## Modulus of Subgrade Reaction (k)

## Modulus of Subgrade Reaction (k)

(OP)

As a geotechnical engineer, I've always been dissatisfied with the way the topic of modulus of subgrade reaction is addressed in geotechnical textbooks and figured I would look to this forum to help clarify some concepts in my mind and hopefully the minds of others.

Firstly, after reading many threads, I now understand that this parameter is a second order problem with interdependence of both the structural system and geotechnical conditions. Asking the question, what is the k-value used for, I am guessing that it is used by the structural engineer to evaluate the deformed shape and resultant stresses in a concrete slab subject to a given load. The structural can then use this value to dimension reinforcement to keep stress levels/deflections within a safe/serviceable range. I'm also guessing that this analysis is somewhat iterative as the amount of reinforcement would influence the slab's structural stiffness and deflection under load. The soil's role in the problem is that depending on how the soil deforms in response to the stress (its stiffness represented by the parameter k) a different portion of the underside of the slab will be supported and influence the reaction force acting on the bottom of the slab.

For structural mats associated with large buildings, I've never seen anything in a geotech textbook showing how to correlate soil data with k. You would think that since the k parameter involves deflection, oedometer tests could be used in some way. I then realize however that depending on the stress level, a linear constant such as k would never adequately characterize the subgrade's reaction. Additionally, depending on the size of the loaded area, there will be deeper or shallower soil strata with varying compressibility characteristics involved. Anyone who has done a settlement calc should realize that you can't just use some USCS or CBR correlation to develop a single k parameter to relate stress and deflection in this instance. In some sense, it is scary to see people on this forum and elsewhere looking to use classification data and index tests to come up with this parameter. One can only hope that they are looking for it's use in a pavement or slab on grade application. My geotech textbook (Das) and at least the classes I took, IMHO, don't do a good job discussing the important boundary conditions that make the published correlations between CBR (and other geotech parameters)applicable.

My epiphany from the other day is that I realized that the available correlation charts generally come from the pavement engineering discipline and that this is an important distinction. In pavement engineering (which for concrete is looking at fatigue) and structural concrete slab on grade (limit state) the problem is relatively narrowly defined. The problem consists of "thin" slabs and lower (compared to buildings anyway) load levels. I've seen others on this site scoff or palm/face at people asking about the k value and correlations with soil parameters, saying it is not a pure geotech parameter. My counter argument however is that given a relatively narrow range of boundary conditions, I would expect there to be a correlation between CBR or R-value and k. In pavement and slab on grade loading scenarios, the stress level in the subgrade below the depth improved by compaction and captured in a geotech parameter such as the CBR is probably relatively unimportant. Therefore, using CBR as a proxy is appropriate considering the difficulty/rarity of performing a plate load test.

If you made it this far and are still reading, any comments refuting or confirming my statements based on your own experience would be much appreciated. I'd also love to know anything about a fundamental approach that could be used to evaluate the appropriate k-value for a large mat foundation.

Firstly, after reading many threads, I now understand that this parameter is a second order problem with interdependence of both the structural system and geotechnical conditions. Asking the question, what is the k-value used for, I am guessing that it is used by the structural engineer to evaluate the deformed shape and resultant stresses in a concrete slab subject to a given load. The structural can then use this value to dimension reinforcement to keep stress levels/deflections within a safe/serviceable range. I'm also guessing that this analysis is somewhat iterative as the amount of reinforcement would influence the slab's structural stiffness and deflection under load. The soil's role in the problem is that depending on how the soil deforms in response to the stress (its stiffness represented by the parameter k) a different portion of the underside of the slab will be supported and influence the reaction force acting on the bottom of the slab.

For structural mats associated with large buildings, I've never seen anything in a geotech textbook showing how to correlate soil data with k. You would think that since the k parameter involves deflection, oedometer tests could be used in some way. I then realize however that depending on the stress level, a linear constant such as k would never adequately characterize the subgrade's reaction. Additionally, depending on the size of the loaded area, there will be deeper or shallower soil strata with varying compressibility characteristics involved. Anyone who has done a settlement calc should realize that you can't just use some USCS or CBR correlation to develop a single k parameter to relate stress and deflection in this instance. In some sense, it is scary to see people on this forum and elsewhere looking to use classification data and index tests to come up with this parameter. One can only hope that they are looking for it's use in a pavement or slab on grade application. My geotech textbook (Das) and at least the classes I took, IMHO, don't do a good job discussing the important boundary conditions that make the published correlations between CBR (and other geotech parameters)applicable.

My epiphany from the other day is that I realized that the available correlation charts generally come from the pavement engineering discipline and that this is an important distinction. In pavement engineering (which for concrete is looking at fatigue) and structural concrete slab on grade (limit state) the problem is relatively narrowly defined. The problem consists of "thin" slabs and lower (compared to buildings anyway) load levels. I've seen others on this site scoff or palm/face at people asking about the k value and correlations with soil parameters, saying it is not a pure geotech parameter. My counter argument however is that given a relatively narrow range of boundary conditions, I would expect there to be a correlation between CBR or R-value and k. In pavement and slab on grade loading scenarios, the stress level in the subgrade below the depth improved by compaction and captured in a geotech parameter such as the CBR is probably relatively unimportant. Therefore, using CBR as a proxy is appropriate considering the difficulty/rarity of performing a plate load test.

If you made it this far and are still reading, any comments refuting or confirming my statements based on your own experience would be much appreciated. I'd also love to know anything about a fundamental approach that could be used to evaluate the appropriate k-value for a large mat foundation.

## RE: Modulus of Subgrade Reaction (k)

An interesting question you pose. However, with this quoted statement, perhaps you can explain why you are concerned. For instance, in your job are you seeing there is some failure, excessive construction cost, or other possibly practical reason involved so that you (or any of us) need a better way than using a k value estimated?.

it is scary to see people on this forum and elsewhere looking to use classification data and index tests to come up with this parameter.As a reader of this forum can you cite examples of some poor engineering or other problem that has resulted from roughing out parameters for design. Guessing that structural designs may be scary, without documentation doesn't fly.

I've found numerous examples through the years where approximations are needed or justified for design and for holding down costs of the job and also the engineering part.

## RE: Modulus of Subgrade Reaction (k)

http://casehistories.geoengineer.org/volume/volume...

I forget how I stumbled upon this particular website but as a sidebar I highly recommend it.

## RE: Modulus of Subgrade Reaction (k)

## RE: Modulus of Subgrade Reaction (k)

The modulus of subgrade reaction does not influence deeper-seated geotechnical issues.

So, knowing that we are interested in the subgrade support immediately below the slab. I always correlated k to soaked CBR value. We know the CBR sample is compacted to 95 or 100 percent relative compaction, we know the CBR is soaked (i.e., the value will be conservative) and correlations have been developed.

I will not comment on using k to address settlement. Structural engineers have been striving to get k to address settlement for years and I don't buy it at all!

f-d

ípapß gordo ainÆt no madre flaca!

## RE: Modulus of Subgrade Reaction (k)

## RE: Modulus of Subgrade Reaction (k)

All of this still leaves the open questions as to whether there is any guidance on the selection of a k-value for a large structural mat application? Also what would be the upper bound loading condition for which the values obtained from the plate load test and correlations with parameters such as CBR would be valid? I feel like trying to come up with a weighted soil subgrade elastic modulus and using that with the Vesic 1961 equation would, short of FEM, be the most reasonable analytical approach? I'm guessing that E values should be selected to represent pre-construction conditions (no consolidation, no strength gain through gradual load application)? Thanks again to any readers and commenters.

## RE: Modulus of Subgrade Reaction (k)

## RE: Modulus of Subgrade Reaction (k)

## RE: Modulus of Subgrade Reaction (k)

## RE: Modulus of Subgrade Reaction (k)

## RE: Modulus of Subgrade Reaction (k)

f-d

ípapß gordo ainÆt no madre flaca!

## RE: Modulus of Subgrade Reaction (k)

http://www.structuremag.org/?p=7840

## RE: Modulus of Subgrade Reaction (k)

Search for "Modulus of Subgrade Reaction - Beating a Dead Horse Perhaps" among others.

k is not constant (of course), and depends on the foundation size and stiffness variation, in addition to the lower zone soil properties, just as SS has noted.

The k used for pavement design has nothing to do with the k used in settlement analysis, but some engineers are often confused and do not separate the two domains.

## RE: Modulus of Subgrade Reaction (k)

And as a structural engineer with some soils experience (and experience working with Geotechs), I know that k is highly variable and the way to deal with that is to allow for a reasonable range of k values. There are no absolutes below your feet.

## RE: Modulus of Subgrade Reaction (k)

I respectfully disagree. k changes, even when the soil properties do not. That is, k reduces as the mat dimension increases, since the pressure bulb deepens.

k changes as load increases (re-compression vs virgin for clays),

k depends on both the structure's foundation and the soil.

## RE: Modulus of Subgrade Reaction (k)

"Because it is so difficult to develop accurate k values, it may be appropriate to conduct a parametric studies [sic] to evaluate its effect on the mat design.

ACI 1999 suggests varying k from one-half the computed value to five or ten times the computed value, and basing the structural design on the worst case condition.".

This is what is appropriate to do and what we typically do. We would use a range of k values in the analysis and design based on the soft values of k and then, using higher values of k can check soil stresses.

It is interesting in the structural world how sometimes, many times, the structure isn't all that much affected by variations in the k.

In some cases, with framed buildings, using a fixed support to replicate a footing in the model is a poor choice and using a spring support - even with widely varying values of k - doesn't affect the structural results all that much except when you compare it to an infinitely rigid support.

Now we do not use a range of k values for estimating settlements or deflections other than to get a "feel" for how the variation of k alters these numbers.

Check out Eng-Tips Forum's Policies here:

FAQ731-376: Eng-Tips.com Forum Policies

## RE: Modulus of Subgrade Reaction (k)

definitionof the Winkler modulus, which is load (pressure)/settlement. This should clarify all doubts.Of course we should specify the dominion. Are we dealing with the limited subset of immediate settlement (as Fattdad strongly implies) or are we dealing with total, time-dependent settlements and at which percentage of total consolidation. Are we dealing with dynamic or static settlements?

The by-the-definition procedure allows us to figure out any situation, at the desired load, once we decided the dominion (immediate or total settlements). Of course the consolidation parameters must be different in both cases.

If we have a slab, we just need to calculate settlements at various points (as described for example in Bowles, Das and other textbooks) by using the appropriate shape modificators. If the soil is layered, we should use appropriate methods relevant to such pattern.

www.mccoy.it