the cross-sectional area of the reef is given approximately by 



A t = (h;) 2 cot e + 3 K (^j (6) 



where cot G is the cotangent of the angle 6 between the "as built" sea- 

 ward and landward breakwater slopes and the horizontal. If the severity of 

 wave attack exceeds a value of the spectral stability number of about six, the 

 reef deforms. A convenient method to quantify the deformation is to use effec- 

 tive response slope for reef breakwaters defined by Equation 5. In Figure 10 

 the response slope C is plotted as a function of N* . This figure is simi- 

 lar to Figure 14.17 presented by Wiegel (1964) showing the relationships among 

 the grain size, beach slope, and severity of the exposure of a beach to wave 

 action. 



26. Because of the narrow range of the effective "as built" reef slope 

 C' (Table 4), it was not possible to quantify the influence of this variable 

 on stability. It is assumed that the flatter the initial slope of the reef 

 the more stable it will be. Future laboratory tests may expand the range of 

 this variable so that the influence of the initial slope can be determined 

 definitively. 



27. Figure 10 suggests that a logical form for a reef breakwater sta- 

 bility equation would be 



J7 = exp ( c i N s) (7) 



where C is a dimensionless coefficient. Regression analysis was used to 



determine the value of C, for tests where N* > 6.0 ; the value obtained was 



1 s 



C = 0.0945. With this value of C , Equation 7 explains about 99 percent of 



the variance in C for the 109 stability tests with N* > 6.0 . Equation 7 



s 



approaches logical limits with 



C -> oo , as N* ■* oo 

 and 



C ■> 1.0 , as N* ■*■ 



22 



