problems were basically the selection of the critical or stable grain size 

 for a borrow distribution, and the quantitative methods by which that dis- 

 tribution was to be modified to resemble native sediments. The adjusted 

 SPM approach assumes the critical grain size to be equal to that chosen by 

 the SPM approach (<f> critical) , except in situations where the borrow is 

 coarser than the native. Then, the stable size is allowed to increase 

 toward a maximum of u - a. Although this maximum is somewhat arbitrary 

 and may not directly relate to processes, it allows for the "retention" 

 of coarser sediments that can play the important role of "armoring" a beach 

 during periods of rapid erosion. As with Dean's approach, this method also 

 assumes that losses to the fill will be from the sizes finer than the 

 critical size, but unlike Dean, the losses are from all sizes finer. The 

 result is a modified fill distribution which is as close as possible to 

 the proportions of the native distribution in the finer size classes, but 

 retains the borrow material characteristics in the coarser size classes. 

 Actual calculations of R^ involve fairly complicated mathematics but 

 accurate graphical estimates can be obtained using the curves in Figure 9. 

 Again, the basic information required is the phi mean and phi sorting 

 values for both native and borrow composites. 



d. Comparison of Fill Factor Methods . The easiest comparisons can 

 be made using the four quadrants defined in Figure 7, where the vertical 

 axis is the log of the ratio of the borrow to native sorting values and 

 the horizontal axis shows the difference between borrow and native means 

 as scaled by the native sorting. In the first quadrant, where the borrow 

 is finer and more poorly sorted than the native, the adjusted SPM value 

 (R4) is between. a low Dean factor (R^,) and a higher SPM value (Rg) . The 

 borrow is coarser but more poorly sorted in quadrant 2 and here the SPM 

 factor is an upper bound, while the adjusted SPM and Dean factors are close 

 to one, except where the borrow is much more poorly sorted and then the 

 adjusted SPM factor is increased while the Dean value remains one. In 

 quadrant 3, the borrow is coarser and better sorted than the native and 

 all three methods predict values of one except where the borrow is much 

 better sorted than the native material (Fig. 7). This situation is unlikely 

 to be encountered but still R^ values are conservatively high as compared 

 with values of unity for Rg and Rp. Borrow sediments are finer and more 

 poorly sorted in quadrant 4 and generally unsuitable as fill. Here, an 

 SPM value cannot be calculated, and the R^ and R^ factors are usually 

 high. 



3. Renourishment Factor (RjO • 



The renourishment factor (Rj-) (James, 1974) is a dynamic approach to 

 answering how beach processes can be expected to modify specific fill sedi- 

 ments. It attempts to predict how often renourishment will be needed and 

 to evaluate the long-term performance of different fill materials with 

 regard to suitability, maintenance, and expense. In general, the conceptual 

 approach is that the active beach system can be viewed as a compartment 

 which receives sediments through longshore transport and from gradual ero- 

 sion of the inactive "reservoir" of sediments that form the backshore. The 

 compartment loses sediments by longshore and offshore transport beyond its 



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