No special technics, just set up the model in your favorite software and run it out.

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.

Thanks for the advice.  
Secondly, Have you heard of applying any external loads on the slope to account for tides, or currents in a river or even wave action(note the top of the slope will be under 50' of water)

Geopavetraffic,
we posted an answer simultaneously!
what about piezometric level?
Water head to slope surface or to water surface?

In theory the answer would be the same if you placed the piezometric level at the top of the soil or if you placed the pieo level at the modeled water level and added a surface pressure to the soil.  A lot of this will depend on how the specific software handles surface pressures and peios in the analysis.  

My personal preference is to model the piezo line to the top of the water surface and add surface pressures due to the weight of the water.

One other thing, if you are doing a pseudostastic analysis be very careful and look at all of the output from the analysis.  You may have to make several models with slight parameter variations to ensure that the results are realistic.

You open/download a copy of Duncan's paper (in a ~1.5 MB .pdf file) by clicking on the following link (right click on the link if you want to save it to your computer):

1999 Spencer J. Buchanan Lecture

Links to other notable papers can be found at:

Spencer J. Buchanan Lecture Series

Dr. Jean Louis Briaud, who holds the Spencer J. Buchanan Chair in Civil Engineering at Texas A & M university, deserves special thanks from the civil engineering community for ably guiding the Spencer J. Buchanan Lecture Series - and providing on-line copies of the lectures.  

Thanks, Jean Louis!

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Basford,
I wonder if stream velocity may have a significant effect on a submerged slope. First, maximum velocity vector is close to the surface, secondly flow lines would be parallel to bottom and banks, maximizing shear component of force.
If turbulence /velocity is substantial, slope profile might be altered by erosion.
Also, the effect of waves rapidly peters out with depth, causing the water particles to move in ever smaller elliptical orbits. 50' to top of slope would require pretty big waves to cause significant effects. This would be a good question for coastal engineers, though.
An anomalous tidal wave caused by big storms or a tsunami may have a tangible effect.
In lieu of better info, to allow for such boundary uncertainties, I would adopt a more conservative factor of safety
                 

How long does the slope have to stand?  How tall will it be?  How far will the embankment extend?

Remember that linear project sites are categorically different than "square" (localized) project sites.  Failures along linear projects aren't governed by the average strengths along the entire project site - they are governed by "local" strengths.  You really need to focus on lower-bound strengths for your analyses, not the averages...

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I dug up Duncan's 1973 article referenced in the recent paper where under water cut slope failed in a soft normally consolidated organic silt like I have at my site. I'm still waiting on my lab resutls, but I think the shear strength are similar mabey a little lower (around 100psf at surface increasing to 350-400psf at 40')  The interesting thing is that they were using a cut angle between 1:1 and .875:1. I was preliminarily thinking of 3:1 or even 5:1 at the top which would put me approx 40 deep.

I have about 150' in plan to get as deep as possible the site plan is 300'x1600'.  I haven’t got a clear answer on the duration the pit will be open but it looks like we are in the 2 months to 1yr range.  Anyone have any comments on when the time frame warrants switching to an effective stress analysis.

If the soil is MH because of a high silt content, the effective stress time frame could range from a few days to a few months, depending on the soil permeability.  However, secondary inclusions could reduce the time drastically - even with a significant clay fraction.  An awful lot depends on drainage paths.

I understand the trench will be about 150 feet long, but I'm still fuzzy on the depth to the top of slope and toe of slope.  Could you kindly describe the entire problem for me?

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the thing about the intrusion (they are mostly organic/root mat/peat.  I guess to be conservative you should assume them to be drainage bounderies.

My goal is to excavated the largest pit/trench with in a 300'x1600' plan area. So I go as deep as I can in 150' (3H:1V gives me 50', 5H:1V gives me 30')or some combination thereof

Why do you need to dig an underwater pit?  What are the consequences should the side slopes fail?  Is bottom stability an issue?

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This is for an under water landfill dredged spoils).  If the slope fail we will exstend outside the boundry given in the environmental permit and we will not have enough room for the spoils.  Bottom stability is not a consern