Modulus of Subgrade Reaction to Linear Elastic Spring

[J1D]

This is an old topic, many similar threads shown in this forum. It is again about the calculation of spring constant, but a bit special.

We typical calculate the spring constant (Cs) of a support joints (which represent the restraint of a area) in computer model, especially for horizontal springs as soils around piles. When the modulus is given with a value (like 50 pci for stiff clay), the spring constant is obtained by multiplying the supporting area. The unit is kip/in. This way seems quite clear to me despite some variable is missed, such as depth of the support joint below the grade.

From time to time, we have geotechnical reports of specific sites. The modulus are given in this format: Kh=nh*Z/B, where Kh is called modulus of horizontal subgrade reaction, nh is the constant of the modulus (in pci or similar), Z is depth below grade, B is pile diameter. My confusion is: in this case the modulus becomes pile diameter dependent, while Cs is not. This means the spring constant of 12” dia pile will be the same as that of 48” dia. pile.

Have you encountered this?

 

[UcfSE]

You are comparing Cs in F/L to Kh in F/L^3. They won't be similar. By your own argument however the Cs is multiplied by area of the pile (supporting area). That would mean that a 48-inch pile would have 4 times the modulus of a 12-inch pile, correct?

Whether the modulus is constant with pile depth is another matter. It depends on the assumptions made in the analysis of the site and the soil profile and the judgment of the geotechnical engineer. The thing is to know what assumptions are made when you do your analysis and to confirm that such assumptions are valid.

 

[BigH]

If I remember correctly Tomlinson in his Pile book goes through a nice discussion of this topic.