Bottomless Culvert Scour Study: Phase I Laboratory Report
6. RECOMMENDED PROCEDURES FOR ESTIMATING MAXIMUM SCOUR FOR BOTTOMLESS CULVERTS
PROCEDURE USING GKY METHOD FOR REPRESENTATIVE VELOCITY AND SMB EQUATION FOR CRITICAL VELOCITY
The GKY method for representative velocity and the SMB equation for critical velocity with the blocked discharge normalized by the acceleration of gravity (g) and the computed equilibrium depth as the independent regression variable gave the best R^{2} value, regressing the K_{ADJ} (see equation 3) to compute the maximum scour for the laboratory data. The SMB method for computing critical velocity, however, is independent of the flow depth and produces much lower critical velocities than the other methods for fine particle sizes. This will, in turn, result in overly conservative scour estimates for field situations.
The procedure is:
Step 1: Compute representative velocity using:
(62)
with
(63)
and
(64)
where:
V_{x}  = velocity in the flow direction, ft/s 
V_{y}  = velocity orthogonal to the flow direction, ft/s 
 = approach flow blocked by the embankment on one side of the channel centerline, ft^{3}/s 
 = total approach flow area on one side of the channel centerline, ft^{2} 
A_{blocked}  = approach flow area that is blocked by the embankments on one side of the channel, ft^{2} 
Step 2: Determine critical velocity by applying the SMB equations. The Shields Manning equations can be combined to yield:
(65)
where:
K_{UM}  = 1.0 for SI units or 1.49 for U.S. customary units 
n  = Manning's roughness 
Blodgett's equations for average estimates of Manning's n for sand and gravelbed channels are:
(66)
(67)
where:
g  = acceleration of gravity = 9.81 m/s^{2} for SI units or 32.2 ft/s^{2} for U.S. customary units 
K_{UB}  = 1/1.49 for SI units or 1.0 for U.S. customary units 
Step 3: Calculate y_{2} using:
(68)
Step 4: Use following regression equation to compute K_{ADJ}:
(69)
with:
(70)
where:
Q_{blocked}  = approach flow blocked by the embankment on one side of the channel centerline, ft^{3}/s 
A_{a}  = total approach flow area on one side of the channel, ft^{2} 
A_{blocked}  = approach flow area that is blocked by the embankments on one side of the channel, ft^{2} 
Step 5: Compute maximum scour according to:
(71)
PROCEDURE USING MARYLAND DOT (CHANG) METHOD FOR REPRESENTATIVE VELOCITY AND CRITICAL VELOCITY
The recommended procedure is based on using the Maryland DOT (Chang) method for computing both representative velocity and critical velocity. For computing the K_{ADJ} factor, the method using the blocked discharge normalized by the acceleration of gravity (g) and the computed equilibrium depth as the independent regression variable was chosen because it is considered to be more applicable to field situations.
The procedure is:
Step 1: Compute representative velocity using the Maryland DOT (Chang) method:
(72)
(73)
where:
K_{V}  = velocity coefficient to account for flow concentration where side flow converges with main channel flow based on potential flow assumptions 
Q  = total discharge through the culvert, ft^{3}/s 
A_{opening}  = average flow area within the culvert, ft^{2} 
W_{opening}  = average flow width in the culvert, ft 
w_{a}  = width of flow in the approach section, ft 
These equations are dimensionally homogeneous and are independent of the system of units as long as they are consistent.
Step 2: Determine critical velocity using the Maryland DOT (Chang) method:
 For D_{50} > 0.03 m (0.1 ft):
(74)
where:
y_{2}  = equilibrium flow depth, m or ft 
D_{50}  = sediment size, m or ft 
K_{U}  = 0.55217 for SI units or 1.0 for U.S. customary units 
 For 0.03 m (0.1 ft) > D_{50} > 0.0003 m (0.001 ft):
(75)
The exponent x is calculated using equation 13:
(76)
where:
y_{2}  = equilibrium flow depth, m or ft 
D_{50}  = sediment size, m or ft 
K_{U1}  = for SI units or 1.0 for U.S. customary units 
x  = exponent from equation 13 
K_{U2}  = 0.788 for SI units or 1.0 for U.S. customary units 
 For 0.0003 m (0.001 ft) > D_{50}:
(77)
where:
y_{2}  = equilibrium flow depth, m or ft 
D_{50}  = sediment size, m or ft 
K_{U}  = 0.55217 for SI units or 1.0 for U.S. customary units 
Step 3: Calculate y_{2} using:
 (78) 
Step 4: Use the following regression equation to compute K_{ADJ}:
 (79) 
with
 (80) 
where:
Q_{blocked}  = approach flow blocked by the embankment on one side of the channel, ft^{3}/s 
A_{a}  = total approach flow area on one side of the channel, ft^{2} 
A_{blocked}  = approach flow area that is blocked by the embankments on one side of the channel, ft^{2} 
(81)
Step 5: Compute maximum scour according to:
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