where 5 is the surf parameter, 9 the angle of the seaward face of the break- 

 water, Lq the deepwater wavelength given from linear theory as 



and a and b are empirical coefficients. Suggested values of a and b 

 are in Table 2. 



Table 2. Rough slope empirical runup coefficients 

 for breakwaters with 1.25 < cot 9 < 5.O.. 



Armor type 



a 



b 



Comment 



rwo layers of rubble 



0.692 



0.504 



Recommended 



Two layers of rubble 



0.956 



0.398 



To obtain 

 an upper 

 limit or 

 conservative 

 estimate of 

 runup and Kp^ 



Two layers of dolos 



0.988 



0.703 





For additional information on wave runup refer to Stoa (1978) and the SPM. 



For irregular wave conditions use the mean wave height (approximately 0.63 

 times the significant wave height; Sec. 3.22 of the SPM) and the period of peak 

 energy density in equations (4) , (5) , and (6) (Seelig, 1980) . 



IV. EXAMPLE PROBLEMS 

 *************** EXAMPLE PROBLEM 1*************** 



GIVEN : A rough impermeable breakwater covered with two layers of rubble on a 

 1 on 3 slope. The structure height is 18 feet (5.49 meters), crest width is 

 12 feet (3.66 meters), and water depth is 15 feet (4.57 meters). 



FIND: The transmitted wave height produced by overtopping for an incident wave 

 with a height of 9 feet (2.74 meters) and period of 11 seconds. 



SOLUTION ; From equation C5) the surf parameter is. 



tan 9 0.333 



? = 



•^H/Lq •^9/C5.12 X ll2) 



= 2.77 



Using the recommended rubble runup coefficients of a = 0.692 and b = 0.504 

 (Table 2), the predicted runup is: 



V ( 0-692g \ „ ( 0.692 x 2.77 \ „ ^ , ^ ^, ^ 



^ = V 1+0.504 J" =V 1+0.504 X 2.77 r ^ = ^'^ ^^^^ ^^'^ ™^^^^^^ 



The breakwater freeboard, F, is h - dg = 18 - 15 = 3.0 feet (0.91 meter). 



From equation (2), C = 0.51 - 0.11 B/h = 0.51 - 0.11 (12/18) = 0.44 and from 

 equation (1), the transmission coefficient is: 



