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# Horizontal Subgrade Reaction of Soil

## Horizontal Subgrade Reaction of Soil

(OP)

When I read this useful thread (thread256-164011: Lateral Loaded Piles - Modulus of Horizontal Subgrade Reaction), I have a question in one of Panars comments. It said that "If k is the spring constant for the finite element model in units F/L, then k is determined by multiplying the coefficient of variation of horizontal subgrade reaction by the depth of the center of the pile segment and by the length of your pile segment."

My question is, assume a vertical pile of 40 ft long embeded in sand. The coefficient of variation of horizontal subgrade reaction = 11.5 pci. Assume the pile segment is every 1 ft. Then, at the bottom element (depth = 39.5' = 474"), the soil spring constant will become k = 11.5 pci x 474" x 12" = 65,412 lbs/inch. It is a very big value. Is that realistic? Is there a limitation to say that, after a certain depth, the k value will not increase?

Thanks!

### RE: Horizontal Subgrade Reaction of Soil

i feel most comfortable with vesic's equation for the modulus of subgrade reaction because it uses the modulus of elasticity of the soil and other parameters understood by geotechnical engineers.  if you feel you can get the horizontal modulus of elasticity, from a pressuremeter test for example, use it.  your spring constant will be dependent on B the width of the pile.

rather than using the so-called coefficient of variation of horizontal subgrade modulus which is depth dependent, why not just plug in different spring constants at different depths after you've divided up the soil into layers?  that way you can have a limit on the k that you are looking for in your question.

another good check is to calculate out the deflection based on your spring constant to see if it is reasonable.  usually, the structural engineer will want the k in pounds per cubic inch (pci) so that each spring can be applied to a tributary area of the foundation.  once the area is known, it is easy to compute the deflection of the spring just like we did in physics class.

### RE: Horizontal Subgrade Reaction of Soil

Mudman, do you mean the Biot-vesic equation underlined by Bowles in chapter 9 of his reference book?

Same as in shallow foundations?

Do you find the output reasonable?

Do you use the same elastic modulus with horizontal reaction as you use in vertical reaction ? I'm saying so because Bowles' simplified approach would entail doubling the subgrade modulus in the horizontal direction with respect to the vertical direction (chapter 16 of the same reference book: 'foundation analysis and design')

### RE: Horizontal Subgrade Reaction of Soil

...not sure what Bowles is referencing, but i've always gotten reasonable spring constant numbers from:

Vesic, A.S.(1961) "Beams on Elastic Subgrade and the Winkler Hypothesis",
5th Int conf Soil Mech Found Eng, Vol 1, Paris, pp 845-850

Ks = (0.65/B)*{(E*B^4)/(EI)}^1/12 * {E/(1-v^2)}

IF = pi *  B^4 /64    EI = Ec * IF

FOUNDATION WIDTH    B
CONCRETE STRENGTH    C
FOUNDATION ELASTICITY    E
FOUNDATION POISSON RATIO    v
CONCRETE ELASTICITY    Ec
MOMENT OF INERTIA    IF
FOUNDATION STIFFNESS    EI

### RE: Horizontal Subgrade Reaction of Soil

Great, thanks mudman, I'm just comparing methods since they don't always yield similar results

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