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

 
  • Information
  • Software
    Advance Design
  • Module
    Advance Design - All
  • Version
    ≥2014
  • Type
    Modeling
  • Difficulty
    **

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:

- a/b ,
- z/b ,

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

What is the algorithm used for the KTZ calculation from elastic supports?
Figure 1. Soil stratification

What is the algorithm used for the KTZ calculation from elastic supports?
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: What is the algorithm used for the KTZ calculation from elastic supports?
• Layer 2: What is the algorithm used for the KTZ calculation from elastic supports?
• Layer 3: What is the algorithm used for the KTZ calculation from elastic supports?

where Es represents the oedometric modulus.

The stiffness, KTZ is then calculated as follows:
• One-layer soil: What is the algorithm used for the KTZ calculation from elastic supports?
• Multi-layer soil: What is the algorithm used for the KTZ calculation from elastic supports?

For example, we consider the slab foundation from Figure 2. It is10 meters in length and 5 meters in width:
a = 10m;
b = 5m;
so the ratio a/b is 10/5 = 2.

What is the algorithm used for the KTZ calculation from elastic supports?
Figure 2. Foundation slab dimensions


The soil stratification is as following:

• Layer 1 ⇒ depth z1 = 5m; Es1 = 58.84 MPa;
• Layer 2 ⇒ depth z2 = 15m; Es2 = 147.10 Mpa;
• Layer 3 ⇒ depth z3 = 30m; Es3 = 220.65 Mpa.

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

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

Layer 3
z3/b = 30/5 = 6 ⇒ So using Table 1, f3 = 1.03
What is the algorithm used for the KTZ calculation from elastic supports?

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

What is the algorithm used for the KTZ calculation from elastic supports?
Figure 4. KTZ value obtained with Advance Design 2014


Figure 4 shows the KTZ value obtained automatically with Advance Design 2014.

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