different projects their planform evolution would be the same. However, if two projects were exposed to the

same wave climate but had different alongshore lengths, then the project with the greatest length would be

predicted to last longer (with all other factors being the same). In fact, according to Equation III-2-32 the

longevity of a project varies as the square of its length. If more than 50 percent of the placed beach-fill

volume remains within the placement area (0.5<p(t)<1.0), Equation III-2-32 can be approximated using the

following relationship (with an accuracy of 15 percent).

g*t*

(V-4-12)

Example Problem V-4-7 illustrates the importance of project length on project longevity. In this

example, a fill with twice the length will last four times as long. The effect of project length on fill

longevity is critical for short fills. It is also important in long fills which may be built in stages. For

example, construction may be limited to a particular season to avoid turtle nesting season or the

tourist season. Therefore it may take 2 or 3 years to complete the work. Projects built in stages will

temporarily perform as short fills until the other portions of the project are completed. Actual loss

rates from the constructed subreaches will likely exceed losses predicted for the completed as

designed project. Any short-term accelerated losses due to construction of the project in stages

should be factored into the advance nourishment quantity.

(b) Effect of wave environment.

The rate of alongshore spreading losses is also a function of the incident wave climate. In

Equation III-2-26 it is seen that the shoreline diffusivity term (ε) varies inversely with the breaking

wave height raised to the 5/2 power. Dean and Yoo (1992) present a method for calculating a

representative wave height and period based on assumptions of Rayleigh-distributed wave height,

shallow-water linear-wave theory, simplified and linearized wave refraction and shoaling relations,

and a constant proportionality between breaking wave height and corresponding water depth. Use

of an effective wave height is recommended in the calculation of the shoreline diffusivity term (ε).

Dean and Yoo (1992) defined the effective wave as one that produces the same spreading of the

beach nourishment material as the actual time-varying wave conditions (expressed as pairs of height

and period). They provided the following equation to calculate the effective wave height, *H*eff ,

1

j ( *K*s Hs )

1

2.4

(V-4-13)

j

1

where *K*s is the proportionality factor between significant deepwater wave height and effective deepwater

wave height and is equal to 0.735 (Dean and Yoo 1992), *H*ns is the significant wave height of the *n*th record

in the time series of *N *wave records, *C*ngo is the deepwater wave group speed of the *n*th record, and *C*n* is the

wave celerity at breaking of the *n*th record. The effective wave period *T*eff is defined as the period

corresponding to the expression in the denominator.

V-4-50

Beach Fill Design

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