Estimation of Subgrade Reaction

[steveyeung]

I am doing preliminary design of a subway and found the midspan deflection of the top slab being very high because the horizontal resistance provided by the soil acting on the wall has been neglected. Now that I have to take the horiz subgrade rection into account and hope it can reduced the midspan deflection of the top slab a liitle bit. However, I don't know how to work out the horiz subgrade reaction based on SPT values????


REgards,

 

[jdonville]

steveyeung,

There really is no (linear) horizontal subgrade modulus. Also, using SPT values as the basis for estimating future soil deformations is terribly crude. I don't suppose that you can throw this question to your geotech?

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

The views or opinions expressed by me are my own and do not necessarily reflect the views or opinions of my employer.

 

[steveyeung]

I understand that soil deformation with horiz stree is not linear. However, just for preliminary design, what method is suitable?

 

[fndn]

To change veryical stress to horizontal stress multiply k(earth pressure coefficient) to the Kv(vertical subgrade reaction). For example your Kv is 150 psi per inch, and you estimate k = 0.3, you horizontal Kv component is 50 psi/inch.

 

[AW12]

steveyeung

With respect to lateral pressures you could refer to the 'lateral earth pressure' entry under 'earth retention engineering'. You will find that for the case where lateral deflections are not desirable you should use K0 = 1. (Kay nought equals one)i.e. lateral earth pressure 'at rest'. fndn seems to be suggesting active earth pressure, but this would tend to underestimate the reaction. I would be interested to know how far is your top slab below ground level. If it is near surface, then using the earth pressure methods may give low reactions anyway.

 

[TDAA]

Since when is K0=1 the "at rest" coefficient for a soil? That would indicate that the vertical and horizontal forces would be the same, ie a fluid. The lateral pressure coefficient is a funcion of the soils strength parameters.

Also, while using 1 may be conservative to reduce lateral deflections in a vertical member, he is using the lateral forces to reduce the deflection of the top slab. I do not believe this would be a conservative approach to that problem.

Steveyeung, as has been stated earlier, I would put this question to the geotech for the project. Even if you are trying to just get a preliminary idea of the deflection, they should be able to give you reasonable values for the materials present at the site. This will likely save some rework for you when finalizing your design.

 

[AW12]

Steveyeung stated that he was hoping to reduce the deflections by allowing for a reaction, which had previously been neglected, hence my earlier response. K0=1 when the friction angle is zero, i.e. in the case of a clay soil in the undrained condition. Given that the reaction had been neglected originally I had assumed that this was the scenario under consideration. Perhaps Steveyeung could clarify this, or give more information on the type of soil and depth of top slab below ground.

Apologies to TDAA if my previous post is not clear.

 

[jdmm]

jdonville is right!

There is no horizontal subgrade reaction. Just because you need one does not indicate that there is one. Soils behave as an elastic-plastic material that behalf in response to the stress distribution. Nothing in structural engineering prepares you for this condition. It is not your fault. The fact remains that soil is very much more complex that simple theorectical analysis predicts. However, you have a problem to solve. I would suggest that you try to solve it with a geotechnical engineer that understands the stress strain relationships of soils.

jim

 

[fndn]

According to Terzaghi(1955)-"Evaluation of Coefficients of Subgrade Reaction", Horizontal Subgrade Reaction , koh = nz/B. Terzaghi's initial constant values were very low. Studies done in 1974 by Reese, Cox and koop suggested higher values for Terzaghi's constants.

As for estimating koh vs SPT, Scott suggests using the following values for loose, medium dense and dense sands: 17, 50 and 110 respectively. Units are in Tons/cubic feet. Note that my earlier post suggested 50 pci and Scott's table says 43 pci(50 tcf) for medium dense sands.

For a thorough discussion on horizontal subgrade reaction see pp 255-259 of R.F. Scott's "Foundation Analysis" 1981 by Prentice Hall.