where R is the wave runup associated with a particular probability of 

 exceedance, P , and Rg is the wave runup of the significant wave height, 

 H . Figure 7-23 is a plot of equation (7-9). For illustration, if the 1 

 percent wave runup (i.e., the runup height exceeded by 1 percent of the 

 runups) is used, then P = 0.01 and equation (7-9) yields 



H(l%) _ ^0.01 _ ( Ln O.Ol V^^ _ , .,, 



This example indicates that the 1 percent wave runup would be about 52 per- 

 cent greater than R , the runup of the significant wave, Hg . H(l%) 

 should not be confused with the term H^ which is the average of the highest 

 1 percent of all waves for a given time period. For the condition of a 

 sloping offshore bottom fronting the structure, a check should be made to 

 determine if a wave height greater than Hg breaks on the offshore bottom 

 slope rather than on the structure slope for which the runup, Rg , was 

 determined. Should the larger wave break on the offshore bottom slope, the 

 runup would be expected to be less than that indicated by the ratio Rp/Rg • 



The following problem illustrates the use of the irregular wave runup on a 

 rough slope using smooth-slope curves. 



************** EXAMPLE PROBLEM 6 **************** 



GIVE N: An impermeable structure with a smooth slope of 1 on 2.5 is subjected 

 to a design significant wave Hg = 2.0 m (6.6 ft) and T = 8 s measured in 

 a water depth (d = 4.5 m (14.8 ft) . The design depth at the toe of the 

 structure d^ = 3.0 m (9.8 ft) at SWL. 



2IND: 



(a) The wave runup on the structure from the significant wave H and the 



H„ and H_ _, waves. 



s 



(b) The probability of exceedance of the wave height that will begin to 

 overtop the structure with a crest at 7.5 m (24.6 ft) above SWL. 



SOLUTION: 



(a) From the example program given in Section 11,1, a. Regular Waves, it is 

 found that R = R = 5.6 m (18.4 ft) . From equation (7-9) or Figure 7-23 



"O.l ^ %A ^ (_ Ln O.l V^^ 



1.07 



and 



Also 



R^ , = 1.07 R,= 1.07 (5.6) = 6.0 m (19.7 ft) 

 U . 1 •= 



7-41 



