The correlation coefficients of the damage profiles provided a convenient 

 means of comparing the damage profiles of the model and the prototype by cal- 

 culating the coefficients for model and prototype tests with approximately the 

 same relative damage. The profiles tests were matched by the location of the 

 Stillwater level on the reference surveys, and the averaged differences from 

 the reference surveys for the model and prototype tests were paired to calcu- 

 late the correlation coefficient. Table 2 provides a tabulation of correlation 

 coefficients for a number of model-prototype profile pairs, including those 

 shown in Figures 8 and 9. In general, the closer the relative depths of the 

 model and prototype tests were the more similar the profile shapes. 



3. Runup . 



In evaluating scale effects between small-scale and large-scale tests the 

 wave runup was also compared. Runup was visually defined as the average point 

 of maximum wave uprush on the riprap surface near the center of the wave tank. 

 The elevation of this point was then measured using the survey apparatus. The 

 runup data in Table 3 indicate that relative runup, R/H, can be considered 

 constant for a fixed value of d/gT^ between 0.0264 and 0.0036. For d/gT^ 

 of 0.0595 or 0.0589, the ratio of the relative runup to the surf parameter, 5, 

 is almost constant, where the surf parameter, 5, is defined as 



5 = (H/Lo)-l/2 tane, 



Lq is the deepwater wavelength, and 6 the angle between the embankment and 

 the horizontal. The runup invariants, R/ll or (R/H)/C, as tabulated in 

 Table 3 and shown in Figure 6, indicate that the runup in the small-scale tests 

 was approximately 20 percent greater than predicted from the prototype tests. 



The small-scale test results at the zero-damage level give more conservative 

 estimates of the stability number and the runup. The zero-damage level stabil- 

 ity numbers are lower and the runup is higher in the small-scale tests than 

 predicted by the prototype tests. The higher runup is probably due to the 

 reduced penetration of the wave uprush in the small-scale tests as compared to 

 the prototype tests. The stone size used in the filter layer was modeled 

 geometrically but should be somewhat larger, according to Keulegan (1973), to 

 obtain proper flow similitude. 



4 . Flow Regime . 



In this study the small-scale tests replicated the prototype tests at a 

 1:10 Froude scale which, assuming no scale effects, required rough turbulent 

 flow in both the small-scale and prototype-scale tests. When using the Froude 

 scale model the model and prototype vrill be dynamically similar with respect 

 to inertial and viscous forces because viscous forces can be assumed insignifi- 

 cant. The existence or nonexistence of rough turbulent flow is determined from 

 the criterion established by Jonsson (1966) . Using definitions similar to 

 Madsen and White (1976), who applied Jonsson's criterion to rubble-mound 

 structures, the Reynolds number, R^, is given by 



b| (1 + cot2e)(|^) 

 Re = '— (5) 



21 



