reduction in runup would be a function of surface roughness, total void 

 space, and friction effects within a porous medium. Runup curves de- 

 rived from Savage's data are given in Figures 29 and 30. These curves 

 are derived from data for the largest stone size, 10.0 millimeters, 

 tested by Savage, and for which H^/k r = 12.7 and 4.8 for d s /H^ = 3.0 

 and 8.0, respectively. His data for all stone sizes show that, for 

 constant wave conditions (d fi /H^ and H^/gT 2 ) , runup was higher on slopes 

 having larger values of H^/kj, (i.e., smaller stones). 



The structure used by Savage was actually intermediate between a 

 permeable rubble mound and impermeable riprap. This structure could be 

 considered to represent riprap with a thickness of many stones; however, 

 this would be unusual because the riprap layer in prototype installations 

 is generally only 2 to 4 stones thick. It could represent the use of 

 stone in front of seawalls, a practice in some locations. Also, the 

 tests are somewhat unrealistic in that the stone size is small rela- 

 tive to wave height and slope stability could have been a problem. 



Direct comparison of the various rubble-slope runup data is diffi- 

 cult because relative stone sizes are not always the same for given 

 wave conditions. Indirect comparisons can be made if the rubble-slope 

 runup values are first calculated as fractions of smooth-slope values. 

 Then, for a specific structure slope and cross section, wave steepness, 

 and relative depth, effects of the relative roughness (H^/k^) may be 

 evaluated. 



The rubble-slope data have been evaluated in this manner using the 

 appropriate smooth-slope curves given earlier. The ratio of rubble- 

 slope relative runup to smooth-slope relative runup is designated r. 

 For a given slope, relative depth (dg/H^) , and relative roughness 

 (H^/k-p) , r appeared to vary with wave steepness, as might be expected, 

 but with no consistent trend. Therefore, r values for several wave 

 steepnesses were averaged for constant relative depth, relative rough- 

 ness, and slope. The r values based on data of Hudson (1958) and 

 Savage (1959) are given in Figures 31 and 32. The horizontal axes are 

 the relative roughness or relative stone size, ti^/k r . Each curve is 

 based on r values averaged over a range of wave steepness for each 

 relative stone size used in the analysis. 



Hudson's data give rather low r values of 0„36 to 0.64. A posi- 

 tive slope trend in the data is noticed for the flatter structure slopes, 

 and might be expected since the stone size becomes smaller relative to 

 the wave as H^/k^, increases. 



The r values for the quarrystone rubble mound tested by Jackson 

 (1968a) are given in Table 8. Jackson's data are for limited condi- 

 tions; r values are 0.48 to 0.52, which are higher than Hudson's data 

 for the given relative stone sizes. This result is expected because of 

 the higher core in Jackson's tests. 



68 



