Please provide good reference, or formula to calculate horizontal and vertical Spring Constant from soil properties to calculate deflection and settlement characteristics of pile foundation...
Kpaudel, the simplest and maybe more coherent references are in Bowles, Foundation Analysis and design, chapters 9 (Kh vertical) and 16 (Kh horizontal). They are pretty good as an input in FEM methods.
Other references are Gazetas 1991, Foundations vibrations, in Feng, foundation engineering handbook. More references: Salgado, the engineering of foundations.
Kh is also the initial, linear part of a p-y curve.