Dear Mehdi,

I think it depends on the type of soil. Anyway, I hope this paper helps you well.

http://ascelibrary.org/doi/pdf/10.1061/41128(384)6

The maximum horizontal movement of the wall in a braced excavation should not exceed 1%H when H is excavation depth.  The allowable value is around 0.5%H to 0.7%H.   If your wall moves less than 0.5%H, your braced system is considered robust.

It's not a simple question. Allowed deformation depends on the type of retaining structure as well as the allowable displacement of adjacent objects if any. 

Could it possible to mention some references Mr.Punlop

Dear Mehdi,

I think it depends on the type of soil. Anyway, I hope this paper helps you well.

http://ascelibrary.org/doi/pdf/10.1061/41128(384)6

 Thank you Mr.Ghavami

I would be appreciate for your recommendation, actually we want to introduce the probability of allowable displacement, thus we need to determine a specific threshold for allowable displacement. It something like the factor of safety 1, which distinct stable and unstable structures.

One classic reference is Mana and Clough (1981) in ASCE.

How much the wall moves depends on many factors, soil type, excavation depth,  excavation width, wall toe depth, wall bending stiffness, the number of strut layers, prestressing, workmanship, etc.   Some are controllable; some are not.  Soil type is not.

How much do you want the wall to move is a different question.  If you have important existing structures close to your excavation, it is important to control your max. wall movement by playing with controllable factors such as wall stiffness or the no. of struts.  The figures 0.5%H or 0.7%H are only a crude guideline.  This does not fully guarantee that the nearby structures will not be affected by your excavation.  

If you have read paper by Marr and Hawkes you will notice that almost all lateral movements fall within the range between 0.005 and 0.025H, where H is excavation depth 

(refer to fig. 2 of the paper, taken from Clough et al, 1989).

However you should be very careful, as decision making in this sense is usually project specific. Maybe a good starting point would be to introduce initial threshold value of 0.01H?

I have to mention that I like the idea, but you should also consider that you are dealing with serviceability limit state not ultimate...

I would search about things like passive and active operating ranges for a retaining wall.. i dont understand are you retaining this or is it a free face and would agree while there are some prescriptions its case by case and you need to look at layering of the material behind the wall.. if the project big enough then think about finite analysis.. i would also ask what re the consequences of a failure both on top of the excavation and failure into it  .. you can fail building around you and cause a lot 10's or 100's of millions of damage  .... do you have access to a professional engineering society and the knowledge base/ references ...  this is a professional design issue and not trivial and my concern would be you are looking here when i would recommend you get the advice of an experienced geotech person who deals with this issue  regularly

It depends on load, height angle. As a simple rule the horizontal displacement with a desired load should not induce more than 80% of the tipping moment (static no heavy wind)