(a) Condition 1. Structure fronted by horizontal bottom. For a 

 given dg/H^ and H^/gT 2 , this geometry results in the highest rela- 

 tive runup. (However, smaller dg/H^ values are obtained when sloping 

 beaches are present, with consequently higher relative runup in some 

 cases .) 



(b) Condition 2. Structure fronted by a sloping beach extending 

 to deep water (same as case 2). For the same dg/H^ and H^/gT 2 

 values noted in condition 1, this geometry gives the minimum relative 

 runup (but the relative runup may be comparable to other geometries for 

 certain conditions) . 



(c) Condition 3. Structure fronted by a sloping beach terminating 

 in shallow water (same as case 3). For the same wave conditions given 

 in conditions 1 and 2, this geometry allows intermediate values of rela- 

 tive runup which is dependent on the relative beach-slope length, t/L. 

 For this study, relative runup was assumed, somewhat arbitrarily, to be 

 negligibly dependent on £/L for £/L > 0.5. (This assumption allowed 

 most of the small-scale smooth-slope data to be incorporated in the 

 design curves of Sec. V,l.) Furthermore, in instances where this 

 assumption is applicable, the geometry is considered essentially com- 

 parable to case 2. As £/L decreases from l/h =^0.5, and keeping 

 dg/H^ and H^/gT 2 constant, relative runup would increase and asymp- 

 totically approach the relative runup for a structure on a horizontal 

 beach with the same dg/H^ value, if applicable. (A value of 



dg/H^ =0.6, for example, would not be obtained in the presence of a 

 horizontal bottom.) 



(d) Condition 4. Varying beach-slope angles. For given dg/H^, 

 H^/gT 2 > an ^ f° r either deep water or a uniform depth seaward of the 

 beach slope, as the beach-slope angle becomes smaller, relative runup 

 increases if the wave does not break in front of the structure. The 

 relative runup would asymptotically approach the values for runup on 



a structure sited on a horizontal bottom. If the wave breaks in front 

 of the structure while passing over a flatter beach slope but does not 

 break over a steeper beach, then relative runup may be higher on the 

 structure fronted by the steeper beach. 



(e) Condition 5. Varying dg/H^ values for a structure fronted 

 by a sloping beach. As dg/H^ increases, the beach slope becomes less 

 important for the relative runup of the higher wave steepnesses. 



The runup expectations in these conditions are based on the assump- 

 tion that the shoaling coefficient, H/H^, for the particular toe depth, 

 dg, is equal to or greater than one. Actually, this assumption is not 

 always true since the steeper waves generally occur in the larger rela- 

 tive depths (dg/gT 2 > 0.009) for which H/H^ may vary between 0.913 

 and 1.0. Any effect of this relationship on relative runup, however, 

 is apparently obscured by data variability and so is not considered in 

 the above examples. 



34 



