Shore Protection Manual guidance suggests a minimum crest width equal 

 to the combined widths of three armor units. Structure slopes normally range 

 from 1V:1.5H to 1V:3H. Selection of crest elevation can be performed using 

 guidance previously discussed in the "Structural Stability" and "Performance 

 Characteristics" sections. The influence of crest elevation on stability of low- 

 crested breakwaters can be estimated using Figure 49 for statically stable low- 

 crested breakwaters and Equations 32 and 33 for reef breakwaters. A series 

 of design curves for reef breakwaters similar to Figures 51 and 52 can be 

 developed to aid in converging on the optimum design. The stability analysis 

 will yield a relationship between crest elevation and armor unit requirements. 

 The performance characteristics for each cross section can be computed using 

 methods previously discussed. Overall analysis of each cross section's 

 stability, performance characteristics, and costs will result in selection of the 

 optimum cross section. 



Armor gradation 



Generally, reef breakwaters have been designed using stone gradations 

 wider than ordinarily used for armor in conventional, multilayered 

 breakwaters, as discussed in the Shore Protection Manual (1984). The 

 advantages of a wide gradation is that it uses a larger portion of the stone 

 produced by a quarry and therefore may be more economical. A wider 

 gradation also makes it easier to satisfy the filter criteria that will be discussed 

 in the following section. Gradation is easily represented in terms of median 

 weight of armor stone W 50 determined from stability analyses discussed 

 previously. W 50 is used to normalize the other percentile weight stones, i.e., 



Wi = _5l (46) 



* Wf 



where x indicates the percentile of armor stone less than the given weight. 

 For example, W 15 ' represents the ratio of W ]5 to W 50 , where W 15 is the stone 

 size exceeding only 15 percent of all stones in the gradation. 



Extensive studies of breakwater and riprap stability conducted in The 

 Netherlands have produced two well-defined stone gradations (Van der Meer 

 and Pilarczyk 1987), which are referred to as the Dutch wide and the Dutch 

 narrow gradations. The wide gradation is defined by: 



W x = fexp(0.01157x - 0.5785)f (47) 



and the Dutch narrow gradation is defined by: 



W x = [exp(0.003192x - 0.1597) f (48) 



where x is entered as a percent to solve for various values of W x . The two 

 Dutch gradations along with the gradation specified in the SPM (Ahrens 1975) 



Chapter 4 Structural Design Guidance 



97 



