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  • US Army Corpsof EngineersHydrologic Engineering Center

    Flow Transitions in Bridge Backwater Analysis September 1995 Approved for Public Release. Distribution Unlimited. RD-42

  • REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188

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    1. AGENCY USE ONLY (Leave blank)

    2. REPORT DATE September 1995

    3. REPORT TYPE AND DATES COVERED Research Document No. 42

    4. TITLE AND SUBTITLE Flow Transitions in Bridge Backwater Analysis 6. AUTHOR(S) John H. Hunt, Gary W. Brunner

    5. FUNDING NUMBERS

    7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US Army Corps of Engineers Institute for Water Resources Hydrologic Engineering Center 609 Second Street Davis, CA 95616-4687

    8. PERFORMING ORGANIZATION REPORT NUMBER RD-42

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    11. SUPPLEMENTARY NOTES 12a. DISTRIBUTION / AVAILABILITY STATEMENT Approved for Public Release. Distribution of this document is unlimited.

    12b. DISTRIBUTION CODE

    13. ABSTRACT (Maximum 200 words) Bridges across floodplains may require special attention in one-dimensional hydraulic modeling if they cause severe contraction and expansion of the flow. The accurate prediction of the energy losses in the contraction reach upstream of the bridge and the expansion reach downstream of the bridge using one-dimensional models presents particular difficulty. Modeling these reaches requires the accurate evaluation of four parameters: the expansion reach length, Le; the contraction reach length, Lc; the expansion coefficient, Ce; and the contraction coefficient, Cc. This report presents research conducted by the author to investigate these four parameters through the use of field data, two-dimensional hydraulic modeling, and one-dimensional modeling.

    15. NUMBER OF PAGES 81

    14. SUBJECT TERMS Bridge, Hydraulics, Backwater, Contraction and Expansion, energy losses, HEC-RAS, RMA-2, Steady Flow Analysis 16. PRICE CODE

    17. SECURITY CLASSIFICATION OF REPORT UNCLASSIFIED

    18. SECURITY CLASSIFICATION OF THIS PAGE UNCLASSIFIED

    19. SECURITY CLASSIFICATION OF ABSTRACT UNCLASSIFIED

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    NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-18 298-102

  • Flow Transitions in Bridge Backwater Analysis

    September 1995 US Army Corps of Engineers Institute for Water Resources Hydrologic Engineering Center 609 Second Street Davis, CA 95616 (530) 756-1104 (530) 756-8250 FAX www.hec.usace.army.mil RD-42

  • i

    Table of Contents Acknowledgements ........................................................................................................................v Abstract......................................................................................................................................... vi Chapter Page 1 Introduction.....................................................................................................................1 1.1 Purpose..................................................................................................................1 1.2 Bridge Hydraulics Concepts .................................................................................3 2 Literature Review ...........................................................................................................5 2.1 USGS Method of Indirect Discharge Measurement .............................................5 2.2 FHWA Method .....................................................................................................6 2.3 Later USGS Research ...........................................................................................9 2.4 Other Literature...................................................................................................10 2.5 HEC Computer Programs ...................................................................................12 3 One-Dimensional Modeling..........................................................................................13 3.1 HEC Model: HEC-RAS......................................................................................13 3.2 FHWA Model: WSPRO .....................................................................................16 3.3 Verification of One-Dimensional Models Using Field Data ..............................17 4 Two-Dimensional Hydrodynamic Modeling ..............................................................19 4.1 Advantages of Two-Dimensional Model............................................................19 4.2 Governing Equations ..........................................................................................20 4.3 Input Parameters .................................................................................................21 5 Analysis of Transition Reach Lengths ........................................................................23 5.1 Two-Dimensional Models of Field Sites ............................................................23 5.2 Idealized Two-Dimensional Models...................................................................28 5.2.1 Geometry and Input Parameters...........................................................28 5.2.2 Recording of Results............................................................................31 6 Analysis of Contraction and Expansion Loss Coefficients........................................35 6.1 Calibration of HEC-RAS Models .......................................................................35 6.2 Expansion Coefficients .......................................................................................35 6.3 Contraction Coefficients .....................................................................................36 7 Results ............................................................................................................................39 7.1 General Results ...................................................................................................39 7.2 Expansion Reach Lengths...................................................................................43 7.3 Contraction Reach Lengths.................................................................................45 7.4 Expansion Coefficients .......................................................................................47

  • ii

    Table of Contents Chapter Page 7 Results (continued) 7.5 Contraction Coefficients .....................................................................................48 7.6 Asymmetric Cases ..............................................................................................49 7.7 Vertical Abutment Cases ....................................................................................49 8 Verification ....................................................................................................................51 8.1 Reliability Within the Range of Regression Data...............................................51 8.2 Applicability to Field Sites .................................................................................51 8.3 Applicability to Larger Scales ............................................................................52 8.4 Applicability to Smaller Scales...........................................................................55 8.5 Effects of RMA-2 Model Refinement and Eddy Viscosity Coefficients ...........57 9 Conclusions and Recommendations ............................................................................59 9.1 Conclusions.........................................................................................................59 9.1.1 Expansion Reach Lengths....................................................................59 9.1.2 Contraction Reach Lengths..................................................................60 9.1.3 Expansion Coefficients ........................................................................60 9.1.4 Contraction Coefficients ......................................................................60 9.1.5 Asymmetric Bridge Openings..............................................................61 9.1.6 Vertical-Abutment Cases .....................................................................61 9.2 Recommendations...............................................................................................61 9.2.1 Expansion Reach Lengths ...................................................................62 9.2.2 Contraction Reach Lengths .................................................................64 9.2.3 Expansion Coefficients .......................................................................65 9.2.4 Contraction Coefficients .....................................................................66 Appendix A References ...................................................................................................

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