where 



H = significant wave height of the incident irregular waves 

 (average height of highest one-third waves at site) 



L = wave length at the site corresponding to the period of peak 

 energy density for the incident irregular waves 



K„ = alternate stability coefficient = L„/NH„ 

 o •' p s 



21. The principal modification of the original Iribarren formula is the 

 substitution of an alternate stability coefficient on the basis that the orig- 

 inal stability coefficient (N in the numerator of Equation 2) is a function 



of the wave steepness H„/L_, . A number of other investigators have proposed 



b p 



similar stability relations (Rybtchevsky 1964, Jensen 1984, and Ahrens 1984). 

 A similar modification to the Hudson formula could be made by substituting K^ 

 = K ,H /L . Ahrens (1984) found that stability by "reef type breakwaters," or 

 low-crested breakwaters without traditional multi-layered cross sections (ba- 

 sically homogeneous rubble-mounds), was reflected with greater confidence us- 



2 



ing a modified Hudson formula with H^Lp in the numerator than with the 



original Hudson formula (Figures 3 and 4). 



22. Engineers at Delft Hydraulics Laboratory in The Netherlands re- 

 cently performed an extensive series of scale model tests of the stability of 

 rock slopes under random wave attack (Van der Meer and Pilarczyk 1984). These 

 tests resulted in the formulation of a set of stability formulae for quarry- 

 stone armor of breakwaters and revetments. Their tests also gave information 

 on how to predict damage rates as a function of the number of incident waves. 

 Armor layer gradation was found to have a lesser effect than that found by 

 other investigators (Ahrens and McCartney 1975). Slope angle was found to 

 have an effect on stability similar to that predicted by the Hudson formula. 

 Wave period effect was investigated as a function of the "Iribarren number" or 

 surf parameter as follows: 



(, = 



tan 9 



H \^^ (4) 



where L = gT^/2ii, based on the average wave period T^ . 



23. The influence of wave period was found to correspond roughly with 

 the traditional distinction between breaking and nonbreaking waves. The ef- 

 fect of variations in the incident wave spectral shape, as measured in various 



15 



