Foundation Modulus

[SteelPE]

I am in the process of designing a slab on grade with a point load applied to the top of the slab. I need to determine the thickness of the slab. The issue is the slab is to be placed on top of a 2” layer of rigid insulation. I ran into a similar problem a few years ago and was able to obtain a document from Owens Corning (OC) that allowed for the calculation of the slab thickness based upon some design parameters including:

Required point Load
Contact Area
Concrete strength
Insulation Foundation Modulus (K)

Inside the document they referenced various OC products and their resultant foundation modulus in pci. I have attached the OC document. Please note that I believe the units for table 3 are suppose to be pci not psi.

I am now trying to put together a proposal for a similar project however, the client is looking to use a different material (one with higher compressive strength). The manufacturer lists the compressive modulus units as psi (in this particular instance the value is 3,700 psi) . How would I go about converting this compressive modulus to a foundation modulus (if this is even the right way to go about doing the analysis)?

I have been thinking about this for a while and cant seem to come to a logical conclusion for something that seems so simple.

 

[JAE]

Perhaps this?

The 3,700 psi is your "modulus of elasticity" of the material.

So for a depth L of your insulation - and an area of 1" x 1" (i.e. A = 1 sq. in.) a load P would result in a deflection based on d = PL/AE.

So for a 6" layer of insulation, a 100 lb. load on a 1 sq. in. area of insulation would be d = 100(6) / (1 x 3700) = 0.1622 inches.

So a 100 lb load creates a 0.1622 inch deflection. Therefore k = 100/.1622 = 617 pci.



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[SteelPE]

JAE, that is what I was thinking after I finished the thread (dividing the modulus by the thickness of the material). Seems logical, but I am not fully sure the is the correct approach.

 

[JAE]

In cases where we don't know for sure what our subgrade modulus really is, we use a parametric approach and vary the K value across a probable range.
This results in a range of possible concrete thicknesses to give us a sense at least of knowing the "right answer" is in there somewhere. Engineering judgement and further comparisons with other resources, methods, project success history, etc. can be included.



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[SteelPE]

In this instance, there may be a correct answer. The project requires me to be responsible for an existing slab that contains radiant heat that is being replaced (and existing 10" thick slab). I have been told that the heating system has failed and needs to be replaced (I have been told this is not a slab failure). So the client is looking to replace the existing slab under the same design parameters but the original EOR has since passed on (an no one has the original structural drawings). I have run an analysis using the approach outlined above and I am "in the ballpark" of the thickness I have been told is currently onsite. I either get the same answer or need to increase the thickness by .5"-1" depending on how I vary the modulus.

 

[WARose]

Assuming the insulation isn't tied to your slab with some sort of tie that makes it composite with the slab......it's almost like springs in a series. (With some more help with a point load in terms of spreading it out.)

 

[WARose]

By the way, are you specifying a subgrade modulus or something else (i.e. consisting of the system as a whole)? The subgrade modulus is (IIRC) independent of the foundation above. As far as "above" goes, you could (for analysis purposes) come up with a plate that reflects the combined stiffness of the slab & the insulation (using the "series" method I mentioned before)......and get your moments & shears that way.