0.053
D
= 0.645 x
(7.11)
VicDx
VcDx
a
=
Critical velocity (m/s or ft/s) for incipient motion for the grain size Dx (m or ft)
VcDx
VcDx = K u y1/ 6 D1/ 3
(7.12)
1
x
y1
=
Depth of flow just upstream of the pier, excluding local scour, m (ft)
V1
=
Velocity of the approach flow just upstream of the pier, m/s (ft/s)
Dx
=
Grain size for which x percent of the bed material is finer, m (ft)
Ku
=
11.25 SI units
Ku
=
6.19 English units
Although this K4 provides a good fit with the field data, the velocity ratio terms are so formed
that if D50 is held constant and D95 increases, the value of K4 increases rather than
decreases. For field data an increase in D95 was always accompanied with an increase in
D50.
The minimum value of K4 is 0.4 and VR must be greater than 0. The bed material size must
have D50 > 2.0 mm and D95 > 20.0 mm.
Correction Factor for Wide Piers
Flume studies on scour depths at wide piers in shallow flows and field observations of scour
depths at bascule piers in shallow flows indicate that existing equations, including the CSU
equation, overestimate scour depths. Johnson and Torrico (1994) suggest the following
equations for a K factor to be used to correct Equation 7.7 for wide piers in shallow flow.
The correction factor to be applied when the ratio of depth of flow (y) to pier width (a) is less
than 0.8 (y/a < 0.8); the ratio of pier width (a) to the median diameter of the bed material (D50)
is greater than 50 (a/D50 > 50); and the Froude Number of the flow is subcritical.
0.34
y
F 0.65 for V / Vc < 1
K 5 = 2.58
(7.13)
a
0.13
y
F0.25 for V / Vc > 1
K 5 = 1.0
(7.14)
a
Engineering judgment should be used in applying K5 because it is based on limited
data from flume experiments. Engineering judgment should take into consideration
the volume of traffic, the importance of the highway, cost of a failure (potential loss of
lives and dollars) and the change in cost that would occur if the K5 factor is used.
7.7.5 Pier Scour in Cohesive Bed Material
The rate of scour in cohesive silt and clay bed materials is many times slower than for non-
cohesive materials. The maximum depth of scour at a pier will often be reached during one
7.19
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