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Rotational Restraint of Soil

Rotational Restraint of Soil

(OP)
Hello,

I’m trying to find a way to model a pile in Space Gass using simplified spring restraints. I have the translational restraints which I calculated using the ks value (modulus of subgrade) taken from J. Bowles’ ‘Foundation Design and Analysis’. My current theory is to assume there are no rotational restraints around the x and z directions- that restraint is provided by the lateral springs acting over the length of the pile. What I can’t seem to find is a value for rotational restraint against torsion.

I have a formula for rotational stiffness, k=M/angle, which would give a value in Nm/radian. The problem is that I’ve only found one journal article which shows results from an experiment, which gave values of around 5700kNm/rad for loose soil and 11400kNm/rad for dense sand, but they don’t mention a way to change these results for different pile diameters and embedment depths, which must have an impact.

Also, with the lateral or vertical restraints, I use the modulus of subgrade to estimate the deflections but to calculate the bearing capacity I use the usual base bearing and skin friction method. What I want is to find something similar to calculate the bearing capacity in torsion. I had thought to use circumference*depth*effective soil pressure*coefficient of friction*pile diameter/2- finding the friction over the surface of the pile and multiplying it by the diameter/2 lever arm, but the only example of something similar that I’ve been able to find comes from the Illinois Department of Transport who use the formula Torsion Resistance=effective soil pressure*(1.5-0.135(distance to mid-depth)^0.5)*circumference*thickness of section*diameter/2 (all in ft and ksf). This is similar but instead of the coefficient of friction (I use 0.4) they use the 1.5-0.135*(h)^0.5<=1.2, which even over a 6m pile doesn’t get below 0.9.

So, does anyone know:

1. A better formula for calculating rotational stiffness of soil, or common values of k?
2. A method of calculating or estimating Torsional resistance capacity of a pile?
3. How piles are normally modeled (Space Gass allows pinned, fixed or spring restraints)?
4. Should I also look into the idea of using the soil reaction on the pile cap to resist torsion? I’ve read that this is often ignored as the first meter or two of soil is often uncontrolled fill, which may not develop passive resistance anyway.

Thanks for your help.

PS. Most of my work is with pipe supports, essentially a vertical member with several horizontal arms which not only catch wind, but also often take lateral loads from the pipes causing torsion about the base, which is commonly supported by a single pile.

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