7.6 Defining Cross-Section Locations and Coefficients

Approach and exit conditions at a culvert are modeled in HEC-RAS similar to bridges as described in Chapter 6. The approach (start of contraction, section 4) and exit (end of expansion, section 1) sections are placed at the same locations as they are for bridge modeling, as shown on Figure 6.1 on (see page 185). Two more sections are placed immediately outside the culvert at the upstream (section 3) and downstream (section 2) ends. Thus, four sections are typically used to model the flow contraction and expansion through a culvert reach.

Section Location

The width of a bridge, parallel to flow, is nearly always much less than the width of the embankment between the embankment toes. This situation is different for culverts, because a culvert extends all the way through the embankment, with the culvert entrance and exit usually located at or beyond the embankment toe. Culverts are therefore normally much longer (parallel to the flow direction) than the bridge width at the same location. Sections 2 and 3 for culverts can be located 1 ft (0.3 m) or more outside the downstream and upstream ends of the culvert, similar to the locations of these sections for bridge modeling. However, while the modeler may choose a foot or so from the culvert entrance or exit to locate the sections, it is more appropriate to locate sections 2 and 3 a distance of 5 to 20 feet from the culvert face, as these locations typically better reflect the headwater and tailwater conditions. Sections 2 and 3 should comprise the full valley cross section, with ineffective flow area constraints specified. If the culvert has wingwalls at the entrance and end walls at the exit, typical locations are just downstream of the end walls for section 2 and just upstream of the wingwalls for section 3.

Two more cross sections are needed to appropriately model a culvert: one at the beginning of the contraction into the culvert and a second at the end of the expansion out of the culvert. These locations are based on the modeler's judgment and supplemented by the equations for expansion and contraction reach length or ratios discussed in Chapter 6. Historically, the rule of thumb calling for 1:1 contraction and 1:4 expansion ratios described in Chapter 6 has been used to locate these sections, although a lower estimate of the expansion ratio is now more appropriate. Expansion ratios (ER) as small as 1:1 are sometimes applied for culverts between sections 1 and 2. This ER is also generally used for the distance between sections BD and 2. The nomographs and equations for expansion and contraction ratios presented in Chapter 6 were developed specifically for bridges. There have been no similar tests for culverts. However, the modeler could choose to assume that the ratios are also applicable to culverts. Figure 7.11 shows the location for the four culvert cross sections required of the modeler, using a 1:1 CR and an ER computed with an appropriate equation from Chapter 6 for L_e or ER. The modeler should develop the appropriate CR or ER for each culvert in the stream reach being modeled.

Figure 7.11 Expansion-contraction reach for a culvert and cross-section locations.

Occasionally, culverts have formal energy dissipaters (further discussed in Chapters 11 and 12) constructed to prevent severe erosion at the culvert exit. These structures serve to control high velocities at the culvert exit and keep the hydraulic jump within the concrete structure or some other selected location. These structures result in flows with lower, nonscouring velocities leaving the energy dissipater. For a culvert with an energy dissipater, the end of expansion location for section 2 could be at or slightly downstream of the end of the dissipater, especially for culvert discharges that remain within the channel bank stations.

Coefficients

Expansion and contraction coefficients for culverts can be selected based on the modeler's judgment or, alternatively, from the values found for bridges, as presented in the previous chapter. When the cross section of a culvert represents a small portion of the overall channel cross section, abrupt expansion and contraction coefficients should be considered. As shown in Table 5.7 on (see page 162), abrupt contraction and expansion coefficient values are 0.6 and 0.8, respectively. Figure 7.12a illustrates a culvert for which these values may be appropriate. When the culvert opening represents a large percentage of the channel width (Figure 7.12b), the typical bridge coefficients shown in Table 5.7 (0.3, 0.5) are more likely to be appropriate. Section 6.5 on (see page 203) presented methods for computing reduced bridge coefficients. Unfortunately, similar studies have not been performed to determine whether these methods and values are appropriate for culverts. It would seem to be a reasonable assumption that contraction and expansion coefficients for culverts should be greater than for bridges. However, the modeler can choose to use the new procedures presented in Chapter 6 to estimate expansion/contraction values at culverts or use the coefficients presented above in conjunction with best judgment.

Figure 7.12 Examples of possible expansion and contraction coefficients for culverts.

In the absence of actual laboratory tests and/or field studies to derive specific equations for contraction and expansion coefficients at culverts, minimum values of 0.3 and 0.5 for the contraction and the expansion coefficients, respectively, are offered as general guidelines for culverts.

Adjustments to Bounding Cross Sections 2 and 3

Specification of ineffective flow area stations and elevations at the bounding cross sections and any necessary modification of the channel and overbank geometry and/or n values should be made to accurately model culvert reaches.

Ineffective Flow Areas.

Ineffective flow areas upstream and downstream of culverts are required for proper modeling of the flow in and around culverts. The information on this subject given in Section 6.6 is applicable for culverts. Figure 7.13 demonstrates the use of the ineffective area option in HEC-RAS at the downstream face of a circular culvert. Typically, culverts are more restrictive to flow than a bridge and the downstream ineffective flow area elevation at culverts is often considerably lower than the upstream constraint elevation. Culverts under high fill may have 10 ft (3 m) or more of head difference between the headwater and tailwater elevations. The downstream ineffective flow area constraint elevations are initially estimated, then adjusted up or down based on computer runs to determine the final, adopted constraint elevations.

Figure 7.13 Example of placing ineffective flow area station-elevation constraints downstream of a culvert.

The locations and initial constraint elevation estimates for culverts are summarized as follows:

Ineffective flow area locations for section 3 - Determine the offset distance from the left and right edges of the culvert by multiplying the selected CR times the distance between section 3 and BU. For example, for a CR of 1:1 and a distance between section 3 and BU of 10 ft, the ineffective flow area stations on section 3 are 10 ft to the outside of both edges of the culvert.
Ineffective flow area elevations at section 3 - The left and right constraint elevations are equal to or slightly greater than the low roadway elevations to the left and right sides of the culvert. The selected value for each side of the culvert should generally represent the elevations when significant weir flow occurs over the roadway to the left and right of the culvert.
Ineffective flow area locations for section 2 - Determine the offset distance from the left and right edge of the culvert by multiplying the selected ER times the distance between section 2 and BD. For example, for an ER of 1:2 and a distance between section 3 and BU of 10 ft, the ineffective flow area stations on section 3 would be 5 ft to the left and right of the left and right culvert edge.
Ineffective flow area elevations for section 2 - The left and right constraint elevations at section 2 are often more uncertain than those for a bridge. An initial assumption for the left ineffective flow area elevation can be an average of the low roadway elevation on the left and the top elevation of the culvert. The right initial constraint elevation can be estimated similarly. These elevations are refined after review of the initial computer runs and inspection of the profiles through the culvert.

Geometry and n values.

Sections 2 and 3 represent full valley cross sections and should not include any portion of the roadway or the embankment in the cross-section data. An intermediate section could be considered if there are large changes in Manning's n between sections 1 and 2 or between sections 3 and 4.

Sections 2 and 3 often require geometric modifications, especially if a new road crossing is being analyzed with multiple culverts. The total width of the culverts may be larger than the width of the existing channel. For example, in the culvert design shown later as Figure 7.15, the multiple box culverts under consideration require trapezoidal channel sections for sections 2 and 3 and are more than double the width of the preculvert channel condition. Although HEC-RAS will operate without a modification of the bounding section's geometry, the losses will not be properly analyzed without correcting the model to reflect the two sections' revised geometry. For significant channel geometry changes between sections 1 and 2 or between 3 and 4, an intermediate section should be considered at the stream location where the preculvert channel meets the postculvert channel.