p(o' s ) 



o;p'V2* 



exp 



In a' -a" 



P" 



(12) 



and the mean and standard deviation for this log-normal distribution are 



a" = mean (In at) ( 13 ) 



= ln[k r (rn^ c + a)] - ±($") 2 



(14) 



and 



p" = s.d. (In o«) 



(15) 



N 



In 



+ a 



+ 1 



(16) 



respectively. In the above equation, the mean of the nondimensional Crescent 

 City static stress distribution is m' cc = 25.8 and the standard deviation is 

 s' = 11.7, as given in Table 4. Note that these values are not natural logs 

 and are not moments of the log-normal distribution. They are computed 

 directly from the data and are used to estimate the log-normal moments. 



53. The above analysis assumes that the static response is not sig- 

 nificantly affected by the armor layer porosity or slope. This assumption has 

 not been validated and must be kept in mind when using the algorithms con- 

 tained herein. 



Long-term static response 



54. Kendall and Melby (1990) showed, using prototype static data 

 through 1989, that the Crescent City static stresses were increasing with 

 time, at a decreasing rate. The exponentially decaying characteristic shape 

 of this long-term time series and the fact that the stress increases were 

 between and 5 percent could have been attributed to creep in the concrete. 

 But continued long-term monitoring of the Crescent City dolosse has shown the 

 static stresses to be increasing linearly rather than increasing with an 

 exponential decay (Coastal Engineering Research Center 1992, Kendall and Melby 



28 



