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# Subgrade modulus of soil

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## Subgrade modulus of soil

(OP)
Hi!
I read few articles and books that describe this soil property.
I dont know if this could be even called soil property since its an mathematical model wich tries to imitate soil behaviour under pressure.
Anyway the formula as we know it is k=pressure/settlement (kN/m2) / m.
As I understood "k" only represents elastic behaviour of soil wich only happens for small deformation (settlements).
Now this is where I get confused.
Small deformations (settlements). How small?

Many authors describe "k" as an tagent to pressure/settlement curve. Is this related to my previous question?
I think it could be couse for small settlements the pressure/settlement curve is prety much linear. But I could be wrong...

Wich field or laboratory test could most accuractly predict "k" value?

Ive seen many graphs from Plate Load Test wich are basicly pressure/settlement graphs. Are they reliable?
I have many doubts here.
First of all, the pressure bulb from small plate and foundation are VERY much different. If the soil properties dont change with depth then its ok.
Second, PLT is only for soils that dont undergo consolidation! So only reliable for soils that only undergo instant settlement. No long term settlements!

Ive found few formulas from "Bowels" that try to coolerate bearing capacity and "k" value.
Can these be safely used while designing?

Ive read aslo few forum discussions where experts say that "k" value should vary under a raft foundation and that one value shouldnt be used under the whole plate. I dont understand this? Why?
If "k" is used based on the elastic behaviour I dont see any problem of using one value for design process.
Ana

### RE: Subgrade modulus of soil

Look at ASTM D3839 for soil modulus. There are tables there.

Richard A. Cornelius, P.E.
WWW.amlinereast.com

### RE: Subgrade modulus of soil

(OP)
Im not interested in tables.
Im interested in understanding the philosopy behind this matter.

### RE: Subgrade modulus of soil

You are correct regarding the Plate Load Test. The pressure distribution is very different from what you actually encounter under a foundation. You are also correct about the "k" value being the result of a mathematical model. As with many things in our field, the value of this number comes from "empirical" correlations than anything else. Don't try too hard to understand it theoretically, as you'll find out that it's just numbers that appear in tables as a result of a lot of scattered data.

Rey Villa, MS, PE
http://geotech-apps.com

### RE: Subgrade modulus of soil

Since K changes with the pressure (nonlinear trend), the point is to select the value corresponding to the applied pressure. This is simplified analysis that represents the soil foundation under the raft with appropriate design value. Now like any problem
you can always go to more detalied analysis considering the facts you mentioned.

### RE: Subgrade modulus of soil

(OP)
So basicly one should define a value that will corespond to real future pressure that the structure will engage on the soil under the foundation?
This could also be the explenation of the fact that k value shouldnt be the same under the whole foundation, wich some authors are saying.
More k values should be defined wich basicly imitate different pressures under the foundations.
What do you think?

### RE: Subgrade modulus of soil

It is fine to spend great effort fussing about the meaning k value. However, it does not make a big difference in the slab thickness. Philosophically, it's a spring constant representing the stiffness of the soil. As soil1999 pointed out, it's nonlinear with applied load. It also needs to be adjsuted for the slab dimensions since tabulated values are normalized to 1 sq. ft plate load test.

### RE: Subgrade modulus of soil

(OP)
I dont understand "does not make a big difference in the slab thickness"?!
What you mean by this?
Are you saying that slab thicknes wont have impact on bending moment diagrams of the slab and necesray reinfrocement?

### RE: Subgrade modulus of soil

(OP)
Thanx!
I found usefull link:
http://www.civil.iitb.ac.in/~kvkrao/CE%20742%20Pav...
It clearly says that if you are using Plate Load test , K coefficient is to be determined for 1.25mm settlement.

### RE: Subgrade modulus of soil

For combined footings/mats and also for lateral piles, changing the k value (vertical or lateral subgrade modulus) by even 300% would do little to the maximum induced shear, monemt, and deflection.

Try it- get the Hetenyi equations and plot two cases - A mat foundation (or even a grade beam) and then laterally loaded pier. In both cases, foundation geometry and compressive strength of concrete has more influence than the subgrade soil modulus value.

### RE: Subgrade modulus of soil

(OP)
Yes, you are right FixedEarth.
What other method can be used for determining modulus of subgrade reaction besides plate load test and CBR test?
For plate load test "k" is determined s described in previous link and also using modification equations provided in the link geobdg gave.
What aboth CBR and maybe triaxial test?

### RE: Subgrade modulus of soil

(OP)
@geobdg
Very interesting text.
That Oasys software seems very powerfull.
Can you tell me whats the difference between soil analysis that Oasys does and SAFE or STAAD?
Seems like a new approach, I might be wrong...
Thank you.

### RE: Subgrade modulus of soil

k value is the basis for the structural design of an industrial floor slab - something where there will be point loads, rack loads and the like.

k value is not a proxy for bearing pressure.

k is a surrogate to evaluate the elastic response of soil to applied loads. Problem is you are dealing with an elastic response in the very near surface of the soil profile (i.e., within the first couple of feet).

I've always used correlations betwseen CBR and k. I typically use the ACI guidance for k atop the subbase, which allows some increase to the soil's k-value depending on the thickness of stone base atop the soil subgrade.

Yes, there are crazy folks in structural engineering that love "k" so much they want to find such a value for deep seated soil behavoir. Some even refer to "long-term" k-values. This is poppycock!

An industrial floor slab is designed as a beam on an elastic founation (well that was prior to computer modeling). When a load is applied to this beam, there will be load spread within the beam and load transfer from the beam to the elastic soil. What happens in the soil? What happens in the beam, what reinforcing is needed? These are structrurally controlled by the materials and the k-value.

Foundation design includes some component of material strength and reinforcing - for sure! It's just the load transfer from the foundation to the soil is not a point load, is uniformly distributed immediatly below the foundation and the soil strength is mobilized to much greater depths. These depths may influence more than one soil material and these soil responses will vary. A simple "k" value cannot address these details - and shouldn't be used!

Just a few of my thoughts.

f-d

¡papá gordo ain’t no madre flaca!

### RE: Subgrade modulus of soil

(OP)
Could software like PLAXIS be used to predict modulus of subgrade reaction under raft foundations?
Basicly user would need to model raft geometry, load it and then analyze stresses under the raft with similiar setllement wich can then be grouped and then used for modulus estimation (i said grouped since K value is never the same under a raft)

### RE: Subgrade modulus of soil

(OP)
Hello.
Can anyone responde maybe regarding PLAXIS usage?
Questions to geotehnical experts.
When testing soil samples is there any test that could be used to determine K value?
An pressure-displacement diagram like in plate load test should be needed or this also isnt a good indication...

### RE: Subgrade modulus of soil

I think you might get some helpful answers if you gave a specific example that you were trying to analyze. Otherwise it's hard to give detailed advice because the questions are sort of jumping around and are very general.

(Note: In my statements below, K is related to overall modulus such as for mat design......not K1 such as from plate load test used for pavement design).

Regarding Plaxis, you could use load/deformation results like you discuss to help define a K value. But this would be going backwards......the point of a Plaxis analysis would be to get away from the over simplified modulus based analysis.

Basically any test on soils that can correlate load to deflection can help with determining K. Most of these would be field tests (Pressuremeter, dilatometer, SPT, etc) although various lab tests and empirical correlations could help.

Not sure this will help but what I frequently do when thinking about what modulus to use for a mat, etc is: make a spreadsheet that has different square footing sizes going down the left column (ex. 2' square, 5', 10', 25', 50'). Then across the top, label different columns with different bearing pressures (100 psf, 200 psf, 500, 1000, 2000, etc). Run a bunch of settlement analyses (such as schmertmann using SPT, cone, dilatometer, etc) and fill in the cells of the excel table with the settlement that corresponds to each pressure/footing size combination. Then I create another duplicate set of columns for each bearing pressure and in each cell of the table calculate the associated modulus (i.e. pressure/settlement). This helps give me a good overall feel for the scatter in K value based on different pressures and different sized loading areas. Then I roll this around in my head to consider what value is appropriate and also provide the excel file to the structural for a discussion on what we should use.

### RE: Subgrade modulus of soil

(OP)
Hi geobdg.
"But this would be going backwards......the point of a Plaxis analysis would be to get away from the over simplified modulus based analysis."
Yes argee. This would basicly be like an simulation of an loaded raft in Plaxis.
One would first define structure geometry, material properties and then define soil properties ( I think PLAXIS soil models use E modulus, poisson ratio, consolidation parametars...).
Second step would be to load the raft geometry with loads determined from analysis and design software (softwares like ETABS, RISA, STAAD...)
Third is running the analysis in PLAXIS and analysing results (settlements, pressures...). WIth pressure-setllement values from PLAXIS users could define overall K modulus wich varies under the raft (somthing that I recentry found out reading some research papers).
With these values user would go back to his analysis/design program and define K value under the raft, run the analysis and design raft together with its superstructure.
You said:
"But this would be going backwards......the point of a Plaxis analysis would be to get away from the over simplified modulus based analysis."
I completly agree with you, but then how to design raft (required reinforcement) in PLAXIS?
Another understanding problem that I have is that loads determined of foundation structure from programs like ETABS, STAAD all depend on the foundation behaviour.

### RE: Subgrade modulus of soil

just correlate the site-specific saturated CBR value to modulus.

f-d

¡papá gordo ain’t no madre flaca!

### RE: Subgrade modulus of soil

personally, i always liked vesic's formulas because it included things i could understand like the elastic modulus of the soil, poisson's ratio, and the width of the foundation. unfortunately, i haven't seen an embedment correction. use the smallest values of elastic modulus you can justify, and you can derive a spring constant that will work in structural computer programs like staad and risa. so, back to your question what is the best field test? i'm not that keen on the plate load it doesn't test deep enough. maybe you want to try a cone penetrometer since it has a good empirical data base to predict the elastic modulus of the soil.

### RE: Subgrade modulus of soil

It's peat stuff, man.

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