variables to explain damage would be one similar to the stability number used 

 by Hudson and Davidson (1975). The following definition is used for the 

 stability number for tests with irregular waves: 



H 

 N = w^ 2 CD 



W \ 1/3 , 

 50\ 



where w is the density of stone and w is the density of water. Since 

 r w -L 



these tests were conducted in fresh water, w =1.0 g/cm . As far as the 



w 



stability tests of reef breakwaters are concerned, it was apparent that tests 

 with a higher period of peak energy density did more damage than similar tests 

 with a smaller period of peak energy density. This finding is consistent with 

 the results of a study conducted by Gravesen, Jensen, and Sorensen (1980) on 

 the stability of high-crested, rubble-mound breakwaters exposed to irregular 

 wave attack. According to the stability analysis of Gravesen, the spectral 

 stability number is defined 



(h 2 lY 



V mo p/ 



/3 



N * = \ "T Y' (2) 



W 50 , , _, _ 



w 

 w 



where L is the Airy wave length calculated using T and the water depth 



P P 



at the toe of the reef d 



s 



20. Figures 4 through 8 show comparisons of the effectiveness of the 

 stability number and the spectral stability number in accounting for damage to 

 reef breakwaters. In Figures 4, 5, 6, 7, and 8 the crest height reduction 

 factor is plotted versus the traditional stability number and the spectral 

 stability number for stability subsets 1, 3, 5, 7, and 9, respectively. The 

 figures show that there is less scatter in the damage trends when they are 

 plotted versus the spectral stability number. They also show that there is 

 little or no damage for spectral stability numbers less than about six but 

 that damage increases rapidly for spectral stability numbers above eight. In 

 the following analysis the spectral stability number will be used to define 



12 



