subgrade modulus to spring stiffness 1

[Lion06]

I have a question about how the subgrade modulus relates to the assumed spring stiffness of a soil.
I have a rather large mat foundation to design (using a beam on elastic foundation) and the geotech report gives a subgrade modulus in kcf. I can input this directly in PCA Mat, but I would like to run a (not so) quick hand calc for comparison since I've never used PCA Mat before. That being said, my notes for beams on elastic foundations only incorporate the spring stiffness of the soil, not the subgrade modulus. Is this a quick and easy conversion?

 

[JAE]

Kips/cu. foot can be looked at as kips/s.f. per foot of deflection.

So if you have 200 lbs/cu. inch soil subgrade modulus, and your spring governs an area of 1 sf, then your spring would be

200 lbs/cu. inch x (1 sf)(144 cu. inch/cu. foot) = 200 lb/ft = 28,800 lbs/inch or 28.8 kips/inch spring.

But keep in mind that soil isn't always linear like this. The spring stiffness is a way to model it in an analysis but can be more complex than this.

 

[Lion06]

Thanks!!

 

[Lion06]

Ok, so it depends on how closely you assume the springs to be? If you assumed the spring governed an area of 0.5 sf, would it end up being 14.4 k/in for the example you have above? If the answer to my first question is yes, how would you account for continuous springs (as you would assume for a hand calc)?

 

[Lion06]

one last thing, would that be 1728 cu. in./cu. ft (instead of the 144) for a spring stiffness of 345.6 k/in?

 

[DaveAtkins]

Yes, in JAE's example, for 0.5 sf you would get 14.4 k/in.

You cannot model continuous springs--it is FINITE element analysis, not INFINITE element analysis. I don't use PCA MATS--I use RISA 3D, and I space the springs 1' oc most of the time.

If you are given k in terms of pcf (which would be unusual--usually it is given in pci), you would multiply by 1728 to convert to pci.

DaveAtkins

 

[Lion06]

The continuous spring question was regarding the hand calc (which would be modeled as continuous - correct?).
PCA Mat allows the input of the subgrade modulus directly, you don't need to use a spring stiffness.

 

[JAE]

I'd concur with all that DaveAtkins said.

I don't know about PCA Mat. It may take your modulus and then convert to discrete springs in a FEA.

 

[Lion06]

I agree when using a program, but when checking by hand and setting up the differential equations I don't agree. The point of the differential equations is to account for the continuous springs and that was all I learned for beams on elastic foundations (by hand), I did not learn how to do a hand calc with discrete springs, just continuous.

 

[kslee1000]

Soil-structure interface is a very complicate issue, I don't think anyone been able to formulate it precisely. As long as the majority of soil beneath the mat behave similarily, the spring constant derived by multiplying the soil (elastic) modulus and the unit area (1 sf) is an acceptable approximation (to generate profile of deflection/stresses flow of the mat). However, you may want to envelop the deformations/stresses of mat by increasing/decreasing the magnitude of spring constant (Es x Area, say 6"x6", 2'x2', 2'x4'...). Depending on stiffness of your mat, the structure could either be very sensitive to the changes, or not at all.

The spring constant has the basic unit - k/in, which implies uniformly continuous from inch to inch (similar to load and pressure terms - klf, psf...). I hope this will help you in thinking if I didn't misunderstand your question.

 

[Lion06]

kslee-
I understand what you are saying. JAE addressed my initial question. So, it seems as though you will get a different spring stiffness for a given subgrade modulus depending on the area of soil that you assume the spring to cover. As the area gets smaller, the spring constant gets smaller (i.e. you have more springs covering the same area, therefore each one can be less stiff to get the same stiffness per area).
The example given had real numbers applied to it.
The question now is how to account for the spacing between springs approaching zero (as you would assume if you are doing this calc by hand).
The whole point of this exercise is that I want to do this by hand before I do anything in PCA Mat so that I don't have their answer in the back of my mind as I'm doing my own calc. I would prefer to do mine first (by hand, hence the springs will be continuous with zero spacing, not spaced at some finite value), then run PCA Mat and compare.

 

[WillisV]

See page 12:

http://www.me.ust.hk/~meqpsun/Notes/Chapter4(202).PDF