When we use finite element software for analyzing deep foundations then it becomes important to model piles with accurate axial stiffness so that the load can distribute properly based on pile stiffnesses.
Some people suggests to calculate pile stiffness by AE/L formula. By doing this method the problem is that as you increase the length of the pile, the stiffness will reduce which is not accurate.
The best thing is to ask Geotech Engineer for the allowable loads and the allowable axial displacement on working loads. Most of the times this allowable displacement is ranged from ¼” to ½” which can be confirmed from geotech report.
Take your allowable load which will vary based on the depth of pile and divide it by the axial displacement, this will be the required pile stiffness.
k = Pile axial stiffness (kips/inch )
P = Allowable load (kips)
Δ = Allowable vertical displacement (inches)