Coefficient of vertical subgrade reaction
Coefficient of vertical subgrade reaction
(OP)
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?
Is this a reasonable method? Is this an acceptable value?





RE: Coefficient of vertical subgrade reaction
RE: Coefficient of vertical subgrade reaction
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!
RE: Coefficient of vertical subgrade reaction
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?
RE: Coefficient of vertical subgrade reaction
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).
RE: Coefficient of vertical subgrade reaction
RE: Coefficient of vertical subgrade reaction
Burland and Burbidge does account for the incompressible layer.
I'll check out Tomlinson's book regarding Winkler method.
Thanks
RE: Coefficient of vertical subgrade reaction
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!
RE: Coefficient of vertical subgrade reaction
I agree with fattdad that elastic theory makes sense as I alluded to.
RE: Coefficient of vertical subgrade reaction
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?
RE: Coefficient of vertical subgrade reaction
RE: Coefficient of vertical subgrade reaction
Without getting into design details, it's hard to know the best course of action.
f-d
¡papá gordo ain't no madre flaca!
RE: Coefficient of vertical subgrade reaction
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.