The experiments used two different toe depths, dg = 0.058 and 0.116 

 meter (0.19 and 0.38 foot), and a uniform water depth, d = 0.381 meter 

 (1.25 feet), seaward of the beach slope, resulting in corresponding 

 changes in the horizontal length of beach slope, Z. Relative runup 

 differences might be expected for tests having different Z/L values 

 but the same incident wave characteristics (H^/gT 2 and dg/H^) ; however, 

 negligible differences were observed for cases of Z/L > 0.5. Conditions 

 of Z/L < 0.5 occurred only for the longer wave periods which also had low 

 wave steepnesses (H'/gT 2 < 0.001, approximately). For these conditions, 

 relative runup was higher rather consistently for the smaller values of 

 Z/L. The tests did not have a sufficient range of conditions to fur- 

 ther define the effects of varying relative beach slopes. To further 

 confuse the question, however, tests of different Z/L values but equal 

 H^/gT 2 and dg/H^ values would be expected to include, because of the 

 differing toe depths (d s ), scale effects which cannot be isolated from 

 apparent beach-slope effects. 



Use of Figures 20 to 23 should be limited principally to conditions 

 where Z/L > 0.5. This particular value is somewhat arbitrary, but seems 

 justified on the basis of the limited testing. For values of Z/L < 0.5, 

 but high dg/H^ (e.g., d s /H^, > 3.0), the runup values from Figures 14, 

 15, and 16 for structures on horizontal bottoms should be used as upper 

 bounds of relative runup on structures fronted by a 1 on 10 slope with 

 the same d s /H^ value. In the case of Z/L < 0.5 with low values of 

 dg/H^ (e.g., 0.6, 1.0, etc.), it should be expected that relative runup 

 will be somewhat higher than predicted from the curves (Figs. 20 to 23), 

 and probably not exceeding 15 to 20 percent higher. The effect of beach- 

 slope length diminishes as the structure slope decreases, and effectively 

 ceases to be significant for cot 6 > 4.0. 



e. Example Problems . Problems may be solved in part by use of 

 equation (2) together with equation (1), or by use of Tables C-l or C-2 

 in the SPM. 



************* EXAMPLE PROBLEM 4************** 



GIVEN : An impermeable structure has a smooth slope of 1 on 3 and is 

 subjected to a design wave, H = 2.5 meters (8.2 feet), measured at 

 a gage located in a depth, d = 10.0 meters. Design wave period is 

 T = 8.0 seconds. The structure is fronted by a 1 on 90 bottom 

 slope, which extends seaward beyond the point of wave measurement. 

 Design depth at structure toe is d s = 7.5 meters (24.6 feet). 

 (Assume no wave refraction between the wave gage and structure.) 



FIND : Determine the height above SWL to which the structure must be 

 built to prevent overtopping by the design wave. 



52 



