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Bridge Scour and Stream Instability Countermeasures: Experience, Selection, and Design Guidance-Third Edition

Design Guideline 3 Check Dams/Drop Structures

3.1 BACKGROUND

Check dams or channel drop structures are used downstream of highway crossings to arrest head cutting and maintain a stable streambed elevation in the vicinity of the bridge. Check dams are usually built of rock riprap, concrete, sheet piles, gabions, or treated timber piles. The material used to construct the structure depends on the availability of materials, the height of drop required, and the width of the channel. Rock riprap and timber pile construction have been most successful on channels having small drops and widths less than 100 ft (30 m). Sheet piles, gabions, and concrete structures are generally used for larger drops on channels with widths ranging up to 300 ft (100 m). Check dam location with respect to the bridge depends on the hydraulics of the bridge reach and the amount of headcutting or degradation anticipated.

Check dams can initiate erosion of banks and the channel bed downstream of the structure as a result of energy dissipation and turbulence at the drop. This local scour can undermine the check dam and cause failure. The use of energy dissipators downstream of check dams can reduce the energy available to erode the channel bed and banks. In some cases it may be better to construct several consecutive drops of shorter height to minimize erosion. Concrete lined basins as discussed later may also be used.

Lateral erosion of channel banks just downstream of drop structures is another adverse result of check dams and is caused by turbulence produced by energy dissipation at the drop, bank slumping from local channel bed erosion, or eddy action at the banks. Bank erosion downstream of check dams can lead to erosion of bridge approach embankments and abutment foundations if lateral bank erosion causes the formation of flow channels around the ends of check dams. The usual solution to these problems is to place riprap revetment on the streambank adjacent to the check dam. The design of riprap revetment is given in Design Guideline 4.

Erosion of the streambed can also be reduced by placing rock riprap in a preformed scour hole downstream of the drop structure. A row of sheet piling with top set at or below streambed elevation can keep the riprap from moving downstream. Because of the problems associated with check dams, the design of these countermeasures requires designing the check dams to resist scour by providing for dissipation of excess energy and protection of areas of the bed and the bank which are susceptible to erosive forces.

3.2 BED SCOUR FOR VERTICAL DROP STRUCTURES
3.2.1 Estimating Bed Scour

The most conservative estimate of scour downstream of channel drop structures is for vertical drops with unsubmerged flow conditions. For the purposes of design the maximum expected scour can be assumed to be equal to the scour for a vertical, unsubmerged drop, regardless of whether the drop is actually sloped or is submerged.

A sketch of a typical vertical drop structure with a free overfall is shown in Figure 3.1 An equation developed by the Bureau of Reclamation (Pemberton and Lara 1984) is recommended to estimate the depth of scour downstream of a vertical drop:

Schematic in profile of vertical drop and check dam with parameters of hydraulic head located. The bed elevation is lower below the drop. Plunging water surface and the Energy grade line are shown.  Upstream of the drop, Vertical distances: Elevation head: Z subscript u. Below ground Datum elevation to channel bed distance  Pressure head: y subscript u. Bed elevation to water surface elevation  Velocity head: [V subscript u] squared divided by [2 times g] is Water surface elevation to energy grade line  Downstream of the drop, Vertical distances: Elevation head: Z subscript d is below ground Datum elevation to channel bed.  Pressure head: y subscript d is bed elevation to water surface elevation.  Velocity head: [V subscript d] squared divided by [2 times g] is water surface elevation to energy grade line.  Head loss: H subscript t, is downstream energy grade line to upstream energy grade line Just below drop structure the local scour depth for a free overfall, d subscript s,is measured from the streambed downstream of the drop, ft (m)
Figure 3.1. Schematic of a vertical drop caused by a check dam.

Local scour depth for a free overfall, d subscript s, equals K subscript u times H subscript t to the power 0.225 times q to the power 0.54 minus d subscript m (3.1)

where:

ds = local scour depth for a free overfall, measured from the streambed downstream of the drop, ft (m)
q = discharge per unit width, cfs/ft (m3/s/m)
Ht = total drop in head, measured from the upstream to the downstream energy grade line, ft (m)
dm,Yd = tailwater depth, ft (m)
Ku = 1.32 (English)
Ku = 1.90 (SI)

It should be noted that Ht is the difference in the total head from upstream to downstream. This can be computed using the energy equation for steady uniform flow:

Equation 3.2: Total drop in head, H subscript t equals [Y subscript u plus ((V subscript u) squared divided by (2 times g)) plus Z subscript u] minus [Y subscript d plus ((V subscript d) squared divided by (2 times g)) plus Z subscript d] (3.2)

where:

Y = depth, ft (m)
V = velocity, ft/s (m/s)
Z = bed elevation referenced to a common datum, ft (m)
g = acceleration due to gravity 32.2 ft/s2 (9.81 m/s2)

The subscripts u and d refer to up- and downstream of the channel drop, respectively.

The depth of scour as estimated by the above equation is independent of the grain size of the bed material. This concept acknowledges that the bed will scour regardless of the type of material composing the bed, but the rate of scour depends on the composition of the bed. In some cases, with large or resistant material, it may take years or decades to develop the maximum scour hole. In these cases, the design life of the bridge may need to be considered when designing the check dam.

The check dam must be designed structurally to withstand the forces of water and soil assuming that the scour hole is as deep as estimated using the equation above. Therefore, the designer should consult geotechnical and structural engineers so that the drop structure will be stable under the full scour condition. In some cases, a series of drops may be employed to minimize drop height and construction costs of foundations. Riprap or energy dissipation could be provided to limit depth of scour (see, for example, Peterka 1964 and FHWA 1983).

3.2.2 Check Dam Design Example

The following design example is based upon a comparison of scour equations presented by the USBR (Peterka and Lara 1984).

Given:

Channel degradation is threatening bridge foundations. Increasing the bed elevation 4.6 ft (1.4 m) will stabilize the channel at the original bed level. A drop structure will raise the channel bed and reduce upstream channel slopes, resulting in greater flow depths and reduced velocity upstream of the structure. For this example, as illustrated by Figure 3.2, the following hydraulic parameters are used:

Design Discharge Q = 5,900 ft3/s (167 m3/s)
Channel Width B = 105 ft (32 m)
Upstream Water Depth Yu = 10.6 ft (3.22 m)
Tail Water Depth dm, Yd = 9.5 ft (2.9 m)
Unit Discharge q = 56.2 ft3/s/ft (5.22 m3/s/m)
Upstream Mean Velocity Vu = 5.3 ft/s (1.62 m/s)
Downstream Mean Velocity Vd = 5.9 ft/s (1.80 m/s)
Drop Height h = 4.6 ft (1.4 m)

Schematic in profile of vertical drop and check dam with parameters of hydraulic head located. Values from above text for parameters of hydraulic head are entered.
Figure 3.2. Design example of scour downstream of a drop structure.

Ht is calculated from the energy equation. Using the downstream bed as the elevation datum gives:

Equation 3.3: Substituting the given parameters, the Total drop in head, H subscript t equals [10.6 plus ((5.3) squared divided by (2 times 32.2)) plus 4.6] minus [9.5 plus ((5.9) squared divided by (2 times 32.2)) plus 0] (3.3)

Using Equation (3.1), the estimated depth of scour below the downstream bed level is:

ds = Ku Ht0.225 q0.54 - dm
ds = 1.32 (5.6)0.225 (56.2)0.54 -9.5
ds = 7.6 ft (2.3 m)

In this case, the unsupported height of the structure is (h + ds) or 12.2 ft (3.7 m). If, for structural reasons, this height is unacceptable, then either riprap to limit scour depth or a series of check dams could be constructed. It should be noted that if a series of drops are required, adequate distance between each drop must be maintained (Peterka 1964).

3.2.3 Lateral Scour Downstream of Check Dams

As was mentioned, lateral scour of the banks of a stream downstream of check dams can cause the streamflow to divert around the check dam. If this occurs, a head cut may move upstream and endanger the highway crossing. To prevent this the banks of the stream must be adequately protected using riprap or other revetments. Riprap should be sized and placed in a similar fashion as for spurs and guide banks. The designer is referred to Design Guide 4 for proper sizing, and placement of riprap on the banks.

3.3 STILLING BASINS FOR DROP STRUCTURES

This section on stilling basins for drop structures is taken from the FHWA Hydraulic Engineering Circular Number 14, "Hydraulic Design of Energy Dissipators for Culverts and Channels" (FHWA 1983).

A general design for a stilling basin at the toe of a drop structure was developed by the St. Anthony Falls Hydraulic Laboratory, University of Minnesota (Donnelly and Blaisdell 1954). The basin consists of a horizontal apron with blocks and sills to dissipate energy. Tailwater also influences the amount of energy dissipated. The stilling basin length computed for the minimum tailwater level required for good performance may be inadequate at high tailwater levels. Dangerous scour of the downstream channel may occur if the nappe is supported sufficiently by high tailwater so that it lands beyond the end of the stilling basin. A method for computing the stilling basin length for all tailwater levels is presented.

The design is applicable to relative heights of fall ranging from 1.0(ho/yc) to 15(ho/yc) and to crest lengths greater than 1.5yc. Here ho is the vertical distance between the crest and the stilling basin floor, and yc is the critical depth of flow at the crest (Figure 3.3). The straight drop structure is effective if the drop does not exceed 15 ft (4.6 m) and if there is sufficient tailwater.

There are several elements which must be considered in the design of this stilling basin. These include the length of basin, the position and size of floor blocks, the position and height of end sill, the position of the wingwalls, and the approach channel geometry. Figure 3.3 illustrates a straight drop structure which provides protection from scour in the downstream channel.

3.3.1 Design Procedures

1. Calculate the specific head in approach channel.

Equation 3.4: Specific Head, H equals y subscript zero plus (V subscript zero) squared divided by (2 times g) (3.4)

where:

yo = normal depth in the approach channel
V0 = velocity associated with normal depth in the approach channel

2. Calculate critical depth.

Equation 3.5: Critical depth, y subscript c equals (2 divided by 3) times specific head, H (3.5)

3. Calculate the minimum height for tailwater surface above the floor of the basin.

Equation 3.6: Tailwater height, Y subscript 3 equals 2.15 times Critical depth y subscript c (3.6)

Schematics of a straight drop stilling basin in profile and plan view. Profile view shows: Height from stilling basin to crest h subscript zero, critical depth at the crest y subscript c, Stilling basin length L subscript B made up of length from vertical to where nape would land L subscript 1 plus distance to floor blocks L subscript 2 plus distance to end of basin L subscript 3, end sill height is 0.4 times y subscript c. At the end sill the Basin side wall height is made up of the depth of the tailwater water y subscript 3, equaling 2.15 times y subscript c 0.85 times y subscript c. Plan View shows the stilling basin width, W subscript zero, the downstream end sill, 45 degree downstream wing walls, optional longitudinal sill through basin, the row of floor blocks across the basin, separation between blocks 0.4 times critical depth at the crest y subscript c, block width 0.4 times critical depth at the crest y subscript c,
Figure 3.3. Straight drop structure stilling basin.

4. Calculate the vertical distance of tailwater below the crest. This will generally be a negative value since the crest is used as a reference point.

Equation 3.7: Vertical distance of Tailwater below crest, h subscript 2 equals negative (h minus y subscript 0) (3.7)

where:

"h" = total drop from the crest of the drop to the flow line of the outlet channel and yo is the normal depth in the outlet channel

5. Determine the location of the stilling basin floor relative to the crest.

Equation 3.8: Distance from crest to stilling basin, h subscript 0 equals h subscript 2 minus y subscript 3. Terms explained in the text (3.8)

6. Determine the minimum length of the stilling basin, LB, using:

Equation 3.9: Minimum length of the stilling basin, L subscript B, equals L subscript 1 plus L subscript 2 plus L subscript 3 plus L subscript 1 equals L subscript 1 plus 2.25 times crest critical depth y subscript c. Terms explained in the following text. (3.9)

where:

L1 is the distance from the headwall to the point where the surface of the upper nappe strikes the stilling basin floor. This is given by:

Equation 3.10: L subscript 1 equals (L subscript f plus L subscript s) divided by 2 (3.10)

where:

Equation 3.11: L subscript f equals y subscript c times {negative 0.406 plus (the square root of [3.195 minus (4.368 times h subscript 0 divided by y subscript c)]} (3.11)
Equation 3.12: L subscript t equals {negative 0.406 plus (the square root of [3.195 minus (4.368 times h subscript 2 divided by y subscript c)]} times y subscript c (3.12)
Equation 3.13: L subscript s equals [0.691 plus 0.228 times (L subscript t divided by y subscript c) squared minus (h subscript 0 divided by y subscript c)] times y subscript c all divided by [0.185 plus 0.456 times (L subscript t divided by y subscript c)] (3.13)

or L1 can be found graphically from Figure 3.4

L2 is the distance from the point at which the surface of the upper nappe strikes the stilling basin floor to the upstream face of the floor blocks, Figure 3.3. This distance can be determined by:

Equation 3.14: L subscript 2 equals 0.8 times y subscript c (3.14)

Design chart for determination of L subscript 1, the distance from the headwall to the point where the surface of the upper nappe strikes the stilling basin floor.
Figure 3.4. Design chart for determination of L1.

L3 is the distance between the upstream face of the floor blocks and the end of the stilling basin. This distance can be determined from:

Equation 3.15: L subscript 3 equals 1.75 ties y subscript c (3.15)
  1. Proportion the floor blocks as follows:
    1. Height is 0.8 yc,
    2. Width and spacing should be 0.4 yc, with a variation of + 0.15 yc, permitted,
    3. Blocks should be square in plan, and
    4. Blocks should occupy between 50 and 60% of the stilling basin width.
  2. Calculate the end sill height, (0.4 yc,).
  3. Longitudinal sills, if used, should pass through, not between, the floor blocks. These sills are for structural purposes and are neither beneficial nor harmful hydraulically.
  4. Calculate the sidewall height above the tailwater level, (0.85 yc,).
  5. Wingwalls should be located at an angle of 45° with the outlet centerline and have a top slope of 1 to 1.
  6. Modify the approach channel as follows:
    1. Crest of spillway should be at same elevation as approach channel,
    2. Bottom width should be equal to the spillway notch length, Wo at the headwall, and
    3. Protect with riprap or paving for a distance upstream from the headwall equal to three times the critical depth, yc,
  7. No special provision of aeration of the space beneath the nappe is required if the approach channel geometry is as recommended in step 12.

The geometry of the undisturbed flow should be taken into consideration in the design of a straight drop stilling basin. If the overfall crest length is less than the width of the approach channel, it is important that a transition be properly designed by shaping the approach channel to reduce the effect of end contractions. Otherwise the contraction at the ends of the spillway notch may be so pronounced that the jet will land beyond the stilling-basin and the concentration of high velocities at the center of the outlet may cause additional scour in the downstream channel.

3.3.2 Stilling Basin Design Example

Using the same problem as was used to estimate scour at the check dam (Section 3.2.2), establish the size of a stilling basin.

Given:

Channel degradation is threatening bridge foundations. Increasing the bed elevation 4.6 ft (1.4 m) will stabilize the channel at the original bed level. A drop structure will raise the channel bed and reduce upstream channel slopes, resulting in greater flow depths and reduced velocity upstream of the structure. For this example, as illustrated by Figure 3.2, the following hydraulic parameters are used:

Design Discharge Q = 5,900 ft3/s (167 m3/s)
Channel Width B = 105 ft (32 m)
Upstream Water Depth Yu = 10.6 ft (3.22 m)
Tail Water Depth dm, Yd = 9.5 ft (2.9 m)
Unit Discharge q = 56.2 ft3/s/ft (5.22 m3/s)
Upstream Mean Velocity Vu = 5.3 ft/s (1.62 m/s)
Downstream Mean Velocity Vd = 5.9 ft/s (1.80 m/s)
Drop Height h = 4.6 ft (1.4 m)

Find: Dimensions for the stilling basin as shown in Figure 3.3.

Solution:

Step 1. Calculate the Specific Head in Approach Channel

Specific Head, H equals y subscript zero plus [(V subscript zero) squared divided by (2 times g)] equals 10.6 plus [(53) squared divided by (2 times 32.2)] equals 11.0 feet or 3.35 meters

Step 2. Calculate Critical Depth

Critical depth, y subscript c equals (2 divided by 3) times specific head, H  Equals two thirds times 11 equals 7.3 or 2.23 m

Step 3. Calculate the Minimum Height for Tailwater Surface Above the Floor of the Basin
y subscript 3 equals 2.15 times y subscript c =equas 2.15 times 7.3 equals 15.7 feet or 4.8 meters  (4.8 m)
Step 4. Calculate the Vertical Distance of Tailwater Below the Crest

This will generally be a negative value since the crest is used as a reference point.

h2 = -(h - yo) = -(4.6 - 9.5) = +4.9 ft (+1.5 m)

where:

"h" = total drop from the crest of the drop to the flow line of the outlet channel and yo is the normal depth in the outlet channel
Step 5. Determine the Location of the Stilling Basin Floor Relative to the Crest
ho = h2 - y3 = 4.9 - 15.7 = -10.8 ft (-3.3 m)
Step 6. Determine the Minimum Length of the Stilling Basin

L subscript B equals L subscript 1 plus L subscript 2 plus L subscript 3 equals L subscript 1 plus 2.55 times y subscript c

where:

L1 is the distance from the headwall to the point where the surface of the upper nappe strikes the stilling basin floor. This is given by:

L subscript 1 equals [L subscript 1plus L subscript 1] divided by 2

where:

L subscript f equals y subscript c times {negative 0.406 plus (the square root of [3.195 minus (4.368 times h subscript 0 divided by y subscript c)]}

L subscript f equals 19.7 feet or 6.02 meters

L subscript s equals [0.691 plus 0.228 times (L subscript t divided by y subscript c) squared minus (h subscript 0 divided by y subscript c)] times y subscript c all divided by [0.185 plus 0.456 times (L subscript t divided by y subscript c)] equals [0.691 plus 0.228 times (0.78 divided by 7.3) squared minus (negative 10.8 divided by 7.3)] times 7.3 all divided by [0.185 plus 0.456 times (0.78 divided by 7.3)]

L subscript t equals {negative 0.406 plus (the square root of [3.195 minus (4.368 times h subscript 2 divided by y subscript c)]} times y subscript c equals {negative 0.406 plus (the square root of [3.195 minus (4.368 times 4.9 divided by 7.3)]} times 7.3

L subscript t = 0.78 t feet or 0.25 meters

L subscript s = 67.9 feet or 20.53 meters

Then, L1 = (19.7 + 67.9) / 2 = 43.8 ft (13.38 m)

or L1 can be found graphically from Figure 3.4

L2 is the distance from the point at which the surface of the upper nappe strikes the stilling basin floor to the upstream face of the floor blocks, Figure 3.3. This distance can be determined by:

L2 = 0.8 (yc) = 0.8 (7.3) = 5.8 ft (1.78 m)

L3 is the distance between the upstream face of the floor blocks and the end of the stilling basin. This distance can be determined from:

L3 > 1.75 yc = 1.75 (7.3) = 12.8 ft (3.9 m)

Step 7. Proportion the Floor Blocks
  1. Height is 0.8 yc, 0.8 (7.3) = 5.8 ft (1.78 m)
  2. Width and spacing should be 0.4 yc, with a variation of ± 0.15 yc, permitted,
  3. Blocks should be square in plan, and
  4. Blocks should occupy between 50 and 60% of the stilling basin width.
Step 8. Calculate the End Sill Height
(0.4 yc) = 0.4 (7.3) = 2.9 ft (0.89 m)
Step 9. Longitudinal Sills

If used, should pass through, not between, the floor blocks. These sills are for structural purposes and are neither beneficial nor harmful hydraulically.

Step 10. Calculate the Sidewall Height Above the Tailwater Level
(0.85 yc) = 0.85 (7.3) = 6.2 ft (1.9 m)
Step 11. Wingwalls

Should be located at an angle of 45° with the outlet centerline and have a top slope of 1 to 1.

Step 12. Modify the Approach Channel
  1. crest of spillway should be at same elevation as approach channel,
  2. bottom width should be equal to the spillway notch length, Wo at the headwall, and
  3. protect with riprap or paving for a distance upstream from the headwall equal to three times the critical depth, yc,
Step 13. Aeration of the Nappe

No special provision of aeration of the space beneath the nappe is required if the approach channel geometry is as recommended in Step 12.

3.4 REFERENCES

Donnelly, C.A., and Blaisdell, F.W., 1954, "Straight Drop Spillway Stilling Basin," University of Minnesota, St. Anthony Falls Hydraulic Laboratory, Technical Paper 15, Series B, November.

Federal Highway Administration, 1983, "Hydraulic Design of Energy Dissipators for Culverts and Channels," Hydraulic Engineering Circular Number 14, U.S. Department of Transportation, Washington, D.C.

Pemberton, E.L. and Lara, J.M., 1984, "Computing Degradation and Local Scour," Technical Guidelines for Bureau of Reclamation, Engineering Research Center, Denver, CO, January.

Peterka, A.J., 1964, "Hydraulic Design of Stilling Basins and Energy Dissipators," Engineering Monograph No. 25, Bureau of Reclamation, Division of Research, Denver, CO.

Updated: 09/20/2011

FHWA
United States Department of Transportation - Federal Highway Administration