Elastic Rotations Of Foundation

[Refaatfaraj]

Dear Colleague

Could someone help me to know a simple approach, how does the elastic rotations of foundation (Rx & RY and RZ) calculate?. I have only the vertical subgrade reaction (Ks ) (I have gotten this value based on this approach : Ks = 40(SF)qa : KN/m3 (Joseph E. Bowels book) .

And am I right or not when I say the horizontal subgrade reaction usually = (1/6 or 1/10 of KS “vertical subgrade reaction”)

Knowing that I using ARS (Autodesk ROBOT Structural Analysis) and the elastic subgrade components are appeared in the attached capture

Thanks in advance for any help

Refaat

 

[Mccoy]

Refaatfaraj,
usually horizontal subgrade reaction is taken as twice the vertical reaction (bowles' handbook).
Anyway, it appears that you need a torsional impedance for the foundation.

You may want to consult the NIST-GCR-12-917-21 publication.
You may also use my spreadsheet, if you have the soil's shear modulus and other parameters.

you can just download the Pais & Kausel link at this webpage.

http://nuke.mccoy.it/SoilStructureInteraction/tabid/72/Default.aspx

http://www.mccoy.it

 

[Refaatfaraj]

Hi Mccog

Many thanks for your correction and guidance, I am really grateful. Especially with your wonderful spreadsheet for equations of foundation stiffness and damping. Also, I would like to greet you to point me to NIST GCR 12-917-21 Publication.

When I concluded the thread some inquiries coming in front of me. I will be highly appreciated to hear your opinion about them

1. May I know, if the translational and rotational stiffness equations which proposed by Pais & Kausel can be applied to any type of foundations such as ( Mat , spread, piled -raft ….etc) ?

2. As I am structural engineer, would I know the general concept of correction the underestimation of rotational stiffness at the foundation edges (clause 2.2.3 - NIST GCR 12-917-21)? . Even Bowles suggested in his book to double the end springs or zone KS with larger values.
Kindly, if you can use the following example in your explanation to help me better to understand the meaning and the purpose of coupling at foundation edges.
I used to model mat foundation for instance as Finite element model (FEM). I also give only (vertical subgrade modulus – Ks (KN/m3) a Winkler foundation) only. Then the software will calculate the vertical stiffness based on tributary areas.
- In which cases should I used this coupling (surface or embedded) (with basement walls or without basement walls)?
- What is the width of strips should I take it along the foundation edge?
- What is the best way to modeling it?

3. Kindly, Could you help me to get a table for common soil ( sand & clay) properties such as ( shear modulus(translational & rotational ) – poison s’ ratio – Shear wave velocity and density ) to use them as reference in my calculations because in some cases the geotechnical data aren't available ?

4. May I know, how did you calculate the of (a0 ) in your spreadsheet?


5. In general would I apply (Kh=2Kv) for any type of foundation (shallow foundations (mat, spread ...etc.) or deep foundations (piles) )?

All the very best in your effort
Refaat

 

[Mccoy]

Refaatfaraj,
maybe you already found the NIST publication, freely available at the following link:

http://www.nehrp.gov/FC4A6BBA-3FA9-...58-8258-D95D3D3947C4/pdf/nistgcr12-917-21.pdf

Clause 2.2.3 of such publication deals with the eventual correction from rigid foundation (the case of the impedance equations) and non-rigid foundations. The conclusion is that in practice you can use the impedance formula for both, without corrections in the non rigid case in translational stiffness.

Liou and Huang (1994) showed that foundation flexibility does not significantly
affect translational stiffness and damping terms for the case of flexible perimeter
walls. For rotational stiffness and radiation damping, Figure 2-7 shows that
foundation flexibility effects are relatively modest for the case of flexible perimeter
walls, and most significant for the case of a rigid core.

Rotational-Rocking stiffness is cited as well as the suggested corrections, translational stiffnes is not. You might as well use the API suggestions for wide rafts (multiplying the central Winkler modulus by a factor 2 or 3 as far as edge springs are concerned). a more rigorous correction would imply to calculate settlements with elastic theory for various verticals across the raft and then to back-calculate th eWinkler modulus applying the definition: Kw=P/y. Pretty time consuming, undubtedly, but it follows a technical logic hard to criticize.

http://www.mccoy.it

 

[Mccoy]

The Pais & Kausel equations in the spreadsheet are applicable to all types and dimensions of rectangular shallow fountations, with various degrees of embedment.

ao = 2πf B/Vs

where f , in the words of the NIST publications:

This can be taken as the frequency
corresponding to the period associated with the dominant response of the structure.
In most cases, this will be the first-mode, flexible-base period.

Vs is shear waves velocity, B is width of foundation

http://www.mccoy.it

 

[Refaatfaraj]

Hi Mccoy


Thanks a lot for your appreciated help .

In addition to your useful information. FEMA-356 has classified to three methods to calculate the stiffness parameters based on the rigidity of foundation with respect to the supporting soil

1. Method 2 (clause 4.4.2.1.3) for not rigid foundations , also suggested to increase the vertical stiffness at the foundation edges but indifferent approach as appear in the attached capture . My inquiry as following :

If I use this approach (central Winkler modulus more stiffener at the edges), shall I use rotational stiffness or not (only vertical stiffness)?


2. May I know, what is the main criteria to classify the foundation as rigid or flexible?


With Regards

Refaat

 

[Mccoy]

Reefat, in the Fema method#2 as you've seen the winkler modulus (per unit lenght) at the B/6 area is taken as over 9 times the modulus elsewhere.
Now, this approximation may be relatively accurate for some geometries, less so for other ones. It's a rule of thumb to be used as a quick reference.

It is explicitely written that the FEMA method should be used for vertical and rotational stiffness (Actually, in rotational stiffness the lack of correction may yield an overly conservative value so it may be even more necessary).

I don't know if there is some official criterion for a rigid foundation, by definition that would be a foundation whose variation in shape after loading is negligible, no matter the entity of loading (until rupture).

To all practical effects though a foundation may retain its shape with a small loading and loose it or 'become flexible' with a large enough loading.

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