density functions of S*, E*, and C*. The number of data sets is 57 for Series A ' lasting 

 28.5 hr, 17 for Series B' lasting 8.5 hr, and 18 for Series C lasting 9.0 hr. For the 

 undamaged profile at the beginning of each test series, 5 = and £ = 0, which yield 

 Sq = 0, Ojo = 0, ^ = 0, and a^^ = 0, where the subscript zero indicates initial values. For 

 an undamaged structure, the probability density functions of S and E are the delta 

 functions with a spike at 5 = and £ = 0, but 5* and E* defined in Equation 5.6 cannot 

 be computed because a^o = and a^^ = 0. On the other hand, the normalized cover 

 depth C for the undamaged profile is a statistical variable related to the placement of the 

 armor layer. The Np undamaged profiles are analyzed in the same way to obtain the 

 mean Q, the standard deviation Oco, and the probability density function PiC*) at the 

 beginning of each test series. 



The probability density functions of 5*, E*, and C* exhibit large scatters but 

 do not indicate any specific variations with damage progression and among the three 

 test series. All 92 data sets of P(S*) and P(£*) are plotted together in Figures 5.2 and 

 5.3, respectively, whereas all 95 data sets of P(C*) are plotted in Figure 5.4. The 

 standard normal distribution given by 



P(y) = expi-0.5y^)/^/2n (5.9) 



with y= S*,E*,otC* is also shown in each figure for reference. Note that a fit to the 

 distribution was not attempted because each data set consisted of too few points to 

 determine the fit error. The data points in these figures scatter about the normal 



87 



