Subgrade reaction complexities

[ONENGINEER]

After going through a number of references I found ambiguities on the dimensional equations. While ks = p/y should be in kN/m3 form, sometimes it is stated as kN/m2. In some references it is given as Ks =ks.x which makes a good sense but this is not consistent. Also modulus of subgrade reaction is sometimes called coefficient of sub-grade reaction with the same dimensional equation. One would expect a coef. be dimensionless. Also did not find a relationship between horizontal and vertical (coefficient of) subgrade reactions. The ks value is used for horizontal subgrade reaction, making the terms “horizontal” and “coefficient” redundant. So would there be a horizontal, a vertical and a resultant modulus or coefficient?

ks is sometimes shown as kc, the latter I think is for cyclic (instead of static) loading (or is it for clays compared to ks for sand.

Could one of the experts shed lights on the above, if possible. Thanks.

PS: this is my second active thread and hope it would be acceptable to the site admin to have two at a time. Thanks again.

 

[DaveAtkins]

It has always been clearer to me to say modulus of subgrade reaction is kN/m2 per meter, because it is the unit pressure which causes a unit of deformation. Think of a square plate being pushed downward through soil.

DaveAtkins

 

[Settingsun]

Coefficients can have dimensions. No problem there and it's just a name in the end.

I've seen the kN/m2 units for clay but that number isn't the coefficient (modulus) of subgrade reaction. You have to convert it to ks using a function of the footing dimensions. For a 0.3m square, the conversion is to divide by 1m, ie the kN/m2 number is numerically equivalent to ks if the footing is 0.3m x 0.3m but not equivalent for other dimensions.

I've seen k,horiz being taken as similar to k,vert for clays but not for sands. It depends on depth for sands.

 

[ONENGINEER]

Thanks steveh49 to clarify that coefficient of Subgrade reaction is indeed the same as modulus of subgrade reaction (ks) and that ks = kh = kv for clays. (I guess for sands with constant compactness with depth the ks, kh and kv values would still be equal).

Although dimensionally the same, conceptually I am curious to know if kN/m3 is pressure per unit deformation or it is pressure per width of foundation. I would appreciate a further feedback.

 

[Settingsun]

Pressure per unit deformation.

For sands, the dependency on depth is similar to passive pressure. Dependent on confining overburden pressure even if the density is the same.

 

[ONENGINEER]

Re the last comment, what the underlined refers to? Dependent on confining overburden pressure?

Another question: I agree ks = p/y, where “y” is deformation. However, some references refer to Ks = ks.x or Ks = ks.B. What is the Ks with a switch from y to B? While ks (being kN/m3) called a modulus, is Ks still called a modulus (being kN/m2)? I like to get to the bottom of this and thanks for helping me on this site. Thanks.

 

[Settingsun]

The shear strength of sand is from friction. Tau = sigma * tan (phi). Sigma (overburden pressure) increases with depth so the strength of sand does too. The stiffness also increases.

ks*B [kN/m2] might be for beams on elastic foundations or strip footings. Was that the context where you found it?

 

[ONENGINEER]

Thank you for the explanation on O/B pressure.

The ks*B was apparently within the laterally loaded pile context, B being the pile diameter.