Coefficient of vertical subgrade reaction

[kcall2]

I am to provide a coefficient of vertical subgrade reaction for design of a mat slab over an older sandy fill material. Based on the dimensions of the mat slab the depth of influence is about 12 ft. Settlement analyses (Burland and Burbidge) indicate that up to 1 inch of settlement can be expected within this zone of influence for a bearing stress up to 2500 psf. Using the definition of subgrade modulus (load/settlement) a k value of 17 pci is calculated. This value is very low in comparison to published ranges for similar soil types (that don't account for relative density).

Is this a reasonable method? Is this an acceptable value?

 

[BigH]

Your "mat" is only 5 to 6 ft in size? Not what I would call a mat - I'd call it a footing. What are the geotechnical properties of your "old sandy fill"??

 

[fattdad]

It seems to me you are confusing subgrade modulus (i.e., spring constant) with soil modulus.

17 pci is way too low. You can correlate a laboratory CBR test to k and that may help. This of course if you anticipate compacting the subgrade to 95 percent compaction as you would the CBR sample.

When I read in the OP that you are striving calculate settlement from a load distrubition with depth from a loaded area, this seems like elastic theory, which is based on soil modulus.

Some folks use 7N or 11N to get soil modulus (TSF). Some folks use a dilatometer. Some guess (local experience and the like).

f-d

¡papá gordo ain’t no madre flaca!

 

[kcall2]

Let me correct myself. My mats range in size up to about 20' by 40' and the depth of influence is cutoff at about 12 feet (beneath base of mat) by very dense bedrock. The 'old fill' is unsaturated, silty sand with relative compaction about 85% and SPT field blow counts of about 12.

The Burland and Burbidge method for estimating settlement of foundations on sand is not based on theory of elasticity but utilizes an empirical approach based on a database of settlement recordings. The results correlate well with Schmertmann's SPT based approach.

My goal is to provide the coefficient of vertical subgrade reaction, or 'spring constant', for design of the mat. It is my understanding that I need to consider the entire column of potentially compressible soil beneath the loaded area, and therefore a plate load test will not yield a representative value.

Am I way off track?

 

[Ron]

I see this age-old confusion still hasn't resolved itself. In the geotech world, the modulus of subgrade reaction, k, would have a typical value between 150 and 300 pci for your noted soil. That's typically used for pavement design.

For mat foundation design, the "k" value for similar soil is generally taken to be between about 25 and 50.

the "k" value for elastic settlement is determined based on very small vertical settlements or deformation as would be expected in pavement design. To transpose that same concept to foundation design for much greater deformations, requires the consideration of a ratio of settlement or deformation, which could be as high as a factor of 10 greater than the deformation achieved in a typical plate load test. Based on that, the "k" value from the plate load test is factored by the ratio of deformations (not an entirely accurate premise, but commonly used), thus when your "k" value from the test is 200 pci, the value used for foundation design might be 10 to 30 percent of that value (inverse of the deformation....assuming 1" expected mat settlement compared to 0.10" test deformation, yields 1/.1 or divide the test value by 10).

 

[BigH]

kcall2 - relative "density" - not relative compaction. If you visit SlideRuleEra's website, you will find charts correlating various engineering parameters with others. Does the Burland and Burbridge method take into account the "incompressible" layer at 12 ft? I'm not sure it does, off the top of my head . . . Have you thought of giving modulus values instead of spring constants? Tomlinson warns against the use of the "Winkler" spring system . . .

 

[kcall2]

Relative compaction, as compared to the max dry density performed on a representative sample.

Burland and Burbidge does account for the incompressible layer.

I'll check out Tomlinson's book regarding Winkler method.

Thanks

 

[fattdad]

Imagine an infinitely-rigid 20x40 ft mat and it's uniformly loaded to 1,000 psf. For your case there's a 12-ft layer of sand that may realize "instantaneous" settlement. That's an elastic behavior (well, there may be some plastic component, but we'll ignore that).

Allow the soil modulus to be 11N (don't really know), so let's use 130 tsf (maybe a little low). Accounting for no load spread (I mean just how much attenuation will you have for a loaded area that large over 12 ft. So, 12 ft times delta sigma V (i.e., 1,000 psf) would be 12,000 lb/ft (6 t/ft - crazy units, eh?).

For a soil modulus of 130 tsf) that'd give you 0.046 ft (0.6 in). Now, in reality, you don't have a rigid mat and you'll get less settlement at the corners and edges, so you have to check for angular distortion.

Now consider a fork lift or a rack leg. This will provide for a point load with stress concentration through the slab and on the subgrade. How the subgrade responds to this stress concentration is governed by the modulus of subgrade reaction. This behavior occurs in the upper few feet of the subgrade - well the affect on the slab design at least.

Schmertman settlement analysis (just like the method that I use) relates to the elastic properties of the soil column.

The use of a consolidation test was referenced by an earlier poster. I'm neither going to agree or disagree. My point is if you believe the soils will consolidate, then this whole subject is moot. Use consolidation theory and move on - you still have to worry about the modulus of subgrade reaction in your mat design, however. If you are dealing with over consolidated soils above the water table or sandy soils, however; elastic theory is more proper. And, you still have worry about the modulus of subgrade reaction in your mat design.

Hope I'm not off track or otherwise off topic, this is how I see it. Just for the record, my professor (Jim Duncan) had no problem with my use of elastic theory to solve for soil compression.

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

I am fully aware of "relative compaction" and "relative density" as estimated from N values (for the most part) - but I am wondering how you determined 85% relative compaction for an old fill? Did you obtain samples (how) and do a compaction test - then how did you determine the in situ density of the fill - was this done in a test pit (I can agree with that) but if in a borehole - undisturbed sample of the sand? It "threw me" when you indicated relative compaction from a site investigation.
I agree with fattdad that elastic theory makes sense as I alluded to.

 

[kcall2]

BigH - Relative compaction was estimated using dry densities measured from driven ring samples and a compaction test of remolded soil from a bulk sample from the same borehole. I realize that ring samples, especially in a sandy soil, are disturbed and that test results may indicate either higher or lower in-situ densities (as a result of dilation/contraction during shearing). The results were used as a location-specific indicator, considering blow count, soil consistency, soil type, etc. as well.

Fatdad - so you're suggesting that the estimated total settlement beneath the loaded mat not be used in evaluation of the "k-value" for mat design, and that it is more appropriate to determine the "k-value" based on the settlement of the upper few feet (hence the term "subgrade") under a concentrated load?

 

[BigH]

Thanks kcall2 for how you did the relative "compaction" - but then I would wonder why? It is not easily translated into engineering properties - few if any direct correlations between it and phi'; "N"; even relative density . . .

 

[fattdad]

Here's what I'm trying to convey: If you took a 1-in thick steel plate and placed it atop your subgrade, you could design an industrial floor slab using a very high subgrade modulus value. You'd do nothing to control or limit settlement of the underlying soils. You can deal with the settlement issue using elastic theory or consolidation theory. You can relate it to Schmertman's methods or other's methods.

Without getting into design details, it's hard to know the best course of action.

f-d

¡papá gordo ain’t no madre flaca!

 

[irawanfirmansyah]

kcall2,
What you need to do is to calculate the average subgrade modulus of the soils along the depth of influence. Then, if you multiply the average subgrade modulus with a unit area of the mat, you will get the spring constant which represents the soils along the depth of influence.