I don't quite understand the spring constants for beams and piles on elastic foundations. Are these parameters of translational, shear, and rotational springs stiffness moduli (MN/m²) or spring constants (MN/m³)?
Translational springs are determined from coefficients relative to surfaces. These are given in kN/m³ and describe the amount of required kN/m² to compress the ground by 1.0 m.
To define the springs for a member limited in its width, the coefficients are multiplied by the width. For a horizontal member with a z-axis pointing downwards, this is the y-dimension. Thus, a translational spring relative to a member is obtained in kN/m². It shows the kN/m required to compress the ground by 1.0 m.
The translational springs always relate to local member axes. Do not use the stiffness modulus for the determination, but the spring constants, which are given in kN/m³.
The shear springs represent a constant rotational spring over the member length and are given in in kNm/rad and per m. If you substitute rad by m/m, you obtain kNm/(m/m x m), which can be simplified to kN.