USGS Scientific Investigations Report 2007-5263

Prepared in cooperation with the North Carolina Department of Transportation

Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. Highway 13 Bridge over the Tar River at Greenville, North Carolina, Using One- and Two-Dimensional Steady-State Hydraulic Models

By Chad R. Wagner

U.S. Geological Survey Scientific Investigations Report 2007-5263, 33 pages (Published December 2007)

This report is available only online in PDF format: SIR 2007-5263 (Opens the PDF file in a new window. ) (2.6 MB)

Cover thumbnailThe use of one-dimensional hydraulic models currently is the standard method for estimating velocity fields through a bridge opening for scour computations and habitat assessment. Flood-flow contraction through bridge openings, however, is hydrodynamically two dimensional and often three dimensional. Although there is awareness of the utility of two-dimensional models to predict the complex hydraulic conditions at bridge structures, little guidance is available to indicate whether a one- or two-dimensional model will accurately estimate the hydraulic conditions at a bridge site.

The U.S. Geological Survey, in cooperation with the North Carolina Department of Transportation, initiated a study in 2004 to compare one- and two-dimensional model results with field measurements at complex riverine and tidal bridges in North Carolina to evaluate the ability of each model to represent field conditions. The field data consisted of discharge and depth-averaged velocity profiles measured with an acoustic Doppler current profiler and surveyed water-surface profiles for two high-flow conditions. For the initial study site (U.S. Highway 13 over the Tar River at Greenville, North Carolina), the water-surface elevations and velocity distributions simulated by the one- and two-dimensional models showed appreciable disparity in the highly sinuous reach upstream from the U.S. Highway 13 bridge. Based on the available data from U.S. Geological Survey streamgaging stations and acoustic Doppler current profiler velocity data, the two-dimensional model more accurately simulated the water-surface elevations and the velocity distributions in the study reach, and contracted-flow magnitudes and direction through the bridge opening.

To further compare the results of the one- and two-dimensional models, estimated hydraulic parameters (flow depths, velocities, attack angles, blocked flow width) for measured high-flow conditions were used to predict scour depths at the U.S. Highway 13 bridge by using established methods. Comparisons of pier-scour estimates from both models indicated that the scour estimates from the two-dimensional model were as much as twice the depth of the estimates from the one-dimensional model. These results can be attributed to higher approach velocities and the appreciable flow angles at the piers simulated by the two-dimensional model and verified in the field.

Computed flood-frequency estimates of the 10-, 50-, 100-, and 500-year return-period floods on the Tar River at Greenville were also simulated with both the one- and two-dimensional models. The simulated water-surface profiles and velocity fields of the various return-period floods were used to compare the modeling approaches and provide information on what return-period discharges would result in road over-topping and(or) pressure flow. This information is essential in the design of new and replacement structures.

The ability to accurately simulate water-surface elevations and velocity magnitudes and distributions at bridge crossings is essential in assuring that bridge plans balance public safety with the most cost-effective design. By compiling pertinent bridge-site characteristics and relating them to the results of several model-comparison studies, the framework for developing guidelines for selecting the most appropriate model for a given bridge site can be accomplished.





Purpose and Scope

Study Site and Data


Data Collection


Simulation of Water-Surface Elevations and Velocity Distributions

Model Calibration

Model Uncertainty

Model Scenarios for Existing Bridge and Pre-Roadway Conditions

Comparisons of One-Dimensional and Two-Dimensional Modeling Results to Field Data

Water-Surface Elevations

Velocity Distributions

Scour Estimates

Suggestions for Selecting Appropriate Modeling Approach


References Cited

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Suggested citation: Wagner, C.R., 2007, Simulation of water-surface elevations and velocity distributions at the U.S. Highway 13 bridge over the Tar River at Greenville, North Carolina, using one- and two-dimensional steady-state hydraulic models: U.S. Geological Survey Scientific Investigations Report 20075263, 33 p. (only online at

For more information, please contact Chad R. Wagner.

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