Calculation of stone size and damage potential 



The USAGE standard for sizing armor units for breakwaters, jetties, and 

 groins is the Hudson formula (SPM 1984; USAGE 1986). The Hudson formula 

 (Equation 4) was developed in the 1950s based on the results from small- and 

 large-scale physical models conducted at WES (SPM 1984). 



W = ^^^^ (4) 



where 



W = weight in pounds of an individual armor unit in primary cover layer 



/,. = unit weight of armor unit in Ib/cu ft (assume equals 165 Ib/cu ft) 



H = design wave height (///«) at structure in ft 



Ki:,= stability coefficient that varies primarily with armor unit shape, 

 roughness, sharpness of edges, and degree of interlocking (see 

 Table 7-8 SPM 1984) 



/ = unit weight of water in Ib/cu ft (assume equals 64.0 Ib/cu ft for 

 seawater) 



= angle of structure slope relative to horizontal (assume 1 :2 slope, so 

 cot 6'= 2) 



The selected stability coefficient, Kp = 1.6. is applicable for rough angular 

 quarry stone, an armor layer two stones thick (i.e.. ii = 2), and breaking waves at 

 the structure head (SPM 1984). However, SPM (1984) cautions that this K,, value 

 is unsupported by test results and should only be used for preliminary design. 

 The New York District experience will confimi selected design stone size. 



Table 7 lists the calculated stone size for each water level and Hjn and ///, 

 value calculated previously. 



Hindcast wave data from the Wave Information Study (WIS) (Brooks and 

 Brandon 1995) were consulted to examine nonbreaking waves and calculate 

 stone sizes for comparison with those calculated for breaking waves. WIS 

 Atlantic Goast Station 72 located in 88.6 ft of water offshore of the north 

 New Jersey coast was selected. The joint occun-ence of wave heights and periods 

 were examined, and each combination of height and period observed during the 

 1976-1993 period was incorporated in the analysis. Using tables from SPM 

 ( 1 984). the deep-water unrefracted wave height was calculated for each height- 

 period combination. Using the nearshore slope for Profile 255 and Figures 7-2 

 and 7-3 from SPM (1984), breaking wave height and depth were calculated for 

 each offshore condition. Where breaking occurred offshore of the groin for each 

 of the three water levels of interest for this study, nonbreaking wave calculations 

 were discontinued. 



44 Chapter 4 Structure Design 



