Correcting for scale effects using Figure 7-13 yields 



k = 1.07 

 and 



R = 1.53 (1.07) 1.5 « 2.5 m (8.2 ft) 



A new hypothetical slope as shown in Figure 7-22 can now be calculated using 

 the second runup approximation to determine Ax and Ay . A third 

 approximation for the runup can then be obtained. This procedure is 

 continued until the difference between two successive approximations for the 

 example problem is acceptable, 



R = 4.8 m (15.7 ft) 



R = 2.5 m (8.2 ft) 



R = 1.8 m (5.9 ft) 



R, = 1.6 m (5.2 ft) 



R = 1.8 m (5.9 ft) 



and the steps in the calculations are shown graphically in Figure 7-22. The 

 number of computational steps could have been decreased if a better first 

 guess of the hypothetical slope had been made. 



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



b. Irregular Wav es. Limited information is presently available on the 

 results of model testing that can be used for predicting the runup of 

 irregular wind-generated waves on various structure slopes. Ahrens (1977a) 

 suggests the following interim approach until more definitive laboratory test 

 results are available. The approach assumes that the runup of individual 

 waves has a Rayleigh distribution of the type associated with wave heights 

 (see Ch. 3, Sec. 11,2, Wave Height Variability). Saville (1962), van Gorschot 

 and d'Angremond (1968), and Battjes (1971; 1974) suggested that wave runup has 

 a Rayleigh distribution and that it is a plausible and probably conservative 

 assumption for runup caused by wind-generated wave conditions. Wave height 

 distribution is expressed by equation (3-7): 



^ r / \Tl/2 



\^ 



ms 



--"'^ 



r~~ " 

 where, from equation (3-9), H^^s" %^ 2 , H = an arbitrary wave height for 



probability distribution, and n/N = P (cumulative probability) . Thus, if 



equation (3-7) is rewritten, the wave height and wave runup distribution is 



given by 



n % / LnP^l/2 



H„ R„ 



(7-9) 

 7-39 



