and Oc of S, E, and C indicate the variability of S, E, and C among the Np profiles. The 

 means and standard deviations of S, E, and C vary with damage progression. 



The Np values of S, E, and C are normalized as 



= ; E = ; c = (5.6) 



where the means, indicated by overbars, and the standard deviations, o, of S*, £"*, and C* 

 are zero and unity, respectively. As an example, the mean and the standard deviation 

 for Series A ' after each 30 min of waves were computed as 



S = ^tK^ ^ = 16 (5.7) 



'*„ n-\ 



°S = 



J-$:(5 -5)2, iV = 16 (5.8) 



where S„ is the individual measured value of S. The probability density functions P(S*}, 

 P(E*), and P(C*} are calculated using the Np values of S*, E\ and C*, respectively, where 

 the range between the maximum and minimum values is divided into eight bins of 

 constant spacing. Admittedly, eight bins do not yield a fine resolution, but the number 

 of data points for this estimation is limited to Np= 16 or 32. 



In summary, the Np damaged profiles measured every 0.5 hr yield one data 

 set consisting of means and standard deviations of 5, E, and C and the probability 



86 



