2. Slope Roughness . 



For rough-slope data, the use of d g /H^ curves has the advantage of 

 having constant H'/k, curves coincident with d /H ' curves. The dis- 

 advantage is that relatively few experiments have been undertaken where 

 the armor unit sizes have been varied to allow differentiation of rough- 

 ness effects from depth effects. Armor sizes have been varied in 

 studies by Hudson (1958), Hudson and Jackson (1962), Jackson (1968a), 

 and Ahrens (1975a). Jackson (1968a) had a rather limited range of d^/H^ 

 values. Ahrens (1975a) tested slopes of 1 on 2.5, 1 on 3.5, and 1 on 5 

 at near-prototype scale (d s = 4.57 meters or 15 feet) with a wide range 

 of H^/gT 2 . Rough-slope results are discussed in Section V,2. 



3. Effects of Beach Slope Fronting a Structure . 



The presence of a slope in front of a structure may or may not affect 

 a wave. Effects of slope will depend on wave conditions and the local 

 geometry or laboratory test arrangement. Three cases may be defined 

 (see also Fig. 2) : 



(a) Case 1. d s /gT 2 > 0.0793. An incident wave that has deepwater 

 characteristics at the structure toe will not be influenced by the slope 

 in front of the structure. A horizontal bottom at the same depth, ds , 

 would also have no effect on the wave. 



(b) Case 2. dg/gT 2 < 0.0793; d/gT 2 > 0.0793. An incident wave that 

 has deepwater characteristics at the toe of the beach slope will not be 

 influenced by the bottom (horizontal or sloping) seaward of the beach 

 slope, but the wave will be modified to some degree by the beach slope, 

 dependent on the toe depth of the structure. This case is the desired 

 condition for laboratory tests where only a particular beach slope (but 

 not the slope length) is specified. The implication is that the beach 

 slope extends into deep water. 



(c) Case 3. d g /gT 2 < 0.0793; d/gT 2 < 0.0793. An incident wave that 

 has transitional or shallow-water characteristics at the toe of the beach 

 slope will be modified by the beach slope. The beach-slope effect is not 

 only a function of relative toe depth, dg/gT 2 , but also a function of 

 the relative depth seaward of the beach slope, d/gT 2 . The latter rela- 

 tionship is expressed equivalently in this study with the dimensionless 

 variable -£/L, where L is the horizontal beach-slope length and L 



is the wavelength for a given period, T, in the uniform depth seaward 

 of the beach slope. Design curves for smooth-slope runup are limited to 

 t/L > 0.5 in this study since there are insufficient data to adequately 

 define the effects of shorter beach-slope lengths on runup. 



However, consideration of the various relations between beach-slope 

 geometry, relative depths, and wave shoaling allows the following 

 expectations (conditions) of runup: 



33 



