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Publication Number: FHWA-RD-06-138
Date: October 2006

Effects of Inlet Geometry on Hydraulic Performance of Box Culverts

 

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Errata for Effects of Inlet Geometry on Hydraulic Performance of Box Culverts Publication No. (FHWA-HRT-06-138)

 

Dear Customer:

A number of technical corrections were made to this report after the report was originally published on the Web site. The following table shows the modifications that were made to this electronic report. 

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FOREWORD

This report describes a laboratory study of culvert hydraulics done at the Turner-Fairbank Highway research Center (TFHRC) hydraulics lab in partnership with the South Dakota DOT (SDDOT). The study focused on rectangular-shaped culverts with a number of inlet geometry conditions representing inlets that are currently available for highway culverts. Design coefficients are recommended for several inlet configurations that are not specifically covered in the Federal Highway Administration Hydraulic Design Series No. 5 (HDS-5). This report will be of interest to hydraulic engineers involved in culvert design and to researchers involved in developing improved culvert design guidelines. It is being published as a Web document only.

Gary L. Henderson
Director, Office of Infrastructure
Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation.

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.

1. Report No.

FHWA-HRT-06-138

2. Government Accession No.

N/A

3. Recipient’s Catalog No.

N/A

4. Title and Subtitle

Effects of Inlet Geometry on Hydraulic Performance of Box Culverts

5. Report Date

December 2006

6. Performing Organization Code

N/A

7. Author(s)

J. Sterling Jones, Kornel Kerenyi, and Stuart Stein

8. Performing Organization Report No.

N/A

9. Performing Organization Name and Address

GKY and Associates, Inc.
5411-E. Backlick Road
Springfield, VA 22151

10. Work Unit No. (TRAIS)

N/A

11. Contract or Grant No.

DTFH61-04-C-00037

13. Type of Report and Period Covered

Final Lab Report 11-02 to 11-04

12. Sponsoring Agency Name and Address

Office of Infrastructure R&D South Dakota DOT
Federal Highway AdministrationOffice of Research
6300 Georgetown Pike700 East Broadway Avenue
McLean, VA 22101Pierre, SD 57501

14. Sponsoring Agency’s Code

SD Project
SD2002-04
FHWA Task Order 3

15. Supplementary Notes

Contracting Officer's Technical Representative: J. Sterling Jones, HRDI-07.
South Dakota Technical Panel: Mark Clausen, Noel Clocksin, Kevin Goeden, Cory Haeder, Terry Jorgensen, Paul Oien, Daris Ormesher, Rich Phillips, Steve Wagner
Brad Newlin designed models and developed preliminary analysis algorithms. Holger Dauster and Amon Tarakemeh provided invaluable assistance with instrumentation, data collection, and analysis.
Donna and Dave Pearson provided senior editing and EDP services.

16. Abstract

Each year, the South Dakota Department of Transportation (SDDOT) designs and builds many cast-in-place (CIP), or field cast, and precast box culvert structures that allow drainage to pass under roadways. The CIP boxes typically have 30-degree-flared wingwalls, and the precast have straight wingwalls with 10.16-centimeter (cm) (4-inch) bevels on the inside edges of the wingwalls and top slab. Previous research conducted on a limited number of single barrel box culverts indicated that further research was necessary to determine (1) the effects of multiple barrel structures, (2) loss coefficients of unsubmerged outlets, and (3) the effects of 30.48-cm (12-inch) corner fillets versus 15.24-cm (6-inch) corner fillets. In order to optimize the design of both types of box culverts, it was also necessary to determine the effects of span-to-rise ratios, skewed end conditions, and optimum edge conditions on typical box culvert installations

17. Key Words

Culvert, inlet, headwall, wingwall

18. Distribution Statement

No restrictions. This document is available to the public through the National Technical Information Service; Springfield, VA 22161

19. Security Classification (of this report)

Unclassified

20. Security Classification (of this page)

Unclassified

21. No. of Pages

158

22. Price

Form DOT F 1700.7 (8-72)Reproduction of completed page authorized (art. 5/94)

TABLE OF CONTENTS

1. INTRODUCTION
     PROBLEM STATEMENT
     OBJECTIVES
     PROCEDURES AND FACILITIES

2. LITERATURE REVIEW

3. THEORY AND DESIGN CALCULATIONS FOR INLET AND OUTLET CONTROL
     INLET CONTROL HYDRAULICS OF CULVERTS
     OUTLET CONTROL HYDRAULICS OF CULVERTS

4. DATA ACQUISITION AND DATA ANALYSIS PROCEDURES
     DATA ACQUISITION FOR CULVERT SETUP
     DATA MANAGEMENT
     DATA ANALYSIS FOR INLET CONTROL TESTS
     DATA ANALYSIS FOR OUTLET CONTROL TESTS

5. EXPERIMENTAL PROCEDURES
     MINIFLUME EXPERIMENTS
     CULVERT SETUP EXPERIMENTS

6. EXPERIMENTAL RESULTS
     EFFECTS OF BEVELS AND CORNER FILLETS
     EFFECTS OF MULTIPLE BARRELS
     EFFECTS OF SPAN-TO-RISE RATIO
     EFFECTS OF HEADWALL SKEW
     OUTLET CONTROL ENTRANCE LOSS COEFFICIENTS Ke FOR LOW FLOWS (UNSUBMERGED CONDITIONS)
     OUTLET CONTROL EXIT LOSS COEFFICIENTS Ko
     FIFTH-ORDER POLYNOMIALS

7. CONCLUSIONS AND RECOMMENDATIONS
     FINDINGS AND CONCLUSIONS
     RECOMMENDATIONS

APPENDIX A. EXPANDED TEST MATRIX

APPENDIX B. INLET CONTROL COMPARISON CHARTS

APPENDIX C. SUMMARY OF REGRESSION COEFFICIENTS

APPENDIX D. EXAMPLE PROBLEM

REFERENCES

LIST OF FIGURES

Figure 1. Photo. Culvert headbox under construction
Figure 2. Diagram. Arrangement of the ceramic class pressure sensors
Figure 3. Sketch. Precast flared end section tested by Graziano and by McEnroe
Figure 4. Equation. HW/D, prefabricated metal end section, unsubmerged condition
Figure 5. Equation. HW/D, prefabricated metal end section, transition zone
Figure 6. Equation. HW/D, prefabricated metal end section, submerged condition
Figure 7. Equation. HW/D, precast concrete end section, unsubmerged condition
Figure 8. Equation. HW/D, precast concrete end section, transition zone
Figure 9. Equation. HW/D, precast concrete end section, submerged condition
Figure 10. Equation. Figure 8 in HDS-5 format.
Figure 11. Sketch. Relationship of entrance loss coefficient to Reynolds number
Figure 12. Diagram. Typical inlet control flow condition
Figure 13. Equation. Unsubmerged form 1, inlet control
Figure 14. Equation. Unsubmerged form 2, inlet control
Figure 15. Equation. Submerged form, inlet control
Figure 16. Diagram. Outlet control for full flow condition
Figure 17. Equation. Head-discharge relationship, outlet control
Figure 18. Equation. Total energy losses
Figure 19. Equation. Entrance loss
Figure 20. Equation. Exit loss
Figure 21. Diagram. Data management flow chart
Figure 22. Equation. Regression analysis, chi-squared
Figure 23. Equation. Fifth-order polynomial for HW/D
Figure 24. Equation. Entrance loss coefficient
Figure 25. Diagram. Technique to determine HLe
Figure 26. Graph. Typical behavior of Ke versus discharge intensity
Figure 27. Diagram and Photo. Miniflume and PIV setup
Figure 28. Photos. Bevel models and PIV camera at culvert entrance
Figure 29. Diagram. Integration of velocity flow field in stream functions to study culvert flow contraction
Figure 30. Diagrams. Tested bevel edge conditions and effective flow depth criterion
Figure 31. Diagram. Culvert setup-side view
Figure 32. Diagram. Culvert setup-top view
Figure 33. Photo. Culvert setup-overview
Figure 34. Photo. Culvert model barrels
Figure 35. Photo. Two-dimensional robot to measure velocity distribution in tailbox
Figure 36. Photo. Groove connectors to assemble models
Figure 37. Diagrams. Effective flow depth at vena contracta for nonrounded bevel edges
Figure 38. Diagrams. Effective flow depth at vena contracta for rounded bevel edges
Figure 39. Graph. Effective flow depth versus headwater/tailwater difference
Figure 40. Sketches. Models tested for effects of bevels and corner fillets
Figure 41. Graph. Inlet control performance curves, FC-S-0 versus PC-A, zero corner fillets
Figure 42. Graph. Inlet control performance curves, FC-S-0 versus PC-A, 15.24-cm (6-inch) fillets
Figure 43. Graph. Inlet control, precast with 15.24-cm (6-inch fillets) and field cast with 15.24-cm (6-inch) fillets
Figure 44. Graph. Inlet control, field cast hybrid inlet with 10.16-cm- (4-inch-) radius bevel on wingwalls
Figure 45. Graph. Inlet control, precast hybrid inlet with no bevel on wingwalls
Figure 46. Graph. Inlet control effects of corner fillets for the field cast model
Figure 47. Graph. Inlet control effects of corner fillets for the precast model
Figure 48. Graph. Inlet control, precast with 30.48-cm (12-inch) fillets and field cast with 15.24-cm (6-inch) fillets
Figure 49. Sketches. Models tested for the effects of multiple barrels
Figure 50. Graph. Inlet control comparison, field cast 0-degree-flared wingwall models
Figure 51. Graph. Inlet control comparison, field cast 30-degree-flared wingwall models
Figure 52. Graph. Inlet control comparison, precast models
Figure 53. Graph. Inlet control comparison, single-barrel models
Figure 54. Graph. Inlet control comparison, double-barrel models
Figure 55. Graph. Inlet control comparison, triple-barrel models
Figure 56. Graph. Inlet control comparison, quadruple-barrel models
Figure 57. Graph. Inlet control comparison, extended or nonextended center walls, field cast model
Figure 58. Inlet control comparison, extended or nonextended center walls, precast model
Figure 59. Sketches. Models tested for effects of span-to-rise ratio
Figure 60. Graph. Inlet control comparison, FC-S-0 span-to-rise ratios
Figure 61. Graph. Inlet control comparison, PC-A span-to-rise ratios
Figure 62. Graph. Inlet control comparison, FC-S-30 span-to-rise ratios
Figure 63. Graph. Inlet control comparison, 1:1 span-to-rise ratio
Figure 64. Graph. Inlet control comparison, 2:1 span-to-rise ratio
Figure 65. Graph. Inlet control comparison, 3:1 span-to-rise ratio
Figure 66. Graph. Inlet control comparison, 4:1 span-to-rise ratio
Figure 67. Sketch. Definition sketch for skew tests
Figure 68. Sketches. Models tested for effects of headwall skew
Figure 69. Diagrams. Plan view of skewed headwall models tested
Figure 70. Inlet control comparison, skew angles
Figure 71. Graph. Entrance loss coefficient versus the Reynolds number, HDS-5 8/3
Figure 72. Graph. Standard deviation of Ke versus the Reynolds number
Figure 73. Diagram. Culvert contraction
Figure 74. Equation. Expansion loss equation
Figure 75. Equation. Exit loss, with coefficient of 1
Figure 76. Equation. Downstream velocity
Figure 77. Equation. Exit loss, with coefficient Ko
Figure 78. Diagram. Flow expansion in the tailbox for high tailwater
Figure 79. Diagram. Flow expansion in the tailbox for low tailwater
Figure 80. Diagram. Vertical flow expansion in the tailbox and projected EGL
Figure 81. Graph. Transition area, unsubmerged and submerged inlet flow conditions
Figure 82. Equation. Transition area, unsubmerged and submerged inlet flow conditions
Figure 83. Graph. PC and FC single barrel models (sketches 1, 7, 11 in figure 93)
Figure 84. Graph. PC and FC multiple barrel models (sketches 1, 2, 7, 8, 11, 12 in figure 93)
Figure 85. Graph. Combined corner fillet data, FC-S-0 and PC-A models (sketches 7, 10, 11, 14 in figure 93)
Figure 86. Graph. Combined multiple barrel data, FC-0 models (sketches 7, 8 in figure 93)
Figure 87. Graph. Combined multiple barrel data, FC-30 models (sketches 1, 2 in figure 93)
Figure 88. Graph. Combined multiple barrel data, PC models (sketches 11, 12 in figure 93)
Figure 89. Graph. Combined span-to-rise data, FC-S-0 models (sketches 7, 9 in figure 93)
Figure 90. Graph. Combined span-to-rise data, FC-S-30 models (sketches 1, 3 in figure 93)
Figure 91. Graph. Combined span-to-rise data, PC models (sketches 10, 13 in figure 93)
Figure 92. Graph. Skewed and nonskewed headwalls, FC-T-30 models (sketches 4, 5 in figure 93)
Figure 93. Thumbnail sketches of inlets recommended for implementation
Figure 94. Graph. Inlet control, FC-S-0 and PC-A, no corner fillets
Figure 95. Graph. Inlet control, FC-S-0 and PC-A, 15.24-cm (6-inch) corner fillets
Figure 96. Graph. Inlet control, FC-S-0 and PC-A, 30.48-cm (12-inch) corner fillets
Figure 97. Graph. Inlet control, FC-S-30, FC-S-0, and PC-A
Figure 98. Graph. Inlet control, PC-A, 15.24- and 30.48-cm (6- and 12-inch) corner fillets
Figure 99. Graph. Inlet control, field cast hybrid inlet with 10.16-cm- (4-inch-) radius bevel on wingwalls
Figure 100. Graph. Inlet control, precast hybrid inlet with no bevel on wingwalls
Figure 101. Graph. Inlet control, FC-S-0, FC-D-0, FC-T-0, and FC-Q-0
Figure 102. Graph. Inlet control, FC-S-0, FC-D-0-E, FC-T-0-E, and FC-Q-0-E
Figure 103. Graph. Inlet control, FC-S-30, FC-D-30, FC-T-30, and FC-Q-30
Figure 104. Graph. Inlet control, FC-S-30, FC-D-30-E, FC-T-30-E, and FC-Q-30-E
Figure 105. Graph. Inlet control, FC-S-0 and FC-S-30
Figure 106. Graph. Inlet control, FC-D-0 and FC-D-30
Figure 107. Graph. Inlet control, FC-T-0 and FC-T-30
Figure 108. Graph. Inlet control, FC-Q-0 and FC-Q-30
Figure 109. Graph. Inlet control, FC-D-0 and FC-D-0-E
Figure 110. Graph. Inlet control, FC-T-0 and FC-T-0-E
Figure 111. Graph. Inlet control, FC-Q-0 and FC-Q-0-E
Figure 112. Graph. Inlet control, FC-D-30 and FC-D-30-E
Figure 113. Graph. Inlet control, FC-T-30 and FC-T-30-E
Figure 114. Graph. Inlet control, FC-Q-30 and FC-Q-30-E
Figure 115. Graph. Inlet control, PC-A, PC-B, PC-C, and PC-D
Figure 116. Graph. Inlet control, PC-A, PC-B-E, PC-C-E, and PC-D-E
Figure 117. Graph. Inlet control, PC-B and PC-B-E
Figure 118. Graph. Inlet control, PC-C and PC-C-E
Figure 119. Graph. Inlet control, FC-S-30, FC-S-0, and PC-A
Figure 120. Graph. Inlet control, FC-D-30, FC-D-0, and PC-B
Figure 121. Graph. Inlet control, FC-T-30, FC-T-0, and PC-C
Figure 122. Graph. Inlet control, FC-Q-30, FC-Q-0, and PC-D
Figure 123. Graph. Inlet control, FC-S-0, various span-to-rise ratios
Figure 124. Graph. Inlet control, FC-S-30, various span-to-rise ratios
Figure 125. Graph. Inlet control, PC-A, various span-to-rise ratios
Figure 126. Graph. Inlet control, FC-S-0, FC-S-30, and PC-A, 1:1 span-to-rise ratio
Figure 127. Graph. Inlet control, FC-S-0, FC-S-30, and PC-A, 2:1 span-to-rise ratio
Figure 128. Graph. Inlet control, FC-S-0, FC-S-30, and PC-A, 3:1 span-to-rise ratio
Figure 129. Graph. Inlet control, FC-S-0, FC-S-30, and PC-A, 4:1 span-to-rise ratio
Figure 130. Graph. Inlet control, FC-T-30 at various headwall skews
Figure 131. Graph. Inlet control, FC-S-30, 0- and 30-degree skew
Figure 132. Equation. Fifth-order polynomial
Figure 133. Graph. Discharge, tailwater variation
Figure 134. Graph. Downstream cross section
Figure 135. Graph. Cross section area versus tailwater elevation
Figure 136. Equation. Downstream flow area for tailwater elevation
Figure 137. Equation. Flow area under headwater elevation
Figure 138. Equation. Downstream channel velocity for Q25
Figure 139. Equation. Downstream channel velocity for Q100
Figure 140. Equation. Critical depth, below top corner fillets
Figure 141. Equation. Critical depth, partially submerged top corner fillets
Figure 142. Equation. Normal culvert depth
Figure 143. Equations. Flow area and hydraulic radius, depth below top corner fillet
Figure 144. Equations. Flow area and hydraulic radius, top fillets partially submerged
Figure 145. Equation. Initial depth
Figure 146. Equation. For Ko equals 1.0
Figure 147. Diagram. Definition sketch for exit loss
Figure 148. Equation. Initial depth, ignoring tailwater velocity head
Figure 149. Equations. For d less than (D-a)
Figure 150. Equations. For d less than D but greater than (D-a)
Figure 151. Equations. For d equal to D (the last iteration)
Figure 152. Equation. Friction slope
Figure 153. Equation. Step length
Figure 154. Equation. EGL at upstream culvert end (the entrance)
Figure 155. Sketches. Entrance loss coefficients (Ke) of culverts in example problem
Figure 156. Equation. Entrance loss
Figure 157. Equation. Headwater energy grade line
Figure 158. Equation. Headwater hydraulic grade line
Figure 159. Diagram. FC-D-30 model, Q100 elevations
Figure 160. Diagram. FC-D-0 model, Q100 elevations
Figure 161. Diagram. PC-B model, 30.48-cm (12-inch) corner fillets, Q100 elevations
Figure 162. Diagram. PC-B model, no corner fillets, Q100 elevations
Figure 163. Equations. Brink depth at culvert outlet
Figure 164. Equation. Headwater EGL
Figure 165. Diagram. Net area used for backwater computations

LIST OF TABLES

Table 1. Effects of bevels and corner fillets-summary of inlet and outlet control coefficients
Table 2. Summary of inlet and outlet control coefficients for models tested for effects of multiple barrels
Table 3. Summary of inlet and outlet control coefficients for models tested for effects of span-to-rise ratio
Table 4. Summary of inlet and outlet control coefficients for models tested for effects of headwall skew
Table 5. Summary of outlet control entrance loss coefficients, Ke, for low flows
Table 6. Summary of outlet loss coefficients
Table 7. Polynomial regression coefficients, models tested for bevels and corner fillets
Table 8. Polynomial regression coefficients, models tested for span-to-rise ratio
Table 9. Polynomial regression coefficients, models tested for multiple barrels
Table 10. Polynomial regression coefficients, models tested for skewed headwall
Table 11. Design coefficients suggested for future editions of HDS-5
Table 12. Fifth-order polynomial coefficients
Table 13. Tests to analyze the effects of bevels for wingwalls and top edges
Table 14. Tests to analyze the effects of multiple barrels
Table 15. Tests to analyze the effects of the span-to-rise ratio
Table 16. Tests to analyze the effects of skew
Table 17. Inlet control design coefficients, all experiments
Table 18. Inlet control fifth-order polynomial coefficients, all experiments
Table 19. Outlet control design coefficients, all experiments
Table 20. Example problem, downstream cross section ground point coordinates
Table 21. Example problem, tailwater rating information
Table 22. Example problem, step 3 solutions
Table 23. Example problem, step 4 solutions
Table 24. Example problem, step 5 solutions
Table 25. Example problem, step backwater and entrance loss results for Q25
Table 26. Example problem, step backwater and entrance loss results for Q100

LIST OF ACRONYMS AND ABBREVIATIONS

2-D two-dimensional
ccd charge coupled device
CIP cast-in-place
DOT Department of transportation
EGL energy grade line
FC field cast
FHWA Federal Highway Administration
HDS Hydraulic Design Series
HECRAS Hydrologic Engineering Center River Analysis System
HGL hydraulic grade line
HW/D headwater depth (ratio)
LDA laser doppler anemometry
NCHRP National Cooperative Highway Research Program
OPM optical pressure measurement
PC precast
PIV particle image velocimetry
PVC polyvinyl chloride
SI International System of Units (the Metric System)
SDDOT South Dakota Department of Transportation
TFHRC Turner-Fairbank Highway Research Center
VI virtual instruments
WW wingwall

LIST OF SYMBOLS

(A comprehensive list can be found in Hydraulic Design of Highway Culverts (HDS-5)(1))
A full cross-sectional area of culvert barrel
c coefficient for submerged inlet control equation
D interior height of the culvert barrel
EGL energy grade line (sometimes E.G.L.)
h height of hydraulic grade line above centerline of orifice
Hc specific head at critical depth (dc + Vc2/2g)
He entrance head loss
Hf friction head loss in culvert barrel
HL total energy loss
HLe, HLc inlet loss (also the inlet head loss or the contraction loss)
HLf, Hf friction loss
HLo exit loss
Ho exit head loss
HGL hydraulic grade line (sometimes H.G.L.)
HW headwater; depth from inlet invert to upstream total energy grade line
HWi headwater depth above inlet control section invert
HWo headwater depth above culvert outlet invert
HW/D headwater depth ratio
g acceleration due to gravity
K coefficient for unsubmerged inlet control equation
Kecoefficient for outlet control entrance loss
Koexit loss coefficient usually assumed to be 1.0 for design purposes
Ku1.811 for SI; 1.0 for the English system
M exponent in unsubmerged inlet control equation
Q discharge
S culvert barrel slope
TW tailwater; depth of water measured from culvert outlet invert
V mean velocity of flow
Vd downstream velocity
Vu approach (upstream) velocity
y depth of flow
Y additive term in submerged inlet control equation

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