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Ann-Kathrin Dannwerth, B.Sc.

2024-07-11

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Overview

Concrete Foundations Add-on

Theoretical Principles

Design Specifications

Design Properties of Single Foundations

Design

Results

Documentation

Load Capacity of Soil

The ultimate limit state design of the soil can be performed in different ways, depending on the standard.
In the Eurocode, the design is performed by comparing design values of actions and resistances (ground failure design), whereas North American standards often use allowable soil pressures.
Both approaches describe the same structural behavior of the soil, but differ in terms of safety concept and design format.

EN 1997-1: Ground Failure Design

In ground failure design according to EN 1997-1, the resistance can be determined either using specified allowable soil pressures or by performing a calculation of the bearing resistance, taking into account the soil layers and soil properties.

Design with Specified Allowable Soil Pressure

In this type of design, the existing soil pressure is compared with the specified allowable soil pressure.
The value of the allowable soil resistance σa is defined in the Geotechnical Configurations of the “Concrete Foundations” add-on in the “Allowable Soil Pressure” section.

Determination of Stresses in Soil Joint and Load Eccentricities

The design shear force with additional foundation loads V_z,+add and the resulting design bending moments M_y,+add and M_x,+add in the foundation base center are required to determine the eccentricity of the effective vertical loads:

e_{x} = - \frac{M_{y, + add}}{V_{z, + add}}

e_{y} = \frac{M_{x, + add}}{V_{z, + add}}

Eccentricity of Resulting Actions Including Additional Foundation Loads in x- and y-Direction

Determination of Effective Foundation Area

In ground failure design, only part of the actual base area is taken into account—the part where the resulting axial force acts in the center.

L^{'} = m a x (w_{x} - 2 \cdot |e_{x}|; w_{y} - 2 \cdot |e_{y}|)

B^{'} = m i n (w_{x} - 2 \cdot |e_{x}|; w_{y} - 2 \cdot |e_{y}|)

A^{'} = B^{'} \cdot L^{'}

Effective Foundation Length L', Foundation Width L', and Base A'

Existing Soil Pressure

This allows the existing soil pressure to be determined:

σ_{v o r h} = \frac{{V^{'}}_{d}}{A^{'}}

Design Value of Ground Failure Action

Design

The existing soil pressure is compared with the specified soil pressure:

η = \frac{{V^{'}}_{d} / A^{'}}{{R^{'}}_{d} / A^{'}} \leq 1.0

Design Criterion of Ground Failure

Bearing Resistance According to EN 1997-1 Annex D

When performing ground failure design according to EN 1997-1 [1], a comparison is made between the actions normal to the foundation level and the design values of the resistances. A calculation method according to [1] 6.5.2.2 is used. Annex D of the standard contains an informative example of the analytical determination of the bearing resistance.

Determination of Bearing Resistance for Drained Soil Conditions

The characteristic value of the bearing resistance can be determined according to [1] Annex D, Equation (D.2) for drained soil conditions as:

R_{k} / A^{'} = \underset{σ_{c}}{\underset{⏟}{c^{'} \cdot N_{c} \cdot b_{c} \cdot s_{c} \cdot i_{c}}} + \underset{σ_{q}}{\underset{⏟}{q^{'} \cdot N_{q} \cdot b_{q} \cdot s_{q} \cdot i_{q}}} + \underset{σ_{γ}}{\underset{⏟}{0.5 \cdot γ^{'} \cdot B^{'} \cdot N_{γ} \cdot b_{γ} \cdot s_{γ} \cdot i_{γ}}}

σ_c	Stress due to cohesion
σ_q	Stress due to foundation depth
σ_γ	Stress due to foundation width

Characteristic Value of Ground Failure Resistance According to EN 1997-1 Annex D (Drained)

Bearing capacity coefficients (N_c, N_q, N_γ): These factors are calculated taking into account the soil conditions and the friction angle.

N_{q} = e^{π \cdot \tan (φ_{d}^{'})} \cdot \tan^{2} (45 ° + φ_{d}^{'} / 2)

N_{c} = (N_{q} - 1) \cdot \cot (φ_{d}^{'})

N_{γ} = 2 \cdot (N_{q} - 1) \cdot \tan (φ_{d}^{'}) sofern φ^{'} / 2 (raue Sohlfläche)

Bearing Capacity Coefficients

Shape coefficients (s_c, s_q, s_γ): These take into account the geometry of the foundation, such as rectangular or square floor plans.

s_{q} = 1 + B^{'} / L^{'} \cdot \sin (φ_{d}^{'})

s_{c} = (s_{q} \cdot N_{q} - 1) / (N_{q} - 1)

s_{γ} = 1 - 0, 3 \cdot B^{'} / L^{'}

Shape Coefficient for Rectangular or Quadratic Ground Plan

Foundation base slope coefficients (b_c, b_q, b_γ): The foundation base slope coefficients take into account the slope of the foundation base α and are always calculated for the design of ground failure.