structure directly. Consequently, although it is likely that the beach slope was most 

 influential on the breaking process, an appropriate slope for E,„ is uncertain and Equation 

 6.9 is simply adopted, although the relation does not contain ^„. The stability number 

 A^^ in Equation 6.9 based on H^ is used here because it will be easier to predict H^ than 

 H2% using time-averaged surf zone models such as Battjes and Stive (1985) and Dally 

 (1992) that will need to be modified to account for reflected waves (Baquerizo et al. 

 1997). The empirical coefficient Q is calibrated using the 16 tests in Table 6. 1. For 

 eight tests with toe depth h, = 0.4 m and H^ Ih, = 0.23-0.39, Q = 0.97-1.21 for A^^ = 

 1,000 and Q = 0.99-1.19 for A^„. = 3,000. For eight tests with h, - 0.2 m and H^ Ih, = 

 0.64-0.72, Q= 1-03-1.27 foriV, = 1,000 and Q= 1.09-1.34 for A^„, = 3,000. The 

 present experiment with H^ Ih, = 0.64-1.1 1 using Table 4.4 is more similar to the eight 

 tests in Table 6.1 with //, = 0.2 m. So Q = 1.2 is tentatively assumed in Equation 6.9. 



Equation 6.9 is rewritten as two damage formulas in the following to 

 facilitate the representation of incident random waves in time series and spectra. The 

 first damage model, based on wave time series statistics, has the form 



f ,^* 





(6.10) 



where ? = 7"^ A'^,^. is the test duration for constant wave conditions. The empirical 

 coefficient a, is related to cot 0, P, and Q, and b in Equation 6. 10 is introduced for long 

 duration tests, where b = 0.5 in Equation 6.9. The second model is based on the wave 

 frequency domain statistics and has the form 



121 



