Dear Tanomy,

In most cases, ultimate lateral displacement of pile at ground surface is a serviceability limit depends on the allowable movements of superstructure.  In the abstinence of certain criteria, some rule of thumb values may be used such as 10% of the diameter or (0.25 to 0.50) inch. If you are looking for a reference, U.S. Army Corps of Engineers, EM 1110-2-2906, "DESIGN OF PILE FOUNDATIONS" suggested a limit of (0.25 to 0.50 inch) 

ultimate lateral capacity of a large diameter pile is governed by BOTH goetechnical and structural considerations.  As teh way FOS or partial FOS are introduced varies between countries/code, and als between structural and geopt code, one need to be careful in adopting equations in design manuals that may have these partial factor built in.

One need to do it from 1st principle if its an important enough foundation.

Good FEM codes can get really close to ultimate condition.  Once again the issue of partial factors need to be considered carefully.

As far as service condition is converrn, it all depends on the structure its supporting!!.

For some structure, such as jetties,  lateral deflection in excess of 50mm may be perfectly acceptableacceptable.

The ratio of live load to sustained load is also a consideration, because movement due to sustained load can be built-out!!

Thanks Mr. Ebid and Mr. Lo for sharing your views. 

Dear Tanmoy,

I think it's better not to use the concept of "ultimate capacity" for such structures, since in practice it is something that probably can't be reached. With such large diameter, you are considering an extremely stiff "pile" (it might be more precise to talk about caisson). This foundation will not behave as a normally slender pile (i.e. with a curved deflected line and eventually a plastic hinge at some depth below the surface) but rather as an almost rigid body, where the ultimate conditions (failure) are reached by failure of the soil. However, since the pile diameter is so large, it seems very unlikely that the loads (either in controlled tests or environmental) can reach the conditions to mobilise the full soil wedge beneath the pile. Thus in practice you will never be able to approach the asymptotic conditions.

Therefore, here it does not seem very appropriate to talk about ultimate capacity in terms of forces, since the structure probably won't reach a mechanical failure, but rather to define the serviceability conditions in terms of ultimate allowable displacements, which are usually imposed by the superstructure (e.g. the allowable inclination of the superstructure). This is of course case-dependent with different limits adopted for different applications.

PS: You may find some literature references in my thesis if you want, but I am afraid they won't be much more specific about your problem...

Thanks Mr. Pablo for your reply. In practice, its unlikely that the loads can reach the conditions to mobilize the full soil wedge beneath the large dia. piles. 

In general, when we analyze the lateral load capacity rigid caissons using FEA packages, some thumb rule is followed where the pile/caisson is loaded upto 10%-30% of dia. which is considered to be the ultimate condition.

Lets consider a case to be analyzed by FEM, for such large a diameter pile or caisson, lateral load corresponding to what percentage of diameter is generally considered to be the ultimate considering the diameter of caisson to be 9 m with max. allowable rotation at its head as 0.5 degrees.

Thanks in advance.

Dear Tanmoy, I am afraid there's no clear, objective answer to your question and I certainly cannot provide you with a percentile quantity of the diameter for orientation. Since the asymptotic state will not be approached (probably by far), all we can provide you is a very subjective opinion on what to "consider" as ultimate. Since such pile diameter is very unusual, there probably does not exist any appropriate "rule of thumb" based on experience. And I would also recommend caution with respect to FEA solutions, especially when using commercial packages if you're not sure on the details of the implementation. Computation of ultimate states and failure is not a straightforward task and there are multiple pitfalls that can alter the result significantly.