Basford,
An interesting case history of the stability analysis of a dredged underwater slope in S. Francisco has been published by Duncan:
Factors of safety and reliability in geotechnical engineering
The paper appears on some recent ASCE journal issue, I downloaded the preview in .pdf format, a simple web search should do. Actually there is no discussion of the used stability methods, suppose the classical ones, with piezo level equal to slope surface level (or to water head to surface?) and density equal everywhere to effective density (density minus buoyancy).
The classical analysis was then (after collapse) studied by probabillistic analysis.
By the way, no offence meant by a guy (myself) whose experience in geotechnical engineering is near to zero compared to the author, the probabilistic method adopted (First order Taylor series approximation, suggested by USACE)is quite inaccurate to the purpose and, as has been shown by recent reliability studies by a NASA commitee, not very effective in the description of the reliability of a system - that is, robust enough in describing the region around the mean, unreliable in describing the regions of the tails, crucial to the comparison between capacity and demand of a system - the factor of safety.
The method requires much less computing power, though.
Sorry for straying. The above paper is dam good anyway.