You are essentially projecting a soil containment device. You have to one side active forces, and passive from the other, you need them for equilibrium, except that you rely on some mass properly placed and founded.

It is clear from the description above that the pile will have to take the tributary containment load, assigned to it by the analysis. It is also clear that if piles are used in the containment scheme, it is because at the projected placement they are thought to positively contribute against slippage of the masses above not yet properly contained (and so not influencing them); this usually means that the piles are in such disposition that are thought to anchor themselves well beyond the expected surfaces of failure; so, as you see, counting on gained fixity, that is always to the expense of passive action on the sound soil thought not to be subject to slippage.


 

I think the easy answer is that it isnt a simple question at all, its actually a pretty complex soil structure interaction problem and you need to carry out an FE analysis to model the interaction of the various elements.  

I am assuming you are using LE software like Slope/w or Slide etc where you can simply slot in a pile and therefore assume a shear resistance. (A structural eng will be able to give you the shear capacity of a pile of a certain diameter)

I think I am right in saying there is a wider problem with this approach, which by the way I see quite often.

The problem is as soon as you put the pile in place you change the shape of the failure surface behind the pile.  Ignoring this for a minute, I dont think you can get the (pseudo)active pressure distrubution on the back of the pile from the LE software, so you start straight away getting into the realm of overestimating (read guessing) the pressure on the pile.  The passive resistance doesnt reach the normal passive limit either because its sloping.

 

I fully agree with IODirt that this is a SSI problem.  When using structures to improve slope stability it is unconservative to think you can simply assign the shear resistance of the pile as a resisting force in a LE model.  As a start you would only be able to use the resistance associated with some allowable deflection such as found from a laterally loaded pile analysis.  That alone is not the whole story.  As you try to decouple the problem to fit into standard tools there are assumptions that need to be made as IODirt mentions.  Still, I expect there are many landslide stabilization projects out there that were designed without the benefit of FEM analysis and using conservative assumptions your design could be done without FEM.  I do like using FEM for SSI problems but since we as an industry don't have a huge amount of experience using FEM for design, I always support doing enough simple analysis to back up the FEM results.