Channel Infilling Rate: The rate of channel infilling, the rate at which the bottom shoals,
is Rz = dz/dt and can be calculated from Eq. 18. For a relatively short time after dredging:
ad
a
q - 2d ( ad + ab ) q2t
Rz =
(21)
W0
W0 z0
The leading-order term is independent of z0, so the rate of channel infilling depends more
strongly on W0 than on z0. The solution indicates that the rate of channel infilling can be
reduced more by increasing channel width than by increasing channel depth.
Bypassing Rate: The bypassing rate, qy = qs + qr , becomes,
z
qy = (1 - ad + ad
)q
(22)
z0
which is a function of time through z (Eq. 14).
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
estimating of the maximum possible time interval ∆tp between dredging events (the
dredging cycle) for a 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, ∆tp can be determined from Eq. 14 by
iteration.
If bedload transport (channel bank encroachment) is not significant, then Eq. 19 can
be solved to give:
W (h - h ) hp - ha
W0 z0 z p
∆t p = -
ln 1 - = - 0 0 a ln
(23)
h0 - ha
ad q
z0
ad q
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
Eq. 23 is expanded or, equivalently, Eq. 18 is solved for ∆tp to leading order, the result is:
W0
( h0 - hp )
∆t p ≅
(24)
ad q
EXAMPLE SOLUTIONS
In the two examples to follow, z0 = 4 m, W0 = 50 m, and time step ∆t = 0.1 year. The
effective channel length, determined as the average width of the surf zone over all tides and
wave conditions, is estimated to be 1,000 m. Equations 8 and 9 (simultaneous non-linear
equations) were solved numerically, and the analytical model developed from the
linearization (Eqs. 14 and 17) was also run. The simulation time was 2 years, and the
Kraus and Larson
8
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