What is the algorithm used for the KTZ calculation from elastic supports?

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Starting with Advance Design 2014 KTZ stiffness is determined from soil layer(s) properties (depth of the soil layer and soil layer oedometric modulus). The method used for this calculation is taken from the German professional literature. The algorithm describing the KTZ determination will be explained in-depth.

Note: 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:

Figure 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:

Figure 2. Foundation slab dimensions

The soil stratification is as following:

Note: In Advance Design 2014, the input data refers to the thickness of the soil layer (Figure 3).

Figure 3. Definition of soil layers thickness in Advance Design 2014

Now, each soil layer has its corresponding f (f₁, f₂, f₃...) and with its contribution to the final KTZ value.

• Layer 1
z₁/b = 5/5 = 1 ⇒ So using Table 1, f₁ = 0.57

Note: For intermediate ratio values, f is determined using linear interpolation

• Layer 2
z₂/b = 15/5 = 3 ⇒ So using Table 1, f₂ = 0.89


• Layer 3
z₃/b = 30/5 = 6 ⇒ So using Table 1, f₃ = 1.03


•; KTZ calculation

Figure 4. KTZ value obtained with Advance Design 2014