and for the 10-second wave , 



r) = 95.. ,.., — _ 



a' a m ft 



(M") = 95.9^^^:^(21,600^^ ) 



*■ A' t m 



(T = 10 s) 



The overturning moments about point B are obtained from equation (7-84) 

 thus 



(m"1 = 85.2 -2.7 (26.5) = 13.7 ^^^ (3,080 ^^^f^ ) 

 '' B' o m ft 



i,M (T = 6 s) 



and for the 10-second wave, 



(m") = 12.7 ^^^tE (2,850 i^ ) 

 ^ S'^c m ft 



[M") . 0^^ 

 ^ B' t m 



As in Examples Problems 31 and 32, various combinations of appropriate wave 

 conditions for the two sides of the structure can be assumed and resulting 

 moments and forces computed. 



*************************************** 



3. Breaking Wave Forces on Vertical Walls. 



Waves breaking directly against vertical-face structures exert high, short 

 duration, dynamic pressures that act near the region where the wave crests hit 

 the structure. These impact or shock pressures have been studied in the 

 laboratory by Bagnold (1939), Denny (1951), Ross (1955), Carr (1954), 

 Leendertse (1961), Nagai (1961a), Kamel (1968), Weggel (1968), and Weggel and 

 Maxwell (1970a and b). Some measurements on full-scale breakwaters have been 

 made by deRouville et al., (1938) and by Muraki (1966). Additional references 

 and discussion of breaking wave pressures are given by Silvester (1974). Wave 

 tank experiments by Bagnold (1939) led to an explanation of the phenomenon. 

 Bagnold found that impact pressures occur at the instant that the vertical 

 front face of a breaking wave hits the wall and only when a plunging wave 

 entraps a cushion of air against the wall. Because of this critical 

 dependence on wave geometry, high impact pressures are infrequent against 

 prototype structures; however, the possibility of high impact pressures must 

 be recognized and considered in design. Since the high impact pressures are 

 short (on the order of hundredths of a second), their importance in the design 

 of breakwaters against sliding or overturning is questionable; however, lower 

 dynamic forces which last longer are important. 



7-180 



