This study has discussed r values, considering some of the vari- 

 ables, principally structure slope and cross section, relative armor 

 size, and relative depth. Variations in r with wave steepness were 

 present but no consistent trends were observed, and r values were 

 usually averaged for the few wave steepness values for each relative 

 depth and relative armor size at which runup was obtained. 



In application, a value (or range of values) of r is determined 

 for the desired structure slope, cross section (high or low core, if 

 applicable), type of armor unit, and relative armor size. This r value 

 is then multiplied by the smooth-slope runup value to give an estimated 

 rough-slope runup. The smooth-slope value is determined from the smooth- 

 slope design runup curves given in Section V,l which are similar to but 

 expanded from those in the SPM. The smooth-slope runup should be deter- 

 mined without any scale-effect correction (discussed in Sec. VI). After 

 determination of the rough-slope runup, it is suggested that the scale- 

 effect correction be applied which is applicable to the data from which 

 the r value is derived, although variability in r values is greater 

 than the applicable rough-slope scale-effect corrections. 



************* EXAMPLE PROBLEM 11 ************* 



GIVEN : Quarrystone rubble- mound structure; cot 8 = 1.5; cot 6 = 40; 

 H<5 = 2.2 meters (7.2 feet); T = 8.9 seconds; h c = 3.4 meters; 

 k r as 0.815 meter (2.7 feet); d s = 3.14 meters (10„3 feet). 



FIND: Determine 



runup. 





SOLUTION: 









d s 



= 1.43; tt- = 2.7; •£■ * 1 

 k r d s 





gT 2 



2 2 

 - - n rift" 1 ° v 





(9.81)(8.9) 2 



This structure is similar in design to the rubble-mound breakwater 

 tested by Jackson (1968a). However, ' dg/H^ is lower than tested, 

 and waves breaking at the structure toe may be expected. Accordingly, 

 an r value needs to be determined along with smooth-slope runup for 

 a similar geometry. From Table 8, for H^/kj, = 2.7 and cot 8 = 1.5, 



r w 0.52 . 



Smooth-slope runup is" determined from the curves in Section V,l. 

 This problem has cot 6 = 40, but the only beach slope available 

 in Section V,l is cot B = 10. Nevertheless, from Figure 22, for 

 dg/H^ «1,S, cot 6 = 1.5, and H^/gT 2 = 0.0028, 



R_ 



iri ss 3 . 6 . 



o smooth 



102 



