boundaries. In this scheme, a fill is viewed essentially as an increase 

 to the backshore reservoir. Sediment particle residence time in the com- 

 partment is longer for coarse-grained sediments than for fine; thus, a 

 comparison between composite-size distributions of native and borrow sedi- 

 ments can be used to predict the lifetime of a fill. The scheme thus 

 becomes a "bookkeeping" problem of monitoring material going in and out 

 of the system by using mass-balance equations that are similar to the more 

 familiar sediment-budget calculations. 



Various simplifications are made to the basic mass-balance equation 

 which result in this relative vetreat-vate equation: 



where 



Log (Rj) 



(Vh ' V 



2 



Ha 



(8) 



Rr = the relative retreat rate (renourishment factor) which 

 is a ratio of the borrow to native retreat rates 



y and a = the phi mean and phi sorting 



b and n = subscripts referring to borrow and native composites, 

 respectively 



A = a dimensionless parameter related to selective sort- 

 ing (winnowing) in the environment. 



The value of the delta parameter, A, is estimated to be between 0.5 and 

 1.5, but to date appropriate fill data have not been collected to obtain 

 more accurate values. Renourishment factors can therefore vary depending 

 upon the A value used. Using a A of unity, Figure 10 shows Rj con- 

 tours plotted against the "standard reference axes" that compare the tex- 

 tural parameters for the native and borrow composites. A renourishment 

 factor of one-third means that the borrow material is three times as stable 

 as the native, or that renourishment with this borrow material would be 

 required one-third as often as renourishment with nativelike sediments. 

 However, an Rj of 3 indicates the borrow is one-third as stable, and if 

 used as beach fill, would require renourishment three times as often as 

 the nativelike sediments. Probably, the most obvious shortcoming of this 

 model is the lack of real values for the "winnowing parameter, A," but 

 the kinds of predictions obtained are nevertheless consistent with general 

 beach-fill guidelines. It is concluded that this model, as is, can be 

 used profitably to solve actual beach-fill problems, and that this kind of 

 approach must be considered in cases where periodic renourishment is 

 anticipated. 



4. Comparison Example . 



Figure 11 shows size-frequency histograms for native and borrow com- 

 posites and phi mean and sorting values from Virginia Beach, Virginia. The 



35 



