Soil Model of Foundation Overlap

Technical Article

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

$${\mathrm c}_1\;=\;\frac{{\mathrm E}_0}{\mathrm H\;\cdot\;(1\;-\;2\;\cdot\;\mathrm\mu\;^2)}$$ $${\mathrm c}_2\;=\;\frac{{\mathrm E}_0\;\cdot\;\mathrm H}{6\;\cdot\;(1\;+\;\mathrm\mu\;)}$$

where

E0  is the elastic modulus calculated as:
$${\mathrm E}_0\;=\;{\mathrm E}_\mathrm s\;\cdot\;\frac{1\;-\;\mathrm\mu\;-\;2\;\cdot\;\mathrm\mu^2}{1\;-\;\mathrm\mu}$$
is the foundation thickness
μ  is the Poisson's ratio

Equation According to Barwaschow

$${\mathrm c}_1\;=\;\frac{{\mathrm E}_0}{\mathrm H\;\cdot\;(1\;-\;\mathrm\mu\;^2)}$$ $${\mathrm c}_2\;=\;\frac{{\mathrm E}_0\;\cdot\;\mathrm H}{20\;\cdot\;(1\;-\;\mathrm\mu^2\;)}$$

where

E0  is the elastic modulus calculated as:
$${\mathrm E}_0\;=\;{\mathrm E}_\mathrm s\;\cdot\;\frac{1\;-\;\mathrm\mu\;-\;2\;\cdot\;\mathrm\mu^2}{1\;-\;\mathrm\mu}$$
is the foundation thickness
μ  is the Poisson's ratio

The foundation overlaps applied to this method should ideally reach far enough 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 a short calculation time, a further advantage of this variant is its consideration of the shear resistance. Furthermore, this method allows you to graphically display the settlement behavior outside of the foundation edge. In this way, it is also possible to represent the interaction between several separate buildings which have an influence on each other via the subsidence basin.

Example

E0  10,000.0 kN/m²
μ  0.2
3.0 m
$${\mathrm c}_{1,\mathrm z}\;=\;\frac{{\mathrm E}_0}{\mathrm H\;\cdot\;(1\;-\;2\;\cdot\;\mathrm\mu\;^2)}\;=\;\frac{10,000}{3\;\cdot\;(1\;-\;2\;\cdot\;0.2\;^2)}\;=\;3,623.19\;\mathrm{kN}/\mathrm m^2$$ $${\mathrm c}_{2,\mathrm v}\;=\;{\mathrm E}_0\;\cdot\;\frac{\mathrm H}{6\;\cdot\;(1\;+\;\mathrm\mu\;)}\;=\;1,000\;\cdot\;\frac3{6\;\cdot\;(1\;+\;0.2\;)}\;=\;4,166.67\;\mathrm{kN}/\mathrm m^2$$

Figure 01 - Support Conditions for Surface Elastic Foundation

Figure 02 - Local Deformations of Base Plate and Foundation Overlap

Figure 03 - Interaction of Two Separate Buildings

Reference

[1]   Barth, C. & Rustler, W. (2013). Finite Elemente in der Baustatik-Praxis (2nd ed.). Berlin: Beuth.
[2]   Kolář, V. & Němec, I. (1989). Modelling of soil-structure interaction. Amsterdam: Elsevier.

Links

Contact us

Contact Dlubal Software

Do you have any questions or need advice?
Contact us or find various suggested solutions and useful tips on our FAQ page.

(267) 702-2815

info-us@dlubal.com

RFEM Main Program
RFEM 5.xx

Main Program

Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements

RFEM Other
RF-SOILIN 5.xx

Add-on Module

Soil-structure interaction analysis and determination of elastic foundation coefficients based on soil data