Culvert Hydrology

culvert hydrology

The primary product or result in engineering culvert design projects is the culvert size.  Obviously, the determination of a design flow is of primary importance, and the hydraulic calculations have the design flow as a key input variable.  Here we will summarize the hydrologic process and calculation procedures.

The Rational Method

As the name suggests, this is a very simple, intuitive method.  It is based on a uniform rainfall over a drainage basin.  If the entire watershed in question has a constant, uniform rainfall for a specified time period, the flow rate at an outflow point should eventually equal that full basin inflow.  As you can probably imagine, this rainfall needs to occur for the time period for which the last drop at the highest point in the basin takes to reach the outflow point.  This time period is called the time of concentration, and it should be calculated first in order to perform a good rational method calculation.

Obviously this method makes a healthy amount of assumptions.  That being said, I think the rational method will always be popular because the many variables are reduced into readily comprehended pieces of information that can be visualized and compared to your “gut feel.”

The SCS Method

This method was developed by the Soil Conservation Service (now Natural Resources Conservation Service) who wanted a way to incorporate the soil infiltration parameters into the calculation.  There are several steps, include the choosing of a “curve number” which is in turn based on a soil type (A, B, C, or D).  The curve number is then adjusted for antecedent moisture conditions (current conditions).  Thus, the calculations are slightly more comprehensive, but it is less intuitive and able to be visualized than the rational method.

The time of concentration is also important for the SCS Method, in fact it is an input variable rather than just information for the designer.  In the SCS Method, the designer needs to choose a “design storm” which is defined by a rainfall intensity and duration.  This is taken from Intensity-Duration-Frequency (IDF) curves, which are normally available in the United States via government environment departments.  The intensity-duration combination must correspond to the time of concentration of the watershed.

Time of Concentration

The three most popular methods of calculating the time of concentration of a drainage basin are:

  • Kirpich Method:  The most-used method.  It requires as input variables the length of water travel down the stream, the difference in elevation from the highest point of the watershed, and the slope of the channel.  It combines both the overland flow (entry time into the channel) and the travel time within the channel.
  • FAA Method:  Back in the 1960’s, the FAA determined a more accurate way to calculate the time of concentration where the slope and surface cover is relatively uniform (think air fields).  This is also widely used in many urban areas since slope and surface cover are often also quite uniform, but one should keep these limitations in mind when using it.
  • Bransby-Williams formula:  This formula takes into account the travel distance and time through the channel, and serves as a good check.  It probably underestimates the time of concentration for permeable basins that hold the water well before depositing it into the channel.

Other Methods and Definitions

The field of hydrology is complex.  The following provides just some of the other methods you should be familiar with:

  1. Hydrograph:  The plot of a stream’s discharge (flow rate) over time.  For the design of culverts, the most important part of the hydrograph is the peak.
  2. Rainfall Hyetographs:  A graphical representation of the distribution of rainfall over time.  If these are available from the local weather office, they can be a good source of information for the rainfall intensity assumption.  One must not confuse the design rainfall event with the data from one single event though.
  3. Return Period:  The theoretical length of time it takes for a certain flow rate to reappear.  For example, a 1:50 year flood will occur once every 50 years.  In the field of culvert design, these are usually specified by the road authority (city, county, state, etc.)
  4. Uplands Method:  Used for calculating the overland flow time.  In other words, it calculates a time of concentration but does not take into account the flow time through the channel.
  5. Kinematic Wave Method:  Another less popular method of calculating the time of concentration.
  6. Infiltration:  The rate at which rainfall enters the groundwater and is effectively lost (for runoff purposes).
  7. Detention:  Ponds, lakes, or other surface features which hold rainfall and release in gradually.
  8. Flow routing:  The process of modelling the flow throughout multiple channels within a drainage basin to determine the flow at a common point.  Various methods exist, such as level-pool routing, distributed flow routing, saint-venant equations, and the muskingum-cunge method.  For culvert projects this is usually only performed for larger site (Drainage area of 50 mi2+).
  9. Antecendent moisture conditions:  The amount of moisture present in the soil before the analysis takes place.  The higher the antecedent conditions, the more the soil is “saturated” and thus the higher the flow rate from the current storm.


About Bernie Roseke

Bernie Roseke, P.Eng., PMP, is the president of Roseke Engineering. As a bridge engineer and project manager, he manages projects ranging from small, local bridges to multi-million dollar projects. He is also the technical brains behind ProjectEngineer, the online project management software for engineers. He is a licensed professional engineer, certified project manager, and six sigma black belt. He lives in Lethbridge, Alberta, Canada, with his wife and two kids.

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