# Determination of Bearing Resistance with "Drained" and "Undrained" Soil Conditions

### Technical Article

This article focuses mainly on determining the bearing resistance according to [1] Annex D and distinguishing between "drained" and "undrained" soil conditions.

#### Example: Hinged Column with Foundation Plate

A foundation plate for a hinged column will be designed to show the differences.

Self-weight, imposed load, snow and wind are applied in four load cases to the column. The following graphic illustrates the load values.

The load combinations for the ultimate limit state design (STR/GEO) are generated automatically according to EN 1990 in RFEM and used for the designs in RF-/FOUNDATION Pro.

#### Input in RF/FOUNDATION Pro

Since the bearing resistance for the foundation plate according to [1] Annex D will be determined, it is necessary to select this option in the "1.1 General Data" dialog box.

The dimensions of the foundation plate are defined with a length and width of 1.25 m respectively and a thickness t of 25 cm.

Additional settings such as concrete grade, column dimensions, possible reinforcement diameters, reinforcement grade, and so on, are of no importance in this article since only the bearing resistance and sliding design has been selected in the details settings. The mentioned parameters are thus not part of the design and can be retained with the default settings.

Presetting the soil parameters is crucial to determine the bearing resistance. It is possible with the "Soil Profile". In this regard, it is worth mentioning an earlier technical article which explains in detail how to enter the soil profile and determine the bearingresistance for a layered soil with drained soil conditions.

In this case, the calculation is carried out with a constant soil parameter below the foundation base. The applied soil parameters are as follows:

Gravel, Gravel-Sand-Clay Mixture (GC)

γ = 21.0 kN/³

φ_{k} = 35.0°

c'_{k} = 0.007 MN/m²

c_{uk} = 0.040 MN/m²

It is important to note that RF/FOUNDATION Pro only displays the used parameters by default. It depends if the "drained" or "undrained" subsoil conditions have been selected in the "1.1 General Data" dialog box. If "Show only used parameters" is not selected, all parameters of the soil layer are displayed.

#### Governing Support Forces and Moments

The support forces of the generated CO4 are governing for determining the bearing resistance. This load combination is defined as follows:

$\frac12\;\cdot\;\mathrm{CO}4\;=\;1.35\;\cdot\;\mathrm G\;+\;1.50\;\cdot\;\mathrm Q\;+\;0.75\;\cdot\;\mathrm S\;+\;0.90\;\cdot\;\mathrm W$

The resulting support forces are displayed in the graphic below.

Figure 06 - Governing Support Forces of CO4

#### Distinction "Drained" and "Undrained"

Die Begriffe "konsolidiert" und "unkonsolidiert" sind in RF-/FUND Pro auch als "drainiert" und "undrainiert" zu interpretieren. Before starting the calculation, it has to be selected by the user and controls if the bearing resistance according to Equation (D.1) or (D.2) is determined.

Figure 07 - Selection "Drained" and "Undrained"

In general, it is assumed that an increase of stress is absorbed or removed by the soil structure (drained state) in case of drained soil conditions. In case of undrained soil conditions, the increase of stress in the soil is not absorbed by the soil structure, but by the pore water which is under overpressure (undrained state).

#### Bearing Resistance for Undrained Soil Conditions

The bearing resistance for undrained conditions results to, according to [1] Annex D, Eq. (D.1):

$\frac{\mathrm R}{\mathrm A'}\;=\;\left(\mathrm\pi\;+\;2\right)\;\cdot\;{\mathrm c}_\mathrm{uk}\;\cdot\;{\mathrm b}_\mathrm c\;\cdot\;{\mathrm s}_\mathrm c\;\cdot\;{\mathrm i}_\mathrm c\;+\;\mathrm q$

with

A' = effective base area B' ⋅ L'

c_{uk} = total cohesion of the undrained soil

b_{c} = factor for the inclination of the base area

s_{c} = shape factors of the foundation base

i_{c} = nclination factor of the load

q = overburden or surcharge pressure at the level of the foundation base

With the mentioned settings for the design, it results in the following intermediate results:

A' = 1.5404 m²

b_{c} = 1.00, since a horizontal position of the soil joint is always assumed in RF-FOUNDATION Pro

s_{c} = 1.197

i_{c} = 0.963

q = 0.005 kN/m²

If this is inserted into (D.1), it results in a charactreristic bearing resistance R_{k}/A' of:

$\frac{\mathrm R}{\mathrm A'}\;=\;\left(\mathrm\pi\;+\;2\right)\;\cdot\;0.040\;\mathrm{MN}/\mathrm m²\;\cdot\;1.197\;\cdot\;0.963\;+\;0.005\;\mathrm{MN}/\mathrm m²$

The design value of the bearing resistance thus results in:

$\frac{{\mathrm R}_\mathrm k}{\displaystyle\frac{\mathrm A'}{{\mathrm\gamma}_{\mathrm R,\mathrm v}}}\;=\;\frac{0.242\;\mathrm{MN}/\mathrm m²}{1.40}\;=\;0.173\;\mathrm{MN}/\mathrm m²$

Figure 08 - Result Details of Ground Failure

#### Bearing Resistance for Drained Soil Conditions

Since the determination of the bearing resistance for drained soil conditions has been already explained in an earlier article, Equation (D.2) is not repeated once again here.

The bearing resistance for drained soil conditions results here in:

$\frac{{\mathrm R}_\mathrm k}{\displaystyle\frac{\mathrm A'}{{\mathrm\gamma}_{\mathrm R,\mathrm v}}}\;=\;\frac{1.124\;\mathrm{MN}/\mathrm m²}{1.40}\;=\;0.803\;\mathrm{MN}/\mathrm m²$

#### Summary

The present example shows the influence of the selection "drained" or "undrained" soil conditions in the 1.1 dialog box on the determination of the bearing resistance according to EN 1997-1 Annex D. In practice, drained soil conditions will be assumed in most cases.

Apart from this, RF-/FOUNDATION Pro provides the selection between the two approaches and offers the option to perform a case study with drained and undrained conditions if the soil conditions are unclear.

The setting "drained" or "undrained" has, besides the determination of the bearing resistance, also an influence on the design of the safety against sliding and the determination of the sliding resistance. More information is available under "Sliding" in Chapter 3 of the RF-FOUNDATION Pro Manual.

#### Keywords

foundation drained undrained

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