ERDC/CHL CHETN-IV-35
June 2001
Bypassing Rate: The bypassing rate is given as q yR = qsR + qrR or
z
q yR = 1 + adR - εd adR
(22)
qR
z0
obtained as a function of time from Equation 14 for z.
Time Interval for Maintenance Dredging: A channel section is dredged to a design depth
including a certain amount of advance dredging and a certain amount of allowable overdredging.
The analytical channel infilling model provides an estimate of the maximum possible time
interval ∆tp between dredging (the dredging cycle) for an assumed constant rate of infilling.
Then for an increase in channel elevation from initial depth h0 (elevation z = 0) to some the
project depth hp (or elevation zp = h0 - hp), at which time dredging must be scheduled, can be
determined from Equation 14 by iteration.
If bed-load transport and channel bank encroachment are not significant, then Equation 19 can be
solved to give
W (h - ha ) hp - ha
zp
W0 z0
=- 0 0
∆t p = -
ln 1 -
(23)
ln
h -h
εdR adR qR
εdR adR qR
z0
0
a
This equation indicates that the time between dredging intervals is directly proportional to the
width of the channel; approximately proportional to the initial depth of the channel with respect
to the ambient depth; and inversely proportional to the input transport rate. If Equation (23) is
expanded or, equivalently, Equation 18 is solved for ∆tp to leading order, the result is
W0 z0
(
)
∆t p ≅
h0 - hp
(24)
εdR adR qR
EXAMPLE SOLUTIONS: In these two examples, z0 = 4 m, W0 = 50 m, and ∆t = 0.1 year.
The effective channel length, determined as the average width of the surf zone over all tides and
wave conditions, was estimated to be 1,000 m.
Equations 8 and 9 (simultaneous nonlinear equations) were solved numerically, and the
analytical model developed from the linearization (Equations 14 and 17) was also run. The
simulation time was 2 years, and the numerical calculation was halted if z reached z0/2 (assumed
project depth) or x reached W0/2 (minimum allowable width of channel).
Example 1: (fine sand) QR = 150,000 m3/year, adR = 0.5, abR = 0.1, εrd = 1
The sediment at this site is fine sand, and calculation of the trapping factor according to Larson
and Kraus (2001) gave , adR = 0.5. This example simulates a shallow-draft channel at an inlet
located on a sandy shore, so most of the fine sand is deposited into the channel or passes over the
channel ( asR = 1 - adR - abR = 0.4 ). If material is deposited into the channel, it can be readily
resuspended. The effective channel length is 1,000 m, so qR = 150,000/1,000 = 150 m3/m/year.
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