Vertical foundation constant (VFC)

KTZ stiffness calculation

KTZ stiffness [Pa/m or N/m3] calculation is based on the assumptions and the algorithm taken from the German geotechnical literature:

KTZ stiffness is determined from soil layer(s) properties (depth of the soil layer and soil layer oedometric modulus). The algorithm describing the KTZ determination will be explained in-depth.

KTZ represents the stiffness associated to the translational degree of freedom along the Z-axis of the coordinate system.

This method applies only on rectangular shaped supports; because of this an equivalent rectangle should be used for complex shapes describing planar supports. Knowing the rectangle dimensions (a, b), the next step is to determine a foundation parameter f. This parameter is determined from Table 1 considering two ratios:

  • a/b
  • z/b

where a = foundation length; b = foundation width; z = soil layer depth.

Soil stratification

Fig 1. Soil stratification


Foundation parameter f

Table 1. Foundation parameter f


For a multi-layer soil, each layer will have its corresponding f (f1, f2, f3 ...) and its contribution to the final KTZ value:

  • Layer 1:
Layer 1


  • Layer 2:
Layer 2


  • Layer 3:
Layer 3

where Es represents the oedometric modulus.


The stiffness, KTZ is then calculated as follows:

  • One-layer soil:
One-layer soil


  • Multi-layer soil:
Multi-layer soil


For the beam structural element, where cross section width(b) is known, KTZ could be re-calculated to the distributed elastic stiffness Cz:


Cz [kN/m3m] = KTZ b.