the lower limit of C may be estimated as (C -2.1 0^). The failure may be assumed to 

 initiate when this lower limit becomes zero. This criterion with Equations 6.5 and 6.6 

 yields the following equation for the mean damage at failure initiation 



0.1^ + 2.7[0.098 - 0.002(^-7)2] = Cj - 2.70^ (6.7) 



This criterion accounts for the initial minimum cover depth and its variability along the 

 structure where (Q -2.70co) = 1.27, 1.06, and 0.79 for Series A', B', and C. Solving 

 Equation 6.7 for mean damage for Series A' yields S= 10.9 at failure initiation, 

 compared with 5= 13 measured. The failure initiation criterion of Equation 6.7 based 

 on the lower limit of C* of all data points plotted in Figure 5.4 yields the lower limit of 

 the mean damage at failure. The upper limit of mean damage at failure may simply be 

 estimated by C = in Equation 6.5. This upper hmit is 5= 16.5 for Series A'. 



6.3 Temporal Damage Development 



If the mean damage can be predicted, then Equations 6. 1 - 6.6 yield O5, E, 

 Of, L, C, and a^. These relationships have been obtained by analyzing the measured 

 profiles of the armor layer and underlayer without regard to the incident waves and 

 water level. This statistical analysis indicates that the damaged profile statistics can be 

 represented by the mean damage S. The next step is to predict the temporal variation of 

 ^'on the rubble-mound breakwater exposed to depth-limited breaking waves in 

 sequences of storms with varying wave conditions and water levels. 



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