You are trying to model a very complex condition.  I'm not familure with GSTABL but you are working on the very edge of what can be expected from any slope stability program.  How the software treats horizontal forces and materials of greatly different strengths will have a significant inpact on the results of your analysis.

My suggestion is to model the slope without the mat foundation.  Relative to a 75 foot cut, a 4 foot concrete mat is insignificant.  You do not indicate what diameter, length or spacing of drilled shaft you are using or how you are modeling the shafts with the slope stability software.  I have had relatively good luck with other software modeling drilled shafts as reinforcement lines then converting the reinforcement line force into drilled shaft designs using LPile.

Good Luck.

I don't know what your excavation and failure surface look like, but if the failure surface wants to cut upward through the mat, that may be unrealistically affecting the result.  The limit equilibrium analysis assumes that it slices through anything there, even though it might actually just lift the concrete out of the way.  It would be reasonable to try replacing the concrete with a surface pressure of 600 lb/square foot.  That might be a tad conservative (because it assumes the concrete has no strength at all, just weight), but in a 75' cut in clay, a little conservatism is generally OK with me.  Also, is the concrete there before the cut is complete, or do you have a period when the cut is done and the concrete is not yet placed?

I am with dgillette on this one.  You may want to discuss this with the GSTABL7 author, Garry Gregory.  He has told me that if you give very strong properties to the concrete, you can get safety factors that are too high.  He recommended to me to use concrete strengths not much stronger than a very good soil.  Call him.  He has been most helpful to me in my use of GSTABL7..

www.PeirceEngineering.com

If the cut is there (complete) before the concrete is placed and fully cured, you should not consider the concrete mat.  
If the excavation would be completed at the same time that the concrete is placed (not cured), then I agree with dgillette, you can model the concrete as a surcharge equivalent with its weight.
If the excavation would be completed after the concrete is placed and fully cured (I can not figure out how, we just assume it is possible), then I slightly disagree with dgillette.  I believe the concrete strength contribute to the stability of the excavation and can be relied upon.  You can consider the concrete strength in your analyses and should model the concrete as a soil layer with phi = 40 degree and C > 500 kPa (72 psi). The C value is way less than the strength of concrete (e.g., 25,000 kPa or 3,600 psi); however, as noted by PEinc you do not want to use the full strength of concrete.  It may give you strange results.  
If the concrete mat is contributing to the stability of the slope (particularly on the third scenario and may be on the second), you may need to consider the applied pressure on the structural design of the mat.  Generally, in an extreme case, it may cause localized tension on the upper portion of the mat which means the excavation has been subject to noticeable movement.  The only way to analyse and design this for the structure of the mat is to run a FEM.  If anybody has a more simpler design approach, I appreciate comments.
 

Sure, geoman, just be clear that there are two mechanisms that limit the resistance, and the slope stability program only knows one of them: shearing through the concrete.  The other one is lifting part of the concrete mat.  Make sure that the program doesn't think it can mobilize more resistance than would be provided by lifting the concrete.

Get slice forces and solve by hand for force equilibrium with the weight of concrete within the circle and a few feet outside of it to be sure that the program's not assuming something impossible.  Assuming the shortest possible shear surface (vertical) and neglecting the comparatively minor frictional part of the strength, the shearing resistance is 4'X72psiX144 = 40,000 lb per unit length of slope, that is, measured into the page if you are looking at a section).  The concrete only weighs 4'x150pcf=600 psf, peanuts compared to the shear strength of the concrete.  Looking at it in section view, the lowest possible resistance of a shear surface through the concrete (vertical, no normal stress so no friction component) is equal to 40,000 lb per foot into the page, equal to the weight of a 4'x66'x1' chunk of concrete.  You can't simply pick a strength for the concrete and assume that it's OK on the basis that it's a lot lower than the real value, because there is another governing mechanism that has to be checked.  If you prefer not to do all the hand calculations to verify that result is OK, just make the concrete into 150 pcf gravel with a high phi', and no cohesion.  That will make the lifting issue go away, and it's a little closer to reality than the 600 psf surcharge, although it won't make much difference in a 75' cut.

I don't know the exact configuration of the OP's cut and the critical failure surfaces, but methinks the lifting mechanism would govern the resistance the concrete can provide.

I completely agree with dgillette.  If you are looking at third scenario and want to rely upon the strength of the concrete (not just weight), there are a few more separate calculations that need to be completed.  In summary, the overall equilibrium of the concrete mat within and outside of the failure circle should be verified and remember that there can not be tension between the base of the mat and subgrade soil outside of the failure circle.

 The verification method explained by dgillette is very amazing (thanks by the way), as you can even use it to figure out the shear and moment for structural design of the mat (instead of running a FEM).  Just need to impose assumption in regard to flexibility of the mat and there you go.  If you do not feel comfortable with simplifying the flexibility of the mat for structural design, then still need to run FEM for structural design.

Notwithstanding all the above, I still can not imagine how you could be in the third scenario.  Unless you are running your analyses for short term and long term soil parameters and the third scenario is for the long term soil parameters.
 
dgillette, I would appreciate to know if you are conducting slope stability analyses for a slope with a building almost close to the top, how do you model the perimeter concrete foundation for the building?  Let assume the goal is to figure out the minim factor of safety for the bulding.
 

There might be some way to construct the third scenario as I described it with a braced cut that is then widened out for completing the project, but I haven't worked the how (or why!) out in my head completely.  Maybe Scenario 3a could be excavating down to uneven bedrock, with the

A more likely version (call it Scenario 3b), is that the initial excavation is modeled without any concrete at all, but that the long-term stability is modeled with it.  Cuts in clay often fail later, once negative excess PWP has dissipated or something like that.

Geoman110, in your last paragraph, are you referring to a building with its footings actually on the upper part of the slope?  Could you post a sketch?

I really appreciate to all of you who have given very knowledgeable responses. Your responses have helped me to understand and solve this problem. The following are my responses to some of your questions/concern/comments:
It is a permanent support system. Temporary excavation support system is already in place. Mat will be inplace even before constructing the permanent stabilizing piers (slurry wall/caissons). I have already discussed this problem with Dr. Garry of GSTABL7 and based on my discussion with Dr. Garry, I am solving the problem as described below:
I have run GSTABL model without concrete surchrage and concrete layer. From this run of GSTABL, I am taking the difference of the driving force and the resisting force, lets say it is 87,000 lb. The weight of the concrete of the mat is 1 ft x 4 ft (thickness) x 200 ft (cross section width) x 150 = 120,000lb.
Just to be conservative, I am using half of the concrete weight, i.e., 60,0000. using half of the concrete results in a difference of about 27,000 lb between driving and resisting force (instead of 87,000 lb). Using this approach of utilizing the conrete mat into stability reduces the stabilizing element sizes about 50%.
Let me know if you agree or disgaree with my approach.

I personally think that this problem should have been solved using more sophisticated program such as Plaxis.
  

tbh64;  I am not sure if I understand what you are referring to as "driving force" and "resisting force". Are you referring to the force which is applied to your stabilizing piers or this is the horizontal internal forces between the slices?  I am not familiar with GSTABL software and maybe there are terminologies associated with the software that I do not know.

dgillette; thank you for the response.  You are correct, I am referring to a footing on the upper part of the slope (more accurately, a short distance behind the crest).  I will prepare a sketch and post it later.  Should I start a new thread for this?  I do not want to hijack this one; however, the topics are pretty close.