a. The SPM Method (R5) . With this approach, the ratios of weight 

 percents of the native to borrow composites are compared across the range 

 of observed grain sizes to determine the phi grain size at which the ratio 

 is a maximum {critical ■phi size). The SPM fill factor (Rg) is the value 

 of the ratio at this size and represents the minimum amount of borrow 

 material which, when selectively winnowed from all size fractions, will 

 produce a unit volume of material with a size distribution identical to 

 the composite native sediments. In process-response terms, this approach 

 assumes that both fine- and coarse-grained sediments will be lost in situ- 

 ations where the borrow material is more poorly sorted than the native 

 material . 



Figure 7 shows isolines of R5 plotted against the reference axes 

 used for Figure 4 in this study. One problem with this method is that it 

 only applies directly to textural conditions defined in quadrant 1 where 

 the borrow composite is finer grained and more poorly sorted than the 

 native composite. Again, an important shortcoming of the method may be 

 the assumption that natural sorting conditions would actually remove coarse, 

 seemingly "stable" sediments from the active beach system to achieve a 

 compatible size distribution for the fill. 



b. The Dean Method (Rp) . Dean (1974) proposed a second fill factor 

 method aimed at overcoming the problem in the SPM of assuming that a part 

 of the coarse, stable sediments are lost by selective sorting. Dean found 

 this concept incompatible with what is commonly observed in nature. His 

 approach assumes that all fill material coarser than the native phi mean 

 reflects stability within the beach environment. Mathematically, a minimal 

 amount of the finest sizes is systematically removed from the borrow gsd 

 until the mean size equals the native mean size. From a process standpoint, 

 this approach is equivalent to assuming that winnowing processes progres- 

 sively wash out the finest sediments from a fill until its average size is 

 equal to that observed for the beach before restoration. The variables 

 required to obtain a graphical estimate of R^ (Fig. 8) are the phi mean 

 sizes of the native and borrow composites and the phi sorting value of the 

 borrow material. The fill factor values obtained for any particular set 



of the composite parameters are lower for R^ than for Rg. Dean's 

 factor is probably a more reasonable approach than that of the SPM in 

 terms of reflecting conditions observed in nature. However, the approach 

 does have drawbacks. First, by ignoring the natural sorting of native 

 sediments, a modified borrow distribution can be created that is quite 

 dissimilar to that for the sediments assumed to be in environmental equi- 

 librium. A second shortcoming is that the approach is somewhat unreason- 

 able in situations where the borrow materials are coarser but more poorly 

 sorted than native sediments. Here, the mathematical model predicts 

 stability for all fill placed although the finer grain sizes will surely 

 be removed by winnowing. 



(c) Adjusted SPM Method (R^) . Shortcomings of the Dean and SPM meth- 

 ods prompted James (1975) to propose a third fill factor method. The 



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