Effect of background shoreline recession.

EM 1110-2-1100 (Part V)

31 Jul 2003

Example Problem V-4-8 illustrates the relative importance of the breaking wave height on the

expected longevity of a beach-fill project, with all other factors being equal. In this example, a

19 percent increase in breaking wave height resulted in a 35 percent decrease in the project's half-

life, which is a measure of fill longevity.

Differences in longevity are even more pronounced if greater differences in breaking wave height

are considered. For example, if the average summer breaking wave height at the project site is 0.6

m, and the average winter breaking wave height is 1.2 m, one would expect that loss rates to be much

higher in the winter compared to those in the summer (because of the diffusivity parameter

dependence on breaking wave height raised to the 2.5 power). Many beach-fill projects are built

during the winter season. The strong dependence of longevity on wave environment helps explain

the high rates of lateral spreading loss that can occur during the winter season.

(c) Effect of background shoreline recession.

The effect of project length and the incident wave environment have been shown to have a significant

influence on expected project longevity. The analysis presented to this point has not considered

losses due to ambient coastal processes, such as a gradient in the longshore sand transport rate, which

tends to produce background erosion at the project site. Equation V-4-12 can be modified to include

the effect of a uniform background shoreline recession rate, E , as follows:

εt

Et

0.5 < p (t) < 1.0

p (t) ' 1 &

(V-4-14)

%

∆yo

a π

Solving Equation V-4-14 for time t yields an expression that predicts the time required for a fraction

(1-p) of the material placed to be lost from the project area (or equivalently the time at which a

fraction p of the material placed remains in the project area). This expression is provided as

& m & m 2 & 4ln

for ε t /a < 1.0

tp '

(V-4-15)

2l

in which

2

E

l'

∆yo

2 E (p&1)

ε

m'

&

∆ yo

πa 2

and

n ' (1 & p)2

V-4-52

Beach Fill Design