It is often said that bigger foundations provide a better geothecnical answer when a constant combination of loads is applyed.
In spite of the fact that this statement is usually valid in spread foundations ,deep foundations are by far trickier.
In this post I would like to show three approaches to analyze the effect of Foundation’s geometry on the bearing capacity of a pile group.
First and foremost, most experts agree on the fact that there are 2 factors that govern the block failure phenomenon in pile groups.
The degree of interference between the stressed zones around each pile.
The stiffness difference between the layers of subsoil which are gone through by the piles,especially near the bottom of the deep foundation.
Although the factors above are both decisive,the effect of the strata under the pile is usually analysed by the design of the reference individual pile of the group.
Thus, Most simplified models for Block failure effect only take into account the interaction between stressed zones around piles.
Regardless of the simplifications in the classic models, authors in the technical bibliography have proved that the group effect is beneficial in group of piles in sand (cohensionless) strata. Have a look at Z.Bazant article for piled slabs!
The denser the sand is, the greater the bearing capacity safety factor is. Of course this fact is not taken into account in real calculations and the group effect in cohensionless strata is neglectable in practice.
So, Problems come up when clay appears.
Let’s start with the first method to consider the block failure,the fictive equivalent pile method.
This method is based on the idea of turning the group of piles into a single equivalent pile.
Once we have obtained the fictive pile geometry we undertake the same calculations we do in a normal individual pile.
The bearing capacity which has been calculated for the equivalent individual pile is taken as the bearing capacity of the pile group. This way we are able to obtain a new safety factor for the pile group which is lower than the bearing capacity safety factor for an individual pile.
Secondly,Let’s continue this brief tour by having a look at Feld’s rule.
Feld’s rule is a good option when it comes to doing a first approximation calculus to gain an insight into the possible capacity of our pile group.
Feld’s rule says that the bearing capacity of a group of piles can be calculated by substracting the fraction n/16 from the bearing capacity of each pile. “n” is the number of piles which are adjacent to each pile. It is easier to be understood with an example.
This method is from 1943 and it goes without saying that it must be used carefully!
Thirdly, It would be a good idea to talk about the formula of Converse-Labarre. This classic formula,which can be found in 2 versions, gives you the efficiency of the pile group by taking into account the geometry of the group and the spacing of the piles inside the pile cap.
Pay attention to the fact that this formula does not consider the ground conditions and it is only an empirical approximation to the real phenomenon as you will be able to see in the next graph.
Last but not least, Whitaker (1957) gives us an excellent synthesis of the block failure effect according to various methods, including his own experiences.
Whitaker’s graph illustrates some important aspects:
-The more amount of piles in each row, the less efficiency the pile group has.
-Converse-Labarre formula according to the Uniform Building Code of the Pacific Coast Building Officials conference’s version is the more conservative model.
-There is a lot of dispersion between the models when the spacing between piles is short and the dispersion decreases when the spacing rises.
– Feld’s rule is a conservative rough estimate for spacings greater than 2 diameters, according to Whitaker’s empirical experiences.
-The length of individual piles affect the efficiency of a pile group when the pile spacing is lower than 2,5 diameters.
-When the pile spacing is greater than 3,5 diameters the group effect is neglectable.
– 3 diameters would be a recommended spacing from a geotechnical point of view,but 2,5 diameters could be accepted as a compromise solution , as the loads still can be transmited by the pile cap as a stiff foundation with a strut and tie behaviour.
In conclusion, block failure in pile groups is complex and it may require numerical analysis in some cases!
References:
Walter E. Hanson, Thomas H. Thornburn. Foundation Engineering, 2nd Edition (1974)
Coming Up Against Structures 