and since 



fix) = O X<0 (22) 



and 



f y (z - x) = (z-x)<0 (23) 



the convolution integral becomes 



f z = j Z f x (x)f y (z - x)dx (24) 



64. Equations 12 and 17 can now be substituted into Equation 24 to 

 achieve a combined PDF 



PO^CZ) = [ Z po' s (x)po' p (Z -X)dx (25) 



Jo 



The resulting output from the convolution integral is a combined stress PDF 

 for static and pulsating stress responses. The convolution is performed 

 numerically in CAUDAID and the resulting combined PDF is then numerically 

 integrated to get a combined exceedance probability function (CEPF) . This 

 CEPF is used to determine a design stress given the design probability of 

 exceedance . 

 Design probability of exceedance 



65. Choosing the design stress from the CEPF requires selection of a 

 design probability of exceedance, which is based on the structure's design 

 life and the number of armor units allowed to break in any given time period. 

 Markle and Davidson (1983) state that a dolos armor layer will continue to 

 remain stable provided dolos breakage does not exceed a uniform 15 percent in 

 the top layer, 15 percent in the bottom layer, and 7.5 percent in both layers 

 or clusters of 5 individual units. One could infer, then, that the design 

 probability of exceedance E for a dolos armor layer must be significantly 

 less than 15 percent for an armor layer. In Appendix A, for Crescent City, 

 the design stress for the 42-ton dolosse is calculated from the CEPF using a 

 probability of exceedance of 2 percent. 



Fatigue 



66. A thorough review of general fatigue concepts should be done prior 

 to estimation of a fatigue coefficient. General fatigue theory is contained 



32 



