Modulus Subgrade Reaction, k- horizontal and vertical, piles in clay 2

[Tabaluga]

Hi,

How do I work out the horizontal and vertical moduli of sub-grade reaction, for laterally and vertically loaded piles in clay?

I want to apply the sub-grade reaction values in a model (using Winkler springs) as I need to confirm the pile moments for the design of reinforcement in piles.

Piles are CFA 450mm dia concrete @ 10m deep, with significant lateral forces resulting from live load surcharge on pile cap.

I have the ground investigation report with the soil SPT and Cu data.

I have seen different approaches used and also note the units sometimes do not agree in the k value (some sources give vales per unit volume(kN/m^3), others are per unit area or unit length).

Which equations or references do I best use? Terzaghi's or are there more reliable recent developments? Are there worked examples that show how the the sub-grade coefficients are worked out and applied that would be greatly appreciated.

Thank you.

 

[r13]

I have seen different approaches used and also note the units sometimes do not agree in the k value (some sources give vales per unit volume(kN/m^3), others are per unit area or unit length).

No difference in the end, as explained below. You shall talk to your geotechnical engineer for other questions.

 

[Tabaluga]

Please see attached as the terminology can be a bit confusing as there are a number of different k's...

 

[r13]

The author has himself confused with inconsistency in the expressions. I am not aware the term "Coefficient of...", also I don't think there is any units associated with the "Coefficient" and "Rate of Increase", which are usually considered as numerical value only. I'll stay away from his article/book, as far as I can.

 

[r13]

Further note:

For the second expression, I think he wanted to relate the vertical modulus of subgrade reaction, K_v, as "p_v = K_v X z". Both K_h and K_v are related to the soil in interest, and should be provided by your geotechnical engineer.

 

[Tabaluga]

Thanks for that, r13.
Are the K_v and K_h values something typically provided by geotech?
I could not find them in the GIR that is why I proceeded to compute them myself to apply to the model...

 

[r13]

Yes, the geotechnical engineer will provide both, only if you asked for. You should also ask if you can rely on friction/adhesion, he/she can provide the required parameters.

 

[Settingsun]

Be cautious of a document that tells you that the "modulus of subgrade reaction" and the "subgrade reaction modulus" are different things. I would hit the delete button, personally.

Also, the original (Terzaghi) definition of "coefficient of subgrade reaction" is what that 'confusing terminology' document referred to as k_h (ie coefficient = modulus; two names for the same thing). See

https://structville.com/2020/07/modulus-of-subgrade-reaction-of-soils.html.

Like r13, I think the author of that document is the one who was confused.

If you're going to ask the geotech engineer, tell them the pile size and loading as this is not an intrinsic soil property and depends on geometry and loading.

Also run a sensitivity check since the method is only approximate.

Many foundations textbooks have information on this, eg Bowles. Definitely try something newer than Terzaghi, as his was the first attempt at quantifying this.

 

[Settingsun]

Forgot to say: I also prefer thinking in terms of kN/m^2/m or kPa/m, but once saw the subgrade modulus described in equivalent fluid terms to explain the kN/m^3 units. Eg water's density is 10kN/m^3 and a piston submerged 1m will therefore be subject to 10kPa pressure. Similar thought process for the footing pressed into the subgrade with modulus in kN/m^3. Different people understand things differently. People raised on equivalent fluid for retaining walls might prefer this. (I don't like equivalent fluid pressure for walls either)

 

[Tabaluga]

Thank you, both.

Would the formulae for horizontal and vertical coefficients be different? Also deep v. shallow foundations: different coefficient in the formulae?


Thanks.

 

[r13]

I am not aware of any formula to calculate subgrade modulus without testing the soil sample. Depth shall have effects on the modulus, due to changes in soil properties, and stresses. Let's see what the geotechnical engineers say otherwise.

 

[Settingsun]

You will need to iterate if using Winkler springs because the top spring will initially try to resist all the load and exceed the capacity of the ground that the spring represents. Try using the theory manuals at this link to calculate trial spring values.

https://www.rocscience.com/help/rspile/RSPile/Documentation/Theory.htm

If your software can handle non-linear springs, it may be quicker to use them rather than iterate. Or use approximate values in your main analysis then use a P-y analysis. There is free software available.

 

[EngMan40]

Tabaluga:

The k value of a soil for a laterally loaded pile is not a constant value but rather a function of the lateral deflection of the pile. The solution for this type of problem is iterative and requires geotechnical engineering experience. You mentioned clay soil and significant lateral load. Did you consider if drained vs undrained loading conditions applies, how about pile spacing, is it enough? Any groundwater? Is the clay normally consolidated or overconsolidated? COM624P is a program specifically developed by USDOT for this purpose. you can read the background information about it in link below (it is located after about page 300 in the document). After reading through it, see if you think you have the expertise needed to take on such responsibility. shifting the liability to the geotechnical engineer for a fee may save you headache later...

https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/PB94108305.xhtml

 

[Settingsun]

Maybe we're going the wrong way. If the pile size and length are known, has it already been analysed by someone else?

 

[Tabaluga]

Thanks for the suggestions and links, steveh48 and EngMann.

I see there is a lot in terms of research on this. I was hoping for a best practice type of approach to use for soil spring values in load model analyses, especially for piles... seems not a clear cut matter, so I will go back to geotech.

Thanks again for all responses.