# Bedding Modulus Calculation

Available in: 3D Structure

In practical design when using surface supports or foundations it is a demand to adjust different surface support stiffness distribution along the surface because the edge, corner or middle parts of the surface support behave in different way to simulate more realistic response. Thanks to two functions of FEM-Design related to surface supports, we can define realistic model-support environment:

- Surface supports with variable stiffness distribution
- Bedding modulus estimation by considering soil parameters applied on linear elastic 3D-solid finite elements

Contents:

# Surface supports with variable stiffness

We can set variable stiffness distribution for all types of surface support objects:

- Simple support item:
*Surface support group* - Complex support items modeled by
*Surface support group*analytical system:*Isolated foundation**Wall foundation**Foundation slab*

For each type, we can assign different stiffness distribution by points in the following steps:

- After creating the surface support or surface support-type foundation object with a general common stiffness value, run the
*Surface support group*command. Depending on whether you want to specify a stiffness different than the common one in a few characteristic points or in given areas, select the*Single point*or*Field*options. - Set the new stiffness value (at
*Default settings*dialog). - Select the initial surface support or foundation object, and
- define a point as the position of the new support stiffness value with the
*Single*option, - define regions for the new stiffness value with requested geometrical shape by using the
*Field*option. Here, the distribution density of the stiffness points can be specified at*Point distance*.

- define a point as the position of the new support stiffness value with the
- Repeat steps 2 and 3 until all points or regions with different stiffness values have been entered.

After defining stiffness points, FEM-Design automatically and continuously distributes - with the aid of interpolation technique - the stiffnesses over the entire support or foundation element. The stiffness distribution can be viewed and checked in Analysis mode (*Analysis/Results/Auxiliary calculations/Bedding moduli*).

The stiffness of the stiffness points can be modified with the *Properties *tool (of *Surface support group*). Points can be deleted with the *Delete stiffness points* tool. The changes are immediately reflected on *Bedding moduli* analysis results.

# Bedding modulus estimation

## Purpose

Estimation of the bedding modulus as springs for elastic surface foundations is always containing several uncertainties. There are several methods in the literature how to estimate the bedding modulus under the bottom surface of the foundations, but it is a very difficult task, because it depends on several things: the properties of the sub-grade soil, the rigidity of the foundation, the position and the distribution of the applied loads, the system of the superstructure, etc.

The purpose of this new feature is to estimate the bedding modulus (spring constants) under the surface foundations with the aim of elastic 3D solid element calculation and to represent the soil sub-grade under the superstructure.

The main idea of the bedding modulus estimation is based on the following formula:

,

where *σ _{0 }*is the normal stress in a point under the surface foundation, and

*s*is the settlement at this specific point perpendicular to the plane of the foundation.The unit of this bedding modulus value is [

*kN/m*] or [

^{2}/m*kN/m*], which represents a surface distributed specific spring constant ("bedding modulus"). Of course, this value varies along the surface of the foundation, which is connecting to the sub-grade. So, the exact values depend on arrangement, material and dimension of the foundations, the type of the superstructure, and the material properties of the soil.

^{3}## Function

After defining foundation objects modeled with *Surface support group *analytical system and with *Stiffness points*, it is necessary to draw a *Soil *block (*Structure *tab) under the superstructure, whose properties affect the calculation of the bedding moduli.

Since we only use the *Soil *object to define the bedding modulus (we don't want to do real calculations for that), we should uncheck the *Calculate soil as solid element *settings option (*Settings *> *Calculation *> *Soil calculation*).

.

To estimate and get the bedding modulus (from *Soil* properties and its connection to the foundation object), run a quick analysis: *Bedding modulus calculation* (*Analysis *> *Calculations *> *Auxiliary calculations*).

We should select a relevant load combination (which contains mainly the vertical self-weight loads). These loads in the selected load-combination will be the basics from where we conclude the stresses and settlements, which will be the inputs for the estimation of the bedding moduli. We may select the mesh properties, which will be used for the solid *Soil *calculation in the background.

According to the used equation, only the bedding modulus perpendicular to the surface support (local z’ direction) can be estimated. The other two (local x’ and y’) directional bedding modulus values are calculated from the z’ value reduced by given stiffness multipliers.

# Results

The analysis gives results of estimated bedding modulus in the stiffness points.

- In the background, only the
*K*_{z’}*compression*value is estimated with the 3D solid element calculation. - The values of
*K*is always assumed to be 0._{z’}tension - The
*K*and_{x’}compression/tension*K*values will be calculated from_{y’}compression/tension*K*reduced by the multipliers set at calculation settings._{z’}compression

The automatically calculated stiffness property values may be modified similarly to a simple surface support stiffness point property.