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001433

Dipl.-Ing. (BA) Markus Baumgärtel

2017-05-03

Soil Model of Foundation Overlap

A previous article presented different variants of surface elastic foundations in addition to the traditional subgrade reaction modulus method. The following article describes another method for surface foundation. This method considers the adjacent ground areas by means of a foundation overlap. In this case, foundation parameters refer to the continuing works by Pasternak and Barwaschow.

Equation According to Pasternak

\begin{array}{l} c_{1} = \frac{E_{0}}{H \cdot (1 - 2 \cdot μ ²)} \\ c_{2} = E_{0} \cdot \frac{H}{6 \cdot (1 μ)} \end{array}

Formula 1

where

E_{s} \cdot \frac{1 - μ - 2 \cdot μ ²}{1 - μ}

Formula 4

H is the foundation thickness,
μ is the Poisson's ratio.

Equation According to Barwaschow

\begin{array}{l} c_{1} = \frac{E_{0}}{H \cdot (1 - μ ²)} \\ c_{2} = E_{0} \cdot \frac{H}{20 \cdot (1 - μ ²)} \end{array}

Formula 2

where

E_{0} = E_{s} \cdot \frac{1 - μ - 2 \cdot μ ²}{1 - μ}

Formula 5

H is the foundation thickness,

μ is the Poisson's ratio.

The foundation overlaps applied to this method should ideally reach until the settlement on the edge of the foundation overlap is close to zero. Moreover, the additional area should not have any additional governing stiffness, which is why the foundation overlap thickness should be kept very low.

In addition to the short calculation time, an advantage of this variant is the consideration of the shear resistance. Furthermore, this method allows you to graphically display the settlement behavior outside of the foundation edge. This way, it is also possible to represent the interaction between several separate buildings that have an influence on each other via the subsidence basin.

Example

E₀ = 10,000 kN/m²
μ = 0.2
H = 3 m

\begin{array}{l} c_{1, z} = \frac{E_{0}}{H \cdot (1 - 2 \cdot μ ²)} = \frac{10, 000}{3 \cdot (1 - 2 \cdot 0.2 ²)} = 3 623.19 kN / m ² \\ c_{2, v} = E_{0} \cdot \frac{H}{6 \cdot (1 μ)} = 10, 000 \cdot \frac{3}{6 \cdot (1 0.2)} = 4 166.67 kN / m ² \end{array}

Formula 3

Image 01 - Support Conditions for Surface Foundation

Image 02 - Local Deformations of Floor Slab and Foundation Collar

Image 03 - Interaction of Two Separate Buildings

References

[1] Barth, C., & Rustler, W. (2013). Finite Elemente in der Baustatik-Praxis, (2nd ed.). Berlin, Beuth. [2] Kolar, V., & Nemec, I. (1989). Modelling of Soil-Structure Interaction. Amsterdam, Elsevier Science Publishers.

Knowledge Base

KB 001433 | Soil Model for Foundation Overlap

Author

Mr. Baumgärtel provides technical support for Dlubal Software customers.

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