runup on a smooth slope, all other conditions being the same (Stoa, 1978a) . 

 Normally, r is determined in laboratory experiments using monochromatic wave 

 conditions but it appears that r factors determined in this manner can also 

 be applied to irregular wave conditions (Battjes, 1974). Values of r for 

 various types of rough and porous slopes are given by Stoa (1979) (shown in 

 App. B). 



Often wave runup on rough slopes must be corrected for scale effects and 

 the correction factors are given in Stoa (1979) (shown in App. C) . Example 

 problem 3 illustrates how the results presented in this report can be applied 

 to a rough and porous slope and the method of applying the rough-slope scale- 

 effect correction factor. 



V. EXAMPLE PROBLEMS 



*************** EXAMPLE PROBLEM 1*************** 



This example illustrates the use of the runup equation, Figures 1 to 6, and 

 the recommended method of interpolation between slopes. 



GIVEN : A plane, smooth slope of 1 on 2.75 is subjected to irregular wave 

 action. The significant wave height, significant wave period, and water 

 depth at the toe of the structure are 6.0 feet (1.83 meters), 7.0 seconds, 

 and 24.0 feet (7.3 meters), respectively. 



FIND : R, R s , and R 2 for the given conditions. Would there be substantial wave 

 overtopping if the freeboard of the structure were 20.0 feet (6.10 meters)? 



SOLUTION : Since there is no figure or set of coefficients for the runup 



equation (eq. 2) for a slope of 1 on 2.75 it is necessary to compute R, R s , 

 and R2 for slopes of 1 on 2.50 and 1 on 3.00 and interpolate between them. 

 To start, calculate the period of peak (maximum) energy density, T p , using 

 equation (1) . 



T p = 1.05 T s = 1.05 (7.0) = 7.35 seconds 



Then compute the steepness parameter, H g /gTp 

 H s 6.0 



>T p 2 32.2(7.35) 2 



= 0.00345 



Using the above value of steepness in equation (2) with the coefficient 

 given in Table 1 allows the computation of R x /H s . For example, to calcu- 

 late R2/H s for a 1 on 2.5 slope 



R 2 



— = 3.39 + [129.0(0.00345)] + [-16 ,100(0. 00345) 2 ] = 3.64 



n s 



The above value of R2/H s can be confirmed, using Figure 4. Therefore, 



R 2 = 3.64(H S ) = 3.64(6.0) = 21.8 feet (6.64 meters) 



The other runup parameters R s and R can be calculated in a similar manner, 

 then used for interpolation to give the values of the runup parameters for 

 the 1 on 2.75 slope as shown in Table 2. 



