A bottomless or threesided culvert is a variation of wellknown culvert configurations such as the box culvert and the arch. Bottomless culverts can have a span ranging from 1.5 feet to more than 35 feet. The difference is that in place of a hard surface (typically concrete) floor, the culvert bottom is the natural stream bed material. Advantages to this are a more environmentally congruous stream path, as well as typically lower construction costs. The engineer's concern then becomes planning for how the natural stream bed will react to the construction of the culvert during all flow regimes and what protective measures might be necessary to protect the culvert from scour or aggradation.
A preliminary study should be done in the area of the proposed culvert to determine local site characteristics. It is important to know whether the stream is aggrading or degrading in the reach. Aggradation/degradation is a longterm process that does not include cutting and filling that may occur during temporary, highflow events. When considering aggradation or degradation, the engineer must consider the planned life of the bridge in addition to the present state of the stream reach. This means assessing longterm changes to the watershed resulting from natural processes or human activities. Changes can include construction of a dam or reservoir upstream or downstream of the reach, modifications in watershed land use such as logging or urban development, and stream channelization. Government agencies such as the U.S. Army Corps of Engineers (Corps), the U.S. Geological Survey, and other local, state, and federal agencies should be contacted for any documentation they may have of longterm streambed elevation changes. If there is no existing data or the data is of insufficient quality, make an assessment using the principles of river mechanics, considering all relative influences on the bridge's crossing.
HEC18, Evaluating Scour at Bridges, outlines a threestep procedure in to determine longterm aggradation and degradation. The threelevel approach consists of the following:
 Level 1 — a qualitative determination based on general geomorphic and river mechanics relationships,
 Level 2 — an engineering geomorphic analysis using established qualitative and quantitative relationships to estimate the probable behavior of the stream system to various scenarios or future conditions, and
 Level 3 — physical models or physical process computer modeling using mathematical models such as BRISTARS and the Corps' HEC6 to make predictions of quantitative changes in streambed elevation due to changes in the stream and watershed.
Methods to be used in Levels 1 and 2 are presented in HEC20 and Highways in the River Environment (HIRE). Once the longterm characteristics have been ascertained, the decision to build a bottomless culvert must be reevaluated to decide if it is the best choice. Provided the decision is made to move forward, the engineer must determine general scour that will occur. For this article, a bottomless culvert with a single barrel will be considered. The general principles may be expanded to multiple barrels provided pier widths and local pier scour are taken into consideration.
figure 1A: Overbank flow conveyed into the main channel approaching a culvert
General scour
General scour is the general lowering of the stream bed in close proximity to the bridge. General scour does not include the longterm changes caused by aggradation or degradation, and it also does not include localized scour that may occur at abutments, piers, and foundations. General scour does include the cutting and filling that may occur during temporary, high flow events. The most common general scour is contraction scour resulting from increased flow velocities as the stream cross sectional area decreases approaching a stream crossing. Other causes of general scour are the planform of the stream, flow around a bend, variable downstream control, or any other changes that result in a decrease in bed elevation at the bridge.
There are two classes of contraction scour, each with equations based on the principle of conservation of sediment. Livebed contraction scour occurs when the sediment transported into the bridge cross section is less than the sediment transported out of the cross section — Q_{s}, in < Q_{s}, out, where Q_{s} = sediment discharge. The result is an increase in the cross sectional area until Q_{s}, in = Q_{s}, out. Clearwater contraction scour takes place under the following two conditions:
 There is no sediment being transported into the cross section from the upstream reach, Q_{s}, in = 0, or
 Any sediment being transported into the cross section is in suspension and does not meet the flow's capacity to carry sediment, Q_{s}, in < Q_{s}, capacity.
figure 1b: Overbank flow conveyed into the main channel approaching a culvert
Again, the cross sectional area will increase, but clearwater scour will continue until the critical shear stress, t_{c}, of the stream bed material is reached through a change in stream velocity (i.e., decreasing velocity due to increasing cross sectional area) or a change in particle size distribution of the stream bed (i.e., bed armoring).
HEC18 provides four types of contraction scour, which depend on the type of contraction and whether there is overbank flow or relief bridges. Each of these cases can be evaluated using either livebed scour or clearwater scour equations. To determine if livebed or clearwater conditions prevail, calculate the critical velocity, V_{c}, of the median diameter, D_{50}, of the bed material and compare it to the average flow velocity, V. If V_{c} < V, livebed conditions exist; if V_{c} > V, a clearwater condition exists.
From HEC18, the equation for Vc is:
Equation 1:
Where:
V_{c} is the critical velocity above which any particle smaller than D will be transported, in feet per second(ft/s);
y is the average upstream depth of flow (feet);
D is the D_{50} (in feet) of the streambed material upstream of the culvert in the upper 1 foot of the bed.
The distance upstream that must be considered is a matter of engineering judgment. In the case where livebed contraction scour is limited by armoring or sediment transport into the culvert cross section, it is acceptable to calculate scour depths resulting from clearwater and livebed contraction scour equations and use the smaller depth.
As previously mentioned, there are four types of contraction scour conditions to consider:
 Condition 1 — Overbank flow is forced back to the main channel approaching the culvert (see Figures 1abc for examples of this type).
 Condition 2 — Flow is contained within the main channel (Figures 2ab).
 Condition 3 — A relief bridge under clearwater scour conditions exists in the overbank area.
 Condition 4 — A relief bridge in the overbank area passes over a secondary stream that carries bed material.
Conditions shown in Figures 1a, 1b, and 2 need to be analyzed for livebed versus clearwater scour using Equation 1 above. It is possible that the bed material will simply be washed through the contraction, as well. To determine this, compute the ratio of shear velocity, V, in the contraction to the fall velocity, ? (ft/s) (Figure 3), of the D_{50} of the transported bed material.
Equation 2:
where:
g is acceleration due to gravity (ft/s^{2}),
y is the average upstream depth (feet),
S is the slope of the energy grade line of the main channel (feet/feet).
If V/? is much larger than 2, a clearwater scour condition may exist as the majority of the bed material from upstream will most likely remain suspended and wash through the contraction.
Condition 3 may not be livebed load even though flow velocity exceeds the minimum critical velocity. Frequently, overbank areas of the main channel are vegetated, which could reduce or eliminate sediment transport, or fine sediment bed material may be transported in suspension as previously discussed. Condition 4 is a combination of Conditions 1 and 3 with livebed load. Under Condition 4, the hydraulic analysis follows Condition 1 with the additional requirement of determining the quantity and distribution of floodplain discharge that will pass through both the secondary and the main channels.
figure 1C: Overbank flow conveyed into the main channel approaching a culvert
The condition shown in Figure 1c is the most complex, with considerations such as the abutment's setback from the bank line, condition of the overbank (such as soil characteristics, vegetative state, and height above stream level), stream width at the cross section versus upstream, quantity of overbank flow that will be forced through the culvert opening, and flow distribution in the culvert cross section. Various software packages such as HECRAS may be used to determine the flow distribution, but engineering experience must be applied as well since studies have shown that conveyance calculations do not properly account for flow distributions under bridges. In addition, HEC18 states that if the abutment setback is less than three to five times average flow depth, the possibility exists that contraction and abutment scour may combine to destroy the bank, so some form of protection should be considered for the bank and bed in the overflow area inside the culvert.
Once the applicable condition has been determined, scour depths may be calculated using the appropriate equation (livebed or clearwater contraction scour). Livebed contraction scour may be computed using Equations 3 and 4:
Equation 3:
Equation 4:
Where:
y_{s} is the average depth of contraction scour (feet),
y_{1} is the main channel average upstream depth (feet),
y_{2} is contraction average depth (feet),
y_{0} is the existing contraction depth prior to scour (feet),
Q_{1} is the upstream main channel discharge (do not include overbank flows) in cubic feet per second (ft^{3}/s),
Q_{2} is the discharge through the contraction (ft^{3}/s),
W_{1} is the main channel upstream bottom width (feet),
W_{2} is the contracted bottom width minus pier width(s) (feet),
k_{1} is a conditional exponent determined from Table 1,
where V and ? are defined.
Table 1: Livebed Contraction Scour Exponent, k_{1}

V/?

k_{1}

Mode of Transport

<0.50

0.59

Mostly rolling, sliding, and saltation

0.50 – 2.0

0.64

Some suspended bed material

> 2.0

0.69

Mostly suspended bed material

Table 2: Abutment Shape Coefficients, K_{1}

Abutment type description

K_{1}

Verticalwall

1

Vertical wall with wing walls

0.82

Spillthrough

0.55

Under Condition 1_{c}, contraction scour must be determined separately for the main channel and the overbank areas, requiring multiple applications of the applicable contraction scour equations using the appropriate depths, widths, and discharges. Clearwater contraction scour may be calculated using Equations 5 and 6:
Equation 5:
Equation 6:
Where:
y_{2} is contraction average equilibrium depth after contraction scour (feet),
Q is the discharge through the culvert or on the abutment's setback area (ft^{3}/s),
D_{m} is the diameter of the smallest nontransportable particle in the bed material of the contraction (equal to 1.25D_{50}) (feet),
D_{50} is the median diameter of the bed material (feet),
W is the contracted bottom width minus pier width(s) (feet),
y_{0} is the average existing contraction depth prior to scour (feet).
If bed material stratification exists, the depth of scour can be calculated using multiple applications of the clearwater scour equation with successive D_{m} sizes. Note: In extreme backwater conditions, low upstream flow velocities can cause upstream sediment storage and change a livebed scour condition to one of clearwater scour.
General scour may also result from channel morphology, changes in the morphology from natural or manmade causes, and shortterm changes in downstream water surface conditions. General scour caused by these other factors is beyond the scope of this article but should not be discounted. If other types of potential general scour are suspected, consult an engineer experienced in hydraulics and river mechanics.
Local scour
In addition to longterm aggradation/degradation and general scour, local scour at the abutments must be considered. Field studies and laboratory experiments have shown maximum local abutment scour typically occurs at the corner of the culvert entrance on the upstream side. The depth of local scour depends heavily on culvert entrance conditions and whether livebed or clearwater conditions exist. Livebed abutment scour can be calculated using Froehlich's LiveBed Abutment Scour Equation:
Equation 7
Where:
y_{s} is local scour depth (feet),
y_{a} is average flow depth in the overbank area (feet),
K_{1} is a coefficient for the abutment shape (see Table 2),
K_{2} is a coefficient for the embankment's skew angle,
L' is the length of active flow obstructed by the embankment (see Figure 4) (feet),
F_{r} is the Froude number of the approaching flow upstream of the embankment.
The Froude number is:
Livebed scour may also be calculated using the HIRE equation developed from field data on the Mississippi River. It is applicable when the ratio of projected abutment length (L) to flow depth (y_{1}) is greater than 25. HIRE may be used when conditions are similar to the conditions under which it was derived:
Equation 9:
Where:
y_{s} is the scour depth (feet),
y_{1} is the depth of flow at the embankment or in the main channel (feet),
F_{r} is the Froude number based on conditions adjacent to and upstream of the embankment,
K_{1} is as before (see Table 2),
K_{2} is as before a coefficient for the embankment's skew angle.
The Maryland State Highway Administration (SHA) has also developed livebed and clearwater abutment scour equations for bottomless culverts that incorporate coefficients to account for the nonuniform velocity distribution and the spiral flow that occurs at the abutment toe. Recent work has also been done by the Federal Highway Administration (FHWA) in conjunction with SHA to develop better methods for predicting clearwater abutment scour depths. Study results are available online.
Once aggradation/degradation, general scour, and local scour have been calculated, the sum of the three provides the design condition. Engineering judgment must be used to determine if the total scour depth seems reasonable, what types of scour countermeasure(s) may be used, and whether a bottomless culvert is still the best alternative.
figure 2A: Overbank flow conveyed into the main channel approaching a culvert
Scour countermeasures
There are many types of scour countermeasures. Selecting the most appropriate countermeasure depends on a thorough understanding of the hydraulics and specifics of the countermeasure installation. A minimum factor of safety of 1.5 is used for design when conditions are well known (Legasse et. al., 2007), and a higher factor of safety is typical around abutments and piers because of the complex hydraulic conditions.
The most commonly used scour countermeasure is riprap or partially grouted riprap; however, it is not necessarily the best choice for every application. Other options include articulating concrete block (ACB) systems, concrete armor units, gabions, groutfilled bags and mattresses, and geotextile containers.
A large body of literature is dedicated to sizing riprap for pier and abutment protection. Riprap has the three following failure modes:
 Failure in shear when local flow velocities exceed the riprap's maximum allowable velocity,
 Failure from winnowing when underlying fines are transported through interstitial spaces in the riprap pile, and
 Edge failure when vortices at the edge of the riprap initiate local scour undermining the riprap.
The National Cooperative Highway Research Program (NCHRP) provides an excellent summary of riprap sizing equations, HEC23 provides a stepbystep method, and the Indiana Department of Transportation has standard drawings of threesided concrete culvert scour protection using riprap available on its website (www.in.gov/indot).
figure 2b: Overbank flow conveyed into the main channel approaching a culvert
ACB systems comprise preformed, interlocking concrete blocks attached to one another using rods or cables in conjunction with a filter fabric to form a continuous mat. The flexible interconnectedness of the blocks provides a system with some flexibility to adjust to changes in bed contours but resist largescale removal of sediment resulting from scour. A typical ACB design needs to account for two possible failure modes — leading edge and uplift. It is important to anchor or trench the leading edge of the system to prevent it from rolling, overturning, or even uplift. All three can occur if the leading edge is not properly addressed. ACB systems such as Armorflex are proprietary systems, and system manufacturers can supply information and assistance on how to best incorporate their ACB systems into a design. Design guidance for this countermeasure can be found in HEC23. Concrete armor units are sometimes referred to as artificial riprap because they are frequently used in place of riprap when natural riprap is unavailable or prohibitively expensive.
Figure 3: Fall velocity as a function of grain size and temperature
Concrete armor units such as AJacks are complex precast concrete shapes designed to interlock with one another. Unlike ACB systems, concrete armor units may be placed individually or in groups (held together similarly to an ACB system). Failure modes of these units are similar to those of riprap; the advantage is the greater stability per unit weight versus riprap. Concrete armor units will typically require a filter layer or geotextile. Concrete armor units are also proprietary and assistance incorporating them into a design can be obtained from the manufacturers. Design guidance for this countermeasure can be found in HEC23.
Gabions are collections of cobbles or crushed stone held together in a container made of wire or some other corrosionresistant material. They can be any shape but are typically boxes, mattresses, or sacks. Though gabions have been used for many years, their effectiveness as a scour countermeasure around piers and abutments has not been well documented. Recommendations for the use of gabions as a pier scour countermeasure may be found in Countermeasures to Protect Bridge Piers from Scour, Volumes 1 and 2 (Parker et al., 1998).
Figure 4: Length of active flow, L'
Groutfilled bags and mattresses are concretefilled fabric containers. They are used when riprap is unavailable or relatively expensive, equipment access is limited, or where environmental concerns prohibit the use of riprap. A groutfilled mattress is a single layer and the groutfilled bags are smaller, single units placed in groups. Groutfilled mattresses fail similarly to ACB systems through uplift or rollback; toeing in the leading edge or placing anchors may be done to protect against this. Groutfilled bags are primarily used as an emergency countermeasure. Edge erosion may undermine the bags or they may be carried away in the flow if the bags are not properly sized and placed.
Geotextile containers are large bags made of mechanically bonded, nonwoven fabrics partially filled with sand and gravel. Scourresistant properties are a result of the filtering characteristics of the material and the filler. The containers are made of material specially chosen for site conditions and arrive on site ready to be filled. Geotextile containers must be carefully placed because any gaps between containers defeats the filtering properties.
Successful design
A successful bottomless culvert design depends on a clear understanding of upstream and downstream hydraulic conditions. This includes influencing factors in the watershed that may change over time, resulting in differing sediment conditions at the culvert. The designer needs to use engineering judgment to account for these potential variances. Scour calculations must be taken seriously and done carefully so proper protective measures may be chosen. A good culvert design will pass the required amount of flow, remain structurally sound, reap the environmental benefits of the contiguous channel bottom, and take advantage of the threesided construction to provide a more economically attractive option.
Bryan N. Scholl, is a research assistant for Colorado State University.
Christopher I. Thornton, Ph.D., P.E., is director of the Hydraulics Laboratory and Engineering Research Center at Colorado State University.
REFERENCES
 Kerenyi, Kornel, J.S. Jones, and S. Stein, Bottomless Culvert Scour Study: Phase I and II Laboratory Reports, FHWA, Nov. 2003, Feb. 2007.
 Lagasse, P.F., J.D. Schall, and E.V. Richardson, Stream Stability at Highway Structures, Hydrologic Engineering Circular No. 20, National Highway Institute, March 2001.
 Lagasse, P.F., L.W. Zevenbergen, J.D. Schall, and P.E. Clopper, Bridge Scour and Stream Instability Countermeasures, Hydrologic Engineering Circular No. 23, National Highway Institute, March 2001.
 Lagasse, P.F., P.E. Clopper, L.W. Zevenbergen, and L.G. Girard, Countermeasures to Protect Bridge Piers from Scour, Report 593, NCHRP, 2007.
 Parker, G., C. ToroEscobar, and R.L. Voigt, Jr., Countermeasures to Protect Bridge Piers from Scour, Vol. 1 Users Guide (revised 1999) and Vol. 2 Final Report, NCHRP Project 247, St. Anthony Falls Laboratory, University of Minnesota, 1998.
 Richardson, E.V. and S.R. Davis, Evaluating Scour at Bridges, Hydrologic Engineering Circular No. 18, National Highway Institute, May 2001.