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

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

Integrated Publishing, Inc. |