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Publication Number: FHWAHRT07026 Date: February 2007 
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.
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.
(28) 
where:
Step 2: Express the critical velocity computed by Laursen’s method (equation 5) in terms of y_{2} as follows.
(29) 
where:
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.
(30) 
This expression can now be rearranged to calculate y_{2} as follows.
(31) 
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.
(33) 
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:
Note that the unit discharge ratio of q_{1} divided by q_{2} can be computed from a width ratio as follows.
(35) 
where:
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.
(36) 
The exponent, x, is calculated using equation 37:
(37) 
where:
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.
(38) 
This expression can now be rearranged to calculate y_{2} as follows.
(39) 
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.
(40) 
Alternatively, the equation for the maximum scour with wingwalls is as follows.
(41) 
Topics: research, infrastructure, hydraulics Keywords: research, infrastructure, hydraulics, Scour, culverts, hydraulics, physical model TRT Terms: research, hydraulics, hydrology, fluid mechanics, earth sciences, geophysics Updated: 04/23/2012
