Culverts are an important aspect of our infrastructure. However, they are so common that they seem obvious in some ways, but without them, life would be more complicated. A roadway has to have gentle curves horizontally and vertically. As a result, this means that roadway designers can only go around some obstacles – including rivers or streams. An obvious solution to this problem is a bridge, but bridges are expensive. A more cost-effective solution for a road crossing a smaller stream is a culvert. A culvert is a pipe or hydraulic conduit that coveys a stream or waterway under a road. In reality, there is a significant amount of engineering that goes into designing a culvert. The Federal Highway Administration (FHWA) guidance on culvert design, Hydraulic Design Series (HDS) 5, is over 300 pages! The purpose of this blog is to distill this large amount of information into a quick start guide that will help engineers develop a basic understanding of culvert hydraulic design and culvert modeling.
A culvert has two jobs: 1) it needs to have the structural strength to hold up the roadway and 2) it needs to be able to pass enough water through it. This blog post is going to focus on job number two.
Culvert Terminology
Understanding the terminology used to discuss culvert hydraulics is fundamental to culvert modeling. When using software programs to perform culvert modeling exercises, it is important to understand what is required for each input. The following image from the HEC-RAS Manual depicts the basic configuration of a culvert. The elements shown on this figure will be discussed in further detail below.
Headwater (HW) – The depth of water at the upstream end of the culvert.
Tailwater (TW) – The depth of water at the downstream end of the culvert.
Hydraulic Grade Line (HGL) – The surface of water flowing in an open channel or a pipe flowing partially full. If a pipe is under pressure, the HGL is the level water would rise to in a small, vertical tube connected to the pipe.
Velocity Head – The kinetic energy in a pipe is referred to as velocity head (v2/2g).
Energy Grade Line (EGL) – The sum of the hydraulic grade line (HGL) and the velocity head.
Head Loss (HL) – Head loss refers to the total pressure losses sustained when water flows from the inlet to the outlet point of the culvert. Head loss includes losses at the culvert entrance/inlet (hen), losses at the culvert exit (hex), and friction loss through the pipe (hf).
Culvert Hydraulics Basics
The following section will discuss the types of flow control used to evaluate culverts and the factors that impact culvert hydraulics.
Types of Flow Control
The Federal Highway Administration (FHWA) categorizes culvert flow in two ways – inlet control and outlet control. The hydraulic capacity and efficiency of a culvert depend on the type of flow control at a particular culvert. The following sections will describe the differences between inlet and outlet control. It should be noted that the term control refers to the point where flow is passing through critical depth.
Inlet Control
For inlet control, the control of the culvert is at the inlet because flow passes through critical depth at the inlet and through the pipe at supercritical flow. If the conditions at the inlet were not restricting the flow, the culvert barrel would be able to convey more water. In other words, the tailwater conditions and the culvert barrel itself can accept more flow than the inlet will allow. Because the conditions at the inlet are restricting flow, inlet control culverts will never flow full. Inlet control culverts are typically on a steep slope and through a partially full barrel at supercritical flow. I have been involved in the design of culverts where the steepness of the culvert resulted in flow velocities close to 20 to 25 fps. In these cases, it is necessary to slow down the water through a series of velocity rings which force a hydraulic jump, thus slowing down the water. The factors that impact hydraulic capacity for a culvert under inlet control are as follows:
- Headwater conditions.
- The shape of the culvert barrel (e.g., pipe, box, arch, etc.).
- Inlet configuration (e.g., square edge with headwall, end mitered to the slope, projecting barrel, and beveled entrance).
- Barrel slope has a little bit of an effect because it affects the exit velocity.
During low flows, the entrance to a culvert under inlet control will be unsubmerged, and flow through the culvert entrance will behave like weir flow. However, during higher flows, the culvert entrance may be submerged. In this case, flow through the culvert entrance will behave like orifice flow. Because the hydraulics associated with inlet flow are complex, empirical methods are used to evaluate inlet control hydraulics. If you are interested in learning more about the equations that govern inlet control hydraulics, I recommend studying FHWA Hydraulic Design Series Number 5 (HDS5).
Outlet Control
In contrast to inlet control, culverts under outlet control are on a flatter slope. If the barrel is flowing partially flow, that flow is going to be subcritical. The only time a pipe is going to flow full is in outlet control. As you may expect, the term outlet control means that the control point is going to be located at the culvert outlet or sometimes farther downstream in the tailwater condition. This means the culvert’s ability to convey water is affected by the entrance conditions, the pipe length, and the pipe roughness. The factors that impact culvert capacity in outlet control are:
- The headwater conditions drive flow to overcome friction losses through the barrel.
- The cross-sectional area (size) of the culvert
- The shape of the barrel (e.g., round, arch, elliptical, etc.).
- Barrel slope.
- Inlet configuration.
- Barrel roughness.
- Barrel length.
- Tailwater condition.
Software
When modeling culvert hydraulics, it is important to select software that will accurately represent the culvert conditions and meet the requirements of the agency reviewing your design. Some software programs typically used to model culvert hydraulics include HY-8, WSPG, and FlowMaster. I have been recently using Hydrology Studio for this type of work. It costs $400/year for this software, but the attractive reports and easy-to-use interface are worth the cost to me.
