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

Effects of Inlet Geometry on Hydraulic Performance of Box Culverts

CHAPTER 2. LITERATURE REVIEW

The most comprehensive publication available in the literature is the FHWA HDS-5,Hydraulic Design of Highway Culverts, a synthesis of culvert research that includes the classic studies done for the Bureau of Public Roads by the National Bureau of Standards during the 1950s and 1960s. (See references 4, 5, 6, 7, 8, 9, and 10.) HDS-5 features sections on design considerations, conventional culvert design, tapered inlets for various types of culverts, storage routing, and special considerations. Appendixes include design methods and equations, barrel resistance, design optimization using performance curves, and design charts, tables, and forms.

HDS-5 defines culvert hydraulics in terms of inlet and outlet control depending on the variables that influence the head required to push flow through the barrel. Inlet control occurs for steep culverts flowing free surface where flow goes through critical depth near the inlet. Flow in the culvert barrel below the critical depth section is supercritical flow that does not propagate downstream surface disturbances upstream. The only variables that affect the headwater are the discharge intensity and the geometry of the inlet. Outlet control occurs for mild slope culverts where free surface flow is subcritical and for any slope when the barrel is completely submerged. In these cases, the tailwater, which is typically known, is the control, and the headwater is affected by tailwater depth, outlet loss, friction loss, elevation difference, and the entrance loss, which is a function of discharge intensity and inlet geometry.

Outlet control is the more general case where the entrance loss is just one component that affects the headwater and usually is not the dominant component compared to the tailwater elevation and the friction in the barrel. The entrance loss is assumed to be a fraction of the velocity head in the barrel and is expressed as a coefficient times the velocity head. HDS-5 lists the entrance-loss coefficients as a single, constant value for each inlet shape. There is no distinction between high flows and low flows, but HDS-5 is a hydraulic design manual; so it is reasonable to expect coefficients to be more related to high flows. Furthermore, it is reasonable to expect some variation in this coefficient at low flows because the effective inlet shape changes when only a portion of it is in the flow zone.

Inlet control is the special case where the inlet geometry and corresponding entrance loss is the dominant component that affects the headwater. Regression equations have been developed for each inlet shape to express headwater as a function of discharge intensity directly or to compute a loss component that can be added to the critical head-to-yield headwater. These regression equations apply for a range of discharge intensities that include low flows. HDS-5 lists the regression coefficients for predetermined equation forms for each inlet shape.

During the late 1980s, there was considerable interest in the hydraulics of long-span culverts, which were frequently proposed as low-cost alternatives to short bridges. Laboratory experiments at the FHWA Hydraulics Laboratory were conducted to investigate effects of some of the characteristic features of long-span culverts, namely the culvert shape, the span-to-rise ratio, and the contraction ratio.(11) Experiments were conducted in a 1.8-meter (m)- (6-foot (ft)-) wide by 21.4-m- (70-ft-) long tilting flume set at a slope expected to generate inlet control. Culvert shapes included circular (which was used as a benchmark), semicircular, high-profile arches, and metal box geometries commonly used for long-span installations. Inlet geometry for all shapes was a thin, projecting edge with no flared wingwalls. Culvert shape seemed to have very little effect at the higher discharges for submerged flow, but the high-profile arch shape appeared to have lower relative entrance losses at the lower discharges for unsubmerged flow. The study found no logical explanation for the apparent advantage for the high-profile arch at low flows.

The span-to-rise ratio was varied by testing three metal box culvert geometries referred to as a high box, a mid box, and a low box with span-to-rise ratios of 2.0, 3.25, and 4.5, respectively. The span was held constant (at 50.8 cm (20 inches)) while the rise was varied. The shapes varied slightly because the metal boxes were not actually rectangles; they had rounded corners and resembled arches more than they did rectangles. The general trend was the higher the span-torise ratio, the lower the efficiency. In other words, for a thin edge projecting inlet where there was no bevel to streamline the flow over the top edge, increasing the span-to-rise ratio actually increased the headwater required to convey a given discharge intensity through the inlet.

The contraction ratio–approach channel width divided by culvert width–varied from 6.0 to 1.5. It appeared that the lower the contraction ratio, the higher the efficiency. But the primary conclusion drawn from this part of the study was that the headwater in HDS-5 was the specific energy head and not just the hydraulic grade line depth as is often presumed. To make the data agree with the performance curves shown in HDS-5 for the benchmark shape, it was necessary to include the approach-flow velocity head in the headwater computations. Typically, long-span culverts are nearly the full width of the approach channel, the contraction ratios are small, and the approach flow velocity is almost as high as the velocity in the culvert. This particular FHWA study was conducted to gain insight about the hydraulics of long-span culverts, but the results were never published.

A study conducted at the FHWA Hydraulics Laboratory for SD DOT compared hydraulic performance of precast inlet configurations to traditional 30-degree-flared wingwall inlets for box culverts.(3)Six culvert models constructed of plywood were tested for both inlet and outlet control. Water depths were measured through ports in the flooring via Tygon® tubing connected to a pressure transducer. Box culverts with single 1.8- by 1.8-m (6- by 6-ft), 2.4- by 2.4-m (8- by 8-ft), 2.7- by 2.7-m (9- by 9-ft), and 3.7- by 3.7-m (12- by 12-ft) barrels with 30-degree wingwalls were modeled in this study. Model scales of 1:10.67, 1:15, and 1:16 were selected to use stock thickness materials to simulate culvert wall thickness and wingwall thickness. Two slopes–3 percent and 1.75 percent–were used in the experiments. Effects of wingwall miters (to the embankment slope), straight-cut bevels, culvert barrel slopes, wingwall flare, and parapets were compared.

Inlet-control design coefficients were developed by regressing experimental data using the inletcontrol design equations found in HDS-5. A benchmark culvert model was fabricated and tested to compare with scale 3 of the HDS-5 chart 8 as a check on experimental procedures. Inletcontrol coefficients were derived for unsubmerged and submerged conditions for each culvert model, and the outlet control entrance-loss coefficient, Ke, was computed for each culvert model. For inlet control, the design coefficients for the benchmark model of the HDS-5 chart 8, scale 3, did not match the values tabulated in HDS-5 very well; however, the outlet control coefficient, Ke, experimental value of 0.68 was a close match to the tabulated value of 0.7. For unsubmerged conditions, the miter slope, span-to-rise ratio, and culvert barrel slope appeared to have insignificant effect on the design coefficients. For submerged conditions, the 3:1 miter was slightly more efficient than a 2:1 miter. In contrast to the observation noted for the long-span culvert study, the higher span-to-rise ratios improved culvert performance (reduced headwater for a given discharge intensity), but these models did not have the thin edge projecting inlet geometry. Parapets used to retain fill over the top plate appeared to improve rather than hinder culvert performance.

Overall, the precast inlets with beveled edges were slightly better than the typical field cast inlets without beveled edges but were not as good as the 30-degree-flared wingwall inlet. No attempt, however, was made in the study to optimize the bevels. A number of general trends were noted, but there were no recommendations about how to modify FHWA manuals or computer programs to implement results from the study.

A study for the Iowa DOT by Graziano, et al., also conducted at the FHWA Hydraulics Laboratory, investigated the hydraulic performance of special Iowa DOT slope-tapered pipe culverts.(12)The culverts consisted of off-the-shelf components including precast end sections, one-eighth bends, and pipe reducers that are readily available from pipe suppliers. The goals of the study were to derive design coefficients for a slope-tapered inlet for circular culverts and to investigate the sensitivity of performance to reducer length and taper ratio. The performance of the precast end section, which was a flared-transition section that conformed to a 3:1 embankment slope, was compared to the performance of the HDS-5 chart 1, scale 1, culvert, which is a circular concrete culvert with a headwall and square edges.

Model scale ratios of 1:6.783 and 1:4.174 were used for the study. The headbox and tailbox were plywood versions of the culvert test facility that is currently in the laboratory. Hydraulic depths were measured by a single-pressure transducer connected through a switching block to pressure ports located along the culvert invert, in the headbox and in the tailbox. An adjustable tailgate was used to submerge the culvert to develop outlet control for a steep culvert.

For inlet control, the precast end section by itself without the other components for the slopetapered inlet performed almost the same as the HDS-5 chart 1, scale 1, inlet. When the precast end section was combined with the reducers and bends to make the Iowa slope-tapered unit, hydraulic performance improved substantially. Performance was not sensitive to the taper ratio or whether one, two, or three reducers were used to transition the taper.

For outlet control, the tabulated Ke value for the HDS-5 chart 1, scale 1, inlet was 0.50, compared to a Ke of 0.35 for the precast end section and a Ke of 0.20 for the Iowa slope-tapered inlet. For inlet control, the design coefficients for the precast end section were K is 0.51 and M is 0.55 for the unsubmerged form 2 equation and c is 0.021 and Y is 0.823 for the submerged flow equation. K is the coefficient for the unsubmerged inlet control equation; M is the exponent for the unsubmerged inlet control equation; c is the coefficient for the submerged inlet control equation; and Y is an additive term in the submerged inlet control equation. The corresponding coefficients for the Iowa slope-tapered inlet were: K = 0.477; M = 0.533; c = 0.025; and Y = 0.659.

GKY & Associates, Inc. consolidated design coefficients, including the fifth-order polynomials that were used to code computer programs such as HY-8.(13) Derivations for the various equations cited in HDS-5, a comprehensive set of design coefficients, and nomographs or performance curves for all of the inlets covered by HDS-5 plus several that were studied later were included in this report.

McEnroe and Johnson tested shop fabricated metal and precast concrete open-flared end sections that are commonly available from pipe suppliers.(14) They also studied the effects of flow bars and debris blockage on the hydraulic performance of the pipes. They noted that HDS-5 provides little information on the hydraulic characteristics of these common end sections other than from limited hydraulic tests hydraulically equivalent in operation to a headwall in both inlet and outlet control. Their experiments with two pipe sizes resulted in outlet control Ke values ranging from 0.24 to 0.31. Both the metal and concrete end sections had the larger value for the smaller pipe size and the lower value for the larger pipe size.

The precast concrete open flare end section tested by McEnroe and Johnson was the same as the end section tested by Graziano, et al., for the Iowa DOT(12) and is illustrated in figure 3. Graziano recommended a Ke value of 0.35, which is comparable to the 0.31 value found by McEnroe and Johnson for that end section.(14)


Figure 3. Sketch. Precast flared end section tested by Graziano and by McEnroe.

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McEnroe and Johnson did not follow the HDS-5 pattern for presenting the inlet-control results; rather, they provided three dimensionless component equations for each inlet. The first component equation essentially represents the unsubmerged condition. The second one represents the transition zone, and the third one represents the submerged condition. Figures 4, 5, and 6 are the component equations for the prefabricated metal end section. In figures 4 through 10, the terms are as follows: HW is the headwater, or the depth from the inlet invert to the upstream total energy grade line; D is the interior height of the culvert barrel; Q is the discharge; and g is the acceleration due to gravity.

Figure 4. Equation. HW/D, prefabricated metal end section, unsubmerged condition.


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Figure 5. Equation. HW/D, prefabricated metal end section, transition zone.


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Figure 6. Equation. HW/D, prefabricated metal end section, submerged condition.


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Figures 7, 8, and 9 are the component equations for the precast concrete end section.

Figure 7. Equation. HW/D, precast concrete end section, unsubmerged condition.

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Figure 8. Equation. HW/D, precast concrete end section, transition zone.


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Figure 9. Equation. HW/D, precast concrete end section, submerged condition.

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The first equation in each set, figures 4 and 7, can readily be converted to the HDS-5 format to compare with Graziano’s results.(12) Figure 10 is the converted first component for the precast concrete end section.


Figure 10. Equation. Figure 7 in HDS-5 format.

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Where: 
  
Ku= 1.0 for English units.
Ku= 1.38 for SI units.
Ku is a coefficient for the unsubmerged inlet control equation.

Figure 10 is the form 2 equation for unsubmerged inlet control flow, which means McEnroe and Johnson obtained values for K and M of 0.51 and 0.55, respectively.(14) These were the exact value obtained by Graziano in a completely independent study.(12)

Umbrell, et al., did a site-specific model study of a culvert installation consisting of a larger concrete culvert in series with a smaller culvert.(15) The inlet was a 30-degree flared wingwall, which was tested with both culvert diameters. The Ke values ranged from 0.12 to 0.24, but the higher values tended to be for the larger pipe size and the lower discharges. Researchers attributed the differences to experimental scatter and proposed an average value of 0.14.

A current National Cooperative Highway Research Program (NCHRP) study at Utah State University is investigating the effects of culvert geometry on hydraulic performance for circular culverts with buried inverts, composite roughness, and other measures used to promote fish passage through culverts. Entrance loss coefficients at low flows are of interest because fish passage criteria are based on average seasonal flows, not the higher flows used for culvert design.

Tullis observed that the entrance loss coefficients for outlet control were not constant values for an inlet geometry as normally presented in the literature.(16) There was considerable variation in the Ke values, especially for low flows. Researchers hypothesized that Ke might be a function of the Reynolds number as illustrated in the conceptual sketch shown in figure 11. The implication of that observation is somewhat distressing because it would tend to complicate an otherwise simple computation. The entrance loss coefficient seems to be higher at the lower Reynolds numbers, which means the larger culverts would tend to have lower loss coefficients. This hypothesis might help explain why McEnroe and Johnson and Umbrell, et al., found smaller Ke’s for the larger models used in the tests.(14,15)

Figure 11. Sketch. Relationship of entrance loss coefficient to Reynolds number.

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Note: The graph is hypothetical and meant to show the general relationship between Ke values and the Reynolds number. Specific Ke values are not given.

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). The hydraulics and hydrology research program at the TFHRC Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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