Jul 12 2012

History of Hydraulic Bridge Design

HDS 7 Background and Purpose

From; FHWA, HDS 7, April 2012

Earliest Methods

Determining the hydraulic capacity of bridges and culverts is a field that has been evolving in the United States since the mid 1800s. The earliest methods of sizing hydraulic openings were largely based on experience and historic performance. However, as the railroads expanded westward many crossings were encountered where there was no flood history or other up or downstream structures to use as the basis for determining bridge or culvert size. Therefore, tabular and empirical methods were developed that related waterway opening to size of drainage area and other coefficients that accounted for drainage basin and stream characteristics. The American Railroad Engineering and Maintenance-of-Way Association (AREMA) published a report in 1911 that presented six formulas for waterway area and 21 formulas for design discharge. A report by V.T. Chow in 1962 listed 12 formulas for waterway area and 62 formulas for design discharge (McEnroe 2007).

The earliest methods for determining waterway openings for bridges and culverts did not consider bridge or culvert configuration. Furthermore, the concept of a “design” discharge or recurrence interval of expected floods to use when determining structure size was not considered. Even though design discharges were not considered an early textbook on highway design and construction by Byrne (1893) suggested that the factors to be considered when determining the capacity of a hydraulic culvert depended on; (1) the rate of rainfall, (2) the kind and condition of the soil, (3) the character and inclination of the surface, (4) the condition of inclination of the bed of the stream, (5) the shape of the area to be drained, and the branches of the stream, (6) the form of the mouth and the inclination of the bed of the culvert, and (7) whether it is permissible to back the water up above the culvert, thereby causing it to discharge under a head. These same concepts were applied to the hydraulic sizing of bridges. As techniques for estimating discharge developed throughout the 1900s these same factors translated into many of the parameters found in methods used today to estimate recurrence intervals, peak discharges, and hydrographs.

Manning Formula

At the same time these methods were being developed in the United States a formula developed by Robert Manning (Manning 1889) was becoming popular. Originally developed in SI units with a coefficient of 1.0, the form of the equation in U.S. Customary units is presented as:



V = Velocity, ft/s

n = Roughness Coefficient

R = Hydraulic Radius, ft

S = Slope

There were two things that Robert Manning did not like about his equation, (1) that it was dimensionally incorrect, and (2) it was difficult (at the time) to determine the cubed root of a number and then square it to arrive at a number to the 2/3rd power. King’s handbook (King 1918) presented a table of numbers from 0.01 to 10 to the 2/3rd power which eliminated the problem of determining a number to the 2/3rd power and is considered to be a leading reason in the early acceptance and of use of the Manning Equation.

As methods were being developed to estimate discharge, it was realized that one could make an estimate of the roughness coefficient based on known values from similar channels and floodplains, determine the slope of the channel, and then use an iterative solution to determine the “normal” depth at a cross-section or hydraulic opening. Through the 1950s this remained a popular method of determining the depth and velocity of flow at a cross-section or through a hydraulic opening.

The problem with using normal depth as the estimate of flow depth (and velocity) for determining the size of hydraulic opening is that it does not consider the effects of backwater. Backwater is the additional depth to accelerate flow through the bridge opening and overcome a variety of resistance and drag forces. These forces depend on a number of factors including bridge type, degree of contraction, embankment skew, pier number and type, debris blockage, etc.

To account for backwater, research was completed and methods were developed that examined the components of backwater (Liu et al. 1957). In HDS 1, the computed backwater was added to the “normal” depth at a location upstream of the bridge to evaluate the overall impacts of a bridge (FHWA 1978).

Modern Developments &  Computer Models

Another significant development that contributed to the development of the current state of bridge hydraulics was the publication of a textbook about open channel flow by V.T. Chow (Chow 1959). The publication presents and applies concepts of energy, momentum, and continuity to the flow of water in open channels. It is also one of the places where the direct and standard step methods for computing water surface profiles were first presented. The direct step method is applicable to prismatic channels and the standard step method to natural channels. The standard step method uses concepts of conservation of energy and flow, and is widely used for water surface profile calculations.

At the same time the physics of open channel flow and water surface profiles were being developed, mainframe computer and programming languages were developing. The application of computer programs made it possible to rapidly complete trial and error solutions required for computing water surface profiles. One of the first computer programs that was developed to compute water surface profiles in natural channels was HEC-2 (USACE 1992) with development dating back to at least 1964. The HEC-2 program has undergone continual development and was ported to the PC in 1984. HEC-2 has evolved into the HEC-RAS (River Analysis System) model (USACE 2010 a, b, c). HEC-RAS performs steady non-uniform flow hydraulic calculations similar to HEC-2, but incorporates enhanced visualization, more complete bridge and culvert hydraulic computations, unsteady flow, and sediment transport. There were many other computer programs developed to compute water surface profiles. The USGS developed E431 (USGS 1976) and the Federal Highway Administration developed WSPRO (FHWA 1998) that had components specifically formulated for the analysis of flow through bridge openings. HEC-RAS has incorporated features from these programs including the WSPRO bridge routine.

More recent developments in the field of bridge hydraulics include the development of two-dimensional hydraulic and hydrodynamic models to compute the entire flow field. These models include FST2DH (FHWA 2003) and RMA-2 (USACE 2009).

Literature cited without a web link:

Manning, R., 1889, “On the Flow of Water in Open Channels and Pipes,” Transactions of the Institution of Civil Engineers of Ireland.

Liu, H.K., J.N. Bradley, and E.J. Plate, 1957, “Backwater Effects of Piers and Abutments,” Colorado State University, Civil Engineering Section, Report CER57HKLI0, 364 pp.

U.S. Geological Survey (USGS), 1976, “Computer Applications for Step-backwater and Floodway Analysis,” U.S. Geological Survey Open-File Report 76-499, 103 p.


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