Pile elastic spring support modeling

[creep123]

Hi!

I'm doing a marine engineering project about 30x30m offshore platform on steel tube piles. The structure need to withstand lateral forces mainly from berthing ship (wind loads) and vertical forces. So as it's 3D structure I created 3D model in Robot structural analyses. I'm going to use both vertical and 1/3 diagonal piles. Most of the horizontal forces would be taken by diagonal piles.
Data that i have in hand about the layered soil includes Young’s Modulus E, cohesiveness c, unit weight γ, porosity, andgle of internal friction φ. So no STP results.
I've tried to find solutions to calculate spring supports for piled foundation and found program called REX piles demo version as robot "Add-in". I think i got quite interesting and reasonable results using it. So i took these results as basis and started to find ways to calculate spring supports by hand to get comparative results.
For lateral supports there are multiple elastic spings solutions for different soils, conditions etc (and of course there are may others):
For example this source Table 1
I used probably quite conservative Vesic's (1961) solution.
And of course classical p-y curve.
And much less conservative solution (fig. 3.1)
Then it comes more difficult part for me. It's the vertical springs that would represent frictional conditions. I've read Tomlinson (and many other) books, googled researchis but haven't found great enough calculations.
Have anyone faced similar problems or just can give some ideas where to look for the solutions?

Cheers

 

[GeoBo]

Hi,

You can use either LPile or PileLAT 2014 to generate p-y curves along the pile shaft and then compare those p-y curves with the values from the program you used. Not sure about your question on the vertical spring. But I guess that refers to t-z curves along the pile shaft which represent the relationship between the pile settlement and skin friction value. For a quick analysis and appreciation about the t-z curves, you can use PileAXL 2014 which automatically generate the t-z curves based on the soil material type, pile installation type and soil strength. Please have a look as the picture attached and see whether this is the information you are looking for.

Regards

 

[Mccoy]

Creep 123,
Kh solution from Vesic is all right, but you should remember to multiply by 2 if you use the solution for shallow foundations.
If you have Es Also Chen's solution may be used, kh=1.6 (Es/d) where d = pile diameter. Chen's value is usually higher than Vesic's.


There is really not much literature on solutions for vertical spring stiffness in foundation piles

The NIST GCR 12-917-12 report (freely downloadable) has a specific solution . Not suitable for FEM models but OK for whole single piles.

The only other one I know is Castelli & Motta, 2010, a solution for the vertical coefficient of subgrade reaction which is good for FEM models as well. You must calculate G from E.

The t-z curves models linked by GeoBo can be used to get vertical spring stiffness since by definition it is K=F/z where F=t applied (shear) force= shaft resistance and z = vertical displacement. From stiffness to subgrade reaction we divide by the lateral surface of the pile element.

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[neukcm]

Hi Mccoy,

Sorry to extend this thread. I am exactly at the same situation now wherein i need to model my pile support as spring. I already generated my t-z curve and yet to establish the spring value. What do yo mean by F/z? is it the maximum side resistance over max displacement?

Thanks,
neukcm

 

[Mccoy]

neukcm,
let's see the t-z output, where the force-displacement behaviour is linearly elastic, then plastic.

Let's take node 7 at depth 2.1 m. The ultimate shaft resistance (the plasticity treshold) is 8.49 kPA, but such treshold is reached following curve #7, which has a linear behaviour.

We see that, with 2 kPa pressure, the pile has a vertical displacement of 0.75 mm; 4 kPa will cause a 1.5 mm displacement and so on, until the plastic treshold. The spring constant for the Whole pile is required according to what unit the analysis software requests.

If the software wants a Winkler modulus, in units of pressure/lenght, than it will be 2 kN/m2/z = 2/0.00075 kN/m3 = 2667 kN/m3 = 2.7 MN/m3; not an exceedingly high value. This is the the value in that depth interval.

If you need the overall stiffness by a gravitational force/displacement units, then, taking a more intermediate elastic relationship (closer to the weaker shallow layers) you would have for example spring vertical stiffness= 2 MN*L/m value, where L = lateral area of pile. That means, with a 20 square meter shaft area, that the pile has a stiffness = 40 MN/m, that is a load of 40 MN (400 metric tons) will cause one meter of vertical displacement. Of course, Since plasticity occurs, according to the API model at a little over 2 mm, that spring stiffness is valid only for very small displacement values, equal or less than 2 mm.

In this case, if it is a large diameter pile, the vertical spring under the base should be considered as well, since the API sand is not contributing much to shaft resistance.

Pls check the above reasonings and units, it's late evening now and I may not be overly clear-minded. Also, I'm really not sure that I've been able to help you in practice, you should maybe produce an example of your t-z curves and elastic modulus of soil if you have it, in the above example the sandy soil and the shallow depth appear to contribute to an overall $h1tty behaviour.

http://www.mccoy.it