underlayer is exposed, then the breakwater can erode quickly. This stractural integrity 

 threshold is uncertain because damage, defined by the eroded volume, may be focused 

 at a point or distributed over a broad area. Because the toe forms a foundation for the 

 armor layer, if the toe armor is mobile, then the entire armor layer can mobile. How the 

 armor layer responds to armor movement at the toe is quite variable. 



The variability in both the loading and boundary conditions demands the 

 consideration of the randomness of each stochastic parameter. Many clients, including 

 the U.S. Army Corps of Engineers, now mandate that a risk analysis be done as part of 

 major breakwater rehabilitation studies. This requirement is intended to provide a 

 standardized engineering economic analysis technique for comparing competing 

 alternatives. The engineering performance study that must form the basis of the risk 

 analysis is often accomplished using a reliability analysis, where the reliability, or 

 conversely, the probability of failure, is quantified for each alternative. In the reliability 

 analysis, all alternatives that fall below a predefined level of reliability are either 

 modified or discarded. For example, a breakwater may have several alternative armor 

 layer designs including randomly-placed stone, pattem-placed stone, and randomly- 

 placed concrete armor units. Each of these alternatives will have a different associated 

 cost and a different probability of failure for the design single storm or sequence of 

 storms. Determining the probability of failure through instability of the armor layer 

 requires knowledge of the rate of deterioration or the rate at which stones are displaced, 

 which has not been quantified for breakwater armor layers. Reliability methods have 



