Adjustment Factor For Spiral Flow At Abutment Toe
The above discussion with respect to the velocity coefficient reflects the limited analysis available using two-dimensional flow concepts.
The flow at an abutment toe is in spiral motion, which is three dimensional. Accordingly, a factor for adjusting two dimensional flow to
three dimensional flow needs to be added to Laursen's Equation. Available scour data for vertical-wall abutments were analyzed (5).
The analyses resulted in the following two equations for determining the value of the spiral flow adjustment factor, kf. In the summer of 2006,
adjustments, as noted below, were made in the kf values for flows with low Froude Numbers based on studies of clear water scour in the FHWA flume
at the Turner Fairbanks Highway Research Laboratory.
For clear-water scour:
kf = 0.13 + 5.85F
For live-bed scour:
kf = 0.46 + 4.16F
Where:
kf = experimental coefficient for spiral flow at the abutment toe. (The values of kf have been determined experimentally to range from 1.4 to 4.0.
If the computed value of kf is less than 1.4, use a value of 1.4; if the computed value is greater than 4.0, use a value of 4.0)
F = Froude number of the flow in the approach overbank subarea (see note below).
F = V1/ (gy1)0.5
Where V1 is the average velocity in the approach subarea, y1 is the average depth in the approach subarea and g is the gravitational constant.
Note: the above equation for kf is derived from the laboratory data by correlating the Froude number at the approach overbank area.