Adjustment for Short Setback Abutment (Case A)

When the abutment has no setback (is at the channel bank), the scour at the overbank will be equal to that for channel. When the setback is small, the scour at the overbank will be very close to the scour in the channel. However, due to the idealization of channel and overbank flow into the rectangular shapes for the ABSCOUR cross-section, the calculated overbank scour may be based on clear water scour (as determined from the Approach Section calculations) whereas it may be subject to live bed scour from the main channel. Some transition is needed between the no setback case and the case where the abutment is set well back on the flood plain.

The limit of the transition zone is defined as five times the flow depth in the downstream channel. When there is no setback, the channel scour flow depth (y2) is used for the contraction scour. When the abutment setback on the flood plain exceeds the limit of the transition zone, separate flow is assumed between the channel and the flood plain and no interpolation is required. When the setback is within this transition zone of from zero to 5yo, the following scheme is used to compute contraction scour:

ABSCOUR separately calculates both clear water scour flow depth and live bed scour flow depth for (1) the channel section and (2) the overbank section

The channel contraction scour flow depth (y2) is the scour when the setback is equal to or less than zero - that is no setback case.

The overbank contraction scour flow depth (y2) is the overbank scour when the setback is located on the flood plain beyond the channel banks a distance equal to 5 times the flow depth in the downstream channel (SB = 5yo)

There are four combination of overbank scour in the transition zone:

  1. clear water scour with no setback
  2. clear water scour with setback = 5yo
  3. live bed scour with no setback
  4. live bed scour with setback = 5yo
The computed channel contraction scour depends on the approach section channel scour type. If the approach section channel scour type is clear-water, then the case 1 will be used as the channel contraction scour. If the approach section channel scour type is live-bed scour, then the smaller of case 1 and case 3 will be used as the channel contraction scour. Note, for the live-bed scour type, the reason to choose smaller of the live-bed and the clear-water scoured flow depth is to account for the armoring effect due to the coarse sediments.

The computed overbank contraction scour will be interpolated between these four cases, depending on the setback distance and the scour type (live-bed or clear water at overbank and channel). Note, for live-bed scour type, the smaller of the live-bed and clear-water scoured flow depth is used and the interpolation applied.

For example:

When the channel is live bed and the overbank is clear water, then the overbank contraction scour for the actual setback (between 0 and 5 times channel flow depth) will be interpolated between smaller of case 1 and case 3 ( live bed scour with no setback) and case 2 (clear water scour with setback = 5yo).

The interpolation depends on the distance that the abutment is set back from the channel bank and the scour type at the overbank and channel sections.

A parabolic interpolation is used for the contraction scour flow depth calculation (y2) since this method provides for a smooth transition that approximates the scour depths computed through the application of Laursen's contraction scour equations. The following parabolic equation is used for interpolation.

y2=(y2)bank+((y2)channel-((y2)bank)*(1-(setback)/(5*yo))p
Where:
p=4.5-Z and p is limited to the values of 1<=p<=4
Z is the approach section bank slope H/V
(y2)bank is the scour flow depth at setback=5y0
(y2)channel is the scour flow depth with no setback

Please note that the bank slope determines the shape of the parabola and therefore the relative effect of the channel scour on scour at the abutment. Steeper bank slopes such as 1:1 will reduce the effect of channel scour whereas flatter slopes such as 4:1 will increase the effect of channel scour. The bank slope can be used as a variable in sensitivity analyses of factors affecting abutment scour.

The contraction scour flow depth is modified as necessary to take into account the effect of any pressure scour and to apply a safety factor to the design.

Next, the abutment scour flow depth (y2a) is computed directly from the interpolated contraction scour value:

y2a=(kf*(kv)k2)*(contraction scour)
Abutment scour (ysa) = y2a-(yo)adj 
where (yo)adj = flow depth before scour occurs.

The final or adjusted abutment scour value (ysa)adj is determined as

(ysa)adj =  Kt * Ke *FS * ysa  								 
Where:
Kt = modification for abutment shape
Ke = modification for embankment skew
FS = factor of safety.
ysa = initial abutment scour estimate noted above (ysa = y2 - (yo)adj)

Please note that any correction for pressure flow is already taken into account in the contraction scour computations.