GIVEN : A smooth-faced levee (cross section in SPM, Fig. 7-21) is sub- 

 jected to a design wave having a period, T = 8 seconds and an equiva- 

 lent deepwater height, H^ = 5 feet. The depth at the structure toe, 

 d s = 4 feet. 



Again, it is assumed that the given design height and period are the 

 significant values. It is also necessary to modify the question slightly 

 to account for the irregularity of actual surf conditions. 



FIND: The elevation which will be exceeded by only 1 wave runup in 20, 



SOLUTION : From example 1: 



R 



-- -^ = 1.22 , 



and from the SPM example, R s -6.04 feet; therefore, 

 R_ 05 = 6.04 x 1.22 = 7.4 feet 



To determine if the above solution provides a conservative runup estimate, 

 estimate the runup of the 5-percent wave, H ; i.e., the wave with a 

 height exceeded by only 1 wave in 20. This approach is adopted since it 

 is initially suspected that the largest waves cause the highest runups. 

 Assuming the Rayleigh distribution holds, the deepwater height of this 

 wave is : 



H.05 = 5 x 1.22 = 6.1 feet 



and the wave period is most likely the same as for the significant wave; 

 i.e., T = 8 seconds, since waves higher than the significant wave usually 

 have a period close to the significant period. Following the procedure 

 given in the SPM example, the runup on the compound slope for H.gs is 

 5.7 feet, which is lower than R s as determined in this example. 

 Although surprising, this result is logical. Because the fronting slope 

 is so flat (1 on 20), the larger wave breaks much farther offshore than 

 the significant wave and therefore loses considerably more energy before 

 encountering the structure. This analysis suggests that R.05 = 7.4 feet 

 may actually be too conservative. However, another component in the 

 incident wave spectrum is probably responsible for the highest runups, 

 e.g., the wave having the maximum breaker height in a water depth of 4 

 feet, the depth at the toe of the 1 on 3 slope. The maximum breaker 

 height for d s = 4 feet and T = 8 seconds is 5.24 feet, and following 

 the procedures in SPM this wave would run up about 7.4 feet, or approxi- 

 mately the value estimated for R.Q5- 



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