have more stone in the cross section than the reefs of subset 9. All the data 

 appear to indicate that when the relative severity of wave attack is based on 

 the spectral stability number the stability of the reef correlates better with 

 the number of stones in the cross section than with the absolute size of the 

 cross section. Other factors being equal, a reef with a large bulk number is 

 more stable than a reef with a small bulk number because there are more stones 

 to dissipate wave energy and to shelter other stones from wave forces. 



25. Effective slope of the reef. The remaining secondary stability 

 factor is a combination of the first two. This factor, referred to as the 

 effective slope of the reef, is obtained by dividing the cross-sectional area 

 by the square of the crest height. Two effective slope variables will be dis- 

 cussed in this report: (a) the effective slope of the structure "as built," 

 defined as 



A 



c* - ~ W 



and (b) the response slope for the reef breakwater to wave action, defined as 



A 



C = -| (5) 



h 

 c 



These variables are considered a cotangent function since dividing A by h 

 one time produces a variable which can be regarded as a horizontal length, and 

 dividing this length by h creates a cotangent-like variable. For low- 

 crested, or submerged reefs, these variables provide a simple way to charac- 

 terize an average slope or shape for what is sometimes a rather complex shape 

 (e.g., see Figure 3). Table 4 shows that the average values of the effective 

 structure slope "as built" are in a relatively narrow range. Since the land- 

 ward and seaward faces of the reef were built to a slope of IV on 1.5H (cot 6 

 = 1.5), the difference between the values of C in Table 4 and 1.5 result 

 from the crest width of the trapezoid which increases the effective slope, as 

 illustrated in Equation 6. The "as built" cross section of the reef is a nar- 

 row trapezoid with a crest width three stone diameters wide. For this study 



21 



