4) should be used as upper bounds of relative runup on structures fronted 

 by a 1 on 10 slope with the same dg/H^I, value. In the case of £/L < 0.5 

 with low values of dg/H^ (e.g., 0.6, 1, etc.), it should be expected 

 that relative runup will be somewhat higher than predicted from the curves 

 (Figs. 8 to 11), and probably not exceeding 15 to 20 percent higher. 

 However, the effect of the length of a 1 on 10 bottom slope diminishes 

 as the structure slope decreases, and effectively ceases to be significant 

 for cot 6 >. 4 . These comments are incorporated in a flow chart (Fig. 12) 

 for determining which figure to use to find the runup on a structure 

 fronted by a sloping bottom. 



Because there are insufficient data available for cases where bottom 

 slopes are flatter than 1 on 10, it is recommended that the curves given 

 in this report, applicable to structures fronted by 1 on 10 bottom slopes, 

 be used; in most cases, results are expected to give higher estimates of 

 R (see Fig. 12). For the larger dg/H^ values (e.g., d^/H^ > 2.5), 

 relative runup on structures fronted by gentle bottom slopes will be 

 equal to or less than that given in Figures 2, 3, and 4 (horizontal 

 bottom) for the appropriate dg/H^ value. Relative runup on structure 

 slopes flatter than 1 on 4 is largely unaffected by changes in bottom 

 slope. Relative runup on steep structures fronted by a gentle bottom 

 slope will be equal to or less than values given in Figures 8 and 9 but 

 may be slightly higher than those given in Figure 10 [dg/H^ = 1.5). 



III. MAXIMUM RUNUP 



This section discusses the maximum runup from regular waves when a 

 range of conditions is possible. Maximum runup from irregular waves is 

 not discussed, but an approach to estimation of maximum runup from 

 irregular waves is given by Ahrens (1977a). In his method, runup result- 

 ing from a significant wave is determined from design curves such as 

 given here, and then runup for the irregular waves is assumed to follow 

 a Rayleigh distribution. 



Maximum runup, R, for a range of regular wave conditions, is not 

 necessarily associated with the maximum relative runup, R/H^. For 

 structures sited on horizontal bottoms, and for a given wave steepness , 

 Wq/ gl^ , both the maximum relative runup and the maximum dimensional 

 runup occur at the minimum value of dg/H^^. 



For structures sited on a 1 on 10 sloping bottom, maximum dimensional 

 runup, R, may or may not be coincident with the maximum relative runup 

 determined for a range of wave conditions. If depth, dg, and wave 

 steepness are assumed constant, then maximum relative runup occurs when 

 1 . <. dg/H^ <. 1.5, but maximum dimensional runup, R, is found when 

 dg/H^ is a minimum (in this report, when dg > 0, then (dg/H^);^,^^ = 0.6). 

 In cases where a bottom slope flatter than 1 on 10 is present, for a 

 given wave steepness, the maximum relative runup will occur for somewhat 

 higher dg/H^ values (1.5 <. dg/H^ <. 2.0). However, if wave height, H^, 

 and wave steepness are held constant, the maximum dimensional runup, R, 

 will be coincident with maximum relative runup as dg/H^ varies (i.e., as 



22 



