PART IV: SUMMARY 



21. All the equations presented within this report were developed from 

 two unpublished laboratory studies. These equations provide an easy way to 

 calculate the R^x of irregular waves on riprap-protected embankments. 

 Table 2 summarizes the important information about two runup equations which 



Table 2 

 Summarized Information for Maximum Runup Formula, Equation 5 



Formula 

 Category 



Recommended 



Wave 



Length 



Used 



Surf 



Parameter 



Used in 



Equation 5 



Runup 

 Coefficients 



5 L (Equation 4) a = 1.154 

 b = 0.202 



Variance 

 Explained 



R 2 = 0.843 



a , Standard 

 Deviation of 

 Percent 

 Error 



12.3 



Alternative 



5 (Equation 3) 



a = 1.022 

 b = 0.247 



R^ = 0.817 



12.9 



represent the most accurate existing method to determine the approximate upper 

 limit of wave uprush on a riprap revetment. The two equations are presented 

 as a recommended method and an alternate method to compute \ iax • The recom- 

 mended method has little or no systematic error such as might be associated 

 with the influence of water depth or nonlinear effects and is slightly more 

 accurate than the alternate method. The alternative method is easier to cal- 

 culate and can serve as a "rule of thumb" estimate. In Table 2 the runup co- 

 efficients are to be used in the general runup equation (Equation 5) by using 

 either the standard or modified surf parameter as noted. A method was devel- 

 oped which provides a reasonable way to make the predicted values of FL 

 more conservative. It was found that the errors in predicting R^x have a 

 normal distribution, and this fact was used to adjust the runup coefficient 

 a so that any predetermined exceedance level for Rmax could be achieved. 

 For example, by increasing the coefficient a by two standard deviations of 

 the percent error gives R^x predictions which would be expected to exceed 

 97.7 percent of the observed values of Kn ax • This technique produces a 

 logical envelope for the data. Table 2 lists the standard deviation a of 



24 



