The crosshatched area in Figure 36 shows that, for a 1 on 1.5 rubble 

 slope fronted by a 1 on 50 beach slope, the maximum absolute runup, 

 coincident with breaking waves at or seaward of the structure toe, 

 occurs for dg/H^ « 1.0 in the high wave steepness range (H^/gT 2 ) , 

 but occurs for progressively higher dg/H^ values as H^/gT 2 dimin- 

 ishes, to djjAil, « 2.6 to 3.0 for HygT 2 « 0.0002. 



Raichlen and Hammack (1974) tested structures with 1 on 2 slopes, 

 having both rough (quarrystone armor) and smooth surfaces. The struc- 

 tures were fronted by a 1 on 200 beach slope (Fig. 33). Smooth-slope 

 runup values from their curves were converted to the variables used in 

 this study and are comparable to the smooth-slope runup values for a 

 structure on a horizontal beach given in Figures 14, 15, and 16. Runup 

 values of Raichlen and Hammack for the quarrystone rubble slope were 

 also converted to variables in this study (Fig. 37) , and were compared 

 with their smooth-slope results. The various r values were each 

 determined as an average of rough-slope runup to smooth-slope runup 

 for varying wave steepness values but constant dg/H^ values. The 

 resultant curve is given in Figure 38. The rather gentle negative 

 slope of the line for the 1 on 2 structure presents a trend similar to 

 that in Figures 31 and 32. 



Ahrens (1975a; personal communication, 1975) tested riprap slopes 

 (Fig. 33) in a wave tank with depth, dg , of 4.57 meters. The armor 

 layer was approximately 1.5 to 2 stones thick, with a filter underlayer 

 lying on a core of bank-run gravel. Ahrens used various armor stone 

 sizes, and for each slope and set of wave conditions, the larger H^/k^, 

 values consistently had the higher values of relative runup. Figure 39 

 shows the effect of H^/k r on relative runup for a range of wave steep- 

 nesses on a 1 on 3.5 slope for dg/H^ = 7, as derived from Ahrens' data; 

 Figures 40 and 41 show runup curves based on Ahrens' data for the spe- 

 cific conditions noted. 



Ahrens 1 data were then compared to the data for smooth structure 

 slopes fronted by a horizontal bottom and the resulting r values are 

 given in Figure 42. Results of his runup data, which were obtained in 

 large-scale testing, can be considered near-prototype scale. The r 

 values were determined by comparison with small-scale smooth-slope test 

 results. A difference in r values between large- and small-scale tests 

 for rubble structures is not apparent. However, the smooth-slope runup 

 curves are expected to underestimate prototype runup (see Sec- VI) ; 

 therefore, application of the values in Figure 42 would give conserva- 

 tive results when used with appropriate smooth-slope values uncorrected 

 for scale effects. 



b. Concrete Armor Units . Concrete armor units have been developed 

 primarily for increased stability under wave attack. In areas where 

 rock is scarce or of insufficient size or quality, concrete armor units 

 may become an economical necessity. Many types of armor units are 

 available in sizes ranging from the 45-metric ton (50 tons) tribar 



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