form DOT 1700.7 (8-69)

20. Security Classif. (of this page) 21. No. of Pages

Unclassified

145

22. Price

TABLE OF CONTENTS
EXECUTIVE SUMMARY ACKNOWLEDGMENTS LIST OF FIGURES LIST OF TABLES LIST OF SYMBOLS
CHAPTER 1 - INTRODUCTION
Background Research Objectives
CHAPTER2- LITERATURE REVIEW
Compound Channel Hydraulics Abutment Scour
CHAPTER 3 - EXPERIMENTAL INVESTIGATION
Introduction Compound Channel and Abutment Geometry Sediment Water Surface Profile and Velocity Measurements Scour Measurements Results
Channel Roughness Discharge Distribution Water Surface Profiles Velocity Distributions Time Development of Scour Equilibrium Scour Depths Critical Velocity
CHAPTER 4 - ANALYSIS OF RESULTS
Equilibrium Scour Depth Alternative Procedure I

Page No.
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v
IX XI
1
1 4
7
7 13
21
21 21 23 24
26 28
28 29 31 31
32 32 34
37
37 38

Theoretical Background

38

Correlation of Results

41

Alternative Procedure II

42

Dimensional Analysis

42

Correlation of Results

44

Discussion

45

WSPRO Predictions

47

Time Development Relationship

50

Proposed Procedure for Abutment Scour Prediction

52

Example

54

Solution

54

Limitations

58

CHAPTER 5 - CONCLUSIONS AND RECOMMENDATIONS

61

LITERATURE CITED

65

APPENDIX

A- Figures

A-1

B - WSPRO Data and Results

B-1

II

EXECUTIVE SUMMARY This report summarizes experimental work on bridge abutment scour in a compound channel with wide, roughened floodplains. Water discharge, abutment length, and sediment size were varied to determine their effects on the time development and equilibrium depth of local, clear-water scour around abutments that terminate on the floodplain. It is shown that the discharge distribution in the bridge approach channel and its redistribution in the contracted section are very important determinants of scour depth. The effects of sediment size are accounted for by the critical velocity at incipient motion. It is demonstrated that scour depth can be related to local values of velocity and depth near the abutment face as well as to approach hydraulic conditions. Based on the experimental results, a dimensionless relationship is proposed for taking into account the effects of time development of scour. A methodology for assessing the expected magnitude of bridge abutment scour is suggested for the purpose of identifying bridges subject to excessive abutment scour so that remedial action can be taken. Finally, the comparisons ofWSPRO results, experimental results, and results from a 2D numerical turbulence model have shown that WSPRO is adequate for estimating the independent parameters needed for abutment scour prediction as long as bridge approach hydraulic conditions are utilized as predictor variables.
111

ACKNOWLEDGMENTS The contributions of graduate students Bahram Biglari, who completed the twodimensional numerical modeling; Sean Williams, who did much of the early fixed-bed and scour time development measurements; William Blackwood, who measured critical velocities; and Antonis Chrisochoides, who completed the scour and velocity measurements and WSPRO analysis contained herein are gratefully acknowledged. Scott Williams assistance in setting up the experimental flume and constructing the abutments was invaluable. The prior work of graduate students Nazar Janjua and Aftab Sadiq did much to set the framework for the advances made in this project. The author is grateful for the careful and thorough reviews of the final report by the FHWA Regional Office, by the GDOT Bridge Design Office under the supervision of Mr. Paul Liles, State Bridge Engineer, and by Mr. David Jared of the GDOT Materials and Research Office. Mr. Jared provided overall guidance as project engineer, and his patience and support in bringing the project to completion is appreciated. Mr. Lamar Caylor, also of GDOT Materials and Research, greatly encouraged the author's efforts during the project initiation phase. The author also acknowledges the support of the FHWA in a parallel research project with additional related objectives, which is still underway. Mr. Sterling Jones and Mr. Johnny Morris of FHWA made numerous helpful suggestions that improved both the GDOT project and the current FHWA project, which at its completion should augment and enhance the present report.
IV

LIST OF FIGURES
Fig. 3.1. Cross-sections Used in Scour Experiments.
Fig. 3.2. Abutment Shapes Used in Scour Experiments.
Fig. 3.3. Sediment Grain Size Distributions.
Fig. 3.4. Manning's n in the Main Channel and Floodplain for Cross-Section B.
Fig. 3.5. Measured and Computed Normal Depth for Cross-Section B.
Fig. 3.6. Ratio of Main Channel Discharge to Total Discharge as a Function ofRelative Normal Depth in the Floodplain.
Fig. 3.7. Discharge Distribution Factor Mas a Function ofRelative Approach Floodplain Depth.
Fig. 3.8. Variation ofMain Channel Discharge Ratio from Approach to Contracted Section with M.
Fig. 3.9. Water Surface Profiles for Vertical-Wall Abutments ofVarying Length and Constant Discharge.
Fig. 3.10. Water Surface Profiles for Vertical-Wall Abutments of Constant Length and Varying Discharge.
Fig. 3. 11. Water Surface Profiles for Spill-Through Abutments of Varying Length and Constant Discharge.
Fig. 3.12. Water Surface Profiles for Spill-Through Abutments of Constant Length and Varying Discharge.
Fig. 3.13. Variation in Backwater Ratios in Floodplain with Discharge and Abutment Type and Length.
Fig. 3.14. Approach Velocity Distributions for Vertical-Wall Abutments ofVarying Length and Constant Discharge.
Fig. 3.15. Approach Velocity Distributions for Vertical-Wall Abutment of Constant Length and Varying Discharge.

Page No. A-1 A-2 A-3 A-4 A-5 A-6 A-7 A-8 A-9
A-1 0 A-ll A-12 A-13 A-14 A-15

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Fig. 3.16. Approach Velocity Distributions for Spill-Through Abutments ofVarying Length and Constant Discharge.

A-16

Fig. 3.17. Approach Velocity Distributions for Spill-Through Abutment of Constant Length and Varying Discharge.

A-17

Fig. 3.18. Time Development of Scour Depth for Sediment A with Varying Discharge.

A-18

Fig. 3.19. Time Development of Scour Depth for Sediment C with Varying Discharge.

A-19

Fig. 3.20. Time Development of Scour Depth for Sediment C with Varying Abutment Length.

A-20

Fig. 3.21. Equilibrium Scour Depths for Sediment A with Varying Discharge and Abutment Length.

A-21

Fig. 3.22. Equilibrium Scour Depths for Sediments B and C with Varying Discharge and A-22 Abutment Length.

Fig. 3.23. Equilibrium Bed Elevation Contours for LjBf= 0.44 (VW) and Q = 3.49 cfs. A-23

Fig. 3.24. Equilibrium Bed Elevation Contours for L/Bf= 0.44 (VW) and Q = 4.00 cfs. A-24

Fig. 3.25. Equilibrium Bed Elevation Contours for LjBf= 0.66 (VW) and Q = 3.51 cfs. A-25

Fig. 3.26. Equilibrium Bed Elevation Contours for LjBf = 0.66 (ST) and Q = 3.50 cfs.

A-26

Fig. 3.27. Measured and Calculated Critical Velocities at Incipient Motion.

A-27

Fig. 4.1. Definition Sketch for Equilibrium Scour in a Long Contraction in a Compound Channel.

A-28

Fig. 4.2. Equilibrium Abutment Scour Relationship Based on Approach and Tailwater Conditions.

A-29

Fig. 4.3. Equilibrium Abutment Scour Relationship Based on Local Velocity Near Abutment Face.

A-30

Fig. 4.4. Estimate ofRatio of Approach Velocity to Abutment Velocity Based on

A-31

Floodplain Flow Depth Near Abutment Face.

Fig. 4.5. Estimate of Ratio of Approach Velocity to Abutment Velocity Based on Tailwater Flow Depth.

A-32

VI

Fig. 4.6. Numerically Predicted Resultant Velocity Distribution at Upstream Face of Bridge by 2D Turbulence Model Applied to Cross-section A
Fig. 4.7. Numerically Predicted Velocity Vectors by 2D Turbulence Model Applied to Cross-section A
Fig. 4.8. Estimation of Abutment Velocity Based on Relationship Between Alternative I and II Scour Prediction Procedures.
Fig. 4.9. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for LJBr =0. 17 and Q=2.0 cfs.
Fig. 4.10. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for LJBr=0.33 and Q=2.0 cfs.
Fig. 4.11. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for L/Br =0.50 and Q=2.0 cfs.
Fig. 4.12. Comparison of Computed and Measured Velocity Distributions in Cross-Section A for LJBr =0.17 and Q=2.0 cfs.
Fig. 4.13. Comparison of Computed and Measured Velocity Distributions in Cross-Section A for L/Br =0.33 and Q=2.0 cfs.
Fig. 4.14. Comparison of Computed and Measured Velocity Distributions in Cross-Section A for L/Br=0.50 and Q=2.0 cfs.
Fig. 4.15. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for L/Br =0. 22 and Q=3.0 cfs.
Fig. 4.16. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for L/Br=0.44 and Q=3.0 cfs.
Fig. 4.17. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for L/Br=0.66 and Q=3.0 cfs.
Fig. 4.18. Comparison of Computed and Measured Velocity Distributions in Cross-Section B forL/Br=0.22 and Q=3.0 cfs.
Fig. 4.19. Comparison of Computed and Measured Velocity Distributions in Cross-Section B for L/Br =0.44 and Q=3. 0 cfs.

A-33 A-34 A-35 A-36 A-37 A-38 A-39 A-40 A-41 A-42 A-43 A-44 A-45 A-46

Vll

Fig. 4.20. Comparisons of Computed and Measured Velocity Distributions in Cross-Section B for L/Br=0.66 and Q=3.0 cfs.
Fig. 4.21. Comparisons of Computed and Measured Approach Velocities for Cross-sections A and B.

A-47 A-48

Fig. 4.22. Comparisons of Computed and Measured Approach Floodplain Depths for Cross-sections A and B.
Fig. 4.23. Comparisons of Computed and Measured Discharge Distribution Factors for Cross-sections A and B.
Fig. 4.24. Time Development of Scour Depth for Cross-section B and Sediment A in Dimensionless Form.
Fig. 4.25. Time Development of Scour Depth for Cross-section Band Sediment B in Dimensionless Form.
Fig. 4.26. Time Development of Scour Depth for Cross-section B and Sediment C in Dimensionless Form.
Fig. 4.27. Consolidation of Dimensionless Time Development Data and Least-Square Fits for Sediments A, B, and C.
Fig. 4.28. Burdell Creek Cross-section for Estimation of Clear-water Abutment Scour.
Fig. 4.29. Design Hydrograph for Burdell Creek.

A-49 A-50 A-51 A-52 A-53 A-54 A-55 A-56

V111

LIST OF TABLES
Table 3.1. Experimental Parameters Table 4.1. Ranges of Dimensionless Variables in Experimental Relationships Table B.1. WSPRO Input Data File for Burdell Creek- Q100. Table B.2. WSPRO Water Surface Profile Output- Q100. Table B.3. Velocity Distribution from HP Record for Unconstricted Flow at Approach Section Table B.4. Velocity Distribution from HP Record for Constricted Flow at Approach Section

Page No. 23 59
B-1 B-2 B-3
B-4

IX

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X

LIST OF SYMBOLS

'b

pier diameter;

floodplain width;

main channel width;

equilibrium scour depth;

theoretical contraction scour depth;

scour depth at time t;

median sediment size;

approach Froude number;

Froude number in contracted section near abutment face;

g

gravitational acceleration;

k

turbulent kinetic energy in k-E turbulence model;

equivalent sand-grain roughness;

spiral flow adjustment factor in Chang's method;

velocity distribution factor in Chang's method;

geometric shape factor for abutment and embankment in Froehlich's equation;

embankment skewness factor in Froehlich's equation;

flow intensity factor in Melville's method;

Ks*

abutment shape factor in Melville's method;

abutment alignment factor in Melville's method;

abutment length;

m

geometric contraction ratio ofbridge contraction;

XI

M n Ns Nsc <Ito Clfl qf2 ql q2 Qmcl Qfpl Qobl Q r R SG = SP t te vl Vru Vn

discharge contraction ratio ofbridge contraction= (Q- Qob1)1Q Manning's roughness factor; Sediment number near abutment face= Vab I [(SG- 1) g d50] 112 critical value of sediment number at incipient motion; flow rate per unit width in floodplain for uniform flow; flow rate per unit width in floodplain at the bridge approach cross-section; flow rate per unit width in floodplain at bridge contraction section; flow rate per unit width in approach section in Chang's method; flow rate per unit width in contracted section in Chang's method; discharge in main channel at bridge approach section; discharge in floodplain at bridge approach section; discharge obstructed by floodplain at bridge approach section; total discharge at any cross-section; ratio of abutment scour to theoretical contraction scour; channel hydraulic radius; specific gravity of sediment= 2.65 for quartz sediment; Shields' parameter= -rc I [(Ys- y) d50] time since beginning of scour; time required to reach equilibrium scour; approach velocity; mean floodplain velocity for uniform flow; approach velocity in floodplain upstream of the end of the abutment;

Xll

maximum velocity in the contracted section near the abutment face;

critical velocity in contracted section near the abutment face;

critical floodplain velocity in uniform flow;

ratio ofVab to critical velocity Vc in contracted section near the abutment face;

Yo

main channel flow depth in uniform flow;

bridge approach flow depth;

Yro

floodplain depth in uniform flow;

Yn

approach depth in floodplain upstream of the end of the abutment;

Yt2

floodplain depth in contracted bridge section;

Yab

floodplain depth in contracted section near the face of the abutment;

y

specific weight of water;

Ys

specific weight of sediment;

E

rate of turbulent energy dissipation in k-E turbulence model;

llf

generalized backwater discharge contraction ratio= M cw/cw;

p

density of water;

Ps

density of sediment;

a

ratio ofManning's n in the main channel in compound channel flow to the

Keulegan value of Manning's n calculated for flow in the main channel alone;

geometric standard deviation of the sediment size distribution;

'[1

bed shear stress in approach flow in Laursen's long contraction theory;

critical value ofbed shear stress at incipient motion;

Xlll

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XIV

CHAPTER 1 INTRODUCTION
Background Recent bridge failures due to local scour around piers and abutments have prompted a
heightened interest in scour prediction and scour-protection measures (Davis 1984, Lagasse et al. 1988, and Richardson et al. 1988). As a result, the Federal Highway Administration has developed a comprehensive technical manual and policy (HEC-18) for dealing with the problem ofbridge scour (Richardson et al. 1993). Unfortunately, the alteration of flow patterns by bridge crossings and the concomitant scour process are quite complex and have defied numerical analysis, for the most part. In this situation, the engineer has been forced to rely on laboratory results that are numerous and sometimes conflicting because of idealized laboratory conditions that have been used in the past. A case in point is abutment scour for which the HEC-18 manual ( 1993) suggests consideration of protective measures because of a lack of confidence in current predictive methods, which are based on laboratory results in idealized rectangular channels.
Laboratory experiments on abutment scour have relied in the past on the abutment length in a rectangular channel as one of the primary variables affecting scour. In an actual river consisting of a main channel and adjacent floodplains, an abutment terminating in the floodplain is not subject to the idealized, uniform approach velocity distribution obtained in previous laboratory experiments in rectangular flumes (Richardson and Richardson 1993). Instead, the scour is a function of the redistribution of flow between main channel and floodplain as flow through the

bridge opening occurs. In other words, abutment length is certainly important, but the same abutment length may result in different scour depths depending on the approach flow distribution in the compound channel and its redistribution as it flows through the contracted opening.
Currently, the FHWA recommends prediction of abutment scour with a regression equation developed by Froehlich (1989) that is based entirely on results from experimental investigators utilizing rectangular laboratory channels. Laursen (1963) has developed an equation for clear-water abutment scour that is based on contraction hydraulics but which relies directly on abutment length. Melville (1992) has proposed a methodology for predicting maximum abutment scour which does not include the effects of overbank flows or of flow distribution in compound channels.
The concept of flow distribution in a compound channel depends on the interaction between main channel flow and floodplain flow at the imaginary interface between the two where vortices and momentum exchange occur. The net result is that less discharge occurs in the compound channel than would be expected from adding the separate main channel and floodplain flows that would occur without interaction. The research by Sturm and Sadiq ( 1991 ), for example, suggests methods by which predictions of flow distribution between main channel and floodplain can be improved in the case of roughened floodplains. Wormleaton and Merrett (1990) have also proposed a technique for predicting flow distribution in compound channels. A more detailed review of the literature on compound-channel hydraulics can be found in Chapter 2 ofthis report.
Sturm and Janjua (1993, 1994) have proposed a discharge contraction ratio as a better measure of the effect of abutment length, and the flow redistribution that it causes, on abutment
2

scour. The discharge contraction ratio is a function of abutment length and compound-channel geometry and roughness. It can be obtained from the output of the water surface profile program, WSPRO (Shearman 1990). The present research reported herein, however, attempts to clarify the influence of bridge backwater on the flow redistribution, and to improve the WSPRO
methodology for computation of flow redistribution by incorporating more recent research results on compound channel hydraulics (Sadiq 1994).
The abutment scour experiments by Sturm and Janjua (1994) and by Sadiq (1994) have used a single, uniform sediment size of 3. 3 mm. The effect of sediment size on the equilibrium scour depth has been incorporated by including, as an independent variable, the ratio of the approach velocity in the floodplain to the critical velocity for initiation of motion, which depends on sediment size. Experiments with three different sediment sizes were conducted in the present research to verify this method for quantifying the influence of sediment size.
Predicted equilibrium clear-water scour depths provide a worst-case scenario for the bridge designer to design the bridge foundations. However, on small watersheds, the time required to reach this scour depth may exceed the hydrograph duration for many rainfall events. In addition, it is important to understand the process of scour development with time in order to ensure that laboratory results for equilibrium scour have indeed reached equilibrium. This research addresses both of these concerns related to time development of clear-water abutment scour.
The latest version ofHYDRAIN (1996) includes options for computation of contraction scour, pier scour, and abutment scour within WSPRO. However, there is little data available to show that one-dimensional models can adequately predict the parameters necessary to estimate

scour in a compound channeL Furthermore, the abutment scour prediction equations in the current version ofWSPRO have the shortcomings discussed above. Accordingly, this research compares hydraulic results from WSPRO with measured laboratory results and with numerical results from a two-dimensional turbulence model. Then a suggested methodology for screening of bridges in Georgia for abutment scour and potential bridge failure is developed utilizing WSPRO. Research Objectives
The objective of the proposed research is to develop better predictive equations for assessing the vulnerability of existing bridges to abutment scour for cases in which the abutment terminates in a floodplain with a defined main channeL Of primary interest is the effect of compound channel hydraulics (Sturm and Sadiq 1991) on the redistribution of the main channel and floodplain flow as the flow accelerates around the end of an abutment. In addition, the effect of sediment size on abutment scour needs to be clarified as well as the time that it takes to reach equilibrium scour. In small watersheds, the equilibrium scour depth may never be reached.
The experimental research reported herein differs from most previous experimental studies of abutment scour which have not had a compound channel as the approach channel and which have not considered the effect of very long abutments in wide, shallow floodplain flow. The results ofthe experimental research have been used to develop a prediction equation for clearwater abutment scour to be used for assessing the vulnerability of bridge abutments that terminate on wide floodplains to scour.
The specific research objectives are: ( 1) Investigate the effect of flow distribution, as affected by abutment length,
4

on clear-water abutment scour in a compound channel; (2) Quantify the effect of floodplain sediment size on abutment scour and the
time required to reach equilibrium scour; (3) Develop numerical techniques for predicting the hydraulic parameters
determined in (1) and (2) that are necessary to predict abutment scour; (4) Combine the experimental results and numerical techniques into a
methodology for assessing field abutment scour.
This report provides a brief review of the literature on compound channel hydraulics and clear-water abutment scour in Chapter 2. Then the experimental investigation is described in detail in Chapter 3. Chapter 4 contains an analysis of the experimental results and a proposed abutment scour prediction equation that addresses the problems of flow distribution, sediment size, and time development. A procedure for implementing the research results for the purpose of identifying scour-susceptible bridges is then suggested in Chapter 4. Conclusions and recommendations are given in Chapter 5.
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6

CHAPTER2 LITERATURE REVIEW
In this chapter, the literature on compound channel hydraulics and clear-water bridge abutment scour is reviewed. The connection between these two topics is an important contribution of this research, so a brief summary of previous research done on each topic is given. Compound Channel Hydraulics
A compound channel consists of a main channel, which carries base flow and frequently occurring runoff up to bank-full conditions, and a floodplain on one or both sides that carries overbank flow during times of flooding. Both channel roughness and depth of flow, and hence flow-channel geometry, can be drastically different in the main channel and floodplains. In general, floodplain flows are relatively shallow with slow-moving flow adjacent to faster-moving flow in the main channel which results in a complex interaction including momentum transfer between the main channel and floodplain flows. This phenomenon is more pronounced in the immediate interface region between the main channel and the floodplain, where there exists a strong transverse gradient of the longitudinal velocity. Because ofthe velocity gradient and anisotropy of the turbulence, there are vortices rotating about both the vertical and horizontal axes along the main channel-floodplain interface (Sellin 1964; Zheleznyakov 1971; Tominaga and Nezu 1991). These vortices are responsible for the transfer of water mass, momentum, and species concentration from the main channel flow into the floodplain flow. The result is that for a given stage, the total flow in the compound channel is less than what would be calculated as the sum offlows in the main channel and floodplain assuming no interaction (Sellin 1964).
7

Several attempts have been made at quantifying the momentum transfer at the main channel-floodplain interface using concepts of imaginary interfaces that are included or excluded as wetted perimeter and defined at varying locations with or without the consideration of an apparent shear stress acting on the interface (Wright and Carstens 1970; Yen and Overton 1973; Wormleaton et al. 1982; Knight and Demetriou 1983; Wormleaton and Merrett 1990). The resulting distribution of discharge between main channel and floodplain due to the interaction at the interface must be correctly predicted in water surface profile computations and in calculations of approach floodplain velocities for the prediction of abutment scour.
The current version ofWSPRO (as well as HECRAS) divides the compound channel into subsections using a vertical interface between the main channel and floodplain, but neglects any contribution ofthe interface to wetted perimeter of the subsections. In effect, the interaction between main channel and floodplain is neglected because this procedure is equivalent to assuming no shear stress at the interface. Wright and Carstens (1970) proposed that the interface be included in the wetted perimeter of the main channel, and that a shear force equal to the mean boundary shear stress in the main channel be applied to the floodplain interface. Yen and Overton (1973 ), on the other hand, suggested the idea of choosing an interface on which shear stress was in fact nearly zero. This led to several methods of choosing an interface, including a diagonal interface from the top of the main channel bank to the channel centerline at the free surface, and a horizontal interface from bank to bank ofthe main channel. Wormleaton and Hadjipanos (1985) compared the accuracy of the vertical, diagonal, and horizontal interfaces in predicting the separate main channel and floodplain discharges measured in an experimental flume of width 1.21 m and having a fixed ratio of floodplain width to main channel half-width of 3.2 (Wormleaton et
8

al. 1982). The wetted perimeter of the interface was either fully included or excluded in the calculation of hydraulic radius of the main channel. The results showed that even though a particular choice of interface might provide a satisfactory estimate of total channel discharge, nearly all ofthe choices tended to overpredict the separate main channel discharge and underpredict the floodplain discharge. It was further shown that these errors were magnified in the calculation ofkinetic energy flux correction coefficients used in water surface profile computations.
In a modification ofthe earlier method, Wormleaton and Merrett (1990) applied a correction factor called the <I> index to the main channel and floodplain discharges calculated by a particular choice of interface (vertical, diagonal, or horizontal) , which was either included or excluded from wetted perimeter. The <I> index was defined as the ratio ofboundary shear force to the streamwise component offluid weight (Radojkovic 1976) as a measure of apparent shear force. If the <I> index is less than unity on the main channel interface, for example, then the apparent shear force resulting from main channel-floodplain interaction resists the fluid motion in the main channel. This modified method was applied to experimental results from the very large compound channel at Hydraulics Research, Wallingford, England. The channel is 184ft long by 33ft wide with a total flow capacity of39 ft3/s. The ratio of floodplain width to main channel half-width varied from 1 to 5.5, and the relative depth (floodplain depth/main channel depth) varied from 0.05 to 0.50. The calculated main channel and floodplain discharges, when multiplied by the square root of the <I> index for each subsection, showed considerable improvement when compared to measured discharges regardless of the choice of interface. The difficulty of the method is in the prediction of the <I> index. A regression equation was proposed for this purpose
9

with the <P index given as a function of velocity difference between main channel and floodplain,
floodplain depth, and floodplain width. The regression equation is limited to the range of experimental variables observed in the laboratory.
Ackers (1993) has also proposed a discharge calculation method for compound channels using the Wallingford data. He suggested a discharge adjustment factor that depends on coherence, which was defined as the ratio of the full-channel conveyance (with the channel treated as a single unit with perimeter weighting ofboundary friction factors) to the total conveyance calculated by summing the subsection conveyances. Four different zones were defined as a function of relative depth with a different empirical equation for discharge adjustment for each zone.
The variation of Manning's n with depth further complicates the problem of water surface profile computations and velocity predictions in compound channels (Myers and Brennan 1990; Sturm and Sadiq 1991 ). In addition, the existence of multiple critical depths can lead to difficulties in both computing and interpreting water surface profiles. Blalock and Sturm (1981) and Chaudhry and Bhallamudi (1988) have suggested the use of a compound channel Froude number in computational procedures for determining multiple critical depths in compound channels. Blalock and Sturm (1981) utilized the energy equation while Chaudhry and Bhallamudi (1988) employed the momentum equation to define a compound channel Froude number. Blalock and Sturm (1983) showed from their experimental results that the energy and momentum approaches resulted in the same values of critical depth. Yuen and Knight ( 1990) have confirmed from their experimental results that the compound channel Froude number suggested by Blalock and Sturm ( 1981) gives values of critical depth that are reasonably close to the measured values.
10

Sturm and Sadiq ( 1996) have demonstrated the usefulness of their compound channel Froude number for computing and interpreting water surface profiles in compound channels having two values of critical depth: one in overbank flow and one in main channel flow alone.
Numerical analysis of flow characteristics in compound open channels, particularly for the case of an obstruction such as a bridge abutment on the floodplain, has received rather limited attention in comparison to experimental studies. Most numerical models have been developed for the parabolic flow situation, which has a predominant longitudinal flow direction with no reverse flow, e.g. uniform or gradually-varied flow. There are, however, a few studies applied to an elliptic flow situation (with flow separation and recirculation allowed), but these are applicable only to a simple rectangular channel. The effect of compound channel hydraulics on flow characteristics in the region close to obstructions is in need of further investigation.
One and two-dimensional numerical models have been used to compute complex flow fields such as those in compound open channel flow. Some of the 2D models (Rastogi and Rodi 1978; Keller and Rodi 1988) are applicable to the boundary-layer type of flow (Patankar and Spalding 1972), in which the flow can be described by a set of differential equations that are parabolic in the longitudinal (flow) direction. The flow situation in a compound open channel can become even more complex by placing structures such as bridge piers or abutments in the floodplain. In this situation, at least for the regions near the structure, the parabolic flow assumption becomes invalid. This is because there is no longer any predominant flow direction in the region close to the structure. The flow will separate downstream of the structure and a recirculating region with reverse flow and an adverse pressure gradient will be formed which violates the parabolic flow assumption. In addition, the water surface elevation no longer varies
11

only in the streamwise coordinate. Due to the presence of the obstruction, there exists a rapid variation of water depth near a bridge abutment both in the longitudinal and transverse directions. The water surface elevation upstream of the abutment increases and forms a backwater profile. These flow characteristics are associated with an elliptic flow field that has additional complexity due to intercoupling of the velocity and pressure (water depth) fields.
Three-dimensional models have been developed and applied primarily to the case of uniform flow in a compound channel (Krishnappan and Lau 1986; Prinos 1990; Naot et al. 1993; and Pezzinga 1994). These models allow the simulation ofturbulence-driven secondary motion in the transverse plane of a compound open channel as well as the Reynolds turbulent shear stresses. Experimental measurements by Tominaga and Nezu (1991) using a fiber-optic laser Doppler anemometer showed a pair oflongitudinal vortices at the main channel-floodplain interface with an inclined secondary current directed from the intersection of the main channel and floodplain bed toward the free surface. The numerical model ofNaot et al. was able to reproduce this behavior. Numerical results ofKrishnappen and Lau (1986) using an algebraic stress model demonstrated good agreement with measured divisions of flow between the main channel and floodplain using data from Knight and Demetriou (1983) and Worrnleaton et al. (1982). The nonlinear k-E turbulence model ofPezzinga (1994) was utilized to compare the effects of various main channel-floodplain subdivisions (vertical, horizontal, diagonal, bisector) on computed subsection discharges. The diagonal interface, and the interface formed by the bisector of the corner angle between main channel and floodplain, gave the best results for both the discharge distribution and the kinetic energy correction coefficients.
In this research, the velocity field is sought in the bridge approach section and near the
12

face of a bridge abutment that terminates on the floodplain where the width-to-depth ratio of the flow is large and the vertical mixing is strong. Under these conditions, the velocity field can be computed adequately from the depth-averaged equations of motion including regions of adverse pressure gradient and flow separation, especially if a k-E turbulence closure model is used (Chapman and Kuo 1985; Puri and Kuo 1985; Keller and Rodi 1988; Tingsanchali and Maheswaran 1990; Tingsanchali and Rahman 1992; Khan and Chaudhry 1992; and Shen et al. 1993). Biglari (1995) applied a depth-averaged, k-E turbulence model in elliptic form to the problem of flow around a bridge abutment on a floodplain. Abutment Scour
Early experimental research on scour around abutments was in some cases motivated by a desire to predict local scour around spur dikes, but the results of these studies have been applied to the problem of abutment scour. Ahmed (1953) proposed a scour-depth relation for spur dikes which utilized the "flow intensity", or flow rate per unit width in the contracted section, as the independent variable in agreement with previous regime formulas. Laursen and Toch (1953) argued that in live-bed scour around bridge piers and abutments, the approach flow velocity had no effect on the equilibrium scour depth because increases in velocity not only increased the sediment transport into the scour hole from upstream, but also increased the strength of the vortex responsible for transporting sediment out of the scour hole.
Garde et al. (1961) studied experimentally the scour around spur dikes in a rectangular channel and related the nondimensional ratio of scour depth to approach depth, d.fy1, to the approach Froude number, F1, and to the geometric contraction ratio, m, which is defined as the ratio of the width of the contracted opening to the approach channel width. In addition, the
13

coefficient of proportionality and the exponent on the Froude number were found to depend on sediment size. Some sediment transport occurred in the approach flow for these experiments.
Liu et al. (1961) considered the scour around bridge constrictions caused by abutment models in a 4-ft wide and an 8-ft wide flume. Their experimental results for live-bed scour indicated that the ratio of abutment length to approach depth, L/y~> and the approach Froude number were the most important influences on the dimensionless scour depth. In one series of experiments, clear-water scour was studied by pre-forming the scour hole and determining the flow conditions necessary to just initiate sediment motion in the bottom of the scour hole. In this case, the dimensionless clear-water scour depth was found to be a function of the approach Froude number and the geometric contraction ratio, m.
Gill (1972) argued from his experimental results on scour of sand beds around spur dikes that the distinction between clear-water and live-bed scour is unimportant for the design determination of maximum scour depth. He proposed that the maximum scour depth be based on the geometric contraction ratio, m, and on the ratio of sediment size to approach depth, D/y1.
Laursen (1960) developed scour-depth relations for bridge abutments that were based on treating the abutment as a limiting case of scour through a long flow constriction. Live-bed scour was considered to be a function only ofL)y1 and the ratio of discharge per unit width in the overbank flow region to discharge per unit width in the scour region. The scour region was assumed to have a constant width of2.75 times the scour depth. In a subsequent analysis of relief-bridge scour (Laursen 1963), which was considered to be a case of clear-water scour, the same approach was taken in relating the abutment scour to that which would take place in a long constriction. The contracted width was assumed to be equal to a scour hole width of2.75 times
14

the scour hole depth. This assumption resulted in an implicit relation for scour depth:

(2.1)

in which La=abutment length; y1=approach flow depth; d.=maximum scour depth; 1:1=bed shear stress in approach flow; and 1:c=critical shear stress for initiation of sediment motion.

In a comprehensive experimental study of the effect of flow depth on clear-water scour

around abutments, Tey (1981) held constant the shear stress ratio, 1:/"tc, at a value of0.90 while

varying the flow depth and the abutment length and shape. The results showed an increasing

scour depth with increasing flow depth but at a decreasing rate as the depth became larger. The

length of abutment obstructing the approach flow and the abutment shape were also found to

influence the scour depth. Longer abutments and blunter abutment shapes caused deeper scour

holes.

Froehlich (1989) completed a regression analysis of some 164 laboratory experiments

from 11 separate sources on clear-water scour around abutments or spur dikes. His proposed

regression equation is:

d

L o.63

y o.43

__:_ = 0.78Kl K2 (~) Ftu6 (-1) ag-1.87 + 1

y1

y1

d50

(2.2)

in which d.=scour depth; y1=approach flow depth; K1=geometric shape factor for abutment and embankment; K2=embankment skewness factor; La=abutment length; F1=approach Froude number; d50=median sediment grain size; and ag=geometric standard deviation ofthe sediment size distribution. Froehlich further proposed that a factor of safety of one should be added to the

15

value of d/y1 obtained from the regression analysis, and it has been included on the right hand side ofEq. 2.2. Currently, HEC-18 recommends the live-bed scour equation obtained by Froehlich's regression analysis of other investigator's results for this case because (2.2) seems to greatly overestimate abutment scour. The live-bed scour equation is given by

L o.43

2.27K1 K2 [~]
y!

F 1 61 + 1

(2.3)

with the factor of safety of one included on the right hand side. Melville ( 1992) summarized a large number of experimental results on abutment scour
from rectangular channels and proposed a design method for maximum scour depth which depends on empirical correction factors for flow intensity, abutment shape, alignment and length. He classified abutments as short (Ljy1<1) or long (Ljy1>25), and suggested that the maximum clear-water scour depth was 2L. for the former case and 10y1 for the latter. For intermediate abutment lengths, equilibrium scour depth was given by

d s

=

2

K I

K s *

K 8 *

(y I

L a

)05

(2.4)

in which K1 =flow intensity factor= V1Nc; V1 =approach velocity; Vc =critical velocity for initiation of sediment motion; K, = abutment shape factor; K6* = abutment alignment factor, y1 = approach flow depth; and L. = abutment length.
Sturm and Janjua (1993, 1994) conducted a series of experiments in a compound channel consisting of a main channel and floodplain with the abutment terminating in the floodplain, and
16

showed that the approach flow distribution and its readjustment by the abutment in the contracted

section is an important factor that should be included in equations for predicting scour depth in

natural channels. On the basis of a dimensional analysis and the application of Laursen's ( 1963)

analysis of relief bridge scour in a long contraction to compound channels, they proposed a

relationship given by

d

V IV

- 5 = 7. 70 [ fJ c - 0.35 ]

Yn

M

(2.5)

in which ds =equilibrium scour depth; Yn = approach floodplain flow depth; Vn =approach floodplain flow velocity; Vc =critical velocity; and M =discharge contraction ratio defined as the fraction of the total discharge in the bridge approach section over a width determined by extending the bridge opening upstream to the approach section.
Young et al. (1993) developed a regression equation for clear-water as well as live-bed abutment scour using the calculated contraction scour as a nondimensionalizing parameter for the abutment scour depth. Melville and Ettema (1993) reported research results on abutment scour in a compound channel but for the case of an abutment terminating in the main channel rather than on the floodplain.
Chang (1996) has applied Laursen's long contraction theory to both clear-water and livebed scour. He has suggested a "velocity adjustment factor" k., to account for the no~uniform velocity distribution in the contracted section, and a "spiral-flow adjustment factor" kf at the abutment toe that depends on the approach Froude number. The value ofk., was based on
potential flow theory, and kr was determined from experiments in rectangular laboratory flumes.
The resulting scour equation was given by

17

(2.6)

in which y2 =flow depth in contracted section after scour; y1 =approach flow depth; q1 =flow rate per unit width in approach section; q2 = flow rate per unit width in contracted section; and 8 = 0. 857 for clear-water scour. Eq. 2. 6 does not include the effect of sediment size on clear-water abutment scour.
An equation in HIRE (Richardson et al., 1990) was developed from Corps ofEngineers' field data for scour at the end of spur dikes on the Mississippi River. It is recommended in HEC18 for predicting scour around long abutments with Ljy1 > 25. The equation is given by

ds

=

4

F o.33
ab

Yab

(2.7)

in which Yab =depth of flow at the abutment; and Fab = Froude number based on the velocity and depth adjacent to the abutment.
Time development of scour was studied in Laursen's pioneering research on scour by jets (Sedimentation 1977). Laursen argued that clear-water scour is an asymptotic process in which scour depth increases linearly with the logarithm oftime. Theoretically, equilibrium would never be reached under these circumstances except at infinity, so as a practical matter, some limiting depth of scour is determined in laboratory experiments at large durations when the rate of change in scour depth is very small. A consequence of developing scour equations from laboratory data for this equilibrium condition is that in the field case for small watersheds, the duration of the design discharge may be considerably shorter than the time to reach equilibrium. The result is an
18

overestimate of field scour for a given design event. Most of the research on time development of scour has been done for situations other than
abutment scour, e.g. jet scour, pier scour, or hydraulic structure scour. Carstens (1966) has proposed a general method for determining the time development of scour by combining (a) the sediment continuity equation; (b) a sediment pick-up function; and (c) an assumed scour hole shape that is geometrically similar at all times. He showed that the simultaneous solution of these three equations agreed with Laursen's experimental results for time development of scour from a horizontal jet, although the experimental data were used to develop the sediment pickup function.
Raudkivi and Ettema (1983) showed from their experimental results on the development of pier scour that dimensionless scour depth (d/b) was linearly proportional to the logarithm of (td50)/b3, in which ds = scour depth; b = cylindrical pier diameter; d50 = median sediment grain diameter; and t =time. Yanmaz and Altinbilek (1991) applied Carstens' method to the problem of time development of scour around bridge piers. The resulting differential equation was solved numerically to obtain a curve of d.lb as function of dimensionless time:
(2.8)
in which SG = specific gravity of the sediment. The function was linear with the logarithm of dimensionless time up to a large value of time after which it leveled off in agreement with their experimental results. Kothyari et al. (1992) proposed a different approach in which the temporal variation of scour around a bridge pier was calculated in successive time steps governed by: (a) the time required for removal of one sediment grain by the primary vortex; and (b) the resulting
19

gradual decrease of shear stress in the scour hole as it grew larger. Chiew and Melville ( 1996) suggested from their experimental results on scour
development around bridge piers an empirical relationship for a dimensionless equilibrium time, t*=Vtjb, as a function ofVNc, in which V =approach velocity; Vc =critical velocity; b =pier diameter; and te = equilibrium time. The equilibrium time was defined as the time at which the rate of increase of scour depth was less than 5% of the pier diameter in 24 hours. The experimental results were then presented as the ratio of scour depth at a given time to equilibrium scour depth (ds/ds) as a function of the ratio of elapsed time to equilibrium time (t/te) for various constant values of(VNc).
20

CHAPTER3 EXPERIMENTAL INVESTIGATION
Introduction Experiments were conducted in a 14 ft wide by 80 ft long flume of fixed slope in the
Hydraulics Laboratory ofthe School of Civil and Environmental Engineering at Georgia Tech. Scour depths were measured as a function of discharge, sediment size, and abutment shape and length for two different compound channel cross-sections constructed in the flume at two different fixed slopes. Velocity distributions at the bridge approach section and complete water surface profiles at the beginning and end of scour were measured. The details of the experiments and some typical results are described in this chapter, and the results are analyzed in Chapter 4. Compound Channel and Abutment Geometry
Compound channel sections were constructed inside the 14 ft by 80 ft flume and are shown in Fig. 3.1. Cross-section A was constructed for a series of experiments reported by Sadiq (1994) and was also used for a few experiments in this study. Subsequently, cross-section A was replaced by cross-section B for use in this study as well as in a separate FHWA study. Crosssection A had a total width of7.00 ft and a fixed bed slope of0.0050, while cross-section B was 13.83 ft wide with a fixed bed slope of 0. 0022 as shown in Fig. 3. 1.
Steel rails on the top of the flume walls were adjusted to serve as a level track for the instrument carriage, which is driven by an electric motor. A pumping system provided the water supply to the flume from a recirculating sump into which the flume discharges. The flume
discharge was measured by calibrated bend meters with an uncertainty in discharge of 0.0 1 ft3Is,
21

and the total capacity of the pumping system was approximately 7.00 ft3/s. The tailwater depth in the flume was adjusted with a motor-driven tailgate at the downstream end ofthe flume. The flume entrance included a head tank and a series of stilling devices to remove flow entrance effects. The compound channel section terminated 10 ft upstream of the tailgate in order to provide a sedimentation tank for settling of any sediment scoured from the channel. As a result of the head tank and sedimentation tank, the actual length of the compound channel was approximately 60ft.
The main channel bed of cross-section A consisted of concrete having a longitudinal slope of 0. 005 with a standard deviation of 0. 003 ft from the required elevation at any station along the channel. Fine gravel with a mean diameter of3.3 mm and with a geometric standard deviation of 1.3 was used to provide the roughness on the main channel bed and walls. Gravel was affixed to the main channel bed and walls with varnish. Roughness in the floodplain was also provided by gravel of the same size. To prevent movement of the gravel in the floodplain for the uniform-flow experiments, the upper 2-in. layer was stabilized by mixing portland cement in the gravel in a ratio of 1:6 by volume. Water was then added until a reasonable workability was achieved to form a fixed bed consisting predominantly of gravel roughness in the resulting matrix. In the case of cross-section B, a lean concrete mix that utilized the 3.3 mm gravel as aggregate was poured to a constant slope of 0. 0022 with a standard error of 0.005 ft in bed elevation. In both crosssections, the bed surfaces were relatively rough as determined by the protruding grains of gravel.
In the case of cross-section A, the bridge abutments were formed by a row of rectangular concrete blocks measuring 0.5 ft high by 0.5 ft wide (in the flow direction) that were fixed to the floor of the flume with cement mortar at Station 32 located 32ft downstream of the flume
22

entrance. The abutments for cross-section B were constructed as a row of concrete blocks poured into custom-built forms to create vertical-wall (VW), spill-through (ST), and wingwall (WW) abutment shapes as shown in Fig. 3.2. The side slopes for the wingwall and spill-through shapes were 2: 1 (horizontal: vertical), and the wingwall angle was 30 degrees as shown in Fig. 3.2. Abutments for cross-section B were located at Station 32. The abutment lengths for both crosssections are summarized in Table 3. 1. The ratio of abutment length La to floodplain width Br in the table indicates the relative length of floodplain obstructed by the abutment. Only the verticalwall abutments are analyzed herein as the worst case, while the effects of abutment shape on scour depth are being studied in a related, current project sponsored by FHWA
Table 3.1. Experimental Parameters

SHAPE

CROSS SECTION

LENGTHS La, ft

L/Br

SED dso mm

Vertical-Wall (VW) Vertical-Wall (VW)
Spill-Through (ST) Wing-Wall (WW)

A

0.50, 1.00, 1.50 0.17, 0.33, 0.50 A 3.3

B

2.62, 5.24, 7.87 0.22, 0.44, 0.66 A,B, 3.3, 2.7,

c 1.2

B

3.87, 6.46, 7.87 0.32, 0.54, 0.66 A 3.3

B

5.28, 7.28

0.44, 0.61

A 3.3

Sediment Three sediments having median sediment grain sizes (d50) of3.3, 2.7, and 1.2 mm were
used in this research as indicated in Table 3.1 where they are referred to as Sediment A, B, and C, respectively. The measured size distributions of all three sediments are shown in Fig. 3. 3. The geometric standard deviation crg (= [d84/d16] 05) of Sediments A, B, and C was approximately 1.3.
23

Thus, these sediments can be considered to be uniform for the purpose of assessing sediment size effects on abutment scour. Water Surface Profile and Velocity Measurements
Both water-surface profiles and velocities were measured in the fixed-bed compound channels just described, first for uniform flow to determine the bed roughness, and then with the abutments in place to obtain the hydraulic conditions at the beginning of scour. In the uniformflow experiments, stations for measuring the water-surface elevations were fixed at 4.00 ft intervals along the length of the channel. The desired discharge was obtained by adjusting the inlet valve, and the tailgate was raised or lowered to achieve the required Ml or M2 profile with no abutments in place. At each station, the water-surface elevation was measured at three points across the cross-section for Cross-section A, and at eight points in the case of Cross-section B. The mean of these elevations was then used to determine the mean elevation of the water surface at each station. The normal depths were determined by taking the mean of the flow depths at a point where both M 1 and M2 water-surface profiles asymptotically approached one another in the upstream direction, which was generally 20 to 30ft downstream of the channel entrance. The relative depth ratio (Yro I y0), in which Yro =normal depth in the floodplain and Yo= corresponding normal depth in the main-channel (see Fig. 3.1), varied between 0.26 and 0.35 for Cross-section A, and from 0. 13 to 0. 32 for Cross-section B.
A miniature propeller current meter with a diameter of0.60 in. was used to measure point velocities averaged over 60 seconds. In the uniform flow experiments, Station 32 (32ft downstream of the channel entrance) was selected for measuring the point velocities across the channel cross section because at this station there were negligible entrance effects, and also
24

because the water surface could be adjusted easily to the normal depth at this station. Depth. averaged velocity distributions were obtained from a point velocity measurement at an elevation
above the channel bottom of0.37 times the flow depth in each vertical profile in the floodplain, and from six to eight point measurements spaced out over each vertical profile in the main channel. A total of 14 to 19 vertical profiles were measured at a single cross-section to establish the depth-averaged velocity distribution. The resulting measured velocity distributions when
integrated over the cross section produced discharges that were within 4 percent of the
discharges measured by calibrated bend meters in the flume supply pipes for the uniform flow experimental runs.
The separate discharges in the main channel and floodplains were determined from the point velocities by integration. This information was combined with the measured normal depths to determine the separate main channel and floodplain roughnesses in uniform compound channel flow from Manning's equation. Normal depth was also determined with flow in the main channel alone in order to determine the equivalent sand-grain roughness of the main channel.
Measurement ofwater-surface profiles and point velocities was also conducted in the fixed-bed channel with the abutments in place. Away from the abutments, the water-surface elevations were measured at stations 4ft apart as in the uniform-flow case. Close to the abutments, water-surface elevations were measured at stations 1 ft to 2ft apart. The depth of flow at the downstream end of the channel was set at the normal depth for each discharge by adjusting the tailgate.
With the abutments in place, detailed point velocity measurements were made across the entire channel cross-section at the bridge approach section, which was Station 28 (located 28 ft
25

downstream of the channel entrance) for Cross-section A, and either Station 22 or Station 24 for Cross-section B depending on the abutment length. This station was located in the region where the maximum backwater occurred as well as where the floodplain velocities were not retarded by the abutment. In general, this location varied between 67 and 133 percent of the bridge opening width measured upstream of the bridge. Depth-averaged velocities were determined at 17 to 19 positions across the cross section. This data was used to determine the discharge contraction ratio Mat the beginning of scour as well as the approach velocity and depth upstream of the end of the abutment. Velocity and depth measurements were also made at the downstream face of the abutment. At this location, the depth of flow in the floodplain was very small; therefore, the velocities were measured in the main channel only, but this still allowed the determination of the discharge in the main channel as well as in the floodplain from continuity.
Resultant velocities were measured at the upstream face of the bridge for both Crosssections A and B. The resultant velocity direction was determined either by flow visualization or by rotating the velocity meter until a maximum reading was obtained. In the case of Crosssection B, additional resultant velocities were measured in the bridge opening to find the maximum velocity near the face of the abutment. Scour Measurements
After the fixed-bed measurements were completed, a movable-bed section was constructed in the vicinity of the abutments. The cement-stabilized floodplain surface was removed between Station 28 and Station 36 for Cross-section A, and between Stations 22 and 42 in the case of Cross-section B. It was replaced by new, clean gravel identical to that in the fixedbed floodplain. The abutments were sealed with cement mortar to the floor of the flume.
26

Scour measurements were made for several discharges at each of the abutment lengths given in Table 3.1. At the start of each experimental scour test, the loose gravel in the movable-
bed test section was carefully leveled to the floodplain elevations corresponding to the constant bed slope. Water was then introduced into the channel very gradually from the upstream and downstream ends ofthe flume with the tailgate raised so that the movable bed remained undisturbed. Once the whole channel was flooded, the desired discharge was obtained by adjusting the valve on the main inlet pipe. The tailgate was then lowered slowly until the corresponding normal depth was obtained at the downstream end of the channel. Scour was allowed to continue for 12 to 16 hours for Cross-section A, and for 24 to 36 hours for Crosssection B. After equilibrium had been reached, the water surface profile and the velocity distributions in the approach section and at the downstream face of the abutment were measured in the case of Cross-section B. Then the channel was carefully drained, and the bed elevations throughout the scour and deposition areas were measured with a point gauge having a scale uncertainty of 0. 001 ft. As a practical matter, the uncertainty in the scour depth measurements was about 0.003 ft. In general, bed elevations in the vicinity of the scour hole were measured at some 100 spatial locations from which scour contours could be plotted.
Time rate of scour measurements were made for Sediment A and for the vertical-wall abutment for some experiments. For these runs, scour depth was measured from a scale inscribed on a plexiglas block that formed the face of the abutment. The scale could be read from above by the use of a mirror. Only those cases where the maximum scour depth occurred at the upstream comer of the abutment face were suitable for this measurement technique. In general, these cases occurred for the larger discharges for each abutment length. Scour depth measurements were
27

generally taken at times of0.08, 0.17, 0.25, 0.50, 0.75, 1, 2, 4, 8, 16, 24, and 36 hours after the

beginning of the experiment.

Results

Channel Roughness

The experimental results for Manning's n in the main channel and floodplain with

compound channel flow are shown in Fig. 3.4 for Sediment A First, the value of the equivalent

sand-grain roughness in the main channel was determined from the normal depth measurements

for flow in the main channel alone (without overbank flow) with the result that~= 0.013 ft (4.0

mm or 1.2 d50). Then the separate discharges were determined in the main channel and floodplain for overbank flow at several discharges as described previously, and the data points are shown in

Fig. 3.4 in comparison with Keulegan's equation given by

R 116 .0928 (-)

n

ks

(3.1)

in which R=hydraulic radius in ft and~= equivalent sand-grain roughness in ft. For the separate flow in the floodplain,~ was found to be 0.013 ft as in main channel flow alone, which is consistent with the fact that the roughness surfaces were identical. In the case of main channel flow, an additional drag due to main channel-floodplain interaction was quantified in terms of
(3.2)
in which I\nc = effective Manning's n in the main channel with overbank flow; and nK = Keulegan's value for Manning's n in the main channel with~= 0.013 ft and no interaction with the
28

floodplain, i.e. zero contribution of the interface to wetted perimeter. The best-fit value of a was 1.23. In effect, the main channel conveyance was decreased by 23 percent due to the main channel-floodplain interaction. Similar results were found previously for Cross-section A (Sadiq 1994; Sturm and Sadiq 1996) with a=1.19. Shown in Fig. 3.5 are the measured values of normal depth in comparison with the calculated values for Cross-section B using Keulegan's equation and the best-fit values ofk. and a. The standard error in normal depth is 0.0025 ft. While it is true that the values ofManning's n were first calibrated with the same data as in Fig. 3.5, the agreement shown in Fig. 3.5 is indicative ofhow well this calculation approach can reproduce the discharge Q over the full range of experimental values. Also shown in Fig. 3. 5 is the calculated critical depth curve, which is below the normal depth curve, demonstrating that the channel is mild over the experimental range of discharges.
Discharge Distribution The purpose of considering floodplain-main channel interaction in developing Manning's n values for compound channel flow is illustrated in Fig. 3.6 in which the ratio of main channel discharge to the total discharge is given as a function of relative depth in the floodplain. In both cross-sections, the calculated discharge distribution agrees well with the measured values. For comparison, the standard WSPRO method of assuming constant Manning's n and no interaction between main channel and floodplain overestimates the relative proportion of main channel discharge as shown in Fig. 3.6 for Cross-section A The correct proportioning of main channel and floodplain discharge is necessary to predict the discharge distribution factor M for which experimental values are given in Fig. 3. 7 as a function of relative floodplain depth in the bridge approach section (indicated by a subscript of 1
29

on the depth). The factor M is defined by

(3.3)

in which Qmci = discharge in the approach main channel; Qfp1= discharge in the approach
floodplain; Qohi = obstructed floodplain discharge over a length equal to the abutment length in the approach cross-section; and Q = total discharge. While the values of M are primarily a function of abutment length and compound channel geometry, Fig. 3. 7 shows that they decrease slowly with increasing relative depth in the approach cross-section. Abutment shape seems to have little influence on M in Fig. 3. 7.
Sturm and Janjua (1993) have shown that for small depth changes from the approach section to the bridge section, M represents the ratio of discharge per unit width in the approach floodplain to that in the contracted floodplain in the bridge section, <Ir/'lrz. This discharge ratio has a significant effect on the equilibrium abutment scour depth as will be shown in Chapter 4. The value ofM, and hence <u-/'lrz, is not the same as the geometric contraction ratio m, which is defined as the bridge opening width over the total channel width. This is because of the behavior of compound channel flow in which some of the approach floodplain flow joins the main channel flow in the bridge section as demonstrated in Fig. 3.8. The ratio Qm/Qm2 represents the ratio of main channel flow in the approach cross-section to that in the bridge section. It is a measure of the redistribution of flow between main channel and floodplain in the contracted bridge section, and it is clearly observed to be proportional toM in Fig. 3.8 for both Cross-Sections A and B.
In the remainder of this chapter, raw experimental results for water surface profiles, approach velocity distributions, time development of scour, and equilibrium scour depths for
30

Cross-Section B are summarized. Water Surface Profiles
Measured water surface profiles are shown in Figs. 3.9 and 3.1 0 for the vertical-wall abutment (VW) and the fixed-bed case (beginning of scour). In Fig. 3. 9, the discharge is held constant and the abutment length is varied. The downstream boundary condition is the same for each profile because it is normal depth for the given discharge as set by the tailgate. The increasing backwater upstream of the abutment that is caused by increasing abutment length is apparent in Fig. 3.9. In Fig. 3.10, the abutment length is held constant but the discharge is varied. In this case, the downstream boundary condition on depth increases with increasing discharge. The backwater is observed to increase with increasing discharge in Fig. 3. 10. Similar results for constant discharge are given in Fig. 3.11 for the spill-through (ST) abutment, and in Fig. 3.12 for constant abutment length in the case of the spill-through abutment. The relative degree of upstream backwater for vertical-wall and spill-through abutments is summarized in Fig. 3.13 in terms of the ratio of floodplain normal depth Yro, which would occur with no abutments, to approach floodplain depth, Yfl The backwater ratio varies from 0.6 to 1.0 as a function of abutment length and shape, and discharge.
Velocity Distributions Velocity distributions in the bridge approach cross-section at the beginning of scour are given in Figs. 3.14 to 3. 17. The main channel velocities are higher than those in the floodplain as expected for a compound channel. If discharge is held constant and abutment length is increased as shown in Fig. 3.14, the increasing backwater causes a general decrease in both floodplain and main channel velocities across the full width of the compound channel. On the other hand, as
31

shown in Fig. 3.15, increasing discharge for the vertical-wall abutment of constant length causes an increase in floodplain velocities even though backwater is increasing. The main channel velocities also increase, but this occurs chiefly in the sideslope region of the main channel. Similar results are given for the spill-through abutment in Figs. 3.16 and 3.17.
Time Development of Scour Some results for time development of scour are given for comparison in Figs. 3.18, 3. 19, and 3.20. It can be observed that the scour depth generally increases proportionately with the logarithm oftime and then levels off to an equilibrium value. Notable exceptions are shown in Fig. 3.18 for Q= 4.0 cfs and 4.5 cfs for which there is a gradual increase in scour followed by a steeper increase that finally approaches an equilibrium value. This would seem to indicate that the scour hole is not self-similar in the early stages of scour development, which may be related to the shift of the location of maximum scour from some distance away from the abutment face to the upstream comer of the abutment face for the larger discharges. Over the full range of discharges, sediment sizes, and abutment lengths, it is apparent from Figs. 3.18, 3.19, and 3.20 that equilibrium is certainly reached in a period of 24 to 36 hours from the initiation of scour, and in even shorter times in some cases. Nevertheless, all equilibrium scour depth measurements were taken at the end of a 24 to 36 hr continuous period of constant discharge.
Equilibrium Scour Depths Raw data for equilibrium scour depth as a function of discharge are shown in Fig. 3.21 for Sediment A and vertical-wall abutments; and in Fig. 3.22 for Sediments B and C, and vertical-wall abutments. The scour depths vary from 0.06 ft to 1.00 ft, and show a consistent increase with discharge. The smaller the sediment size, the larger the scour depth as expected for clear-water
32

scour. It should be noted that these scour experiments cover a range of values ofL/Yn from 12 to 78 and thus cover both intermediate-length and long abutments according to Melville's classification.
Typical scour contours are shown in Figs. 3.23 to 3.26. The contours are given in terms ofbed elevation; the undisturbed floodplain and main channel elevations at the station corresponding to the centerline of the abutment (Sta. 32) are approximately 1. 060 ft and 0. 55 5 ft, respectively. A typical scour hole is shown in Fig. 3.23 for an intermediate vertical-wall abutment length of5.24 ft and a discharge of3.49 cfs. The bottom ofthe scour hole is displaced laterally from the abutment face and the long axis of the scour hole is skewed from the approach flow direction as an indication of the deflected streamlines in the contracted section. A prominent bar deposit can be seen on the downstream side of the abutment in the region where the flow is expanding. An increase in discharge to 4.00 cfs is shown in Fig. 3.24, and the shape and location of the scour hole have changed. The maximum depth of scour occurs at the upstream corner of the abutment face, and the scour hole shape is more nearly conical. The effect of increasing the abutment length is shown in Fig. 3.25 with essentially the same discharge as in Fig. 3.23. The scour hole is obviously larger in both depth and volume. Finally, the influence of abutment shape can be observed in Fig. 3.26 for the spill-through abutment with the same length (measured to the toe) and discharge as for the vertical-wall abutment in Fig. 3.23. In this case, the maximum depth of scour occurs immediately adjacent to the sloping abutment face next to the upstream quadrant. A shallow trench trails downstream from the scour hole with a deposition area on the downstream side of the abutment.
33

Critical Velocity

Critical velocity for the initiation of sediment motion at the abutment face was measured

for all three sediments. The tailwater was raised higher than normal depth for a given flowrate;

the flowrate was set; and then the tailgate was gradually lowered until normal depth for that

flowrate was reached. If sediment motion did not occur then the tailgate was raised again and the

flowrate was increased. This process was repeated until sediment motion had just begun at the

face of the abutment. The determination of the conditions for initiation of sediment motion

necessarily involved some qualitative judgment; hence there is scatter in the data points shown in

Fig. 3.27. For sediment Conly, it was possible to initiate motion on the floodplain with no

abutments in place and for uniform flow. This experimental point is also shown in Fig. 3.27.

Shown for comparison in Fig. 3.27 are various relationships that can be used to calculate critical

conditions in terms of the critical value of the sediment number Nsc:

PAROLA: N = _ _1_.6_1_
sc [d5o I y] o.m

(3.4)

LAURSEN: N = 385 !:J'P

sc

[d
50

I

y

]116

(3.5)

KEULEGAN:

N
sc

=

5.75

[SP] 112

lo g

[

122d2 Y]

50

(3.6)

in which Nsc = Vc I [ (SG- 1) g d50] 112 ; Vc =critical velocity; SG =specific gravity of sediment; d50 = median sediment grain diameter; y = flow depth; and SP = critical value of Shields' parameter. Based on the results in Fig. 3.27 and the best fit of the scour data, which will be discussed in the next chapter, the uniform flow critical velocity Yeo was calculated from

34

Keulegan's relationship with SP determined from Shields diagram for the given sediment size (Julien 1995). However, Laursen's relationship was found to give a better fit to the data for critical velocity at the abutment face Vc with SP varying from 0.035 for Sediment C to 0.039 for
Sediment A. (The value of0.039 corresponds to -rc = 4 d50 in English units.)
35

THIS PAGE LEn BLAHK
36

CHAPTER4 ANALYSIS OF RESULTS
Equilibrium Scour Depth Clear-water scour at a bridge abutment located on the floodplain of a compound open-
channel is influenced by the flow distribution between the floodplain and main channel in the approach and contracted bridge cross-sections. It has been shown that the effect of the flow contraction can be accounted for by the discharge contraction ratio M that depends on both abutment length and the discharge distribution in the approach section of a compound channel (Sturm and Janjua 1994). In addition, previous equations for predicting clear-water scour depths at abutments have depended on the ratio of floodplain velocity V1 to critical velocity Vc in the bridge approach section (Melville 1992, Sturm & Janjua 1994) with maximum clear-water scour occurring when V1 approaches Vc (see Chapter 2 ). In this formulation, the independent variables for scour prediction are determined from one-dimensional numerical models.
A possible alternative to parameterizing scour depth in terms of approach velocity and discharge distribution is to relate it directly to local hydraulic conditions near the abutment face, although these conditions can only be predicted by two or three-dimensional numerical models. Possible advantages of this alternative formulation include: ( 1) it may provide a means of unifying scour prediction equations obtained from experiments in rectangular channels with those based on the more realistic compound channel geometry; and (2) it may offer greater sensitivity of scour predictions to changes in local depth and velocity at the location of scour initiation near the abutment face. Theoretically, local scour is initiated when the ratio oflocal flow velocity to
37

critical velocity exceeds unity, and it continues at an ever decreasing rate until equilibrium is reached. The initial rate of scour and limiting equilibrium depth of scour might be expected to depend on the excess ofthe local velocity ratio in comparison to unity.
The implementation procedure for prediction of clear-water abutment scour that is described herein is based on laboratory experiments in two different compound channel crosssections as described in Chapter 3. Abutment length, abutment shape, discharge, and sediment size were varied, and the resulting equilibrium scour depths were measured as well as the water surface profiles and local depth-averaged velocities at the beginning and end of scour. Alternative Procedure I
The first proposed procedure is based on Laursen's long contraction scour theory (Laursen 1963) as modified by Sturm and Sadiq (1996) for abutments ending on the floodplain of a compound channel. The theoretical development is given first followed by correlation of the scour data for both Cross-sections A and B.
Theoretical Background With reference to Fig. 4.1 for equilibrium scour conditions in a long contraction, it is assumed that the approach conditions tend toward the undisturbed depth and velocity on the floodplain, Yro and Vro, respectively. This assumption is consistent with the assumption of an idealized contraction with negligible head loss and velocity-head changes made by Laursen (1963) in his analysis of clear-water contraction scour. The continuity equation for the floodplains from the approach section to the contracted section at equilibrium is written as
(4.1)
38

in which Vro and Yro are the average undisturbed velocity and depth in the approach floodplain, respectively; V12 and y12 are the average velocity and depth in the contracted floodplain; and llr is a generalized discharge contraction ratio that depends not only on the ratio of the floodplain widths, but also on the discharge ratio between the approach and contracted floodplain sections as some of the approach floodplain flow joins the main channel flow in the contracted section. For equilibrium clear-water scour conditions, the velocity in the contracted floodplain section, V12 , is set equal to the critical velocity, Vcz If this substitution is made in Eq. 4.1 and it is divided by the critical velocity in the approach section, Vc0, the result, after noting that the ratio of critical velocities is proportional to the depth ratio to the 1/6 power (Sturm & Sadiq 1996), is
(4.2)

An equation of this form has been suggested by Richardson et al. (1993) for estimating clear-

water contraction scour except that llr is evaluated as a geometric contraction ratio. Utilizing the

assumption that velocity-head changes and head losses at equilibrium contraction scour are small

(Laursen 1963), it can be shown that y12 = dsc + Yro (see Fig. 4.1). Then Eq. 4.2 can be written in
terms of the theoretical contraction scour depth, dsc

~ d

+

1 =

[

V
jV

I VcO] 617

YJV

llr

(4.3)

The assumption of Laursen (1963) is that local abutment scour d.= r dsc' in which r is

some constant greater than one that multiplies the contraction scour depth given by Eq. 4.3.

~

Although the contraction scour predicted by Eq. 4.3 is for a fictitious long contraction with

~

several restrictive assumptions, including the assumption that the approach depth and velocity

J~ \

~~<~zl

39

,,~'
.;;j

.'
~'al

tend toward their undisturbed values as scour approaches equilibrium, it suggests that an equation for abutment scour might take the form
(4.4)
in which Cr and C0 are constants to be determined by experiment; and the exponent in Eq. 4.3 has been taken to be approximately unity as found in several experimental investigations (Melville 1992; Sturm and Janjua 1993).
There are two dimensionless ratios of interest on the right hand side ofEq. 4.4. The velocity ratio in the numerator is the undisturbed floodplain velocity in the approach section in ratio to the critical velocity under the same conditions. Theoretically, once this velocity ratio reaches the value of unity, maximum clear-water scour occurs and live-bed scour begins assuming that the approach depth and velocity tend toward their undisturbed values as equilibrium is reached. The other independent dimensionless variable in Eq. 4.4, which is especially relevant in the present experiments, is the discharge contraction ratio at equilibrium, IJ.r Sturm and Janjua ( 1994) suggested the use of the discharge contraction ratio M, which is defined as the ratio of unobstructed discharge in the approach channel to the total discharge at the beginning of scour, as an estimate of !lr They showed that M was a good estimate of IJ.r for small depth changes in the contraction, which was indeed the case for their experiments with a contraction experiencing negligible changes in depth through the contraction because the tailwater was high with respect to critical depth. However, ifthere is choking in the contraction and significant upstream backwater at the beginning of scour, then an improved estimate of IJ.r is needed. If it is assumed that M is an estimate of ~I'In with small depth changes as shown by Sturm and Janjua ( 1994), then IJ.r can be
40

estimated as

(4.5)

in which M is evaluated for the approach depth at the beginning of scour and can be obtained from WSPRO output (Shearman 1990); ~= Vro Yro at the end of scour as estimated by the
undisturbed approach floodplain velocity and depth; and em= VnYn at the beginning of scour
determined by the approach floodplain velocity and depth obtained from the disturbed watersurface profile in WSPRO output. Substituting Eq. 4.5 into Eq. 4.4 results in

(4.6)

in which <lroc = Vco yro and Vco is the critical velocity in the floodplain for the undisturbed floodplain depth Yro Eq. 4.6 provides a working equation for fitting the experimental results.
Correlation ofResults The correlation of scour depth measurements according to Eq. 4.6 is presented in Fig. 4.2. Results for vertical-wall abutments are given for both cross-sections (A and B) and for relative abutment lengths LJBrvarying from 0.17 to 0.66. Sediment sizes ofl.2 mm, 2.7 mm, and 3.3 mm are included in the results in Fig. 4.2. Shown for comparison in Fig. 4.2 is the proposed relationship suggested by Sturm and Janjua (1994) from a much more limited data set in a short, horizontal laboratory compound channel. In the latter data set, the tailwater essentially submerged the contraction so that the backwater was small, but this data agrees with the present data if the undisturbed floodplain depth is substituted for Yro even though it is not normal depth.
41

The best-fit relationship for all of the data is also given in the figure for which C, = 8.14 and C0 =
r 0.40 in Eq. 4.6. For this relationship, the coefficient of determination is 0.86, and the standard
error of estimate in (d/yro) is 0. 68. Alternative Procedure II
Clear-water scour at a bridge abutment located on the floodplain of a compound openchannel occurs at an ever decreasing rate from initiation of scour until equilibrium is achieved. Theoretically, local scour is initiated when the ratio oflocal bed shear velocity U. to its critical value U.c, or the ratio oflocal flow velocity V to critical velocity Vc, exceeds unity. Furthermore, the initial rate of scour and limiting depth of scour have been shown to increase with the value of V/U*c in experiments on scour by jets (Sedimentation 1977). Thus, although the local depthaveraged velocity near the abutment face is continually decreasing as the scour hole grows larger with time, it seems possible to relate the maximum depth of scour to the maximum depthaveraged velocity near the abutment face Vab at the beginning of scour as shown in Fig. 4. 1. This velocity cannot be predicted by one-dimensional models. Biglari and Sturm ( 1996) have applied a depth-averaged, k-E turbulence model to predict the flow field and Vab around an abutment on the floodplain of a compound channel using Cross-section A and vertical-wall abutments. For Crosssection B, Vab was measured for several discharges for each abutment length.
Dimensional Analysis As a test of the hypothesis that scour depends on the local depth-averaged velocity near the abutment face, a relationship for the equilibrium clear-water scour depth is sought in the form

ds =f[Ytv, Yah' Vab' p, (Ps- p), g, dso]

(4.7)

42

in which d.= equilibrium scour depth; Yro= undisturbed flow depth in the floodplain set by uniform

flow downstream of the bridge; Yab =floodplain flow depth at the location ofVab in the contracted

section; v.b =maximum velocity near the upstream comer of the abutment face; p =fluid density;

Ps = sediment density; g = gravitational acceleration; and d50 = median sediment diameter. Dimensional analysis of (4. 7) results in

d
_s

=J[y ~N

F

~d ]

' s' ab'

Y1o

Yjo

Yab

(4.8)

in which Fab = V.j(gy.b)05 = Froude number in the contracted floodplain near the abutment face;

and

Ns

=

v

.j[(SG-1)gd50]

05

=sediment

number

in

the

contracted

section

as

defined

by

Carstens

(1966) with SG =specific gravity of the sediment. The value of the relative roughness (d5Jy.b)

can be replaced by the critical value of the Froude number Fe or the critical value ofthe sediment

number Nsc for the case of fully-rough turbulent flow (Pagan-Ortiz 1991) as in these experiments.

For quartz sediment and water, either Fab or Ns can be considered redundant with respect to the

other. If it is further assumed that scour is related to the excess ofvelocity (or sediment number)

with respect to its critical value as suggested by several sediment transport formulas (Carstens

1966, van Rijn 1984, Brownlie 1985, Karim & Kennedy 1990), a relationship for dimensionless

scour can be presented in terms of

ds =f[N -N Yab]

.

s

sc'

Yt. o

Yr. o

Alternatively, the scour relationship could be given as

(4.9)

(4.10)

43

Correlation of Results Fig. 4.3 illustrates the correlation of scour data in terms of the excess velocity ratio suggested by (4.10). The experimental scour data for Cross-section A were measured by Sadiq (1994) and reported by Sturm and Sadiq ( 1996), while the scour data for Cross-section B were collected as part of this contract and the concurrent FHWA contract. The values ofVab and Yab were predicted by Biglari's numerical 2D turbulence model (Biglari 1995) for Cross-section A, while they were measured for Cross-section B. For Cross-section A, the left and right floodplains were slightly asymmetric due to finite construction tolerances so that slightly different scour depths were measured for the left and right abutments. These two scour depths in each experiment were averaged for comparison with the numerical model runs which assumed perfect symmetry. The value ofVc was calculated from Keulegan's equation as a function of d5ofYab with appropriate values of Shields' parameter. The results in Fig. 4.3 include experimental data for six different values ofLJBr and for three different sediment sizes. The value ofLJyro varied from 3 to 90 which includes both intermediate and large scale abutment lengths according to Melville's classification (1992). The variable Yat!Yro in (4.10) is an indication of relative local water surface drawdown near the upstream comer of the abutment, but it was found not to be a significant explanatory variable for the observed scour depths in these experiments. The coefficient of determination for the least-
r squares-fit relationship in Fig. 4.3 is = 0.88. Correlation of the results according to the excess
sediment number given in (4.9) was not as successful as the form suggested by (4.10).
44

Discussion In comparing Figures 4.2 and 4.3, there appears to be relatively little difference in using
Alternative I or II for scour prediction. Alternative I is based on variables easily determined by WSPRO, while Alternative II requires output from at least a 2D, depth-averaged numerical model. It is not clear that FESWMS will satisfy this need with its assumption of constant eddy viscosity. Biglari's model used a k-E turbulence closure in order to capture the interaction between main channel and floodplain flow, and there is the possibility that even higher order turbulence closure models may be needed to model the large-scale eddies of separation at the abutment. Only 3D numerical models can be used to even attempt prediction of the action of the horseshoe vortex and its effect on scour depths. Nevertheless, Alternative II is attractive because of expected rapid development and use of2D and 3D numerical models in the next few years, and also because of the possibility of unifying experimental results on abutment scour from rectangular channels with those from compound channels.
There is a strong temptation to take the "hydraulic approach" and develop a simple method for predicting Vab until more advanced numerical models are readily available and usable. Fig. 4.4, for example, is an attempt to correlate the acceleration indicated by the ratio ofV1 in the bridge approach section to Vab in terms of the discharge contraction ratio M and the depth ratio Yat!Yn that might be inferred from simple continuity considerations. The results in Fig. 4.4 are based on Biglari's numerical model for Cross-section A and experimental measurements for Cross-section B for both vertical-wall (VW) and spill-through (ST) abutments. The data show considerable scatter and still require a prediction ofyab' which is the drawdown depth near the upstream comer of the abutment face. Ifyab is replaced by Yfth which is more easily predicted by
45

lD models, the correlation improves slightly as shown in Fig. 4.5. Another possible method of predicting Vab is to relate it either to the average floodplain
velocity, or to the mean cross-sectional velocity at the upstream face of the bridge. A typical set of comparisons between measured and numerically predicted resultant velocities at the upstream face of the bridge are shown in Fig. 4.6. As the discharge is increased while holding the abutment length constant (LJBr = 0. 17), Figs. 4. 6(a) and 4. 6(b) show a large increase in the floodplain velocity relative to the main channel velocity. On the other hand, if the discharge is held constant while increasing the abutment length to LJBr = 0.50 as shown in Figs. 4.6(a) and 4. 6(c), the shape of the velocity distribution changes so that there is a smaller difference between maximum and minimum floodplain velocities for the longer abutment.
Relating Vab to the average cross-sectional velocity for the whole cross-section is complicated by the fact that WSPRO predicts the average cross-sectional velocity at the downstream face of the bridge, whereas Vab occurs at the upstream face of the bridge. As shown by the computed velocity vectors in Fig. 4.7, there seems to be no simple one-dimensional flow relationship between these two velocities. Also apparent in Fig. 4.7 is the entrainment of floodplain flow into the main channel in the approach to the contraction. It is this interaction which complicates the simple hydraulic approach to prediction ofVab
A final method of obtaining Vab is suggested by relating the independent dimensionless groups in Figs. 4.2 and 4.3 used to estimate the scour depth. Because the correlation of scour data is similar in these two alternative procedures shown in Figs. 4.2 and 4.3, the independent
r dimensionless groups must be related to one another. The correlation is shown in Fig. 4.8 with
= 0.88.
46

WSPRO Predictions In order to determine the adequacy of 1-D hydraulic computations to be used in
Alternative I scour predictions, WSPRO simulations of the water surface profiles and approach velocity distributions for both Cross-sections A and B are compared to measured laboratory results in this section. Some comparisons are also made with the results from Biglari's 2-D numerical model.
In the WSPRO runs for Cross-section A, Manning's n was assumed to be constant with depth with values of0.020 for the main channel and 0.0174 for the floodplain based on the experimental data for uniform flow. Computed and measured water surface profiles are compared in Figs. 4.9, 4.10, and 4.11 for a constant Q of2.0 cfs and varying vertical-wall abutment lengths of0.5, 1.0, and 1.5 ft, respectively, in Cross-section A (LJBr = 0.17, 0.33, 0.50). The backwater becomes much larger as the abutment length increases, but Biglari's numerical model tracks the experimental results for depth very closely both upstream and downstream of the abutment. It is particularly interesting to note how faithfully the 2D model reproduces the depths in the flow expansion zone downstream of the abutment where WSPRO merely produces a constant depth. This is clearly a limitation of the 1D model. Of more interest, however, are the comparisons upstream of the abutment where WSPRO consistently overestimates floodplain depths by about 10 percent.
Velocity distributions in the bridge approach section are compared in Figs. 4.12, 4.13, and 4.14 for the same conditions as the previous three figures for water surface profiles. For abutment lengths of0.5 ft and 1.0 ft, both WSPRO and Biglari's 2D numerical model predict approach floodplain velocities reasonably well. There are some difficulties with the WSPRO
47

results, however, at the main channel-floodplain interface, and at the main channel centerline. The WSPRO results are computed from the cross-sectional areas of 20 streamtubes having equal conveyances and assumed equal discharges. The vertical wall of the artificial main channel where the depth changes abruptly is apparently the reason for the very low velocity computed by WSPRO near the interface. The WSPRO data points are very close together near the centerline of the main channel because of the large conveyances there, but the reason for the slight decrease in velocity at the main channel centerline is unclear. Biglari's numerical results using a k-E turbulence model do a much better job of predicting the smooth transition in the velocity distribution at the interface. For the longest abutment length of 1.5 ft, the results shown in Fig. 4.14 show that Biglari's model underpredicts floodplain velocities while WSPRO tends to overpredict the floodplain approach velocities. The problem with a very low velocity predicted by WSPRO at the main channel-floodplain interface persists and may account for the overprediction of floodplain velocities to maintain continuity.
Water surface profiles for Cross-section Bare compared in Figs. 4.15, 4.16, and 4.17 for a constant discharge of3.0 cfs and varying abutment lengths of2.62 ft, 5.24 ft, and 7.86 ft, respectively (L/Bf = 0.22, 0.44, 0.66). The values of Manning's n were held constant for the WSPRO simulations based on the measured values over the range of depth variations experienced. These n values were 0. 0190 for the main channel and 0. 015 5 for the floodplain. In spite of the change in cross-sectional shape and channel roughnesses, the WSPRO results are very similar to those for Cross-section A. Downstream of the abutment, the WSPRO depth is nearly constant for uniform flow, while upstream of the abutment, the computed WSPRO depths are larger than the measured values by about 0. 0 1 to 0. 02 ft giving a percent error in floodplain depth
48

of about 10 percent. In general, the computed WSPRO depths at the downstream face of the bridge agree rather well with the measured values.
Computed and measured velocity distributions for Cross-section B, and for the same conditions as the three previous figures of water surface profiles, are shown in Figs. 4. 18, 4. 19, and 4.20. Good agreement between measured and WSPRO floodplain velocities occurs for the first two abutment lengths in Figs. 4.18 and 4.19. For the longest abutment in Fig. 4.20, there tends to be an underestimation of main channel velocities with an overestimation of floodplain velocities in the obstructed floodplain area. The measured and predicted velocity distributions cross one another in the vicinity of the approach to the end of the abutment at a transverse station of approximately 8 ft, which would correspond to the location of the approach velocity defined previously as VI. Part of the disagreement for this case of the long abutment may be of experimental origin with some deceleration occurring at the chosen approach location near the left floodplain boundary. On the other hand, some of the difficulty may also be due to the inadequacy ofWSPRO in modeling the interface region and its influence on velocities in the floodplain near the interface. This point will be raised again in the comparisons, which are to follow, of computed and predicted values ofM, the discharge distribution factor.
More detailed comparisons of computed and predicted values of V~> the approach floodplain velocity upstream of the end of the abutment; y0 , the approach depth at the location of VI; and M, the discharge distribution factor, are given in Figs. 4.21, 4.22, and 4.23 for Crosssection A, and for Cross-section B for both the vertical-wall and spill-through abutments. The approach velocity VI is predicted well by WSPRO for Cross-section B as shown in Fig. 4.21 with a mean square deviation between measured and calculated values of about 0.05 ft/s giving a
49

coefficient ofvariation of0.05. The WSPRO comparisons for V1 in Cross-section A are somewhat scattered due to experimental uncertainty, but the 2D numerical turbulence model performs reasonably well for Cross-section A The approach depth Yn is consistently overestimated by WSPRO in both Cross-sections A and Bas shown in Fig. 4.22. The mean percent error is about 12 %. The 2D numerical model slightly underpredicts approach floodplain depths. In Fig. 4.23 it can be observed that the discharge distribution factor M is predicted equally well by WSPRO and the 2D numerical model in Cross-section A; however, WSPRO underestimates M for the smaller values in Cross-section B. This problem is rooted in the differences in velocity distributions noted earlier for this case as well as in the overprediction of yn by WSPRO. The results forM show that at least some of the effect of main channel-floodplain interaction has been accounted for by the adjustment ofManning's n values, but this achieves only the correct split between main channel and floodplain flow, not the correct detailed velocity distribution near the interface. This is a problem with the one-dimensional analysis afforded by WSPRO that can be overcome by a full 2-D numerical model. Time Development Relationship
Based on the dimensional analysis result given by Eq. 4.10, time can be added as a variable in the scour development process to produce an expected relationship of the form

~ d

=J[

v v ~b,

t
_c_

]

YJD

f' c Ym

(4.11)

in which d81 is the scour depth at any timet. The influence ofyaJYro in (4.11) has not been included based on the experimental results. The experimental measurements of scour depth with

50

time are presented according to Eq. 4.11 for Sediments A, B, and C in Figs. 4.24, 4.25, and 4.26, respectively. These results for time development of scour include only those cases for which the maximum scour depth developed near the upstream comer of the abutment as discussed previously in Chapter 3. However, the location of the scour hole at the upstream comer occurred for the larger discharges so that the worst cases are included in these results. Close examination of these figures reveals that the choice of dimensionless variables ofEq. 4.11 results in very similar curves for the three different sediment sizes having similar values ofV.JVc. The curves have a functional form that begins with a linear development of scour depth with the logarithm of time followed by an abrupt leveling off to a nearly constant value equal to the equilibrium scour depth that depends only on V.JVc as shown previously in Fig. 4.3.
The functional behavior and collapse with respect to sediment size shown in Figs. 4.24, 4.25, and 4.26 suggest the possibility of a universal set oftime development curves that can be applied to field cases provided that the dimensionless variables fall in the same range as in the laboratory experiments. Accordingly, least-squares regression analysis was applied to the data and suggested interpolated curves were developed and plotted as solid lines in Fig. 4.27. Thus,
for a given sediment size, which determines Vc; a given abutment velocity v.b, which is
determined by the abutment shape, degree of floodplain contraction, and flow velocity distribution; and a given time corresponding to the design flood duration, an estimated depth of
scour can be obtained. For example, ifV.JVc = 1.5, approximately 2/3 of the equilibrium scour
depth is reached in a flow duration of only about ten percent of the equilibrium time. Figure 4.27 shows very clearly the interplay of time, flow distribution, and sediment size in determining a design value of abutment scour depth.
51

Proposed Procedure for Abutment Scour Prediction As a result of the experimental results on equilibrium depth of clear-water abutment scour
in Fig. 4.2 and time development of scour in Fig. 4.27, a prediction procedure that accounts for discharge distribution, sediment size and time can be developed. Based on the extensive comparisons between WSPRO estimations of scour parameters and parameter estimation by a 2D numerical turbulence model, it is assumed that the WSPRO predictions provide a reasonable estimation of the independent parameters for the prediction of clear-water abutment scour. It is further assumed that the abutment velocities to be used in the time development determination in Fig. 4.27 can be obtained from the relationship developed in Fig. 4.8 that depends only on parameters that can be calculated from WSPRO results. The steps in the proposed procedure are:

(1) From field data, obtain at least one surveyed cross-section, and preferably three sections (bridge exit, downstream face of the bridge, and bridge approach). Also

estimate Manning's n for the floodplains and main channel, and obtain bridge geometry data and sediment size d50. (2) Determine the 100 year and 500 year design discharges based on drainage area and

regional frequency estimates (available from NFF in version 6 ofHYDRAIN). (3) Run WSPRO and obtain M, V0 , y0 , and Ym from the results. Also estimate the
value of Voc from ymand d50, and the value of V lc from y0 and d50 using Keulegan's equation, Eq. 3.6, which is repeated below:

v c
JCSG -l)gd50

(4.12)

52

in which SG =specific gravity of the sediment= 2.65; SP =Shields' parameter determined from Shields' diagram for the given sediment size d50 ; andy= flow depth at which critical velocity Vc is to be determined. (4) Calculate the equilibrium depth of abutment scour from the best-fit relationship in Fig. 4.2 modified by a factor of safety FS:

ds =8.14 [ qfl - 0.4] + FS

}jv

M qfDc

(4.13)

where ~c = Vac yto and Cin = Vn yn The maximum value of d/yto should not be

taken any greater than 10 based on the experimental results. In addition, if

Vn2:V1c , then maximum clear-water scour occurs so set Vn=V1c . It is recommended that the value of FS = 1.0, which is slightly greater than the standard

error of estimate of 0.68 for d/Yto in the best-fit relationship.

(5) From the watershed size and a hydrologic estimate oflag time of the watershed,

use NFF in HYDRAIN to generate a hydrograph corresponding to the peak design

discharge from which a flood duration can be estimated.

(6) For the duration obtained from step 5, determine the percent of equilibrium scour

depth that will occur from Fig. 4.27. To estimate VaJVc needed in Fig. 4.27, use

Fig. 4.8 for which the best-fit relationship is given by

V

i.TI

_3.!!._ = 1 + 1.56 [ __!!p_ - 0.4]

Vc

M qjDc

(4.14)

(7) Compare the estimated abutment scour depth with the abutment foundation depth and determine if riprap protection is needed or not.

53

Example A bridge with a 750ft opening length spans Burdell Creek which has a drainage area of 375 mi2. The exit cross-section is shown in Fig. 4.28 with three subsections and their corresponding values of Manning's n. The slope of the stream reach at the bridge site is constant and equal to 0.001 ft/ft. The bridge has a deck elevation of22 ft and a low chord elevation of 18 ft. It is a Type 3 bridge with 2: 1 abutment and embankment slopes, and it is perpendicular to the flow direction (zero skew). There are six bridge piers each with a width of 5 ft. The sediment has a median grain diameter d50 of2.0 mm (0.00656 ft). Estimate the clear-water abutment scour for the 100 year design flood.
Solution From HYDRAIN, the NFF (National Flood Frequency) program can be used to estimate the design flood flows. For the given drainage area and for Region 3 in Georgia (coastal plain), the predicted Q100 is 14,000 cfs and Q500 = 20,000 cfs. Calculations are done in this example for
QIOO
The WSPRO input data file is shown as Table B.1 in App. B for Q100= 14,000 cfs. The
program was actually run twice, first to obtain the water surface elevations for both the unconstricted and constricted cases at the approach cross-section, and second, with the HP 2 data records to compute the velocity distribution in the approach section for the unconstricted (undisturbed) water surface elevation of 13.25 ft and the constricted water surface elevation of 13.64 ft. These elevations can be extracted from Table B.2 where the results ofthe water surface profile computations are given. Tables B.3 and B.4 give the results of the velocity distribution computations for the unconstricted and constricted cases, respectively.
54

Now the scour parameters can be calculated from the WSPRO results. The value ofM(K)
from Table B.2 is 0.189, which by definition gives M = 1- M(K) = 0.811. For consistency with
current FHWA methodology, the unconstricted and constricted floodplain depths and velocities are determined by the procedure given in HEC-18 for Froehlich's equation. First for the constricted case, the abutment length is determined from Table B.2 by

La = LEWBRDG - LEWAPPR = 937 - 173 = 764ft

(4.15)

Then from Table B.4 the blocked flow in the approach section up to X STA. 937 is 1.97 streamtubes by interpolation. Therefore, the blocked flow Qn is (1.97/20)*14,000 = 1379 cfs since each of the 20 streamtubes carries 1/20 of the total flow. Also, the blocked flow area An is
659 + .97*506 = 1150 ft?. Now we can calculate Vn = Qn/An = 1379/1150 = 1.20 ft/s, and Yn = An/La = 1150/764 = 1.50 ft. In a similar way, the value ofy10 is found for the equivalent
blocked flow area in the unconstricted cross section from Table B.3 to be 1.17 ft. The critical velocities for coarse sediments are determined by substituting into Eq. 4.12.
First, for the constricted approach section in the floodplain, we have for a depth of 1.50 ft:

v 1 = v(2.65 -1)(32.2)(.00656)(0.035)*5.75*10g(12 .2)(1. 50) = 2.0ft/s

c

2*0.00656

(4.16)

in which the Shields parameter was taken to be 0.035 for this sediment size (Julien 1996). In a similar manner, the value of Yeo for an unconstricted floodplain depth of 1.17 ft is 1. 93 ftls. Because Vn < Ve1, it is apparent that we have clear-water scour.

55

To compute the scour depth, substitute into Eq. 4. 13 to obtain

ds = 8.17 [ (1.20)(1.50) - 0.4] + 1.0 = 5.5

y fO

(0.81 )(2.0)(1.17)

(4.17)

Finally, the scour depth is 5.5*1.17 = 6.4 ft. The NFF program can be used to develop a design flood hydrograph. Assuming that the
watershed is 30 miles long with a lag time of 15 hours, the resulting hydrograph can be computed and is shown in Fig. 4.29. As a conservative assumption, the flood duration is estimated as the time required for a constant discharge equal to the peak discharge to give the same volume of direct runoff as the original hydrograph. This results in a duration of 16 hrs.
The critical velocity at the toe of the abutment is computed from a depth equal to the water surface elevation in the bridge opening, which is 12.47 ft (Table B.2) minus the ground elevation at the toe (10.35 ft) to give Yab = 2.12 ft. Then using Eq. 4.12 again for consistency, the critical velocity Vc = 2.1 ft/s, and Vc tl Ym= (2.1)(16)(3600) I (1.17) = 1.0 x 105. From Eq. 4.14, VaJVc = 1.54, and Fig. 4.27 indicates that more than 90 percent of the equilibrium scour will occur over the flood duration of 16 hours. Under these circumstances, the reduction in scour due to equilibrium not being reached is small so that the final result for clear-water abutment scour depth is left at the value of 6.4 ft that was previously estimated.
Because scour holes can develop as a result of several floods over time, the time analysis proposed herein is intended as a judgment factor in reducing the estimated scour only when (a) the estimated scour is significantly higher than actually observed on an existing bridge; or (b) the watershed is so small that only a small fraction of equilibrium scour is reached in a typical design
56

flood. It is strongly recommended that a whole range of discharges be considered and that the percent of equilibrium scour be investigated in each case. Fig. 4.27 provides for the first time a method for estimating percent of equilibrium scour for floods of differing magnitude, and it should greatly enhance the engineer's judgment in making a final evaluation for scour susceptibility.
It should be noted that the estimated equilibrium scour has been determined for a verticalwall abutment and could be further reduced by a shape factor for a spill-through abutment currently recommended by HEC-18 to be 0.55. However, the results currently being obtained under the FHWA contract do not support such a large reduction for very long abutments, and so for the time being the worst case of the vertical-wall abutment is assumed. In addition, the estimated scour could be increased by a skewness factor for abutments not perpendicular to the flow as recommended by HEC-18, but for this example, the skewness factor was taken to be 1.0 for a perpendicular abutment.
Finally, for purposes of comparison, it is reasonable to calculate the abutment scour for this case using Froehlich's live-bed scour equation or the HIRE equation as recommended by HEC-18. Substituting into Froehlich's equation given previously as Eq. 2.3, and using the values ofL3, Yn, and Vn already determined, we have

5._ = (2.27)(1.0)(1.0)( 764 )0.43 (

1.20 )0.61 + 1 = 12.3

Yn

1.50 J(32.2)(1.50)

(4.18)

so that ds = (12.3)(1.5) = 18.4 ft. (Froehlich's clear-water abutment scour equation gives a value
ofds =39ft!) 57

For the HIRE equation, which is recommended by HEC-18 for long abutments, the value ofyab is taken to be 2.12 ft as determined previously from the water surface elevation in the bridge section. However, the value ofVab is estimated to be equal to 3.2 ft/s as determined from Fig. 4.8 or Eq. 4.14 developed in this research. It is not recommended to use WSPRO results from the bridge section to estimate Vab because conveyance ratios cannot predict the local acceleration occurring near the abutment face. Now substituting into the HIRE equation given by Eq. 2. 9, we have

ds = (4.0)(

3 2 .

113
)

= 2.9

Y ab

J(32.2)(2.12)

(4.19)

from which ds = (2.9)(2.12) = 6.2 ft. This estimated scour depth is in much better agreement with
the one predicted from the results of this research (6.4 ft), but the agreement is partly due to the choice of sediment size for this example. Much more extensive field testing is required to verify the relationships developed herein.
Limitations The experimental results developed herein are for the case of clear-water abutment scour and should not be applied at the present time for abutment lengths and cross-sections that produce M values less than about 0.5, or for abutments that approach the bank of the main channel. The ranges of variables covered in the experiments reported herein are given in Table 4.1. If the livebed scour case occurs, then it is recommended that Vn be set equal to Vnc for maximum clearwater scour. In any case, the value of d/y10 without the factor of safety should not exceed a maximum value of 10, which was obtained both from these experimental results and those of
58

Melville (1992). Additional experiments are currently underway under the sponsorship ofFHWA to consider the case of the abutment terminating at the edge of the main channel, the case oflivebed scour, and the effect of abutment shape. These results may require some minor modification of the proposed scour prediction procedure but they are certain to enhance it.
Some bridge scour data for the Georgia flood of 1994 was reviewed, but this data was collected for the purpose of closing bridges during the flood. It is not detailed enough for field verification of the proposed scour prediction procedure, so additional research is suggested in Chapter 5. Nevertheless, the field example problem that has been presented should assist the engineer in implementing the results of this research.
Table 4.1- Range of Dimensionless Variables in Experimental Relationships

Variable M
Yr/Vflc Vrr/Vft)c YtofYo L/Br Qn/(MqmJ

Range 0.60-0.95
0.4-0.8 0.5-1.0 0.6-1.0 0.17-0.66 0.4-1.6

59

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60

CHAPTERS CONCLUSIONS AND RECOMMENDATIONS
It is concluded that the experimental results and methodology developed from this research can be utilized to estimate the depth of abutment scour and protect those bridges that may be scour susceptible. It has been determined over a much wider range of variables than was previously available that the effects of discharge distribution, sediment size, and time development on scour depth can be predicted from the relationships given in Figures 4.2, 4.8, and 4.27. The comparisons ofWSPRO results, experimental results, and results from a 2D numerical turbulence model have shown that the results from WSPRO are adequate for estimating the independent parameters needed for abutment scour prediction so long as bridge approach hydraulic conditions are used as predictor variables. It is recommended that the proposed procedure for abutment scour estimation be used alongside current FHWA procedures subject to the limitations on ranges of dimensionless variables given in Table 4.1. Full implementation of the proposed procedure should await completion of the present FHWA research for the case of the abutment approaching the banks of the main channel and for the case oflive-bed scour. In addition, it is strongly recommended that verification of the proposed procedure with field data be undertaken to develop confidence in its use.
It is recommended that further research be conducted to advance to the next level of confidence in abutment scour predictions in the field in order to protect bridges that are subject to scour and possible failure. Suggested areas for further research are:
61

a. A well planned, detailed field study of a bridge subject to abutment scour in cooperation with the USGS is needed. The bridge should be instrumented and scour determined over a three year period with detailed field measurements of velocity and bed elevation changes. If resources are available, it is further recommended that more than one bridge be instrumented to allow for different regions in Georgia such as wide, heavily vegetated river floodplains as well as tidal zones in estuaries.
b. A laboratory model of the instrumented field bridge should be constructed and tested to compare scour predictions based on the laboratory data with those actually measured in the field.
c. Numerical model results from both WSPRO and FESWMS should be compared with the field data to determine their performance in an actual field case with respect to estimation of scour-prediction parameters.
d. A laboratory study of scour countermeasures is needed in order to design the most efficient abutment scour protection schemes. The study should consider (a) the extent, size, and placement of riprap at abutments; (b) the effectiveness of spur dikes; and (c) procedures for using rock riprap to repair an ongoing abutment scour problem.
e. The next level of research needed in order to refine equations for abutment scour prediction is the application of a 3D numerical model combined with 3D velocity measurements in the scour-hole area as the scour hole develops with time. Such a 3D model could also enhance the proposed field and scour countermeasure
62

studies.

f.

A combined laboratory and numerical model study for the case of embankments

and abutments skewed to the oncoming flow would broaden the applicability of

the proposed abutment scour prediction procedure through the development of a

skewness correction factor.

63

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64

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69

Hyd. Div., ASCE, 99(1), 219-238. Young, G. K., M. Palaviccini, and R. T. Kilgore. "Scour Prediction Model at Bridge Abutments." Hydraulic Engineering '93, Proc. ofthe 1993 Conference, ASCE, 1993, pp. 755-760. Zheleznyakov, G.V. (1971). "Interaction ofChannel and Floodplain Streams," Proc. 14th IAHR Conference, Paris, 145-148.
70

APPENDIX A. FIGURES

c---~---~------,v---~- -~-,

I I o.5o

k---BJc_r i

, B

T

---"""""'.:'""'>K'---'m!L::-"'e:1<-::<C--- ----___:;;

I

3.06

0.88

3.06

CROSS-SECTION: A

Yr

SLOPE= 0.0050

!

':8 \;:

1 ~~

'-~-------~--.-,,--~------~---B-r_-----~-~--~~-.~--~--~-"'~f-0_-l

'

12.02

I 1.29 0 .52

CROSS-SECTION: B

SLOPE= 0.0022

(All dimensions in ft)

Fig. 3.1. Cross-sections Used in Scour Experiments.

A-1

'!

I

vw

0.15 m

I
_j

I
.I
La

1
I I
rI I
I
ST
i
..I,.

T
I

2:1

t
I

IT~\~

/I I
0.15 m

I
~~

I
12:1 't

J '::J ____./

30

i
I

/1

I
I

I

T

/1

I 2:1 I

1---------

l l{ I \

I
I

'I
I

I WW

10.15 m

____________________:-_.L_______

I
I 1/

l2:1 t/

t

2~
I
l . I
1II '//-

L

Fig. 3.2_ Abutment Shapes Used in Scour Experiments. (VW =vertical wall; ST =spill-through; WW = wingwall)_

A-2

100

80 - - - - - - _,

c0>

- - - - .. - J

60 rJ)
rJ)

- - - - - - -'

-a.S.
c

,_ - - - -

--

Q)
0 40
!.....

Q)

a..

- - - - - - I

I-t-

I
+- - .___ - 1--- -1- I-

_I_

I I L _ L _I_ L l_
I

I

__ i __

_I_ _I_ I_ _!_ I

-~-

I - - 1-
I
- r - r r -~-

-t -
+ - 1- -+ -j -
I I J _j
_ J _ l _ I_ 1

-------
1

- 1-

-I

I

I

- - r - T ~-

-~- ~ ~-

20

- - - - - - -t

-1 -

I

I

L- - - - - ~--- -1-

- ~- 1- -1-

- I- - - I- - -+ - _j_ - 1- -+ ---! -

I

L _____ o

_;___~~~-j___j____L_.L__j.---J......""'!'!~=----_L_ ___J_ __L_ _[__L___L__u

0.1

1

10

Sieve Size, mm

i ~ Sediment A ....... Sediment B ...... Sediment C I

Fig. 3. 3. Sediment Grain Size Distributions.

A-3

0.10

_j -

L

~- - -:--

I - - i - - I-

'

- - - - - - ' -- - MAIN CHANNEL

,- :

- - - -T

ks=0.013 ft

r

~ _______ I__ _ l

~ -_I_ - -

I

I_ -

- - - - - - l

SIGMA=1.23

--<0
.T.."._" .
-<
(/) ~
c

!

l_

- I-

L - - - - - - _I_

'

.... l

J - I- - I- - -- L J - i -

l -

., ...."'-<- I I ' I
j_ - - _j - _I_~- _I_. _j _I - - - - - - - l

I - - I-
I
_I_ - - I- -

- _j - l - - II
I
_j - l - - I_

FLOODPLAIN

- - - - - - -~-

ks=0.013 ft

-,- - - - - - - T

I

I I II

-,- ' ' - -r -

I I

- ---, -

r -~-

I

0.01
1

10

100

Rlks

Fig. 3. 4. Manning's n in the Main Channel and Floodplain for Cross-Section B

A-4

0.80 ~-------

' i

'

0.75-

.:= 0.70
>.

I
Iaw.-.

0.65

0 0.60

0.55

. / // /

0. 50 '-._j___..L..._.L..._...C___c_~__L._.~..L__..._____.c--'----'-___L__~-'----'~--'-_L__j__~L......_l.__L.--'-~

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Q,cfs

, - CALC. NORMAL DEPTH i - - - CRITICAL DEPTH

I
MEASURED NORMAL DEPTH I
I
I '

Fig. 3.5. Measured and Computed Normal Depth for Cross-section B.

A-5

0.5 ~~~ 0.4 ~
0.3 ~

--------~--
1

0.2 i

0.1

0.0 ~~-L- ~1__~--'-~--~L~--"~ ____] 0.0 0.1 0.2 0.3

... ~-L-~
0.4

L____L______l~__L__ ~ _l________!__ ~~-~_j_- ___j_~J____ --"- _ __j
0.5 0.6 0.7 0.8 0.9 1.0

QIQ
m

e 1 MEAS., XSECT. A

.A MEAS., XSECT. B

II - CALC.; n VARIABLE; A & B - - - CALC.; n CONSTANT; A

Fig. 3.6. Ratio ofMain Channel Discharge to Total Discharge as a Function ofRelative Normal Depth in the Floodplain

A-6

1.0 c - ,- - - - -

0.8 !
I
0.6 ~ I
0.4 i-
0.2 l..
!

_ _ X-SECTION A - - - - - - X-SECTION 8

0.0

0.1

0.2

0.3

0.4

~1 I y1

; -~ VW; La/Bf=0.22 -.s VW; La/Bf=0.44 -G VW; La/Bf=0.66
1-~ ST; La/Bf=0.32 - ST; La/Bf=0.52 - ST; La/Bf=0.66
I ~ VW; La/Bf=0.17 --- VW; La/Bf=0.33 ~ VW; La/Bf=0.50

Fig. 3.7. Discharge Distribution Factor Mas a Function of Relative Approach Floodplain Depth

A-7

1.0 ~,~~~~~~~~~--~--~---,

0.9

0.8

0.7

0.6

0.5 ~-~-~'--L~~- -----".-~~----"~~~.L__---'

0.5 0.6 0.7

0.9

1.0

Fig. 3.8. Variation ofMain Channel Discharge Ratio from Approach Section to Contracted Section with M.

A-8

CROSS-SECTION B ABUTMENT VW; Q=3.0 cfs

0.85 ,~~~~~~~ ---~-~~...-----~--~-~-~--

0. 80 - - - - - - - ~ - - - - - - - + - - - - - - - +
I

ABUTMENT
- - - - - 4 - - - - - - - ~- - - - - - -

0.75

-- - - - - - - - - - T--- - - - - "T

' ' - - - - -

I
--- ---- - ----- -

.::=_ 0.70 :_-- ----- ~I -- ~-! --- ~ - ~

~

t~

a~.. 0.65 rf -------,'_ --

I

I

' ' I
---- - -- -----

- ------

I
- - - - - I - - - - - - - - -~ - - -

::: L_- :- - -,- --: a.6a r~ -------~I --- ----+i - - - - - - -- ~I

I - - - - - - - -: - - - - - -

-1

~

'

I

I 11

I

I

11-- --i- -- - :--

'
--~

0

1 0

20

30

40

50

60

X-STATION, ft

~ La/Bf=0.22 ___.__ La/Bf=0.44 ~ ~a/Bf=0.66_]

Fig. 3.9. Water Surface Profiles for Vertical Wall Abutments of Varying Length and Constant Discharge.

A-9

CROSS-SECTION 8 ABUTMENT VW; La/Bf=0.44

0.85 ---------------;1..,.-i----------~

: :: ____ ~ :::: ___ ::: :::) ~UTME:NT: :: ~ ___ :-

~

I

I

I

I

~ ~ ~-~:~=~ ;_ _ _ _: I

I

r- - ---- -,------ __ ________ I 0.70 I

I

i

~-

---.~-

- - - - - - ~ - - - - - - ~ - - - - - - -

0.65

0. 60 ~ - - - - - - - : - - - - - - - : - - - - - - - :

_____:_______ -:_______ i

I

I

I 1

I

0.55 I _____ : ______ : __ __ : u~

I
I
-~

0.50 r

' I I

0

1 0

I '
20

I

I

I

, I

30

I

I

'

I

'

I

I

I

I

I

I

40

50

I __c___j
60

X-STATION, ft

i --- Q=2.5 cfs --.- Q=3.0 cfs --a-- Q=3.5 cfs 1
----------'
Fig. 3.10. Water Surface Profiles for Vertical Wall Abutments of Constant Length and Varying Discharge.

A-10

CROSS-SECTION B ABUTMENT ST; 0=3.0 cfs

:::: ~-------~------~----_-_-_~__-___+_________________+_:i~i~1------------~-,-~---------~--~-:------------~-.-

0.75

i' '
~ ~- ~ ~ ~ ~ - - - - - - r - - -

I

I

-- - - - - - - - - -

l ABUTMENT

I

- - - - - 1 - - -- - - - -

- - - - - -- -

I

!

! I

I

I

i \

I

t-- --- -- ------ ~ 0.70

~-

I -- -=----._..1. I '_---- ~------- ~------- -~

f--:-- : : -- ----- - ---- Q..
O W

0.65 f~

------~

~ I .....-

I

:

I

[

~I ,

I

I

1 - - - - - - - -1 - - - - - - - -

t 0.60 ~ - - - - - - - ~ - - - - - - - +- - - - - - -

I

I

I - - - - - - - -, - - - - - - - -~

!

o.55

f r

-

-

-

-

-

-

-

I
~

-

-

-

-

-

-

-

I
~

-

-

-

-

-

-

-

I
~

L
0.50

:

:1

~~~~~~~~~~~~~-_J~~~~~~~~

0

10

20

30

40

50

60

X-STATION, ft

/-e- La/Bf=0.32--.- La/Bf=0.54 -a- La/Bf=~:_66_j

Fig. 3.11. Water Surface Profiles for Spill-Through Abutments of Varying Length and Constant Discharge.

A-ll

CROSS-SECTION B ABUTMENT ST; La/Bf=0.54

0.80
0.75 ------------
.;:=
I 0.70
ID...
~ 0.65
0.60

0. 50 '----'----'----'---"-- '~~~~ ..l.__c__..L..._"--.L._L.b.~

0

10

20

30

40

50

60

X-STATION, ft

I -e- 0=2.5 cfs -.- 0=3.0 cfs -a- 0=3.5 cfs I
L___----------------------------------~----_j
Fig. 3.12. Water Surface Profiles for Spill-Through Abutments of Constant Length and Varying Discharge.

A-12

1.0,---

CROSS-SECTION 8

0.8
y Iy
fO f1
0.6

0.4

0.2

0. 0 L _ '_ 0.0

_ _ J __

! ___i_ _-'----~---'---~-___c---'------L--------'--------'----

1.0

2.0

3.0

4.0

5.0

6.0

Q,cfs

)', VW; La=2.62 ft z VW; La=5.24 ft + VW; La=7.86 ft o ST; La=3.86 ft
ST; La=6.47 ft - ST; La=7.78 ft - VW (Exp. Fit) - ST (Exp. Fit)
- - - - - - - - - - - -----1

Fig. 3.13. Variation ofBackwater Ratios in Floodplain with Discharge and Abutment Type and Length.

A-13

CROSS-SECTION B ABUTMENT VW: Q=3.0 cfs
2.0

1.6

~ 1.2 : - - - - - - - - -

-4 - - -- - - ,_ -

~.
- -! --- j r

_._- 1--
0

!------ I~. tI =-~----=I t=~--~-' cc--- I

J I
/-J

g w
>

0 .8

i~.>-----~-=-=-'~--_-__-___.,I. --~~--~.+-.-------~-I ---I --

~~-~---------I~

I'

I

1 ~---
0.4 !Y' - . - - - - I- - - - -

'
I - -- - - -' - - - -

!
.. - - - - ,_ - - - - - - ,- - - - - - . iI

I
I I
i

0. 0 L______L_

_ j __

_L.___L....

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

TRANSVERSE STATION, ft

I -e-- NO ABUTMENT --&-- La/Bf=0.22

---- La/Bf=0.44

__.__ La/Bf=0.66

l

Fig. 3.14. Approach Velocity Distributions for Vertical Wall Abutments of Varying Length and Constant Discharge.

A-14

CROSS-SECTION B ABUTMENT VW; La/Bf=0.44

2.0 ~-------------------------------------------------------------

1.6

f
i

r------ I

r - - - - - - ~------ r - - - - -

-~------

-~------

-~--

I

I

I

I

I

(/)

1.2 ~

i

I

~------ ~------ ~------ L - - - - - - 1- - - - - - - 1 - - - - - - -1-

~

I

I

I

'

i

I

I

I

0~ 0.8t~.~~ ~ ~ : ~- : ~- : -- I ---- / 1I1

> ..--------,

I

I

i

I

I

~

'

I

I

I

I

I

I

I

I

I

0.4 ~- - - - - - r - - - - - - r

I

I

I

I

I

- - : - - - - - - :- - -- - - - -:- - - - - - -:- - - - - - -~

~
o.o L~--~-~-"----~

I

I

0.0

2.0

4.0

6.0

8.0

10.0

TRANSVERSE STATION, ft

:

___j

12.0

14.0

1--- I = = = Q 2.5 cfs -..- Q 3.0 cfs -a-- Q 3.5 cfs ____________________________ _j
Fig. 3.15. Approach Velocity Distributions for Vertical Wall Abutments of Constant Length and Varying Discharge.

A-15

CROSS-SECTION B ABUTMENT ST: 0=3.0 cfs
2.0 ----------------------------------------- ----------

1.6 - - - - - - r - - - - - - ~------ r - - - - - - 1 - - - - - - -~------ -~--

~

- 1.2 - - - - - - ~

i-- - - - - -- - 1- - - - - - - L - - - - - -I_ - - - -

>- I I

I

I

I - 1- - - - - - - 1-
I

...

I-
--=--------- ------- ; --- 0

L~ -~ I

~ r~~---~-~~~~---:------- > 0.8 I /

I

'

~

I

_ ____________..-

-.-.-.-. ---....::..-=---=----==~--

~-~-~:

0.4 I~

I

~------- c

!

I

I

- - - - -~------- r - - - - - - -~- --

I - - - -~------ -~-------

I
r
0.0 l
0.0

2.0

. _ L __

_ L __ __ J __

___,_ _ ___L__ _ __c_ _ _ _ _ _ _,

4.0

6.0

8.0

10.0

12.0

14.0

TRANSVERSE STATION, ft

' --- NO ABUTMENT ___..,._ La/Bf=0.32

----- La/Bf=0.54

__._ La/Bf=0.66

Fig. 3. 16. Approach Velocity Distributions for Spill-Through Abutments of Varying Length and Constant Discharge.

A-16

CROSS-SECTION 8 ABUTMENT ST: La/Bf=0.54
2.0 ~---------------------------------------------------------------

I

i

1.6 ~------ ~------ ~------ ~------ :-------:-------:-------I

f

I

I

I

I

I

en

>--~

!

'

'

1.2 1- ______ L __ . ___ L - -

-

-

I - -L - -

-

' - - - I_ - -

-

-

I - - 1- - - -

-

-

: - J_ -

1-

- - -~I I

0

0

_J
w

0.8

-I =i:=:=====~.c=-=--~~-~--=-=----=----- :- - - - - - I

>

I

I

1- -----' -- !
0.4

I

I

I

I

I

I

- - - r - - - - - - ~-- - - - : - - - - - - - : - - - - - - - : - - - - - - -~

f
o.o L_______L___L____L_____

I

i

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

TRANSVERSE STATION, ft

= = = ~ Q 2.5 cfs ....._ Q 3.0 cfs --- Q 3.5 cfs I
Fig. 3. 17. Approach Velocity Distributions for Spill-Through Abutments of Constant Length and Varying Discharge.

A-17

CROSS-SECTION B ABUTMENT VW; SEDIMENT A
1.0 ,---------------------------------------------------------

0.8
I
!:L 0.6
w
0
60::: 0.4 0
(f)
0.2

- - - - - - - - - - - T- - - - - - - - - - - I - - - - - - - - - - - I - - - - - - - - - - -



I I

I

1e

X I ::::X

- - - - - - - - - - - L - - - - - - - - - - - -- -l - - - - - - - - _:x__-- - 1 - - - - - - - - - - -

I

e e

I X

X

i

X X



I. I

X

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - I - - - - - - - - - - -

X

X
x



I

I
- - - - - - ~ - - - - - - - - - - - ~ - - - - - - - -

0 0 L ______ -'-----'----~-L-LLLLI --------"----'--__L__L_L_LL.LL___"---'--_J__J_-'---L_L_L[__

____j__L__l___j__L_L_L__Lj

1

10

100

1000

10000

TIME, min.

[ La=2.62 ft, 0=4.0 cfs x La=2.62 ft, 0=4.5 cfs La=2.62 ft, 0=5.0 cfs
Fig. 3.18. Time Development of Scour Depth for Sediment A with Varying Discharge.

A-18

CROSS-SECTION B ABUTMENT VW; SEDIMENT C
1.0

i
0.8 Ir

- - - - - - - - - - - - - - - - - - ~----------- -~------------

I
b= 0.6
w 0
6a::: 0.4
0
(f)

I

- - - - - - - - - - - ~----------- ~----------- - 1 - - - - - - - - - - - -

'

XX X XX



I X

I

:



I

I

--= ________ _ - - - - - - - - - - - .'.. - - __ - - _X _X__ _I _______ -.- --. IIIII _

I



X

X





I.

-I

. . :I;

I

0.2
L

----X------ --

- - - - ~ - - - - - - - - - - - I - - - - - -

0. 0 I

:

L~-~_j_____j_______l___._..L.~..--.l--- __ .._ __l___L~~.L_L.l_..LJ._~_ _L_____J________j____j_j__J______L__l___L__~____J-'---.l..__L__L_j_JJ

1

10

100

1000

10000

TIME, min.

I La=2.62 ft, 0=2.0 cfs x La=2.62 ft, 0=2.5 cfs La=2.62 ft, 0=3.0 cfs I

Fig. 3. 19. Time Development of Scour Depth for Sediment C with Varying Discharge.

A-19

CROSS-SECTION 8 ABUTMENT VW; SEDIMENT C

1.0

0.8

- - - - - - - - - ~ - -

---- - -i---- -- --

I.
f----~~

I
b= 0.6
w
0
60::: 0.4
0
(/')



X

I X -II1--------.-.----..---------

- - - - - - - - - - - 4- . - - - - - ;;:_--



X

I.

I

XX

I

I

0.2 :I-- - - - - - - - - - - -.i - - - - - - - - - - - - I - - - - - - - - - - - - ,i- - - - - - - - - - - -

IJt

0' 0 c____"-- - -'---'----"-~.__u_L_____~ -~~< ~ ~L-'-'-'-'-L

1

10

100

TIME, min.

1000

10000

La=2.62 ft, 0=2.0 cfs x La=5.24 ft, 0=2.0 cfs La=7.91 ft, 0=2.0 cfs /
Fig. 3.20. Time Development of Scour Depth for Sediment C with Varying Abutment Length.

A-20

CROSS-SECTION B ABUTMENT VW; SEDIMENT A

ds ,ft

1.0

~~~~-----------------------------------------------------------,



I A

0.8 0.6 0.4

- - - - - - 1 - - - - - - - - - - - - - -. .- - - - - - -~------ -~-------------

I

A



- - - - - - ~- - -
I

I

e - -- - 1-- - -

-I - - - - - - -1-- - - - - - -I- - - - - - -I - - - - -

... ...... ..I

- - - - - - - - - !- - - - - - - I- - - - - - - I- -

- - - I- - - - - - I- - - - - - - I - - - - - -

i

I ...... I I

I

I

I

:

0.2 ~ - - - - - - ~ -

f

L o.o

---'--~_L _____l_

I
-- - t- -A- - - - - i- - - - - - - r- - - - - -- --~- -- - - - - -~ - -

I



I

!

____ _________[_

____,______]__

-----'-----'

I

:

j ___L__ _____cL___ _...L__ _ _ _ L _ _ __L__ _ _ _

0

1

2

3

4

5

6

7

Q, cfs

1



La=2.62 ft La=5.24 ft La=7.86 ft 1

------------------------~-.-....J

Fig. 3.21. Equilibrium Scour Depths for Sediment A with Varying Discharge and Abutment Length.

A-21

CROSS-SECTION B ABUTMENT VW; SEDIMENTS B & C

1.0

0.8 0.6

~

- - - - - - ~------ 1 - - - - - - - ! - - - - - - - 1 - - - - - - - 1 - - - - - - - 1 - - - - - -
I



I

G

12:;

I

_ _ _ _ _ _ i_ _ _ _ _ _ _e_ _[]_ _ _ _ _ I _ _ _ _ _ _ _ I _ _ _ _ _ _ _ I _ _ _ _ _ _ _ I _ _ _ _ _ _



,G

------,-------I-- 0.4

I

'

8---

-I~------

-!~------

-~I -

I
-------,------

.L

0.2 ,_. - - - - - e - - - - - - - - - - - - - - - - - - - - - - - _,_------~-------I---

I 0.0
0

--~----'----------.L--~-

1

2

3

4

5

6

7

Q, cfs

r

I .0. La=2.62 ft; SED B G La=5.24 ft;SED B D La=-7.86 ft; SED B I

... La=2.62 ft; SED C

La=5.24 ft; SED C

I
La=7.86 ft; SED C j

Fig. 3.22. Equilibrium Scour Depths for Sediments B and C with Varying Discharge and Abutment Length.

A-22

40.

: <(

I

f-

w N

(/)

><

31.

30. []--!C...,.....,-i--'-;"-T--'~,.....r-:ri--.,.-,----r-r--r--i'-r-r"+-+-'-r-"i-T'>r-t"+"'-i-"'r"'-i~ 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

8.0

Z- STA. (ft)

9.0 10.0 11.0 12.0 13.0

Fig. 3.23. Equilibrium Bed Elevation Contours for La/Bf= 0.44 (VW) and Q = 3.49 cfs.

Elevation (ft)
1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40
= Q 3.49 cfs

X

32.

3 0. 0 -+-r...,....,.....,.-,-T-'!--,--,i-T--,-,-,.,--,-,-.,-'-rT-rT"1"'..,.,-" 0.0

11.0 12.0

Fig. 3.24. Equilibrium Bed Elevation Contours for La/Bf= 0.44 (VW) and Q = 4.00 cfs.

Elevation (ft)
1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30
Q =4.00 cfs

40.0

39.0

38.0

37.0

~

~ I

<( f-

36.0

N

(f)

Vl

X
35.0

34.0

33.0

32.0

31.0

Elevation (ft)
1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10
= Q 3.51 cfs

Fig. 3.25. Equilibrium Bed Elevation Contours for La/Bf= 0.66 (VW) and Q = 3.51 cfs.

42.0

39.



~ 36.0

;J>

<{

I

f-

N 0'

x(/)

33. 32. 31. 30.
Fig. 3.26. Equilibrium Bed Elevation Contours for La/Bf= 0.66 (ST) and Q = 3.50 cfs.

Elevation (ft)
1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30
Q = 3.50 cfs

10 ------N
sc

1 0.01

: VW-SEDA
i D ST-SEDA
I
I ~ LAURSEN (SP=.039)

e VW-SED 8

.&. VW-SED C

L UNIFORM-SED C

- - - PAROLA

-LAURSEN (SP=0.035) - KEULEGAN (SP=0.047)

Fig. 3.27. Measured and Calculated Critical Velocities at Incipient Motion.

A-27

'1 Bl

A
L

APPROACH
i ;or v,

,2
BRIDGE

~ ABUTMENT
B._) PLAN

====> Q
FLOODPLAIN

'--------------- -- --~lc'__---
SEC. A-A

tJY
SEC. B-B

Fig. 4. 1. Definition Sketch for Equilibrium Scour in a Long Contraction in a Compound Channel.

A-28

10 .~------------------------------------------~,----

9 [SYMBOL ~FILL
8 ~ None
rf Solid
7 Dots

d50, mm
3.3 2.7 1.2

I Best Fit


5

4

______L 3 ~..;:;& Janjua, 1994

c:=~

l '-.........__

2

""/ cZ

1

:z

0 ~~~--~~~--~----~--~~--~~--~~--~~--~~

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

qf/ (M qfOc)

SYMBOL SHAPE
r
XSECT. 8: i :z La/Bf = 0.22 6 0.44
XSECT. A: i c La/Bf=0.17 v 0.33

D 0.66 EB 0.50

Fig. 4.2. Equilibrium Abutment Scour Relationship Based on Approach and Tailwater Conditions.

A-29

10

9

r
L

8

k i8est Fit
~---~ ~-

d/Ym 7
6

5

SYMBOL

4

FILL

d50, mm

None

3.3

3

Solid

2.7

2

Dots

1.2

1

0

0.0

0.5

1.0

1.5

2.0

(V IV)- 1
ab c

SYMBOL SHAPE

XSECT. B: I :z: La/Bf=0.22 L- La/Bf=0.44 o La/Bf=0.66 I

XSECT. A: I c La/Bf=0.17 v La/Bf=0.33 EB La/Bf=0.50 I

Fig. 4.3. Equilibrium Abutment Scour Relationship Based on Local Velocity Near Abutment Face_

A-30

1.0

-- - - - - - I - - - - I

- -I - - - -

Ii I

I

I

I -- - - ~-- -, - -

~ ~--- ~- ~ ~- ~- 4 ~-- ~- ~-- 4 ~

~I----~~-- - 1 - - - ~-- ~- ~- ~i

- - - - - - - - - - - - - - - - - iii;-, - ~ ~ ~ ~ ~ ~-

I

~

~

~ ~

I

~ ~

~ -~

~

~ ~~ ~

I

i I

I

I

i ~ r ~ - r - -~ - -

,

,

1

1

-------- ---t--------'----- _,_ 6-- -1--- _,_-

-I , ul

1

1

-- r--- -1-

I

I

I

~ ~ ~ ~ ~ ~ ~ -

... -

---

- - - - - - - - _I - - - - - -:

I

I

I

I

~I-

-~- ~ -~ - -:-

:- -:-

;

I I .

I

I

I I

:~.- -~- ---: ---: --:~ -~: --I

I
-~-----_I_--- _ I - - - _ I _ - - L - - L - _I--


r - - r - - - - - - - - - - - - - - - ~-------- T - - - - - - , - - - - -~--- - , - - -

-~--

I

I

I

I

0.1 L _ _ __ 0.1

I

I

I

I

L---~--~-----L-~1 ~J

1.0

I ... XSECTION B 0/W) XSECTION B (ST) 6 XSECTION A 0/W) I
Fig. 4.4. Estimate ofRatio of Approach Velocity to Abutment Velocity Based on Floodplain Flow Depth Near Abutment Face.

A-31

1.0

- - - - - - ~- -

- - - - - - - I_ - - - :_ - - J - - _l _ _ '_ _

- - - ~ - - - - - - - - ~ - - - - - - 1- - - - - 1- - - - ~ - - 4 - - 4 - - ~ -

:- :- :- -~ - - - -

I

I

I

I

I

I

--

- - --

- --

,- - - ~ - ~ -

V/V
1 ab

-: :- ~ - -

-

---

-

-- -

~ - - - -

-

---

- ---

- - - -

--

-- -

I

I

I

I

I

r - - - - - - - - - - - - - - -', - IBEST FIT)2= 0.77 ( - ~ .D._ I_

I

I

~-~-I -I -

I
~-

-

-

I I

-

--III-III

-

-

I -

-

:
~---
1

"' . : L-------,---~--' 1--,~

I

I

---------~--------~-- __ --~-L------~--~--L-

I~

- - - - - -- - - I - - - - - -- ~- - - - - 1- - -

- 'I

-

- --

-r

i
0.1 i L_________ _ 0.1

_ _j _ __ _

I
______]__ - ________[__ _ ____j__

I I ______l_

!
j _ _ l _ _ _ L _ ____

1.0

My ly
to t1

.a. XSECTION B 0/W) XSECTION B (ST) Leo. XSECTION A 0/W) ]

Fig. 4.5. Estimate ofRatio of Approach Velocity to Abutment Velocity Based on Tailwater Flow Depth.

A-32

3.5 ~---,Sia.:---c3c:-2---------------------------, 3.5

3.0 ~
~
i-2.5 -
] >" 2.0-

Q = 2.02 cfs; lA = 0.5 ft

-!-3.0
-;-2.5
.-~
" -2.0 Ui

Transverse Distance, ft

(a)

:-Computed Velocity

X Exp. Velocity (Sadiq 1994)

- - WSE

-BED

3.5 . . , - - - - S l a . : c - - : : - : 3 2 = - - - - - - - - - - - - - - - - - - - - - - 3.5

3.0-
~
ig- 2.5 -;-
u> 2.0-

Q = 3.83 cfs; lA- 0.5 ft

I
-;-3.0

0

2

3

4

6

7

Transverse Distance, ft

(b)

-Computed Velocity

x Exp. Velocity (Sadiq 1994)

1-WSE

-BED

3.5 - - - - - - - - - - - - - - - - - - - - - - - - 3 . 5 Sla. 32
Q = 2.02 cfs; lA ~ 1.5 ft

0

2

4

6

Transverse Distance, ft

. - Computed Velocity

X Exp. Velocity (Sadiq 1994)

(c)

-WSE

-BED

Fig. 4.6. Numerically Predicted Resultant Velocities at Upstream Face of Bridge by 2D Turbulence Model Applied to Cross-section A.

A-33

3.5

3.0

-c::: 2.5

'-"
>-

8
s c

2.0

0"'

u
~

1.5

~"' 1.0

0.5

0.0 28

Velocity Vector Distribution Q = 2.89 cfs, 12 in. Abutment, Exp. 53

. _______ _.. __--t.....,

_,_...._...._...,..,.
---- --- --------_ -- . -.. ------------- ----.~..-_:....-$:::;

.. t
..
e

_..._..:::;

_,....,..,,..,/~

~-

-- --- -- __ -------- _,....,....,.......//~--

,....,.......,....,,....,~-

,....,....,......,...............-::;

-- ---- ----...... ////,

......
-- :::~ ......

/// //

.~- -..--~-- :-::--:-:-- :-::---~ ----- -- -~~~-

---- ----- -- ;;~ ::::::
-- --- ----- --- -- .;....

~
~ ~
..-

:~:::;
~ ~
..~ :..:....:..

~:~ ~ :::;::;~~!!.~~ ~::::
:.___.-/.-.;-,,.;-,;--I..-__...f,,~,,,,

-- ---- .---. .- . .

~~~ ~~~~

~
~ :::::-;;::

~8::::;ts::-:-;::::::::--:~o:

........ .:.:.:.:-

.. ...... ":~.~.~~...~:.....-.:.~.:.:....:.-.:....:.:..:...::.i:-.:.-.::...:..-:...:..:::.:::.::::.:-::.::.:::..:...-:...:....:..:.~:::: ~

~

~

29

30

31

32

33

34

35

36

37

38

Longitudinal Distance X (ft )

Fig. 4.7. Numerically Predicted Velocity Vectors by 2D Turbulence Model Applied to Cross-section A.

A-34

10.00 - - - - - - - - - - - - , - - - - - - - - - - - - - - - - - - - , (V IV)- 1
ab c
1.00

r

L__ 0.10

.L.

0.1

I I --~~~~~~

1.0

[q I (M q )] - 0.4

f1

fOe

6 CROSS-SECTION A A. CROSS-SECTION B
~---------------~----------- ------~----- - - - - - - - - - - - '
Fig. 4.8. Estimate of Abutment Velocity Based on Relationship Between Alternative I and II Scour Prediction Procedures.

10.0

A-35

CROSS-SECTION A ABUTMENT VW; La/Bf=0.17; Q = 2.02 cfs 0.85 ----------------------------------------------------------~

0.80

- - - - - - - ~------- ~------- ~------- _ : _ - - - - - - -
I

0.75 I 0.70

I

- - - - - - - ~------- ~------- ~------- - 1 - - - - - - - -

I

11

I

I

~ -

--- - - -

~ :~-

- --

-: -~- -

-- - - - -

- - -- --

1--

0w... 0

0.65

---------

I

/

I iI
, I -III ~-----
1 ~~

'
_

_

_

_

_

__

_

_

I
1

_

_

_

_

_

_

_

_

I

,

0.60

~--=~~~.;;..<......;_......;;____.,...;;;;,.~---...J+.<.'.......~ / ~-~ -cQ-,~-~- ~ -c-x~_ --.....,c~ ;i---:.,:-: -~3.,><_..I~1 ..t.; _.~ij;'-- -~

'J

I 'J

lJ

T

I

I

0.55 l -------:-------:- ------~ -I- -----: ------ - i- - - - - - - -I

0. 50

LLL.L..L..L.L..L...L...L...L..L..L...L...L.~ .L.L_L_l_ '

-"---'...L..L....L..L...L..~..l_j_LL.L.L.L..L.L..L.L..L.L..L.L..L.L..L..L.L...L..L...L..L...L

LL.L..L.J

0

10

20

30

40

50

60

X-STATION, ft

' - BIGLARI (NUMERICAL) c SADIQ (MEASURED) x WSPRO

Fig. 4.9. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for La/Bf= 0.17 and Q = 2.0 cfs.

A-36

CROSS-SECTION A ABUTMENT VW; La/Bf=0.33; Q= 2.01 cfs

0.85 r
'

0.80

- - - - - - - L - - - - - - - ~ - - - - - - - ~ - - - - - - - ~ - - - - - - - ~- - - - - - -

0.75
:.::
I 0.70
Ia.-.. w 0.65
0
0.60
0.55

II - - - - - - - ~ - - - - - - - + - - - - - - - 4 -rr - - - - - ~ - - - - - - - ~ - - - - - - -

i

I

I

I

-----. -:-------' .------ i~f----. ~---- .. -J_------

i

'

I : !

'

I

I
- - -- - - - - I - - - - - - - T - - - - - -X- .::L -

- -- - - - I - - - - - - - -1 - - - - - - -

CJ,__'--..J

G IG

I

:or::

X 1A

I

- - - - - - - ~- - - - - - - l - - - - - - - J

I

I

- - - - - J - - - - - - - _I - - - - - - - -
I

0. 50 L_j_L__L_._c__~___j_L_.L..L_l_L_L_-'--'--'---L-L~L..L..l___L_L_L-L_L_i_U.'--.LJ____J_L_~___l___j__~_L_L__l___L_l___l_t__l___L_l___L_L~

0

10

20

30

40

50

60

X-STATION, ft

- BIGLARI (NUMERICAL) o SADIQ (MEASURED) X WSPRO

Fig. 4.10. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for La/Bf-=0.33 and Q=2.0 cfs.

A-37

0.85

CROSS-SECTION A ABUTMENT VW; LaBf=0.50; Q=2.02 cfs

0.80 ~ - - - - - - - ~ - - - - - - - ~ - - - - - - - ~ - - - - - - - ~ - - - - - - - -:- - - - - - -

e

- 0.75

--

-

-

-

-

-

~

-

-

-

-

-

-

-

~

-

-

-

-

-

-

-

~

-n -

-

-

-

-

I
~

-

-

-

-

-

-

-

-:

-

-

-

-

-

-

-

-i'

.......

'

I

I 0.70

- - - - - ~- - - - - -

1--

0w...
0

0.65

----- T-------; /

I

0.60

~-:-------

-~

/ I

0.55 - - --- -- ~ - ----- ~ -- -----~-If-----~--- ---- ~-------

0. 50 ___L_.L_L_j_.L_L__L_L_l_l___L_j_L_.L_L_~__L.

I '!

I

I

_L_j_L_L_j__L_.L_L_L_L_.LUJ_L_L_.L_.L_.L_.L_.L_.L_.L_.L_L_L_L_L_j__L_.L_.L__L_L_~--"-__J__j_____L . ;'

0

10

20

30

40

50

60

X-STATION, ft

'~ - BIGLARI (NUMERICAL) o SADIQ (MEASURED) x WSPRO
-----

I
-.-J

Fig. 4.11. Comparison of Computed and Measured Water Surface Profiles in Cross-section A for La/Bf= 0.50 and Q = 2.0 cfs.

A-38

CROSS-SECTION A: APPROACH ABUTMENT VW; La/Bf=0.17; Q = 2.02 cfs
3.5 6. 0 ~,-------;-----,-------,---~----;---------,-------,-

3.0

_ _ _ _ _ _ ! _ _ _ _ _ _ l _ _ _ _ _ _ I_ _ _ _ _ _ ~ _ _ _ _ _ _ 1 _ _ _ _ _ _ ;_ _ _ _ _ _

I

I

5.0 ~

2.5
~

- - 1 - - - - - - ~-----_I_-----

~ 2.0
1-
g 0 1.5

-----

-~------

I
~------

- - - - - - T - - - - - - ,- - - - - -

3.0

> w

I

>:

{

X

'

1....__ _X_..__X ___..A.1_~...,..,..~2.0

1.0

- - - - - -~------------- ~-------------I------------



0. 0 c_____c__ ..L__~---___j___.L__....J.__~_J._______j_

0

1

2

3

4

_ _ l __
5

TRANSVERSE STATION ,ft

_ _ _ L __

_ _ _ l __
6

0. 0 _L____L
7

! - BIGLARI SADIQ ~ WSE -BED

X WSPRO I

Fig. 4.12. Comparison of Computed and Measured Velocity Distributions in Cross-section A for La/Bf= 0.17 and Q = 2.0 cfs.

A-39

CROSS-SECTION A: APPROACH ABUTMENT VW; La/Bf=0.33; Q=2.01 cfs

3.0

I

I

I

I

------~------I------~-------~-------------~------

5.0

z

2.5

-- _;_----- l--

__ I __

0

4.0 ~

I

~ 2.0

- - - - - - 1 - - - - - - ~------ 1-

---1------

w

_J

0

3.0 w

0
_J

1.5

> w

1.0

---t---

-- - 1- - -- - - -

I ~

I

I

- - 1 - - - - - - - 1 - - - - - - T - - - - - -~----X-

2.0

0
m w
~
w

0 5 1==:::;;:;::::;;:;::!;;;;;;;:;::;;:;::::;;:;:::::;;;;;;::;;:;::~:;-=-:::--::-=----::-;!xI::;;:;::::;;:;::;;;;;;:I:::::::;;:;::::;;:;::::::::!:::;;:;::::;;:;::~ 1.0 ~

.

1

0. 0 L_~--

_

0. 0 ______j __L__ _ _ ____________j__ _ _ _l _ __ _ _c _ __ _ _____j_ _ ____l__ _

0

1

2

3

4

5

6

7

TRANSVERSE STATION, ft

r I - BIGLARI SADIQ -

WSE

-BED

X WSPRO I

_ _ _ _ _ _ _ _j

Fig. 4.13. Comparison of Computed and Measured Velocity Distributions in Cross-section A for La/Bf=0.33 and Q=2.0 cfs.

A-40

CROSS-SECTION A: APPROACH ABUTMENT VW; La/Bf=0.50; 0=2.02 cfs
3.5 6. 0 ,---------------,---~------,--------,------,---~-----,

- x - - - -.- - - e- - Te- - - -


- - - -.- - -e - - ~- - -.- x -

w

en

0.5 ~==:::::r::====::::::::====:r;-------=---~::.::::==:::::c====::r:::==~ 1.0 s

I
0.0 I ------+----~----+----+-------+----:1-----,

0

1

2

3

4

5

TRANSVERSE STATION, ft

- Biglari SADIQ - WSE__-_-:__B_E_D___x_W_SPRO]
1

Fig. 4.14. Comparison of Computed and Measured Velocity Distributions
in Cross-section A for La/Bf= 0_50 and Q = 2.0 cfs

A-41

CROSS-SECTION 8 ABUTMENT VW; La/Bf=0.22; Q=3.0 cfs

0.85

0.80

_______ L _______ ~ _______ ~ ________I ________ I_______ _

_______ _______ _______ -n _____ 0.75

~

~

~

-1- ______ -I- ______ _

I

i

I

I

I

I

r ; :T .---, ~
I

0.70

r-------

~---

---- i-------

~

-~~----- ,------- -!--------

1o._-
w 0.65
0

:
--li --li-' ~--

:

: I'

:

Tx ~.-;; -.- rr~. ~.

:

I

~-

r 1- l--- 0.60 ~ ~ ~ ~ ~ ~- ~-- ~ ~-- ~

~ ~-- ~ ~ ~-

~- -~---- ~-- ~~-----~~~I

l 0.55 I

r - ----- ----: ~ - ---- -~J- --- -i- -

- ! ---

-

0. 50 l__LJ~_L_L__LJ_L_LJ_~__j__L...LJ_L...L...C....L.L_...L...L._L...L...L...L_L~L_L_J_...LJ_.L..C..-'___L__L...L...L._L_L_J__J_J__L_L__'--l_L_L..j_..L..l.....L.J

0

1 0

20

30

40

50

60

X-STATION, ft

MEASURED DEPTH - NORMAL DEPTH X WSPRO
Fig. 4.15. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for La!Bf= 0.22 and Q = 3.0 cfs.

A-42

CROSS-SECTION 8 ABUTMENT VW; La/Bf=0.44; Q=3.0 cfs

0.85 ~--------------~---------~

r------- ------- ------- rr
o.8o

I

I

~

~

I

I

I

_jl- - - - - - - -:- - - - - - - -:- - - - - - - -

t-

I

I

o. 75

fIf

---

-

--

-

I
~

-

---

---

~

----

---

i
~

-n------:I --------:I-

------

-

~

t , ! I1

I

i

~ II , ,

.

I

0.70 ~------- + - - - - - - - - - t - - - - - - - 4 -~ - - - - - -~------- - 1 - - - - - - - -

I

r

I

,

.

I I,

I

,

t:L 0.65 - - - - - w

If

< /:

.: !

I -.-- - - . - - i - - - - - - - "l -

0

1

'

1

I
X 1 ~X:

0.60

t --- ""
l

---:i -------:Ii --------:1i -----:- -~-~l---e..I

-- -

----:II-

------

-I1 I

-' --------: -:--- ----:------ - 0

.

5

:
5

[-.

-

-c~----: :-------

I

I -~I:----- I

I

:

_i

050

i

'

-->--L-L.L_L_U_L

I i

I

I

I


0

1 0

20

30

40

50

60

X- STATION, ft

I MEASURED DEPTH - NORMAL DEPTH X WSPRO
Fig. 4.16. Comparison of Computed and Measured Water Surface Profiles in Cross-section B for La/Bf=0.44 and Q=3.0 cfs.

A-43

CROSS-SECTION B ABUTMENT VW; La/Bf=0.66; Q=3.0 cfs

0.85

0.80

I

I

~ ~ ~ ~ ~ ~ ~ L ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~ ~ ~ ~ ~ ~ ~ ~~~ ~ ~ ~ ~ ~ ~ ~

I

MEASURED DEPTH - NORMAL DEPTH x WSPRO
Fig. 4.17. Comparison of Computed and Measured Water Surface Profiles
in Cross-section B for La/Bf= 0.66 and Q = 3.0 cfs.
A-44

CROSS-SECTION 8: APPROACH ABUTMENT VW; La/Bf=0.22; Q=3.0 cfs
2.0

1.6

X ~

:

I

,

I

I

I



- -- - - - :,..._ - - - - - - r- - - - - - - !-- - - - - - - i- - - - - - - 1- - - - - - - 1- - ->~- ~-

I



U)
~
>--
1--
0
0uj

1.2 0.8

L- - - - - - L - -

I

~ I -~ .
, - _ - -

-

'
;

-

-I~-

--

-

--
,""'
--

-

-L -
'
- :- -

-

-v "
--

-

- :_ -
~: -
:
- I~- -

-

-/
--

-

.- I_ x
I I - 1- -

-

--
x
'
--

-

.- I_ ::><
- II~- -

-

-

-

-

.I.I ~
- I_ - - -
xl - II~- - - -

-

--
X-

>

0.4 ~- - -~ - - - - r

-- - - - - - ~ - - - - - - - ~- - - - - - 1- - - - - - - !- - -

r
0' 0 l___L__~_..L_......J__~"--L---~~_

_L_.____~_l____L__o _t____L___L_~~ _L_.....L.___L.__j____L---'~

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

TRANSVERSE STATION, ft

' MEASURED VELOCITY x WSPRO
Fig. 4.18. Comparison of Computed and Measured Velocity Distributions
in Cross-section B for La/Bf= 0.22 and Q = 3.0 cfs.

A-45

CROSS-SECTION 8: APPROACH ABUTMENT VW; La/Bf=0.44; 0=3.0 cfs
2.0 ~---------------------------

l

I

I

1.6 [- - e ! ~ ~ ~

~ ~ II~ ~ ~

-

-

~ ~ t,~ ~ ~ ~ ~ ~ ~ II~ -

I ~ ~ ~ ~ ~ ,-

~ ~ ~ ~ ~ ~!! ~ ~ ~ ~ ~ ~ ~II ~ ~

~ ~

~
~ 1.2
1-
0 0
_j
> w

I

I

'

I

i

I

--- i------- 1----- ---I------ -1-

I







X

r

0. 4 rI

I

~ ~ ~ ~ ~ ~r

I

I

I

I

I

~ ~ ~ ~ ~ ~ !~ ~ .. ~ ~ ~ ~ I~ ~ ~ ~ ~ ~ ~ I~ ~ ~ ~ ~ ~ ~I~ ~ ~ ~ ~ ~ ~I~ ~ ~ ~ ~ ~

r

o. o L--'---'---'-"-----'-----'---.L..--L___L____L___j__J______L___j___L__L____L___L____j_..L..__C--.L.___j__-'----~

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

TRANSVERSE STATION, ft

' MEASURED VELOCITY x WSPRO

l

Fig. 4. 19. Comparison of Computed and Measured Velocity Distributions in Cross-section B for La/Bf=0.44 and Q=3.0 cfs.

A-46

CROSS-SECTION 8: APPROACH ABUTMENT VW; La/Bf=0.66; Q=3.0 cfs
2.0 ~----~------~------~------~----~------~-------

1.6

- - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - -

~ >-- 1.2
1-
0
0u:l 0.8
>

I

I

I

I

i

I

l

l

I

~

_ _ _ _ _ _ I_ _ _ _ _ ~- _ I_ _ _ _ _ _ _ I_ _ _ _ _ _ _ I_ _ _ _ _ _ _ ~~- _ _ _ _ _ _ I__ _e_ _ ._ _

I

1

X

I

X e

I

I

I

I

I ~

I

:-:x:- -I I

i

I

I

>- - - - - -;:: - :- x- -

~c - ;Y:- - ; :- - ;-;::_- - 7-

I



!

-7 - -~ - -x - -x :-:;,: - - - -

I

:



~

I

I

:

0.4

Ir
~------ ~~------ 1 - - -
~

I

1

X

i'

- I -~--- ~------- ! - - - - - - - - r - - - - - - - t - - - - - -

I

I

I

I

I

0.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

TRANSVERSE STATION, ft

MEASURED VELOCITY x WSPRO
Fig. 4.20. Comparison of Computed and Measured Velocity Distributions in Cross-section B for La/Bf= 0.66 and Q = 3.0 cfs.

A-47

2.0

1.5
en
~
'I-

>...--

0

w
f-

1.0

:5

:::>

0
_J

<(

0

0.5

I
I

ID

L

I I

-~~~.
~DL ~ .A.

/'-'

, - - - - - - - -c~ll/_ - - - - - - - - .._ -

41

I

I I

~~~ ... :

I

~

'D-

-

-

-

-

-

-

-.761/

-

-

-

-

-

-

-

-

--I

-

-

-

-

-

-

-

-

-

I T

-

-

-

-

-

-

-

-

-

/ '

IL 1 w:PRO: xs-A; vw
120: XS-A; VW
I D I WSPRO: XS-8; vw
I
I WSPRO: XS-8; ST

0.0

t

1/

___ l'~.

_____j _

_L___..l......__!__-.---.L...,.~

0.0

0.5

1.0

MEASURED V1, ft/s

1.5

2.0

Fig. 4.21. Comparison of Computed and Measured Approach Velocities for Cross-sections A and B.

A-48

0.40:

0.30

D
- - - - - - - - - 1 - - - - - - - - - ~- - - - - - - - -

r-::-~-------
1 ~

.>..---
0w~ 0.20 '~ ---.

I WSPRO: XS-A; vw

D /.

I

I ,.

12: :

~-

~~- W~PRO: :- - - - - --- -

,

o& J21

- . - - - - !. - . - - - - - - - I

I

I

XS-A;VW
XS-8; vw

::J 0
_.J
<(
0
0.10

.,Q : s:l ~v/ I

I

I

I

1

Q~

:

:

II

- - - - - - - - - ~~- - - - - - - - - ~ - - - - - - - - T - - - - - - - - -

WSPRO: XS-8; ST

,

,

'

I

0.00 I l'--.. _ _ _ _L. _ __ _ j _ __~-----_L_~-

0.00

0.10

0.20

MEASURED yf1, ft

I
.J_____j ___L_._ _

0.30

0.40

Fig. 4.22. Comparison of Computed and Measured Approach Floodplain Depths for Cross-sections A and B.

A-49

1.0
0.8
~
6J 0.6 ~
::::> 0
~ 0.4
0

'

~:~ ;

. '\L /

:

;

~ :y.

..

-

-

-

-

-.

-

-

-

-

-

-

_, ;

-

-

-

-

-

-

.J :

-

-

- - :.
~I
./tt:J.I I

_" - - -- -

'//

; ./....If._

I

- - - -~--
I

-

-

~ I /-

,.
----

-

I
T -

-

-

-

-

-

-

./ 21 ?D1e

1
I

I

I

[]

I

I

- - - - l - - - - - - - T- - - - - - -

D

lu
WSPRO: XS-A; VW A
20: XS-A; VW D
WSPRO: XS-B; VW

WSPRO: XS-B; ST

0.2

L--
i

~

I

- - - - - I - - - - - - - -I - - - - - - -

I

I

0. 0 "'~-~ ~.~._J_.L_ __ -'----L_

0.0

0.2

0.4

0.6

0.8

1.0

MEASURED M

Fig. 4.23. Comparison of Computed and Measured Discharge Distribution Factors for Cross-sections A and B.

A-50

CROSS-SECTION B SEDIMENT A: All Abutment Lengths 10.0 --------------------------------------------------------

9.0

dst I Ym

I

8.0 '

7

.

o

L
i

r

6.0 ~

5.0 ~

4.0 3.0

. .... ... ... ~~+



~

2.0



1.0 ~

o. o L_____~ --~--'-~~-~ -~-Ll. ~ - -----1".. ___j____l___j...........J_L____l__Lj_ _ _____________..___

__j __;__L_.l__L_L_

i I
---'------'---'---'--~

1.0E+03

1.0E+04

1.0E+06

1.0E+07

Vr=1.23 z Vr=1.26 Vr=1.29 6 Vr=1.51 + Vr=1.58 Y Vr=1.86l
1
Fig. 4.24. Time Development of Scour Depth for Cross-section B and Sediment A in Dimensionless Form.

A-51

CROSS-SECTION 8
SEDIMENT 8: All Abutment Lengths 10.0 ------------------------------------------------

9.0.

d I y 8.0 ~
st fO
7.0 :

6.0 ~. 5.0 c-

.... ....

.... ....

4.0 : 3.0 ~ 2.0 .
1.0 '

,.,. ......

.A. X
,X/-

X

-..








yx




0. 0

i
L_________j_______j-

__.L__.i_____._l____._L___L_j____l____ _ _ _ _ l___ _____L__ _____L________L_j___L___l___]~_ _____L__ __J___l_______l___.L_l--L.L....__

1.0E+03

1.0E+04

1.0E+05

1.0E+06

~ t/ yfO

1.0E+07

Vr=1.24 x Vr =1.32 Vr=1.35 .& Vr=1.61 j

Fig. 4.25. Time Development of Scour Depth for Cross-section B and Sediment B in Dimensionless Form.

A-52

CROSS-SECTION 8 SEDIMENT C: All Abutment Lengths 10.0 --------------------------------------~~~-~YY~.-.__V_r_=_V_a_b/_V_c__

d Iy
st fO

9.0 r-

a.o

r
1

t I
7.0

r I
6.0

r 5.0

l4.0 f
3.0

+ ,:::,. + +
~

2.0 i
1.0 ~

o.o L-----'---'----'--'--'--'-Ll__--'-_____L_"--'---'.--'-LLJ_---'---'----L___l_L_L..L.L.L_-'------''---'-"--'--'-LLJ

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

Vet/ yfO

.., -

I I
I

Vr=1.52 z Vr=1.59

Vr=1.79 !'c. Vr=1.90 I

I + Vr=2.02

Vr=2.23 X Vr=2.45 [81 Vr=2.55 I

--------------~----

Fig. 4.26. Time Development of Scour Depth for Cross-section B and Sediment C in Dimensionless Form.

A-53

10.0 ------------------------------------==~--------~

SYMBOL
L,'

--~~- 2.50



d Iy
st fO

9.0 ' FILL d50 mm " - - - - - -

-- - - -1I

3-.~- ~ ~ 8.0 r-N-on_e___

r- - - - - - - - --- + - -- - -- - - - - - ___________

t Solid

2.7

7.0 r Dots

1.2

f

j
'

6.0 ~ - - - - - - - - - - r - - - - -

~

1.0E+04

1.0E+06

1.0E+07

SYMBOL SHAPE ; Li Vr=1.25 c Vr=1.50

D Vr=2.0

z Vr=2.5 - BEST FIT I

Fig. 4.27. Consolidation ofDimensionless Time Development Data and Least-Squares Fits for Sediments A, B, andC .

A-54

BURDELL CREEK
D.A. = 375 SQ. MI.
25 --------------------------------------------------~

I

I

f EXIT SECTION !

20

I i

I

I

I

I---------,---------'-------

I

I

I

I !

-- T--------- I---------;

I

'

'

f--

r\1 1

'

I '

' I

I I

~I

2 -.--A u_

~ ,

i

:

I

i

~15 ""\, ---- :-~~0~;2- ~1-n-~~-~~~~-~~-0-;3~-:

~ 10 l . --~~-~~~-------- b~- -!

w I

I

I~

.,.

I

'

---------;- -------- f

I

I

\

;:

1

!

5 r---------~- -- --- ---~- --~.-I- ~

I

w

0 ~-~---~L- ________l__________ _ J _ _ __ _j _ _ _~

0

500

1000

1500

TRANSVERSE STATION, FT

2000

2500

Fig. 4.28. Burdell Creek Cross-section for Estimation of Clear-water Abutment Scour.

A-55

BURDELL CREEK
D.A. =375 SQ. MI.; 0100; TL =15 HRS
20000 ~I----------------~----------~----~----~--~

18000 ' - - - - - I - - - - - - - - - - - ' - - - - - ' - - - - - I - - - - - -~ - - - - - - - - - - - -

16000 ~ ~ ~ -1 r - - - - - - - - - - T - - - - - T - - - - - , - - - - - - - - - - - - - - - -1- - - - -

I

I

I

I

I

I

I

14000

I I

I

i - - - - - t- - - - - - + - - - __.._ - - - - - -+ - - - - - -j - - - - - -j - - - - - -I - - - - - -

I

I

.



I

I

I

I

I

I



!

12000 _ _ _ _ _ L ___ - - L ) - ' - - - ~- - - - J - - - - - ~-----~------I------~

.\~~: ~ (/)
LL
0 10000
a : : ..:. f. :::/.:. :. ;: .

: : . : . : . : :: ... : :: ... : :

8000

I

J I

I

I



I

I

I

I

6000

I

I

I

I

- - - - - I - - - - I - - - - - T-

I



I

I

I

- - I - - - - . ; I - - - - - -1 - - - - - -r - - -

:

4000

---

-

-

,_I

'

I



~

-

-

-

I
,
~ -

--

-

-

I I
~- - -

-

-

I
~ -

--

' -:-

I

I

I.

I

I

- - -----~~- - - - -

-- - -

2000

~-~- ~ ~ ~- i - -

-

-

-

-

-

- - - - - T - - - - -- -f - - - - -

-----

-- -

0

0

5

10

15

20

25

30

35

40

TIME, HRS

Fig. 4.29. Design Hydrograph for Burdell Creek.

A-56

APPENDIX B. WSPRO DATA AND RESULTS

Table B.l - WSPRO Input Data File for Burdell Creek - QlOO.
*F SI 0 T1 ABUTMENT SCOUR EXAMPLE * Q 14000 SK 0.001 * XS EXIT 750 0.0 0.5 0.0 0.001 GR 0, 19 100, 15 200, 11 500, 10.75 900, 10 1100, 9.0 GR 1215, 5.5 1250, 4.9 1300, 3.05 1350, 4.85 1385, 5.1 GR 1500, 9.0 1700, 10 2100, 10.75 2400, 11 2500, 15 GR 2600, 19 N 0.042 0.032 0.042 SA 1100 1500
*
XS FULV 1500 0.0 0.5 0.0
*
BR BRDG 1500 * 0.0 0.5 0.0 * BL 0 750 1100 1500 BC 18 CD 3 50 2 22 0.0 0.0 0.0 AB 2 2 PD 0 5.65 30 6 N 0.042 0.032 0.042 SA 1100 1500
* xs APPR 2300 0.0 0.5 0.0
* HP 2 APPR 13.25 0 13.25 14000 HP 2 APPR 13.64 0 13.64 14000 * DA BRDG 1 1 * * 14000 1 * EX 0 ER
B-1

Table B.2 - WSPRO Water Surface Profile Output for Burdell Creek - QlOO

************************* W S P R 0 ***************************

Federal Highway Administration

U. S. Geological Survey

Model for Water-Surface Profile Computations.

Input Units: English I Output Units: English
*---------------------------------------------------------------*

ABUTMENT SCOUR EXAMPLE

WSEL VHD

EGEL

HF

CRWS

HO

Q
v
FR #

AREA
K
SF

SRDL

LEW

FLEN

REW

ALPHA

ERR

Section: EXIT

Header Type: XS

SRD:

750.000

Section: FULV Header Type: FV S RD : 1 5 0 0 . 0 0 0

11.696 .268
11. 964 ****** 9.447 ******

14000.000 2.965 .504

4721.088 *********

442473.00 *********

******

1. 960

182.604 2417.396
******

12.449 12.716 10.197

. 267 14000.000 4728.060

.750

2.961 443183.70

.000

.502

.0010

750.000 182.526

750.000 2417.474

1. 959

.003

<<< The Preceding Data Reflect The "Unconstricted" Profile >>>

Section: APPR Header Type: AS SRD: 2300.000

13.250 13.517 10.997

.267 14000.000 4730.357

.798

2.960 443418.00

.000

.502

.0010

800.000 182.500

800.000 2417.500

1. 959

.003

<<< The Preceding Data Reflect The "Unconstricted" Profile >>>

<<< The Following Data Reflect The "Constricted" Profile >>> <<< Beginning Bridge/Culvert Hydraulic Computations >>>

Section: BRDG Header Type: BR SRD: 1500.000

WSEL VHD

Q

AREA

SRDL

LEW

EGEL

HF

v

K

FLEN

REW

CRWS

HO

FR #

SF

ALPHA

ERR

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

12.470 .470 14000.000 3038.370 750.000 936.685

12.940 .921

4.608 386306.30 750.000 1663.315

10.668 .055

.474

******

1. 424

-.004

Specific Bridge Information c
Bridge Type 3 Flow Type 1 ------

Pier/Pile Code 0

.8380

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

P/A PFELEV BLEN

XLAB

XRAB

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

.067 18.000 750.000 940.750 1659.250
-------- -------- -------- --------

Section: APPR Header Type: AS SRD: 2300.000

WSEL VHD

Q

AREA

SRDL

LEW

EGEL

HF

v

K

FLEN

REW

CRWS

HO

FR #

SF

ALPHA

ERR

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

13. 635 .186 14000.000 5595.480 750.000 172.865

13.822 .780

2.502 536819.40 776.571 2427.135

10.997 .100

.387

.0010

1. 914

-. 017

Approach Section APPR Flow Contraction Information

M( G ) M( K )

KQ

XLKQ

XRKQ

OTEL

.675

.189 438924.8 938.577 1661.368 13.635

B-2

Table B.3 - Velocity Distribution from HP Record for Unconstricted Flow at Approach Section - QlOO.

************************* W S P R 0 ***************************

Federal Highway Administration

U. S. Geological Survey

Model for Water-Surface Profile Computations.

Input Units: English I Output Units: English

*---------------------------------------------------------------*

ABUTMENT SCOUR EXAMPLE

***

Beginning Velocity Distribution For Header Record APPR

***

SRD Location: 2300.000

Header Record Number 4

Water Surface Elevation:

13.250

Element # 1

Flow: 14000.000 Velocity: 2.96 Hydraulic Depth: 2.116

Cross-Section Area: 4730.38

Conveyance: 443419.90

Bank Stations -> Left:

182.500 Right: 2417.500

X STA. A( I V( I D( I

182.5

803.7 628.6
1.11 1. 01

1045.3 454.8
1. 54 1. 88

1141.7 279.4
2.51 2.90

1181. 9 184.1
3.80 4.58

1209.7 156.0
4.49 5.62

X STA. A( I V( I D( I

1209.7

1232.9 146.1
4.79 6.30

1253.5 138.2
5.07 6.69

1271.9 133.4
5.25 7.27

1288.1 128.5
5.45 7.91

1302.5 121.2
5.77 8.46

X STA. A( I V( I D( I

1302.5

1317.4 124.2
5.64 8.29

1333.9 127.1
5.51 7.73

1352.7 133.8
5.23 7.10

1373.2 138.2
5.07 6.76

1394.8 141.8
4.94 6.55

X STA. A( I V( I D( I

1394.8

1421.9 157.2
4.45 5.81

1458.5 172.9
4.05 4.73

1558.5 290.7
2.41 2.91

1799.0 449.8
1. 56 1. 87

2417.5 624.5
1.12 1. 01

B-3

Table B.4 -Velocity Distribution from HP Record for Constricted Flow at Approach Section - QlOO.

************************* W S P R 0 ***************************

Federal Highway Administration

U. S. Geological Survey

Model for Water-Surface Profile Computations.

Input Units: English I Output Units: English
*---------------------------------------------------------------*

ABUTMENT SCOUR EXAMPLE

***

Beginning Velocity Distribution For Header Record APPR

***

SRD Location: 2300.000

Header Record Number 4

Water Surface Elevation:

13.640

Element # 1

Flow: 14000.000 Velocity: 2.50 Hydraulic Depth: 2.487

Cross-Section Area: 5605.83

Conveyance: 537996.80

Bank Stations -> Left:

172.750 Right: 2427.250

X STA. A( I V( I D( I

172.7

684.7 658.8
1. 06 1. 29

945.3 506.4
1. 38 1. 94

1101. 6 423.1
1. 65 2.71

1161.2 241.3
2.90 4.05

1195. 4 187.3
3.74 5.47

X STA. A( I V( I D( I

1195. 4

1223.0 176.6
3.96 6.40

1246.6 163.5
4.28 6.93

1268.0 159.7
4.38 7.47

1286.0 147.8
4.74 8.19

1302.5 144.8
4.83 8.81

X STA. A( I V( I D( I

1302.5

1319.1 143.9
4.87 8.65

1338.0 151.0
4.64 8.01

1359.2 156.4
4.48 7.35

1382.3 163.7
4.28 7.09

1407.8 169.5
4.13 6.64

X STA. A( I V( I D( I

1407.8

1441.5 190.1
3.68 5.64

1497.0 229.2
3.05 4.13

1658.1 435.6
1. 61 2.70

1917.6 502.4
1. 39 1. 94

2427.3 655.0
1. 07 1. 29

B-~