is *R*z = *dz*/*dt *and can be calculated from Eq. 18. For a relatively short time after dredging:

(21)

The leading-order term is independent of *z*0, so the rate of channel infilling depends more

strongly on *W*0 than on *z*0. The solution indicates that the rate of channel infilling can be

reduced more by increasing channel width than by increasing channel depth.

)*q*

(22)

which is a function of time through *z *(Eq. 14).

including a certain amount of advance dredging and a certain amount of allowable

overdredging. The analytical channel infilling model provides an explicit expression for

estimating of the maximum possible time interval ∆*t*p between dredging events (the

dredging cycle) for a constant rate of infilling. Then, for an increase in channel elevation

from initial depth *h*0 (elevation *z *= 0) to some the project depth *h*p (or elevation *z*p = *h*0 -

iteration.

If bedload transport (channel bank encroachment) is not significant, then Eq. 19 can

be solved to give:

∆*t * p = -

ln 1 - = - 0 0 * a *ln

(23)

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 ∆*t*p to leading order, the result is:

( h0 - *h*p )

∆*t * p ≅

(24)

In the two examples to follow, *z*0 = 4 m, *W*0 = 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

Integrated Publishing, Inc. |