EXAMPLE PROBLEM V-4-8

FIND:

The "half-life" of the specified beach fills (time at which 50 percent of the beach-fill material

remains within the placement area).

GIVEN:

Both projects have a rectangular planform with an alongshore length of 6 km. The effective

breaking wave height at beach fill A is 0.80 m whereas the effective breaking wave height at beach

fill B is 0.95 m.

ρs/ρ = 2.65

SOLUTION:

Equation III-2-26 gives: (for beach fill A)

0.77 (0.80)2.5 9.81/0.78

m2

1

1

1

ε'

.

.

.

' 0.02322

8

(2.65 & 1) (1 & 0.4) (2.5 % 6.0)

sec

(for beach fill B)

ε = 0.03568 m2/sec (see EXAMPLE PROBLEM V-4-7)

Solving Equation V-4-12 for *t *and p(t) = 0.5 gives

'

4ε

Half-life of beach fill A

(3000)2 (3.14)

' 304.420 X 106 sec 9.65 years

'

(4) (0.02322)

Half-life of beach fill B

(3000)2 (3.14)

' 198.102 X 106 sec 6.28 years

'

(4) (0.03568)

where *∆ y*o is the initial dry beach width (after cross-shore equilibration), *E *is the historical shoreline

recession rate and *a *is the beach-fill half length. Example Problem V-4-9 illustrates the effect of background

erosion rate. Comparison of results from this example with results from Example V-4-7 show that the

specified background erosion rate decreased the half-life of the fill by about 20 percent. Note that the

historical shoreline erosion rate *E*, may underestimate the postnourishment erosion rate if the preproject beach

is armored or otherwise features a deficit in sand volume or sand supply.

Beach Fill Design

V-4-53

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