#### KTZ stiffness calculation

KTZ stiffness [Pa/m or N/m^{3}] 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.

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.

Fig 1. Soil stratification

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 2:

- Layer 3:

where Es represents the oedometric modulus.

The stiffness, KTZ is then calculated as follows:

- One-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/m^{3}**⋅**m] = KTZ **⋅** b.