Analysis of Culvert Systems

When engineers analyze culvert systems, they are usually trying to make one or more of the following basic determinations:

x Determine the size, shape, and number of new or additional culverts required to pass a design discharge.

x Predict the hydraulic capacity of an existing culvert system under some allowable headwater elevation.

x Predict the upstream flood level at an existing culvert system resulting from some check discharge or other discharge magnitude or special interest.

x Develop hydraulic performance curves for a culvert system for assessing hydraulic risk at a crossing or as input to another hydraulic or hydrologic model.

CulvertMaster models complete culvert systems. A roadway cross-drainage culvert system is typically designed to safely carry flood flows from one side of the road to the other. The culvert system consists of the following hydraulic components:

x Hydrology – An upstream watershed drainage area discharging design and check storm flows to the culvert system. The magnitude of these discharges is computed using an accepted hydrological method such as Rational, SCS Peak, application of a state Regression Equation, or some other suitable methodology.

x Culvert Hydraulics – One or more culvert barrels along with associated headwalls, wingwalls, and other types of end treatments, which convey flow through a roadway embankment. The performance of these culverts is described using culvert hydraulics.

x Roadway Overtopping – A roadway embankment may be subject to overtopping flows if the total capacity of the culvert(s) is exceeded. Such overtopping flows are analyzed using weir hydraulics.

x Tailwater – A natural stream, improved channel, or other waterway at the discharge or tailwater side of the roadway embankment. The hydraulic response of the downstream discharge areas affects the capacity of the total culvert system. Tailwater is analyzed using uniform flow assumptions or separate floodplain analyses.

54 Chapter 5 – CulvertMaster Theory

5.2 Hydrology

CulvertMaster offers the rational method, SCS peak discharge method, and user-defined peak discharge for input of the design and check storm flows.

5.2.1 Rational Method

The rational method solves for peak discharge based on watershed area, rational coefficient, and rainfall intensity for the watershed.

The rational method is based on the simple rational equation:

Q CiA

Q AiR

Where Q = Design flow rate (cfs, m³/s)

C = Rational coefficient for drainage area R = Rational coefficient for drainage area i = Rainfall intensity (in/hr, mm/hr) A = Drainage area (acres, hectares)

In English units, CulvertMaster uses the conversion factor 1.008 ac-in/hr per cfs. This factor converts the units of intensity in inches/hr and the drainage area in acres to flow units of cubic feet per second. In SI units, the conversion factor is 0.002778 hectare-mm/hr per m³/s. C, the rational coefficient, is the parameter that is most open to engineering judgment. Engineering references contain tables that will help you estimate C. The following table shows rational coefficients for common land uses. In many cases, an area weighted average of C coefficients is used for the entire drainage area. CulvertMaster will calculate the weighted C for drainage areas.

Table 5-1 - Table of Rational Coefficients

Area C Values

Business Downtown

Neighborhood 0.70-0.95

0.50-0.70 Residential (1.2 acre lots or

more) 0.30-0.45

Industrial Light

Heavy 0.50-0.80

0.60-0.90 Parks and Cemeteries 0.10-0.25

Playgrounds 0.20-0.40 Drives and Walks 0.75-0.85 Lawns, Sandy soils

5.2.2 Intensity-Duration-Frequency (IDF) Curves

The rainfall intensities for which you will be designing your culverts are determined by regulatory agencies. Historical rainfall information has been analyzed and compiled into IDF Curves based on the frequency of the storm events. These curves provide a quick reference for determining the intensity of rainfall that will occur at given return periods.

56 Chapter 5 – CulvertMaster Theory Figure 5-1 - Linear Intensity Duration Frequency Curve

IDF curves can be extremely useful when performing hand calculations using the rational method. They are less useful when used for computer programs or spreadsheet calculations because you have to look up values and enter them each time you need intensity data. For this reason, it is often easier to use rainfall tables or rainfall equations to calculate IDF curves.

Rainfall Tables

CulvertMaster lets you enter data in a rainfall table and saves the data so you may use it again for other projects. Entering the design intensities for your culvert analysis is simply a matter of looking up data from a graph and entering it into the Rainfall Table. Once the rainfall intensities are gathered, it is helpful if you make a table to enter the data.

Table 5-2 - Table of Rainfall Intensities

Duration Return Periods

2-year 5-year 10-year 25-year 50-year 100-year

5 min 7.20 7.86 8.42 9.33 10.01 10.80

10 min 6.02 6.67 7.20 8.04 8.71 9.38

15 min 5.20 5.84 6.35 7.14 7.77 8.40

30 min 3.88 4.42 4.84 5.48 5.98 6.49

60 min 2.50 2.94 3.26 3.74 4.12 4.50

CulvertMaster has provided a tabular format for entering rainfall volumes obtained from the National Weather Services’ Hydro-35 technical report. Hydro-35 provides a methodology for estimating rainfall volumes for durations of 5 minutes to 60 minutes for the eastern United States.

Rainfall Equations

IDF curves can be fit to equations with high accuracy. The most common form of these equations is:

 ^{b D} 

Other equations supported in CulvertMaster are:

5.2.3 SCS Peak Discharge Method

The SCS Peak Discharge method solves for peak discharge based on watershed area, site specific hydrologic conditions expressed through the curve number (CN), rainfall distribution type, and rainfall depth.

SCS Peak Discharge method is based on the following equations:

p

S = Potential maximum retention after runoff begins (in, mm) Ia = Initial abstraction (in, mm)

58 Chapter 5 – CulvertMaster Theory

The CulvertMaster implementation of the SCS-graphical peak discharge follows the procedures and methodology set forth in Chapter 4 and Appendix F of the SCS-TR-55 (1986) manual.

Table 5-3 - Runoff Curves for Urban Areas

COVER DESCRIPTION CURVE NUMBERS FOR

HYDROLOGIC SOIL GROUP

Cover type and hydrologic condition Average percent impervious area

A B C D

Fully developed urban areas (vegetation established) Open space (lawns, parks, golf courses, cemeteries, etc.):

Poor condition (grass cover < 50%) Fair condition (grass cover 50 to 75%) Good condition (grass cover > 75%)

68

Paved parking lots, roof, driveways, etc.

(excluding right-of-way) Gravel (including right-of-way) Dirt (including right-of-way)

Natural desert landscaping (pervious areas only) Artificial desert landscaping

(impervious weed barrier, desert shrub with 1- to 2-inch sand or gravel mulch and basin borders)

63

Commercial and business Industrial Residential districts by average lot size:

1/8 acre or less (town houses)

Newly graded areas (pervious areas only, no

vegetation) 77 86 91 94

Idle lands (CN’s are determined using cover types similar to those in Runoff Curve Numbers for other Agricultural Lands)

Notes: ¹Average runoff condition, and Ia = 0.2S.

Other runoff curve number tables can be found in Chapter 2 of the SCS-TR-55 (1986) manual.