Figure 22 exhibited a slightly decreasing reflection coefficient with 

 increasing incident wave amplitude which is not reproduced by this 

 simple relationship for the slope friction angle. However, the feature 

 of (j) being independent of aj^, when equation C126) is adopted, is 

 extremely convenient for use in problems where the incident wave is 

 given in terms of its amplitude spectrum rather than as a monochromatic 

 wave. This is the reason for including equation (126) in the present 

 report and it leads to reasonably accurate results. 



Upon substituting the relationship for f^^, given by equation (125) 

 in equation (109) a less convenient but more accurate implicit equation 

 for <J) is obtained. 



tan2* - 0.29(^)°-'(^JM_^)°-%^ . (127) 



O s 



This equation may be solved iteratively by assuming a value of <j) 

 and evaluating |a| = R^ 2a£ and F^ from Figures 16 and 17, respectively. 

 With these values a new value of i> may be obtained from equation (127) 

 and the iteration may be continued until convergence is achieved. Since 

 |a| is a function of a^^, the incident wave amplitude, cj), is a function 

 of aj^; the use of equation (127) will therefore reflect the observed 

 decrease in reflection coefficient with increasing incident wave 

 amplitude. Although seemingly more cumbersome, it should be mentioned 

 that equation (127) is solved after a limited number of iterations (two 

 iterations generally suffice) . 



For given incident wave and slope characteristics, a^^ , L, h^, i^, 

 and d, either of the relationships for ^ may be solved; the reflection 

 coefficient is then obtained from Figure 15. To use this procedure to 

 "predict" the reflection coefficients observed for the slope angles 

 tanBs = 1/2.0 and 1/3.0 does not constitute a test of the procedure since 

 these data were used in establishing the empirical relationships for f^^ 

 and hence the procedure. However, with the degree of scatter exhibited 

 in Figure 22 this may be a meaningful comparison in that it will indicate 

 the ability of the procedure to reproduce the experimentally observed 

 reflection coefficients. 



To perform a more meaningful test of the procedure two separate 

 sets of experiments were performed as previously described in 

 Section III.3.b but for values of the slope angle tan3 = 1/1.5 and 

 1/2.5; each of these tests consisted of 48 individual experiments. 

 From knowledge of the incident wave and slope characteristics the 

 procedure was used to predict the reflection coefficient of the slope. 

 For each experiment two predicted values of the reflection coefficient, 

 Rp3 and Rp, were obtained depending on whether the slope friction 

 angle <^ was obtained from equation (126) (Rpg) or from equation (127) 

 (Rp) . The predicted reflection coefficients were compared with the 



70 



