From curve B in Figure 2-65, x < 0*01 for the beach. The 1 on 50 beach 

 slope reflects less wave energy and is a better wave energy dissipater than 

 the 1 on 5 structure slope. 



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The preceding example problem and Figure 2-65 indicate that the reflection 

 coefficient depends on incident wave steepness. A beach or structure will 

 selectively dissipate wave energy, dissipating the energy of relatively steep 

 waves while reflecting the energy of longer, flatter waves. 



*************** EXAMPLE PROBLEM 13*************** 



GIVEN ; Waves with a height H^ = 3.0 meters (9.84 feet) and a period T = 7 

 seconds are normally incident to a rubble-mound breakwater with a slope of 1 

 on 2 (cote = 2.0) . 



FIND ; A high estimate (upper bound) of the reflection coefficient. 



SOLUTION ; Calculate 



o 2-n Iv 



and from equation (2-86) 



,. '■'- 2.52 



2.OV3.O/76.4 



From curve C in Figure 2-64, x - 0.29 which is the desired upper bound on 

 X. The actual reflection coefficient depends on wave transmission, internal 

 dissipation, overtopping, and many other factors. Techniques described in 

 Seelig and Ahrens (1981) and laboratory tests by Seelig (1980) should be 

 used to obtain better wave reflection coefficient estimates for breakwaters. 



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Revetments faced with armor stone dissipate more wave energy and allow 

 less reflection than smooth slopes; therefore, reflection coefficient values 

 from curve A in Figure 2-65 should be multiplied by two reduction factors, 

 a. and a„ . The reduction factor a , given in Figure 2-66, accounts for 

 reduction due to relative armor size and wave breaking at the structure toe. 

 In Figure 2-66, d is the armor diameter, L the wavelength at the toe of 

 the structure, and H^ the maximum possible breaker height at the structure 

 toe (see Ch. 7 for estimating H, ) . The factor a„ depends on the number of 

 armor layers n and the ratio of armor unit diameter d to the incident 



o 



wave height H^. Table 2-3 gives an estimate of a2 based on laboratory tests. 



2-119 



