Table 2. Empirical wave runup prediction coef- 

 ficients for smooth impermeable slopes. 



Front-face slope 

 of breakwater 



Ci 



t^2 



s 



Vertical 



0.958 



0.228 



0.0578 



1 on 0.5 



1.280 



0.390 



-0.091 



1 on 1.0 



1.469 



0.346 



-0.105 



1 on 1.5 



1.991 



0.498 



-0.185 



1 on 2.25 



1.811 



0.469 



-0.080 



1 on 3.0 



1.366 



0.512 



0.040 



runup on an impermeable rough slope armored with one layer of stone. Ahrens 

 and McCartney (1975) present an empirical method for estimating the runup on 

 two layers of riprap overlying a 0.2-meter thick underlayer (Fig. 11). In 

 their method the runup is predicted as a nonlinear function of the surf param- 

 eter, E,, 



as 



1 + b5 



C = 



tan_0 



(12) 



where a and 

 b = 0.398. 



b are empirical coefficients with values of a = 0.956 and 



Both the Madsen and White and Ahrens and McCartney prediction methods tend 

 to give high or conservative estimates of wave runup for predicting wave trans- 

 mission coefficients. However, Hudson (1958) made numerous observations of 

 runup over a wide range of breakwater conditions; the Ahrens and McCartney 

 empirical curve (eq . 1) was fitted to the Hudson data to give the recommended 

 runup coefficients of a = 0.692 and b = 0.504 (Table 3). These coefficients 

 gave a lower prediction of runup than that given for riprap (Fig. 12). The 

 equation 



0.692 g 

 1 + 0.504 C 



(13) 



is recommended for predicting runup on stable permeable and impermeable stone 

 breakwaters until a more comprehensive model becomes available. Coefficients 

 for dolos were also estimated using Bottin, Chatham, and Carper's (1976) data 

 for breaking and nonbreaking waves (Table 3) . Stoa (1978) provides additional 

 information on runup; runup data for nonbreaking waves on breakwaters are pro- 

 vided in Jackson (1968)'. 



Runup predictions were made for the conditions tested, and observed wave 

 transmission by overtopping coefficients, K^o , were plotted as a function of 

 F/R (Fig. 13). This figure shows the case of breakwaters with a slope of 1 on 

 1.5. The upper part of Figure 13 shows results from BWl for tests that had a 



26 



