Bottomless Culvert Scour Study: Phase II Laboratory Report
Chapter 6: Scour Calculation Examples
This section gives stepbystep instructions for calculating the maximum scour depth for unsubmerged bottomless culverts. Two different scenarios from the results section will be shown.
USING k_{S} AS A FUNCTION OF V_{RA}, V_{CL}, AND F_{1}
The first example is based on using V_{RA}, V_{CL}, and F_{1}. The procedure is as follows:
Step 1: Compute the representative velocity of the flow using the average velocity in the approach section (equation 2) as follows.

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where:
 Q
 is volumetric flow through the culvert (m^{3}/s).
 y_{0}
 is depth of flow in the approach to the culvert before scour (m).
 w_{CULV}
 is width of the culvert inlet (m).
Step 2: Express the critical velocity computed by Laursen’s method (equation 5) in terms of y_{2} as follows.

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where:
 y_{2}
 is equilibrium flow depth (m).
 D_{50}
 is sediment size (m).
Step 3: Everything in the previous two equations should be known except for y_{2}. Now we can substitute the previous two equations into equation 1 as follows.

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This expression can now be rearranged to calculate y_{2} as follows.

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Step 4: Now use the scour equations from the first entry (k_{s}) in table 2 to calculate the maximum scour, recalling that only the intercept of these equations should be used.
Without wingwalls, the maximum scour is computed with the following equation.

(32) 
Alternatively, the equation for the maximum scour with wingwalls is as follows.

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USING k_{s} AS A FUNCTION OF V_{RM}, V_{CN}, AND Q_{blocked}
The second example is based on using V_{RM}, V_{CN}, and Q_{blocked}. The procedure is as follows:
Step 1: Compute representative velocity of the flow using the calibrated velocity in the culvert inlet (equation 22) as follows.

(34) 
where:
 Q
 is volumetric flow through the culvert (ft^{3}/s or m^{3}/s).
 y_{0}
 is depth of flow in the approach to the culvert before scour (ft or m).
 w_{CULV}
 is width of the culvert inlet (ft or m).
 q_{1}
 is unit discharge in the approach section (ft^{2}/s or m^{2}/s).
 q_{2}
 is unit discharge in the contracted section (ft^{2}/s or m^{2}/s).
Note that the unit discharge ratio of q_{1} divided by q_{2} can be computed from a width ratio as follows.

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where:
 w_{CULV}
 is width of the bottomless culvert inlet (m).
 w_{a}
 is width of the approach section to the culvert (m).
Step 2: Express the critical velocity computed by Neill’s method (equations 6, 7, and 8, or 9) in terms of y_{2}. For example, for D_{50} sediment size greater than 0.0003 m (0.001 ft) but less than 0.03 m (0.1 ft), the equation for Neill’s critical velocity is given as follows.

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The exponent, x, is calculated using equation 37:

(37) 
where:
 y_{2}
 is equilibrium flow depth, m or ft.
 D_{50}
 is sediment size, m or ft.
 K_{U1}
 is 0.3048^{(0.65x)} for SI units, or 1.0 for U.S. customary units.
 x
 is the exponent from equation 8.
 K_{U2}
 is 0.788 for SI units, or 1.0 for U.S. customary units.
Step 3: Everything in the previous three equations should be known except for y_{2}. Now we can substitute the previous two equations into equation 1 as follows.

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This expression can now be rearranged to calculate y_{2} as follows.

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Step 4: Now use the scour equations from the first entry (k_{s}) in table 2 to calculate the maximum scour.
Without wingwalls, the maximum scour is computed with the following equation.

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Alternatively, the equation for the maximum scour with wingwalls is as follows.

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