EXAMPLE PROBLEM III-2-12

FIND:

The level of protection (i.e., width of beach) afforded to a historical lighthouse as a consequence of

the nourishment project at the end of 3, 6, 8, 9, and 12 months after initial fill placement. The lighthouse

is situated at the shoreline 1 mile (. 1,609 m) south of the south end of the proposed beach at the

initiation of the project fill.

GIVEN:

A long beach fill is placed along a north-south directed stretch of shoreline along the east coast of

the United States (i.e., the azimuth of the offshore direction is 90 deg). The project is to be constructed

and maintained continuously to design project width throughout the project fill area. The project will

be constructed in two stages; Stage 1 will provide a fill width of 50 m, and Stage 2 (to be placed

3 months after initial placement) will add another 50 m of beach width, making the total finished project

width = 100 m. Assume that: *H*b = 1 m; *T *= 10 sec; αb = 5 deg (from the north) *K *is assumed = 0.77,

and *κ *= 1.0. Sediment density to water density ratio (i.e., specific gravity) = ρs/ρ = 2.65; porosity *n *=

0.4; *d*B + *d*c = 6 m. Note that except for breaking wave height *H*b, these are the same wave and sediment

parameters as given in Example III-2-8.

SOLUTION:

For *H*b = 1 m, with other parameters the same as the previous problem;

0.77 (1)2 9.81 @ 1

1

1

1

ε'

8

2.65 & 1

1 & 0.4

6

m2

0.0508

sec

At the end of the first 3 months, the solution of Equation 2-37 (graphical solution provided by Figure III-

2-34) can be utilized with *t *= 3 months . 7.78 106 sec, and *x *= 1 mile . 1,609 m:

1,609

meters

2 0.0508 @ 7.78 106

. 50 @ *erfc *(1.28)

. 50 (0.07) 3.5 m

(Continued)

III-2-76

Longshore Sediment Transport

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