Table 1. Average values of £ U /H and ^^/H and the standard 



deviations, a, for slopes of 1 on 2.5, 3.5, and 5.0. 



Slope 



V H 



a 



V H 



a 



1 on 2.5 



1.20 



0.38 



-0.65 



0.33 



1 on 3.5 



0.56 



0.24 



-0.76 



0.29 



1 on 5.0 



0.48 



0.29 



-0.85 



0.34 



height, H, which caused the damage. The parameters £ u and l^ are meas- 

 ured in the vertical from the SWL. Table 1 indicates that typically the 

 vertical range of damage was about 1.8 wave heights on a 1 on 2.5 slope and 

 1.3 wave heights on slopes of 1 on 3.5 and 1 on 5. When inspecting for damage, 

 it is necessary to consider the water level which may have existed during a 

 storm. 



8. Wave Runup . 



Wave runup on riprap may be estimated using the method in Stoa (1979) . 

 Stoa indicates that runup on riprap ranges from 60 to 72 percent of the value 

 for smooth embankments with similar slopes and wave conditions. An alterna- 

 tive method has been developed using the runup data from Ahrens (1975) . Run- 

 up, R, is given by the general equation 



b + 



(e/l ) 



1/2 



cot e 



(8) 



where a and b are the dimensionless coefficients, H the wave height at 

 the toe of the structure, and L the deepwater wavelength, given by 



L ° 2T7 



where T is the wave period and g the acceleration of gravity. The best fit 

 coefficients for predicting runup on riprap in equation (8) are a = 0.956 and 

 b = 0.398; these coefficients were rounded off to 1.0 and 0.4, respectively, 

 for the runup prediction method given in ETL 1110-2-221 (U.S. Army Corps of' 

 Engineers, 1976). Equation (8) has been determined to give reliable estimates 

 of monochromatic wave runup for d s /H > 3.0 and for slopes from 1 on 2 to 1 on 

 10. If there is no clearly defined toe, equation (8) may still be used as 

 shown in the following example . 



*************** EXAMPLE PROBLEM 3*************** 



This example illustrates how to compute the maximum runup for situations 

 where there is little truncation of the wave height distribution due to depth- 

 limit breaking. Three different methods are used to illustrate the runup 

 calculations and to show comparative answers. 



GIVEN : An earth dam is being constructed to form a deep reservoir. The up- 

 stream face of the dam will have a 1 on 3 slope which will require riprap 

 protection. The design wave has a significant height of 1.52 meters and a 

 period of 4.7 seconds. No wave refraction is assumed for the design con- 

 dition. 



