which is only approximate because the maximum d^ and the minimum d^ may not occur 

 at the same location due to variability in the original layer thickness. 



The eroded length l^ is defined herein as 



K = -J- (5.4) 



e 



and the normalized eroded length is given by 



D... dJD_,„ E 



Here the dimensional eroded length Ig is not measured directly, but is a derived value. It 

 is roughly equivalent to the surface length of the eroded region along a profile. As seen 

 in Figure 5.1, the eroded length characterizes the along-profile length of the roughly 

 triangular eroded area and describes the along-slope extent of damage. 



53 ProbabUity Density Functions of Damage, Eroded Depth, and Cover Depth 



The number of damage profiles measured at a given time during damage 

 progression is denoted by Np in the following, where A'p = 16 for Series A ' and N^ = 32 

 for Series B' and C. The Np values for S, E, and C are analyzed statistically to reduce 

 the number of measured values and separate the variability along the structure from the 

 temporal variation associated with damage progression. First, the mean and standard 

 deviation of the A'p values of 5, E, and C are calculated. The standard deviations O5 o^ 



85 



