and the roughness term, aim/k, by 



im 



R„ (1 + cot^e)l/2 



k - / W5oNl/3 



(6) 



where R^ is the wave runup associated with the zero-damage wave height, Hg; 

 T the wave period; and v the kinematic viscosity. The values of runup used 

 to compute the Reynolds number and roughness are tabulated by test in Table 4 

 and represent the estimated runup which would be caused by the zero-damage 

 wave height. The estimates of Rz are calculated using the values of Hz in 

 Table 1 with the runup invariants tabulated in Table 3. Since the Reynolds 

 number defined in equation (5) uses wave runup, the calculations of the flow 

 regime refer to surface conditions, not conditions in the filter layer. In 

 Figure 10 the Reynolds number and roughness values tabulated in Table 4 are 

 shown with the flow regime boundaries as updated by Jonsson (1978) . The 

 figure shows that both the small-scale and prototype tests are in the rough 

 turbulent flow regime. 



V. COMPARISON WITH OTHER SOURCES OF DATA 



Scale effects at the zero-damage level were compared with the scale effects 

 test results of Dai and Kamel (1969) and Thomsen, Wohlt, and Harrison (1972) in 

 Figure 11; Dal and Kamel used rough quarrystone in their rubble-mound stability 

 tests and Thomsen, Wohlt, and Harrison used dumped Kimmswick limestone in their 

 riprap stability tests. The comparison was made by dividing the individual 

 value of Nz by the average prototype value of Nz for the tests having the 

 same relative depth (designated Nzp^, as tabulated in Table 1 for this study, 

 to form the scale effects factor Nz/Nzp. Figure 11 shows the scale effects 

 factor plotted versus a Reynolds number, R^, which is given by 



(gHz) 



1/2 





where H^ is the zero-damage wave height, and v the kinematic viscosity of 

 water (assumed to be 1.1306 x 10~^ square meters per second corresponding to 

 a water temperature of 15.6° Celsius). At the zero-damage ] evel the stability 

 numbers were approximately 20 percent lower for the small-scale test than for 

 the prototype test, as shown in Figure 11. The figure also shows that at the 

 zero-damage level the scale effects observed in this study were somev/hat less 

 severe than those observed by Thomsen, Wohlt, and Harrison and comparable to 

 those observed by Dai and Kamel. 



The small-scale test results of this study were also compared with a 1975 

 study conducted by the Hydraulic Research Station (HRS) , Wallingford, England, 

 for the Construction Industry Research and Information Association (CIRIA) 

 (Hydraulic Research Station, 1975) . The HRS study on riprap stability under 

 irregular wave attack was conducted at small scale. Table 5 tabulates the HRS 

 tests with a 1 on 4 or 1 on 3 slope which were used for comparison. These slopes 



23 



