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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: FHWAHRT09028 Date: May 2009 
Publication Number: FHWAHRT09028 Date: May 2009 
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The Hydrodynamic Forces on Inundated Bridge Decks Study described in this report was conducted at the Federal Highway Administration's (FHWA) TurnerFairbank Highway Research Center (TFHRC) J. Sterling Jones Hydraulics Laboratory and at the Department of Energy's Argonne National Laboratory's (Argonne) Transportation Research and Analysis Computing Center (TRACC). The study was in response to a request of several State transportation departments asking for new design guidance to predict hydrodynamic forces on bridge decks for riverine conditions. The study included experiments (physical modeling) at the TFHRC J. Sterling Jones Hydraulics Laboratory and High Performance Computational Fluid Dynamics (CFD) modeling at the Argonne National Laboratory. This report will be of interest to hydraulic engineers and bridge engineers who are involved in estimating loads for 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
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Technical Report Documentation Page
1. Report No.
FHWAHRT09028 
2. Government Accession No.  3 Recipient's Catalog No.  
4. Title and Subtitle
Hydrodynamic Forces on Inundated Bridge Decks 
5. Report Date May 2009 

6. Performing Organization Code  
7. Author(s)
Kornel Kerenyi, Tanju Sofu, and Junke Guo 
8. Performing Organization Report No.


9. Performing Organization Name and Address GKY and Associates, Inc. 4229 Lafayette Center Dr., Suite 1850 Chantilly, VA 20151
University of Nebraska 312 N. 14th Street Alexander Building West Lincoln, NE 685880430 
10. Work Unit No. (TRAIS) 

11. Contract or Grant No. DTFH04C00037 

12. Sponsoring Agency Name and Address
Office of Infrastructure Research and Development Federal Highway Administration 6300 Georgetown Pike McLean, VA 221012296 
13. Type of Report and Period Covered
Laboratory Report November 2005June 2008 

14. Sponsoring Agency Code FHWA Task Order 16 

15. Supplementary Notes
Contracting Officer's Technical Representative (COTR): Kornel Kerenyi, HRDI07 

16. Abstract
The hydrodynamic forces experienced by an inundated bridge deck have great importance in the design of bridges. Specifically, the drag force, lift force, and the moment acting on the bridge deck under various levels of inundation and a range of flow conditions influence the design and construction of the bridge. This report explores the forces acting on bridges in two ways. First, through physical experimentation on scaleddown bridge deck models tested in a flume and then with computational fluid dynamics (CFD) simulation models. Three bridge deck prototypes were used for the experimentation: a typical sixgirder highway bridge deck, a threegirder deck, and a streamlined deck designed to better withstand the hydraulic forces. The forces (expressed as nondimensional force coefficients) on each of the bridge deck shapes were measured in the laboratory with an ultraprecise force balance under a range of inundation scenarios (including partial inundation) and at four different velocities characterized by Froude numbers in the range of 0.16 to 0.32.
CFD modeling was performed using both the Fluent^{®} and STARCD^{® }software packages. The CFD models were calibrated to the flow conditions of the sixgirder bridge, and these same conditions were used for the other two bridge shapes. A range of model options were tested including twodimensional versus threedimensional models, different mesh resolutions, boundary conditions, and turbulence models; their effect on the accuracy of results and processing efficiency were noted.
Fitting equations were generated to create an envelope around the experimental data and create design charts for each of the bridge types and force coefficients.
Finally, the CFD models, though they can match some of the general behavior of experimental models in terms of the relationship between inundation ratio and force measured at the bridge, do not yet faithfully reproduce the critical values of the hydraulic forces and show very little response to velocity. The CFD simulations seem promising as a method to test bridge designs, but more research is needed before complex designs can be tested wholly in the CFD realm. However, the design charts from the experimental results should be a valuable tool for the bridge designer in a wide range of design applications. 

17. Key Words
Hydrodynamic Forces, Force Balance, CFD, Inundated bridge decks 
18. Distribution Statement
No restrictions. This document is available to the public through the National Technical Information Service (NTIS), Springfield, VA 22161. 

19. Security Classification Unclassified 
20. Security Classification Unclassified 
21. No. of Pages 44 
22. Price 
Form DOT F 1700.7  Reproduction of completed page authorized 
SI (Modern Metric) Conversion Factors
3. Computational Fluid Dynamics Setup and Validation
5. Deck force calculation examples
Figure 2. Equation. Inundation ratio
Figure 3. Equation. Froude number
Figure 4. Diagram. Definition sketch of forces acting on bridge deck
Figure 5. Equation. Drag coefficient
Figure 6. Equation. Lift coefficient
Figure 7. Equation. Moment coefficient
Figure 8. Diagram. Dimensions of the sixgirder bridge deck
Figure 9. Diagram. Dimensions of the threegirder bridge deck
Figure 10. Diagram. Dimensions of the streamlined bridge deck
Figure 12. Diagram. Test section of deck force analyzer showing strain gauge configuration
Figure 13. Photo. Deck force analyzer system at the TFHRC hydraulics lab
Figure 15. Image. Segment of bridge used for 3D model
Figure 16. Diagram. Coarse meshes for STARCD^{®} simulation
Figure 17. Diagram. Partially refined meshes for STARCD^{®} simulation
Figure 18. Model. A rendering of the 3D sixgirder bridge deck in Fluent^{®}
Figure 19. Image. Velocity profile from the 2D Fluent^{®} model
Figure 20. Image. Velocity profile from the 3D Fluent^{®} model
Figure 21. Diagram. Fluent^{®} unstructured mesh in the vicinity of the bridge
Figure 22. Image. Velocity profile from the Fluent^{®} κε CFD model for the sixgirder bridge
Figure 23. Image. PIV velocity profile for the sixgirder bridge
Figure 24. Image. Velocity profile from the Fluent^{®} κε CFD model for the threegirder bridge
Figure 25. Image. PIV velocity profile for the threegirder bridge
Figure 26. Image. Velocity profile from the Fluent^{®} κε CFD model for the streamlined bridge
Figure 27. Image. PIV velocity profile for the streamlined bridge
Figure 28. Graph. Drag coefficient versus inundation ratio for the sixgirder bridge
Figure 29. Graph. Lift coefficient versus inundation ratio for the sixgirder bridge
Figure 30. Graph. Moment coefficient versus inundation ratio for the sixgirder bridge
Figure 31. Graph. Drag coefficient versus inundation ratio for the threegirder bridge
Figure 32. Graph. Lift coefficient versus inundation ratio for the threegirder bridge
Figure 33. Graph. Moment coefficient versus inundation ratio for threegirder bridge
Figure 34. Graph. Drag coefficient versus inundation ratio for streamlined bridge deck
Figure 35. Graph. Lift coefficient versus inundation ratio for the streamlined bridge
Figure 36. Graph. Moment coefficient versus inundation ratio for the streamlined bridge
Figure 37. Equation. Drag coefficient fitting equation for three and sixgirder bridges
Figure 38. Equation. Lift coefficient fitting equation for three and sixgirder bridges
Figure 39. Equation. Moment coefficient fitting equation for all bridge types
Figure 40. Equation. Drag coefficient fitting equation for the streamlined bridge
Figure 41. Equation. Lift coefficient fitting equation for the streamlined bridge
Figure 42. Equation. Upper fitting equation for drag coefficient as a function of h*
Figure 44. Equation. Velocity, v, at h*_{crit}
Table 1. Fitting equation coefficient values for sixgirder (6g) and threegirder (3g) bridges
Table 2. Fitting equation coefficient values for the streamlined bridge
Table 3. Critical coefficient values by bridge type
Table 4. Bridge example dimensions
Table 5. Flow conditions for example design floods
Table 6. High and low force coefficients for the two example floods
2D  Twodimensional 
3D  Threedimensional 
ADV  Acoustic Doppler Velocimeter 
Argonne  Department of Energy's Argonne National Laboratory 
CFD  Computational fluid dynamics 
FHWA  Federal Highway Administration 
LES  Large Eddy Simulation 
PISO  PressureImplicit SplitOperator 
PIV  Particle Image Velocimetry 
PVC  Polyvinyl Chloride 
R&D  Research and Development 
RANS  Reynoldsaveraged NavierStokes 
SIMPLE  SemiImplicit Method for Pressure Linked Equations 
TFHRC  TurnerFairbank Highway Research Center 
TRACC  Transportation Research and Analysis Computing Center 
VoF  Volume of fluid 
C_{D}  Drag coefficient 
C_{L}  Lift coefficient 
C_{M}  Moment coefficient 
F_{D}  Drag force 
F_{L}  Lift force 
Fr  Froude number 
g  Gravitational acceleration 
h*  Inundation ratio 
h*_{crit}  Critical Inundation ratio resulting in maximum forces 
h_{b}  Height from bottom of flume to bottom of bridge 
h_{u}  Height of water from bottom of flume 
κε  Turbulence model 
L  Bridge length 
M_{cg}  Moment about the center of gravity 
Re  Reynolds number 
s  Deck thickness 
V, v  Free stream velocity 
W  Bridgewidth 
ρ  Fluid density (or water density) 