GIVEN : An impermeable structure with a smooth slope of 1 on 2.5 and sub- 

 jected to a design wave, H = 7 feet, measured at a gage located where 

 the water depth, d = 15 feet. The design period, T = 8 seconds. 

 Design depth at the structure toe at high water, d s = 10 feet. 

 (Assume no change in the refraction coefficient between the structure 

 and the wave gage . ) 



FIND : 



(a) The height above the Stillwater level (SWL) to which the struc- 

 ture must be built to prevent overtopping by the design wave. 



(b) The reduction in required structure height if uniform-sized 

 riprap is placed on the slope. 



SOLUTION : Although the given wave is not specifically defined, it is 

 convenient to consider the wave as the significant wave of the design 

 storm. In addition, instead of no overtopping by the design wave, 

 assume that it is required to compute the elevation overtopped by only 

 1 wave in 20 during the design storm; i.e., p = 0.05. In the SPM, 

 R s was 21.3 feet; therefore, from equation (2): 



05 "'.05 



= 23—3 = °-707 (In 20) l / 2 =1.22 



and R 05 = 1-22 (21.3) = 26.1 feet. 



To find (b) above, the roughness and porosity factor from the Table 

 is estimated as: 



r = 0.50 

 This yields: 



R s = R s (smooth) * r = 21.3 (0.50) = 10.65 feet. 

 The 5-percent runup corresponding to R s = 10.65 feet is 



R 05 = 10.65 x 1.22 = 13.0 feet . 

 **************** EXAMPLE 2*************** 



Saville (1958) presented a method for determining R s on composite 

 slopes using the results obtained for constant slopes (see SPM example, 

 pp. 7-33 to 7-37). The technique discussed in this report can be applied 

 to composite slopes and should give conservative results for Rp/R s > 1.0, 

 if Rg is found to exceed the berm or slope break elevation. This can 

 be shown by using the conditions given in the SPM example. 



II 



