Spring Factors

[Okiryu]

I am involved in a project to provide soil parameters to the project's structural engineer for a seismic evaluation of an existing building.
The structural is asking for:

1. Bearing Pressures with spring factors
2. Soil Passive Pressure with spring factors

For #1, I am assuming that the spring factor which the structural is asking for, is the modulus of vertical subgrade reaction, "k" with Force/Length^3 units. This "k" value is also the same "k" value provided for slab-on-grade design. Is this assumption correct?

For #2, I will provide the passive equivalent fluid pressure depending on the type of soils. However, I am confused about what "spring factor" is. If the building were on piles, I will be able to provide the lateral modulus of subgrade "kh", however the building is constructed on shallow footings. I was checking my geotech books and most of the equations to calculate "kh" requires the diameter of the pile, but in my case since I have shallow footings I do not know what will be the best approach.
Does somebody have an idea what (lateral) spring factor mean? and how to calculate it for shallow footings? or any book references?

Thanks in advance for your help.

 

[Mccoy]

Okiryu, the classic reference is Gazetas, 1991, in Foundation Engineering handbook, which probably you can find in Googlebooks.

Some slightly different relationships are illustrated in the FEMA 273 october 1997 guidelines, maybe there even is a more recent installment. Section 4.4.2 is mostly on spring constants and unit subgrade modulus (or spring coefficient).

In the FEMa guidelines the equivalent radius case is exposed (best for square to near-square sections), in Gazetas you have any foundations geometry.

http://www.wbdg.org/ccb/DHS/ARCHIVES/fema273.pdf

These are the basic relationship for the various cases. Watch out, stiffnes for passive pressure in figure 4-4 can be applied only if there is effective and efficient coupling between foundation and soil- no gaps.

 

[BigH]

Actually the classic is Barkan (1962), then Richard Hall and Woods' 1970 book. But being that I am older, I can see where others have different, newer, classics. There is a book out there, too, by Arya that goes into all this detail.

 

[Okiryu]

Mccoy and BigH, thank you for your replies. I found the FEMA guidelines very useful. Also, I was able to download the Barkan's book and realized that it is an classic Russian book (translated into English by Tschebotarioff)

Regarding the FEMA guidelines, I have few more questions:

1. The spring constants "k" in the FEMA guidelines are calculated based on the size of the footings (BxL), my building has continuous wall footings and in that case "L" is very large and therefore "k" becomes very large as well. My approach is to consider "L" as unitary length (L = 1 meter) when calculating the spring constants. Is that a reasonable approach?

2. The units are force/unit displacement/unit area, so is it valid to express "k" with Force/L^3 units?

 

[Mccoy]

Actually the classic is Barkan (1962), then Richard Hall and Woods' 1970 book. But being that I am older, I can see where others have different, newer, classics. There is a book out there, too, by Arya that goes into all this detail.

bigH you're absolutely right, I've should have said 'recent classic reference', although I didn't know much Barkan and the Others, on the subject of foundation vibrations and dynamic spring moduli I've been reading Gazetas, Wolf and Prakash but I'm realizing the Indian school has written a lot about that as well.

Okyriu, actually with long beams and foundations which deviate significantly from a circular shape the methods based upon circular radius may be are not very well suited.
In this case the rigid massless model of Gazetas would be best. About using smaller elements, if your program allows you to break out the beam in smaller elements then it would be an excellent way to proceed. also, if the soil is laterally inhomogenous as may be the case in your Japanese project, you may use different spring constants along the beam in a realistic fashion.

 

[Okiryu]

McCoy, thanks much for your advice. Actually I calculated the strip footing spring factor considering an unitary length. I already sent my recommendations to the structural and I am waiting for their comments.
Also, I am confused about if the vertical spring factor and modulus of subgrade reaction are the same thing. I normally provide modulus of subgrade reaction "k" for slab on grade design. For my current project, the structural asked for spring factors to be used at shallow footings. When checking the numbers, the spring factor and "k" value were quite similar, so I would want to know if there is any difference between those two parameters.

Thanks again for your help !!

 

[Mccoy]

You are welcome okyriu, I'm not sure about spring factor but if units amd numbers are the same they are probably two definitions for the same parameters.
Whereas 'spring stiffness' or simply 'static stiffness' or 'dynamic stiffness' is different, it is measured in units of Force/L and is the weight-force which causes a unitary displacement of the rigid block