For lesser steepness, some waves may still be breaking. Figure 4 shows 

 minimum values of H^/gT 2 for breaking waves as a function of d g /gT 2 . 

 The flow chart in Figure 6 describes use of the equations. Runup of 

 nonbreaking waves on a structure fronted by a horizontal bottom, to- 

 gether with breaking wave runup (if desired) , may be obtained by using 

 the smooth-slope empirical runup curves in Figures 14, 15, and 16. 

 These curves are modified from those in the SPM. 



Runup on smooth structures fronted by a sloping 1 on 10 beach should 

 be determined by use of Figures 14 to 23. The beach-slope length is an 

 important variable. The runup curves were developed from results of 

 tests where the beach-slope horizontal length was equal to or greater 

 than one-half the wavelength at the toe of the sloping beach. As the 

 relative beach-slope length (£/L) decreases, for a given dg/H^ and 

 H^/gT 2 , relative runup would be expected to increase (unless the wave 

 breaks in front of the structure toe) to a maximum relative runup equiv- 

 alent to that obtained for the given d s /H in the presence of a 

 horizontal beach. 



Maximum absolute runup, R, for a given wave ■period will be pro- 

 duced for the maximum wave steepness possible unless the wave breaks 

 before reaching the structure. If a wave of given period breaks at the 

 higher steepness values, maximum runup will be produced by a wave which 

 begins breaking near the structure toe. The smooth-slope runup curves 

 (Figs. 14 to 23) give data for constant dg/H^ values. For a given 

 dg/H^ value and constant dg, higher runup, R, will occur at lower 

 wave steepnesses, H^/gT 2 . Conversely, for a given wave steepness and 

 depth, dg , higher runup will occur at the lower values of relative 

 depth, dg/H^,. For structures on sloping beaches, runup, R, for a 

 given wave steepness may be approximately the same for different dg/H^ 

 values because of effects from the waves' breaking. Design wave condi- 

 tions usually assume the design wave is associated with high wave steep- 

 nesses, but certain environments might have a design wave associated 

 with low wave steepness. A range of wave conditions encompassing the 

 selected design conditions needs to be evaluated to determine maximum 

 runup. Most importantly, maximum absolute runup may not be coincident 

 with the maximum relative runup for a given range of conditions. 



Runup on rough slopes was developed in this study with emphasis on 

 structure cross section, relative depth, and relative roughness. In 

 cases where sufficient experimental data were available, relative runup 

 was plotted in a manner analogous to the smooth-slope data; i.e., R/H^ 

 versus cot 9 for isolines of H^/gT 2 and for specific dg/H^ and 

 H /k r values. In all cases, also, the ratio between the rough-slope 

 runup and smooth-slope runup, r, is given. The ratio r is given as 

 r = ffH^/kp, 0) . Thus, for any given H^/kj, and dg/H^ , r is an 

 average of several values over a range of* H^/gT 2 and is expected to 

 be a function of dg/H^ and H^/gT 2 , but insufficient data exist to 

 further develop the relationship. Runup for structures or wave condi- 

 tions not tested may be estimated by using the equivalent smooth-slope 



122 



