for predicting the reflection coefficient of rough impermeable slopes 

 is warranted. This comparison of predicted and observed runup, which 

 is independent of the determination of the reflection coefficient, may 

 also be taken as an independent check of the soundness of the procedure 

 and the theoretical analysis developed here. 



a. Limitations of the Procedure . The preceding comparison of 

 measured and predicted values of the reflection coefficient of rough 

 impermeable slopes has shown the semiempirical procedure to yield quite 

 accurate results. However, it is important to realize that the 

 significance of this favorable comparison is limited by the range of the 

 independent variables tested here. Therefore, it should be used with 

 caution whenever the values of d tanBg/JAl and d/h^ are outside the 

 range indicated by the experimental data in Figure 22. 



Furthermore, the procedure relies on an experimentally established 

 empirical relationship for the wave friction factor, f^^. In this 

 investigation the empirical relationship was established from experiments 

 in which the slope roughness elements were modeled by gravel. The 

 procedure as it appears here is therefore applicable only for slopes whose 

 roughness may be considered adequately modeled by gravel, i.e., natural 

 stones, quarry stones, etc. To utilize the procedure for slopes 

 protected by concrete armor units, an empirical relationship for f^^, 

 representative of these armor units, should be established in a manner 

 similar to that presented in Section III. 3. It is beyond the scope of 

 the present research to establish more general relationships for f . 



Finally, the manner in which the theoretical results were used in 

 the analysis of the experimental data to obtain values of f^^ makes the 

 resulting empirical relationships for f^^ part of the procedure itself, 

 i.e., the empirical relationships for f^^ can be used with confidence 

 only in conjunction with the present procedure for estimating the 

 reflection coefficient of rough slopes. 



As mentioned in Section Ill.S.b, experiments were performed also for 

 smooth slopes. For smooth slopes the roughness is negligible and the 

 empirical relationships for <}) (eqs. 126 and 127) are invalid. The type 

 of empirical formula anticipated for f^^ was based on an assumption of 

 fully rough turbulent flow conditions. To investigate if the experiments 

 performed with rough slopes in this study do correspond to fully rough 

 turbulent flow, the criterion established by Jonsson (1966) may be 

 examined. For the present experiment the maximum value of |A|/(d tang^) 

 is seen from Figure 22 to be of the order 20. Since this value 

 corresponds to the parameter a^^j^/k used by Jonsson (1966, Fig. 6) it is 

 seen that fully rough turbulent flow should exist for values of the 

 Reynolds number 



I i2 

 Re = -^ — ^ — > 10 , (131) 



V tan 3 



74 



