How to calculate ks value ( modulus of sub-grade reaction ) and what its proper unit?

[Usmi09]

Here I am confused with the ks value that is ks=p/s where P (kg/cm2) is contact pressure and S (mm) is Settlement.
what is the the ks unit, According to
((Apurba Tribedi ( the Code Writer for STAAD ) Software
Senior Product Manager
Bentley Systems Inc.
Yorba Linda, CA, US ))

this is a ratio and ks unit should be kN/m2/m
and as I read from some other books it's unit is (ks) kN/m3

Can any one help me?

 

[fattdad]

I just correlate the modulus of subgrade reaction to saturated CBR.

f-d

ípapß gordo ainÆt no madre flaca!

 

[BigH]

kN/m3 = kN/m2/m - that's math.

 

[Signious]

kN/m3 =/= kN/m2/m

just like kN-m/m =/= kN

 

[BigH]

I know that many do not like Bowles' books but, he does explain the concept of the units in Section 9.6 in his 5th Edition. ks is q/d where q is pressure (kPa) and d is deflection in linear terms (m). Hence some would write kPa/m which is kN/m2/m. In final form, ks is put into kN/m3 (see equations 9-9).

 

[ATSE]

Big H is correct. Low powered math: kN/m3 = kN/m2/m. This is for an area spring. Contact pressure divided by vertical displacement.
If ks is a discrete spring (like a single pile under vertical load), units are kN/mm (or kips/inch).
If ks is an area spring (like a spread footing under vertical load), units are kPa/mm or kN/m^2/m (or kips/in^2 per inch, or kips/in^3).

 

[Usmi09]

Thank you for all good friends clearing my concept .
Usually many people assume the kn/m3 as density thought is correct numerically.
I think Kn/m2/m is more correct.

 

[BigH]

Your choice

 

[mudman54]

coming from the lateral load on piles community, we've always seen it as pci (pounds per cubic inch)as per Terzaghi 1955. however, we really want to get it right for STAAD, the Ks="spring constant" in metric would be kN/m3 as BigH says. in rock we are using MN/m3. by the way, it is in no way constant and varies with size of the foundation and with depth requiring a very important interaction between the structural engineer and the geotechnical engineer.

 

[Mccoy]

The actual unit is weight-Force/(L[sup]2[/sup]L[sup]1[/sup])
Which is the same as: pressure/L
Ks has by coincidence the same dimensions as density but it is not a density.

There is really no fixed value used in practice, softwares should have a conversion capability and when we evaluate Ks we should Always be aware that conversion can be very, very Tricky, I'm speaking out of personal experience, once I got it wrong by two orders of magnitude...

popular units in metrics are kg/cm[sup]3[/sup] which is the same as daN/cm[sup]3[/sup], also MN/m[sup]3[/sup]is used

There are four orders of magnitude between kN/m3 and daN/cm[sup]3[/sup], if I'm not wrong

Popular units in America are pci and kcf as far as I've seen

http://www.mccoy.it

 

[Okiryu]

Would like to hear from structural engineers how they use our "k" value in their designs....do they assume this value to be constant throughout the entire slab? Or under point loads, do they assume other different value comparing to the "overall" recommended "k"?

 

[killi_82]

Hi Okiryu,

Basically, in structure analysis we could divide our elements into many nodes, and possibly during iterations with geotechnical engineer, the result (k) will not same for entire slab.
and I believe that subgrade modulus is also correlated strongly to the shape of the structure (behaviour) itself.

 

[Okiryu]

Thanks for the information. Just one comment/question: The k value (modulus of subgrade reaction) is not a property of the soils since it depends on the geometry of the loaded area. Normally we use plate loading tests of correlations to CBR to obtain the k values. But I am wondering how to calculate it manually. Do I just need to assume an area, say 1m x 1m and check the load that is necessary for a specific settlement, say 10mm? If so, I am assuming that the settlement is computed based on elastic theory and considering an influence depth of 2 to 4 times the loaded area?

 

[killi_82]

Modulus subgrade is the distribution of soil reaction,beneath the foundation structure against the foundation load.
It would be reflected accurately if you could do loading test like that, but in case you make an underground structure like MRT station, it would be so much hassle to do that.
So far I think it is difficult to do it manually, but your explanation seems very good. have to try it once.
in case that your structure is quite uniform in shape, not significantly differ between width and length, it should be fine to use formula.
in practical we need to compute it using software, in which the first value we can take from vesic formula or else, then iterate between structural engineer and geotechnical engineer. Basically this process is to find the settlement like your proposal for manual calculation.

please see this paper if you are interested.

 

[Usmi09]

Thank you for your helpful response. Basically I am geotechnical engineer in an independent laboratory. We only do on site test and provide the KS value to the client. How they use I cant say it.

I was only to be sure which unit should I use so they can use it in their proper way.
Thank you for All. I m really appreciated.
I think I invest my time in the right forum.

 

[rconner]

While most on this forum have far more experience than I in this area, I do think it is probably important to understand that soil "modulus" (or various "moduli"), as well as "coefficient of subgrade reaction" depend on many factors and also fields of application. There is e.g. a "coefficient of vertical subgrade reaction" (e.g. for footings) and a "coefficient of horizontal subgrade reaction" (e.g. for horizontally loaded piles). While you probably deal most often with the former and perhaps also without some of the other complications, you may nevertheless also be interested in the explanations of some of these factors in the paper at

https://ceprofs.civil.tamu.edu/briaud/Intro to Moduli/Intro to Moduli.pdf.

 

[Okiryu]

I have read Professor Briaud's paper in the past. It gives good idea of the different soil modulus. Interesting thing is that he mentions that the typical 25 mm allowable settlement which we use as a standard relates to some amount of strain.