Buckling Capacity of a Partially Embedded Pile

[alighalib]

Hi all, Happy New Year

I am designing a pile supported off-shore structure. The structure is supported on timber bearing piles. The piles are embedded in a 40+ ft of dense sand and extends 10+ ft above mudline. As such, the piles are in fact unsupported laterally throughout the length above the mudline. I am trying to determine the allowable axial capacity for this pile. To be more specific, what is the unsupported length of this pile/column and what bottom end condition should be considered. Any suggestions!!

Thanks

 

[ishvaaag]

If you don't find better reference I would proceed by making different analysis specifying some initial imperfection at the mud-line, i.e., a sharp angle there, then some lateral restrainnt along the within-the-ground length, and some restraint at the tip. Alternatively you may use some curve to define your imperfect pile, divide it in segments, then analyze it in the same way. Iclude in all cases P-Delta at-nodes effects. If the slenderness between considered nodes is small, you might even disregard P-delta (or in-such-submember) additional effects and you wouldn't need to design but for mere sectional analysis (squashing load) without any regard to buckling, that would be explicited by the initial imperfection plus P-Delta at so short sub-members.

For sand, if you deem it to remain stable, the stiffer assumptions for the modulus of subgrade reaction (and its lateral counterpart to derive supporting springs' stiffnesses) would be best, and the contrary if you see it unreliable, mainly if you see that your would love go even deeper for stability. This is critical, for if scour occurs nothing of we are talking is of relevance.

However your problem most surely is tabulated somewhere. Have not looked deeply nor my books nor the web but if I find something will post.

 

[ishvaaag]

By mere chance I was downloading pile information worth to see for cases like yours

http://www.tdi.state.tx.us/general/pdf/wscgsec400.pdf

 

[oldrunner]

The reference book "Design and Construction of Ports and Marine Structures" by Alongzo DeF. Quinn has a section on the design of piles and cylinders for the support of docks. There is also some information on Wood Piles.

 

[austim]

Hi, alighalib.

In my younger days, my standard reference was a paper presented to a Symposium on Bearing Capacity of Piles. If you can get hold of a copy, it may be some help to you.

Authors :A.J. Francis, L.K.Stevens and D.H. Trollope,
Title :"Flexure and Load-carrying Capacity of Slender Piles in Soft Soil"

Regrettably, my ancient dog-eared copy does not specify the date, which I believe would have been about 1965 or so (the most recent reference quoted in the paper was 1964).

Similarly there is some doubt as to precise location of the symposiom. My copy of the paper is annotated in hand-writing "Symposium on Bearing Capacity of Piles - India" (Originally it said Hong Kong, but that was over-written).

I hope this may help you.

 

[Ron]

alighalib...
The "unsupported length" is actually longer than the ten feet above the mudline. The condition you have is a cantilever beam of length y, with "y" being determined by the fixity of the pile. If you do an analysis of the soil-pile interaction (L-Pile or similar) you can find the inflection point for the moment, thus its fixity. You can do this by hand analysis, finding the minimum depth to handle the lateral load moment (use iteration to find).

Once this is done, the problem is just a simple cantilever beam bending problem.

 

[Ron]

alighalib...
Sorry...I didn't read your question correctly. Disregard my prior post (unless you have lateral loading, which then you will need to add to the compressive axial loading).

For buckling, the effective length considered is, just as in the lateral bending, the point of fixity of the pile. Typically, for dense sand, you can assume an additional depth of 1x the height above the mudline, in this case, your unsupported length would be 20 feet. From that, compute the critical load (Pcr) from Euler's equation with k=2.0.