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Federal Highway Administration Research and Technology
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REPORT 
This report is an archived publication and may contain dated technical, contact, and link information 
Publication Number: FHWAHRT09041 Date: October 2009 
Publication Number: FHWAHRT09041 Date: October 2009 
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The Bridge Pressure Flow Scour for Clear Water Conditions Study described in this report was conducted at the Federal Highway Administration's (FHWA) TurnerFairbank Highway Research Center (TFHRC) J. Sterling Jones Hydraulics Laboratory. The study was in response to a request of several State transportation departments asking for a new design guidance to predict bridge pressure flow scour for clear water conditions. The new pressure flow scour procedure will replace the existing pressure flow scour prediction method in the FHWA Hydraulic Engineering Circular No. 18 (4th edition) Evaluating Scour at Bridges. The study includes experiments (physical modeling) at the Hydraulics Laboratory. This report will be of interest to hydraulic and bridge engineers who are involved in estimating pressure flow scour for inundated bridge decks. This report is being distributed as an electronic document through the TFHRC Web site (www.fhwa.dot.gov/research/tfhrc/).
Cheryl Allen Richter
Acting Director, Office of Infrastructure
Research and Development
Notice
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TECHNICAL REPORT DOCUMENTATION PAGE
1. Report No. FHWAHRT09041 
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15. Supplementary Notes 

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CHAPTER 1. INTRODUCTION
CHAPTER 2. LITERATURE REVIEW
CHAPTER 3. EXPERIMENTAL STUDY
CHAPTER 4. ANALYTICAL STUDY OF MAXIMUM SCOUR DEPTH
CHAPTER 5. DESIGN PROCEDURE AND APPLICATION EXAMPLES
CHAPTER 6. FURTHER RESEARCH NEEDS
CHAPTER 7. CONCLUSIONS
APPENDIX A. MAXIMUM SCOUR DEPTH FOR CASE 1
APPENDIX B. DERIVATION OF PRESSURE UNDER BRIDGE DECK
ACKNOWLEDGEMENTS
REFERENCES
Figure 1. Photo. Partially inundated bridge deck at Salt Creek, NE
Figure 2. Photo. Completely inundated bridges at Cedar River, IA
Figure 3. Equation. Arneson and Abt's scour depth equation
Figure 4. Equation. Upstream critical velocity
Figure 5. Equation. Lyn's scour depth equation
Figure 6. Equation. Umbrell et al.'s scour depth equation
Figure 7. Equation. Modified Umbrell et al. scour depth equation
Figure 8. Photo. Approach section of the test flume
Figure 9. Illustration. Plan and side schematic of the test flume
Figure 10. Illustration. Detail of sand bed and sediment recess in test flume
Figure 11. Illustration. 3D view of a sixgirder bridge deck
Figure 12. Illustration. Cross section view of a sixgirder bridge deck
Figure 13. Illustration. Cross section view of a threegirder bridge deck
Figure 14. Equation. Operating discharge Q
Figure 15. Photo. Automated flume carriage with laser distance sensor perched over the test flume
Figure 16. Graph. 3D scour map at equilibrium scour
Figure 17. Graph. Scour profiles at various bridge openings for the threegirder bridge deck
Figure 18. Graph. Scour profiles at various bridge openings for the sixgirder bridge deck
Figure 19. Graph. Scour profiles at various bridge openings for the sixgirder bridge deck (d_{50} = 0.078 inches (2 mm))
Figure 20. Graph. Similarity profile for equilibrium scour for the threegirder bridge deck
Figure 21. Graph. Similarity profile for equilibrium scour for the sixgirder bridge deck
Figure 22. Equation. Similarity scour profile, x is less than or equal to zero
Figure 23. Equation. Similarity scour profile, x is greater than zero
Figure 24. Equation. Xcoordinate of scour initiation
Figure 25. Equation. Xcoordinate of scour initiation normalized to bridge width
Figure 26. Equation. Upstream dimensional abscissa, x1
Figure 27. Equation. Dimensionless abscissa upstream
Figure 28. Equation. Distance from scour initiation position to bridge deck face
Figure 29. Equation. Initiation of sediment deposition position
Figure 30. Equation. Dimensionless abscissa downstream
Figure 31. Equation. Distance from bridge deck to deposition position
Figure 32. Equation. Scour depth at deck edges
Figure 33. Graph. Normalized scour profile
Figure 34. Graph. Arneson and Abt's scour depth equation agreement with experimental data
Figure 35. Graph. Lyn's scour depth equation agreement with experimental data
Figure 36. Graph. Umbrell et al.'s scour depth equation agreement with experimental data
Figure 37. Illustration. Plan view of bridge over stream
Figure 38. Illustration. Pressure flow for case 1
Figure 39. Illustration. Pressure flow for case 2
Figure 40. Illustration. Pressure flow for case 3
Figure 41. Equation. Energy equation along streamline 12
Figure 42. Equation. Pressure under the bridge, p2
Figure 43. Equation. Energy equation including curvature coefficient
Figure 44. Equation. Model describing difference bridge energy loss coefficient and curvature coefficient
Figure 45. Equation. Energy equation including empirical parameters
Figure 46. Equation. Rearrangement of energy equation including empirical parameters
Figure 47. Equation. Continuity equation
Figure 48. Equation. Pressure flow scour design equation
Figure 49. Equation. Downstream flow depth approximation
Figure 50. Equation. Inundation Froude number
Figure 51. Equation. Pressure flow scour design equation including inundation Froude number
Figure 52. Equation. Effective velocity equation
Figure 53. Graph. Scour number versus inundation Froude number
Figure 54. Equation. Unit discharge
Figure 55. Equation. Velocity at maximum scour section
Figure 56. Equation. Pressure flow scour design equation including effective velocity
Figure 57. Equation. Deck block depth for cases 2 and 3
Figure 58. Equation. Inundation Froude number for cases 2 and 3
Figure 59. Equation. Effective velocity for cases 2 and 3
Figure 60. Equation. Maximum scour depth calculation
Figure 61. Graph. Maximum scour depth versus bridge opening height
Figure 62. Graph. Maximum scour depth versus bridge thickness
Figure 63. Equation. Critical velocity
Figure 64. Equation. Manning coefficient
Figure 65. Equation. Critical velocity
Figure 66. Equation. Dimensionless diameter
Figure 67. Equation. Critical Shields number
Figure 68. Equation. Critical approach velocity
Figure 69. Equation. Deck block depth evaluation
Figure 70. Equation. Inundation Froude number evaluation to determine pressure flow
Figure 71. Equation. Scour depth evaluation
Figure 72. Equation. Maximum scour depth position
Figure 73. Equation. Equilibrium scour profile equation, x is less than or equal to zero
Figure 74. Equation. Equilibrium scour profile equation, x is greater than zero
Figure 75. Equation. Simplified equilibrium scour profile equation, x is greater than zero
Figure 76. Graph. Scour profile for example problem
Figure 77. Equation. Scour depth at the upstream deck edge
Figure 78. Equation. Maximum scour depth solution
Figure 79. Equation. Downstream flow depth
Figure 80. Equation. Critical Shields number approximation by Guo
Figure 81. Equation. Shields number
Figure 82. Equation. Dimensionless diameter
Figure 83. Equation. Energy equation between points 1 and 2
Figure 84. Equation. Scour depth
Figure 85. Equation. Bernoulli equation across streamlines
Figure 86. Equation. Bernoulli equation applied to circular streamlines
Figure 87. Illustration. Radii of curvature
Figure 88. Equation. Integration of figure 86
Figure 89. Equation. Bernoulli equation solved at point 2
Figure 90. Equation. Pressure at point 2 when V_{b} equals zero
Figure 91. Equation. Solution for integration constant
Figure 92. Equation. Pressure at point 2
Figure 93. Equation. Curvature coefficient
Figure 94. Equation. Pressure at point 2 with curvature coefficient simplification
Table 1. Experimental results for the threegirder bridge (d_{50} = 0.039 inches (1 mm))
Table 2. Experimental results for the sixgirder bridge (d_{50} = 0.039 inches (1 mm))
Table 3. Experimental results for the sixgirder bridge, (d_{50} = 0.078 inches (2 mm))
Table 4. Maximum scour depth estimates by four different methods
LIST OF ABBREVIATIONS AND SYMBOLS
Abbreviations  

2D  Twodimensional  
3D  Threedimensional  
FHWA  Federal Highway Administration  
TFHRC  TurnerFairbank Highway Research Center 
Symbols  

a 
Deck block depth  
b  Thickness of bridge deck including girders  
B  Width of a river  
d_{*}  Dimensionless sediment diameter  
d_{50}  Median diameter of sediment  
F  Inundation Froude number  
Fr  Froude number  
g  Gravitational acceleration  
h  Downstream flow depth in case 1  
hb  Bridge opening  
hd  Bridge downstream flow depth  
hu  Depth of headwater  
Kb  Bridge energy loss coefficient  
Kp  Curvature pressure coefficient  
Ks  Critical Shields number  
m  Fitting parameter in the bridge energy loss coefficient  
n 
Manning coefficient, or normal direction of a streamline  
p1  Pressure at point 1  
p2  Pressure at point 2  
Q  Operating discharge in the flume  
q  Unit discharge of a river  
q1  Unit discharge through the bridge  
R  Local radius of curvature of a streamline  
R_{0}  Radius of curvature at the maximum scour point  
R^{2}  Correlation coefficient  
Re  Reynolds number  
s  Specific gravity of sediment  
ν  Kinematic viscosity of water  
V_{a}  Velocity through the bridge before scour  
V_{b}  Velocity through the bridge at the maximum scour depth  
V_{c}  Critical velocity  
V_{u}  Velocity of the headwater  
V_{uc}  Upstream critical velocity  
V_{ue}  Upstream effective velocity  
W  Width of bridge  
x  Coordinate along a river  
x_{1}  Coordinate of upstream face of deck  
x_{2}  Coordinate of downstream face of deck  
xd  Coordinate of initiation of deposition  
x_{s}  Coordinate of initiation of scour  
y_{s}  Maximum scour depth  
z  Vertical direction  
α_{1},α_{2}  Energy correction coefficients  
ß  Correction factor for hydrostatic pressure under bridge  
λ  An empirical fitting factor  
γ  Specific weight of water  
τ_{c}  Critical shear stress 