# 750.2 Culverts

## 750.2.1 General

The design procedures and design aids presented herein are to be used in the design and analysis of all highway culverts. The hydraulic design of highway culverts is based on the theory and procedures presented in Hydraulic Design of Highway Culverts - HDS No. 5. These methods are also to be used in the design of median drains. Storm sewer systems may be analyzed by the models of culvert hydraulics, in order to determine water surface elevations at critical points in the system such as at manholes and drop inlets.

The responsibility for analysis, design and final plans preparation is sometimes shared between districts and Bridge Division. See EPG 750.7.4.3 Summary of Responsibilities. This is particularly important information for multiple opening culverts since these culvert types can be classified as bridges and are required to have a bridge number for identification on the system.

## 750.2.2 Hydraulic Analysis of Culverts

The FHWA HY-8 computer program as well as other programs may be used for the hydraulic analysis of culverts.

Hydraulic design of culverts requires analysis of both the "natural conditions" and the "proposed conditions" at the site. In order to show that structures meet Backwater and National Flood Insurance Program Requirements. It is also necessary to analyze the "existing conditions", when replacing an existing structure.

For these reasons, models for culverts shall be developed for three conditions:

• Natural conditions - Includes natural channel and floodplain, including all modifications made by others, but without MoDOT structures,
• Existing conditions - Includes natural conditions and existing MoDOT structure(s),
• Proposed conditions - Includes natural conditions, existing MoDOT structures if they are to remain in place, and proposed MoDOT structure(s).

## 750.2.3 Culvert Hydraulics

Many different types of culvert flow have been observed and classified. However for the purpose of design, only two types of flow are recognized. These are termed inlet control and outlet control. A culvert barrel may flow full over its entire length or may flow partly full. Full flow results in pressure flow within the culvert barrel, while partly full flow is a form of free surface or open channel flow.

It is possible by means of hydraulic computations to determine the type of flow which will exist in a culvert under a given set of conditions. This is done by assuming that inlet control exists and computing the headwater depth at the inlet based on this assumption. Normally inlet control exists for slopes of 1% or greater. Next it is assumed that outlet control exists and the headwater depth at the culvert inlet is again computed. The larger value of headwater depth, obtained from these computations is the true value and defines the flow regime which exists in the culvert. Type of control is a function of the location of the control section.

Headwater is defined as the depth of the upstream water surface measured from the invert at the culvert entrance. The invert is the lowest point inside the culvert at a particular cross-section.

### 750.2.3.1 Inlet Control

Inlet control exists when the headwater elevation depends on the culvert entrance configuration and the barrel is capable of conveying more flow than the inlet will accept. The properties of the inlet, such as the size, shape and edge treatment control the capacity of the culvert. The control section is at or just inside the culvert inlet. The water surface passes through critical depth at this location, and flow is supercritical in the culvert barrel immediately downstream.

When a culvert is operating under inlet control the barrel of the culvert has a greater hydraulic capacity than does the inlet. For this reason the capacity of the culvert is dependent only upon the inlet properties and is independent of barrel properties. Under inlet control the culvert behaves as an orifice.

Nomographs have been developed which provide a headwater-discharge relation for culverts operating under inlet control. These inlet control nomographs are based on an analysis of experimental data obtained from various sources and provides a direct solution to inlet control culvert flow. The following inlet control nomographs may be used in the design and analysis of culverts.

Inlet Control Nomograph for CMP
Inlet Control Nomograph for CMP Arch
Inlet Control Nomograph for Concrete Pipe
Inlet Control Nomograph for Elliptical Concrete Pipe
Inlet Control Nomograph for Box Culverts

Given the size of the culvert and the flow rate of the culvert the submergence ratio of the culvert, i.e. headwater depth divided by the Depth of the Culvert (HW/D), may be read directly from these nomographs. Use of these nomographs is illustrated on each figure by means of an example.

### 750.2.3.2 Outlet Control

Outlet control exists when the headwater elevation depends on the culvert barrel geometry or downstream conditions and the inlet is capable of conveying more flow than the barrel will accept. The control section is either at the downstream end of the barrel or further downstream.

Outlet control may be of two types; full flow and part full flow. Outlet control with part full flow will occur only when the submergence ratio (HW/D) is near or less than 1.0 and when the culvert is on a mild (subcritical) slope. This type of flow does not occur often in small culverts. Also part full flow under outlet control is very complex and requires the computation of a backwater curve. For these reasons this type of flow will not be treated in detail in this article. However, part full outlet control flow is recognized in the computer program which is available for culvert design computations and occasionally culvert design will be based on this flow regime.

Full flow outlet control occurs when the culvert barrel flows full throughout its length. This is the most common type of outlet control and the only type to be considered when design computations are carried out by hand. Hereafter the term outlet control will refer to full flow outlet control unless otherwise specified.

#### 750.2.3.2.1 General Outlet Control Equation

Culverts flowing under outlet control may be modeled by the pipe flow formula as follows:

${\displaystyle H=\left[1.0+K_{e}+{\frac {29n^{2}L}{R^{1.33}}}\right]{\frac {Q^{2}}{2gA^{2}}}}$
where:
ke = entrance loss coefficient for a given inlet. Design values for the coefficient "ke" are given in the Entrance Loss Coefficients Table
n = the roughness coefficient of the culvert barrel. Design values for the coefficient "n" are given in the Roughness Coefficients for Various Materials Table and EPG 750.1.4.1.1, Composite Roughness
L = length of culvert barrel, ft.
R = hydraulic Radius of the culvert barrel, ft.
Q = the culvert discharge in ft3/s
A = culvert waterway area in ft2
Entrance Loss Coefficients
Type of Structure and Entrance Coeficient, ke
Pipe, Concrete
Projecting from fill, socket end 0.20
Projecting from fill, square cut end 0.50
Beveled to conform to fill slope 0.70
End section conforming to fill slope (flared end section) 0.50
Socket end of pipe (previously used by MoDOT) 0.20
Square edge 0.50
Pipe, or Pipe-Arch Corrugated Metal
Projecting from fill (no headwalls) 0.90
Headwall or headwall and wingwalls - square edge (previously used by MoDOT) 0.50
Beveled to conform to fill slope 0.70
End section conforming to fill slope (flared end section) 0.50
Box, Reinforced Concrete
Headwall parallel to embankment (no wingwalls)
Square edge on 3 edges 0.50
Rounded on 3 edges to radius of 1/12 barrel dimension or between edges on 3 sides 0.20
Wingwalls Parallel (extension of sides)
Square-edge at crown or square edge (0° flare) (used by MoDOT) 0.70
Wingwalls at 30° to 75° to barrel
Square edged at crown or square edge (30° - 75° flare) (used by MoDOT) 0.40
Crown edge rounded to radius of 1/12 barrel dimension or beveled top edge 0.20

The above equation accounts for energy losses in the culvert due to the development of the velocity head, entrances loss, and friction loss. Outlet control nomographs have been developed which provide a graphical solution to this equation for various culvert material, cross section, and inlet combinations. Use of these nomographs is illustrated on each figure by means of an example.

Outlet Control Nomograph for CMP
Outlet Control Nomograph for Structural Plate CMP
Outlet Control Nomograph for CMP Arch
Outlet Control Nomograph for Structural Plate CMP Arch
Outlet Control Nomograph for Concrete Pipe
Outlet Control Nomograph for Elliptical Concrete Pipe
Outlet Control Nomograph for Square Concrete Box Culvert

#### 750.2.3.2.2 Head Loss Due to Bends

Occasionally it is necessary to build a culvert which has one or more bends in the alignment. If this culvert is operating under outlet control then these bends will reduce the capacity of the culvert. The head loss due to bends may be estimated by the following formula. To minimize these losses, the culvert should be curved or have bends not exceeding 15° at intervals of not less than 50 feet. Under these conditions, bend losses can normally be ignored. If the culvert alignment is changed by means of a circular curve with a radius equal to or greater than four culvert diameters, then energy loss in the bend may be ignored.

${\displaystyle H_{b}=K_{b}{\frac {v^{2}}{2g}}}$
where:
Kb = the bend loss coefficient. The bend loss coefficient "Kb" may be estimated as follows:
${\displaystyle K_{b}=0.50{\sqrt {\frac {\Delta }{90}}}}$
where:
Δ = the angle of the bend in degrees.

If bend losses are encountered in design, these losses should be computed by the above equation and added to the total head obtained by application of the general outlet control equation. In this manner the total required energy head will be obtained.

The actual headwater depth at the culvert inlet depends on the total head as discussed above, the culvert outlet conditions, and the length and slope of the culvert barrel. These items will be covered in detail in the discussion of outlet control computations.

## 750.2.4 Design Data

The design data which are necessary for the hydraulic design of a given cross road structure are as follows:

• Design Discharge, Q, ft3/s
• Allowable Headwater depth, AHW, ft.
• Type of culvert
• Length of culvert, L, ft.
• Slope of culvert, So, ft./ft.
• Tailwater depth at culvert outlet, TW, ft.

The design discharge is obtained by means of a hydrologic analysis of the watershed being drained using the guidance in EPG 749.2.1 Design Frequency Criteria.

The allowable headwater depth is defined as the maximum depth of water which may be allowed at the culvert inlet.

The type of culvert (barrel material) and inlet type, is usually governed by the type of highway being designed. The designer does, however, have the option of considering both a box culvert and a circular culvert at any given location. At locations where it is questionable which type of structure will yield the most economical design, both structure types should be considered and the least costly type should be selected.

The length and slope of the culvert are functions of the stream being enclosed, the geometry of the highway embankment and the skew angle of the culvert. Design values may be obtained by scaling from the strip map or cross-sections.

The tailwater depth is influenced by conditions downstream of the culvert outlet. If the culvert outlet is operating in a free outfall condition then the tailwater is taken as 0. If the culvert discharges into an open channel, then the tailwater is equal to the normal depth of flow in that channel. If the culvert outlet is located near the inlet of a downstream culvert, then the headwater elevation of the downstream culvert may define the tailwater depth for the upstream culvert. In any case the tailwater depth is defined as the depth of water measured from the flow line of the culvert (invert) at the outlet, to the water surface elevation at the outlet.

## 750.2.5 Backwater

The design headwater elevation may be dependent upon the culvert length. Therefore, an iterative procedure may be necessary to determine the optimum culvert design. See also EPG 748.4 Headwater and Backwater.

## 750.2.6 Selecting a Trial Culvert Size

The hydraulic design of culverts is a trial and error procedure; whereby a culvert size is assumed and this trial culvert is analyzed to determine if it satisfies the design conditions. For this reason the amount of work involved in the hydraulic design of culverts is highly dependent upon how close the first trial size is to the final culvert size selected.

One method which may be used to select a trial culvert size is the Talbot formula. The Talbot Formula relates required waterway area to watershed drainage area. This formula is well known and will not be presented here. The Talbot formula may also be used to obtain rough estimates of culvert requirements at an early stage of design such as in the preparation of the preliminary strip map.

Another method which may be used to obtain a first estimate of the required waterway area is by assuming an average velocity of flow at the culvert inlet. By this method the trial culvert waterway area, "a" is set equal to the design flow rate, "Q" divided by the assumed velocity of flow. The entrance velocity is generally near 10 feet per second.

## 750.2.7 Inlet Control Computations

All inlet control computations are carried out with the aid of the inlet control nomographs. Knowing the size and flow rate of the culvert, the submergence ratio "HW/D", may be read directly from these nomographs. For pipe or pipe arch culverts the submergence ratio is presented as a direct function of the culvert size and discharge. For box culverts it is necessary to first determine the flow rate per foot of width, "Q/B", expressed in cfs per foot. The submergence ratio is then given as a function of the height of the box "D", and the flow rate being conveyed per foot of box, "Q/B".

Knowing the submergence ratio "HW/D", the headwater depth "HW", expressed in feet is computed as follows.

${\displaystyle H={\frac {HW}{D}}D}$
where:
D = the height or diameter of the culvert, ft.

Each nomograph has three submergence ratio scales and each of these scales corresponds to a different inlet treatment. Care should be taken to use the scale corresponding to the inlet type being investigated.

## 750.2.8 Outlet Control Computations

The computation of headwater depth based on outlet control is somewhat more complex than are the inlet control computations. Several separate steps are involved.

### 750.2.8.1 Computation of Total Head (H)

The total energy head required to pass a given flow rate through the culvert may be computed by the pipe flow formula as previously discussed, or by use of the proper outlet control nomograph.

On the outlet control nomographs the total head "H" is presented as a function of the entrance loss coefficient "Ke", the length of the barrel "L", the size of the culvert, and the discharge "Q". Two steps are required to use these nomographs. First given the entrance loss coefficient "Ke", the barrel length "L", and the culvert size a point on the turning line of the nomograph is established. Next, given the discharge "Q", and the point on the turning line, the total head "H" is read directly from the chart. This procedure is illustrated on each of the outlet control nomograph.

These nomographs provide a graphical solution to the pipe flow equation assuming that there are no losses due to bends. If bends are encountered in design, the bend loss, "Hb", should be computed by means of the previously discussed equations for head loss due to bends. The computed value of the bend loss is added to the value of total head "H" obtained from the proper outlet control nomograph in order to obtain the true value of total head.

It should be noted that Outlet Control Nomograph for Square Concrete Box Culverts applies to square box culverts only. When analyzing box culverts of rectangular cross section the total head must be computed by means of the general pipe flow equation. The nomograph does not apply in this case.

### 750.2.8.2 Determination of the Design Tail Water (DTW)

The tailwater condition which prevails during the design event is termed the design tailwater "DTW". The design tailwater may be a function of downstream conditions, or of the culvert outlet conditions. The depth of water at the culvert outlet due to downstream conditions is termed the tailwater "TW", and has been previously discussed under "Design Data".

The distance from the flow line at the culvert outlet, to the elevation of the total energy line at the culvert outlet, is termed the head at the outlet "ho" and is computed as follows:

${\displaystyle h_{o}={\frac {D+d_{c}}{2}}}$

where:

ho = the head at the culvert outlet, ft., for a nonsubmerged outlet condition. D = the depth of the culvert, ft. dc = the critical depth at the culvert outlet, ft.

The critical depth for various sizes and types of culverts may be determined from the following graphs:

Critical Depth for Circular Pipe
Critical Depth for Box Culverts
Critical Depth for Elliptical Concrete Pipe
Critical Depth for CMP Arch
Critical Depth for Structural Plate CMP Arch

If the critical depth "dc", read from the charts is greater than the depth of the culvert "D", then "ho" is set equal to "D".

Knowing the tailwater depth at the outlet, "TW" and the total head at the outlet "ho" the design tailwater "DTW" is determined as follows:

 for ho > TW → DTW = ho for ho < TW → DTW = TW

Having established the total head and the design tailwater depth, the headwater depth is computed as follows:

${\displaystyle HW=H+DTW-S_{o}L\,}$
where:
HW = the headwater depth for outlet control, ft., and all other terms are as previously defined.

It should be noted that the product of the culvert slope times the culvert length "SoL", is equal to the difference in elevation between the culvert inlet and the culvert outlet. This value may be substituted for the "SoL" term in the above equation.

## 750.2.9 Culvert Design Procedure

The procedure which is to be used for the hydraulic design of crossroad drainage structures is given in five steps as follows:

STEP 1. Assemble Design Data.
STEP 2. Assume a culvert size then adjust the size of the culvert by means of inlet control computations and environmental requirements for culverts. The smallest size culvert which will meet environmental requirements and pass the design flow rate at or below the allowable headwater depth is selected as the trial culvert size.
STEP 3. Find the actual Headwater Depth "HW", for trial culvert.
a. Inlet Control Computations.
b. Outlet Control Computations.
c. Compare headwater depths found in Step 3a and 3b. The large value governs.
STEP 4. Compare HW to AHW.
a. If HW < AHW, culvert is adequate. However a smaller culvert may be considered.
b. If HW > AHW increase culvert size and go to Step 3.
STEP 5. Compute Outlet Velocity for Design Discharge.
a. For inlet control use the Manning Equation.
b. For outlet control use V = Q/A.

## 750.2.10 HY-8 Culvert Analysis

The FHWA HY-8 computer program is available for the analysis and design of culverts.

### 750.2.10.1 Required Input Data

Below are the data required for HY-8 culvert calculations.

Discharges - Both the design discharge and a maximum discharge are required inputs. HY-8 will compute a hydraulic performance curve for a range of discharges based on the minimum and maximum discharges, and will also perform calculations for the design discharge.

Culvert Invert Data - The station and elevation for both the inlet and outlet inverts are used to determine the length of the culvert. Another option allows the input of information defining the embankment and streambed slopes. HY-8 will then use this information and the culvert height to compute the culvert length.

Roadway Data - Various information regarding the roadway is required. This information is used in weir flow calculations when the roadway is overtopped. A fixed roadway crest elevation and length can be input or coordinates describing the top of roadway can be used. The type of roadway (paved or graveled) or a weir coefficient must be input, along with the roadway width.

Tailwater Data - Tailwater depths must be provided for the various discharges used in the analysis. Several input options are available, including providing a tailwater rating curve (depth vs. discharge at the culvert outlet), providing either a natural or a prismatic channel cross-section, or providing a constant tailwater elevation. HY-8 will calculate a tailwater rating curve when a channel cross-section is input. It is recommended that either a channel cross-section be used or a tailwater rating curve be developed independently of HY-8; using a constant tailwater elevation can result in incorrect headwater elevations for the outlet control computations.

Culvert Geometry - The culvert geometry must be provided, including the number of barrels, culvert span and rise, and inlet configuration. The inlet configuration options include conventional and improved inlets, with various combinations of headwall bevels and wingwall flares for each. The "Square Edge (0 deg. flare)" and "Square Edge (30-75 deg. flare)" wingwall options should be used for standard MoDOT culverts with straight and flared wingwalls, respectively.

### 750.2.10.2 Minimize Culvert Span

HY-8 provides an option for determining the minimum culvert span for a given culvert rise and design headwater elevation. The design headwater elevation required for this input is the normal water surface at the culvert inlet plus any allowable backwater.

### 750.2.10.3 Improved Inlets

For culverts operating under inlet control, cost savings may be realized by using an improved inlet. This is especially true for extremely long culverts. Side-tapered inlets are the most often used type of improved inlet. Refer to Hydraulic Design of Highway Culverts - HDS No. 5 for details on design of improved inlets.

## 750.2.11 Data Required on Plans

In addition to the type, size and length of the culvert certain design data are shown on the construction plans for crossroad culverts. This data can also be provided for entrance culverts when deemed appropriate. Among these data are the drainage area of the watershed, the design discharge, the design frequency and the overtopping flood. The following is an example of how these data may be presented on the plans:

D.A. = 70 ac.
Q25 = 160 cfs
QOT = 200 cfs (50-year)

The above indicates that the culvert provides drainage for 70 acres of land, the 25-year design flood peak is equal to 160 cfs and the road overtops at the 50-year flood equal to 200 cfs.

In addition to the above data, the elevation of the culvert flow line at the inlet and at the outlet should be shown on the profile portion of the plan-profile sheets. These elevations may be below the natural stream bottom in accordance with EPG 750.7.3 Environmental Requirements.

The design flood elevation is shown on the profile portion of the plan-profile sheets, at locations where discharges of 500 cfs or more are potentially present, and at other locations where special consideration is required of inlet and erosion control problems.

For data requirements when Bridge Division is responsible for the plans, see EPG 750.7.4.3 Summary of Responsibilities.