Modulus of Subgrade Reaction - Beating a Dead Horse Perhaps

[DirtEngineer08]

I posted this in the soil mechanics thread and then realized it is probably best suited here.

First post here, so go easy. I have read through the many threads about the modulus of subgrade reaction (MSR), I have read many articles and consulted with senior level engineers within my company... Perhaps I am dense but I am turning to you fine people.

Background:
When providing recommendations for a mat foundation, I typically use the Vesic 1961 equation as it seems more thorough then some of the other equations IMO. I usually play with the modulus of elasticity of soil input (typically based on blow counts in sand/gravel) so that the 1 foot foundation width is near a generally acceptable and published 1 foot plate MSR value. I then present a graph in my reports of the foundation specific modulus of subgrade reaction versus foundation width. I have attached the spreadsheet I use for this, it also includes a few other methods, but I prefer vesic.

Question:
For large mats (anything over ~ 20 feet) the resulting value becomes very small (relatively). for a 1' Plate MSR of 350pci a 100 foot square mat has a foundation specific MSR of 11pci. The senior engineer at my firm says that is right where it should be as that is equivalent to ~ 1500psf per inch of settlement and the recommended max bearing pressure at the site is 1500 psf. Now the structural engineer is saying this value is to small and they typically see values of 100 to 200pci. while I respect my colleges opinion, and do see what he is saying, I don't think that we can directly specify the MSR based on our max bearing pressure recommendations. I need to discuss this further with the structural and I want to make sure I am as educated as possible before the call. From what I have read most structural software inputs for MSR are the foundation specifc MSR values not the MSR for a 1' plate.

Your input is appreciated and I look forward to being part of this online community!!

 

[Okiryu]

Somebody posted the attached before that I found interesting and may help you.

 

[Okiryu]

To follow up that paper, since the modulus of subgrade reaction is a soil-structure interaction parameter, I got an advice that for mat foundation it may be better to consider the modulus of subgrade reaction as the ratio of the average contact pressure below the mat and the average settlement within the depth of influence of the mat. I think that this make more sense than using plate bearing plates to get this value for large mat foundations.

 

[JoshPlumSE]

What does the engineer need it for? I ask because it may not be primarily for settlement.

One of the things that I've been working on a lot lately is support for dynamic equipment. Where the goal is to calculate the natural frequency of the system and then calculate the vibration response. We have to be cautious what elastic stiffness we're using in our analysis. Because at these very low force levels, the soil tends to be a lot stiffer obviously than it would be at ultimate load. And, using a lower MOSR value would not necessarily be conservative when calculating the vibration response.

 

[ATSE]

DirtEngineer08,
Your fellow senior engineer is much more correct than the structural engineer client.
Do not use plate load test results for equivalent linear subgrade springs for foundation modeling. k=100pci is way too high (too stiff) for most soil profiles for typical mat loading and dimensions.
Let's assume you are only dealing with static loading for now. You didn't mention your soil profile, but let's say that you have some compressible soil (and not simply very dense sand over bedrock).
Start with expected vertical loads and expected long term vertical settlement, and then calculate your k. Structural engineers sometimes forget the depth of soil effective stress (and resulting settlements) is greater for larger mat dimensions.
If you have a 100'x100' mat, you need to consider deep settlement - at least down to 200' depth, or until you hit bedrock. My SE brethren sometimes think only in terms of allowable bearing pressure, not settlement. if you have consolidating clay, then this SE is going to have a cow when you tell him that the k in the middle of his mat is 10% to 30% lower than near the edges.
For the same soil profile, 2,000psf net pressure on a 10'x10' spread footing will produce significantly less settlement than 2,000psf net pressure on a 20'x20' spread footing, and the 20'x20' ftg will have a softer response (lower k).

 

[Okiryu]

For a past project, I have reported 25 pci for soft loam soils based on plate bearing tests and the SE was very very surprised for that such low value. My feeling is that SEs normally expect around 100 pci. I think this is because most correlations relate 100 pci to clays. Also CBR-k values charts relate 100 pci to a CBR of 3. Anyway, MSR depends on the geometry of the loaded area and for large mats low MSR may be expected due to the reasons that ATSE mentioned above.

 

[hawkaz]

Good topic! I learned something new (I can go home now).

As a structural engineer, I normally use the subgrade modulus when checking a slab on grade capasity for racking or forkllifts. The PCA method charts start at 50 pci for this application (50, 100, 200). As stated above- I normally expect to see this in the 100-150 range.

The other application is for mat slabs (where I am using an FE program) on poor or liquifiable soils. This number can be all over the map.