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Hedi Boukraa, M.Sc.

2024-07-11

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Concrete Foundations Add-on

Theoretical Principles

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Design Properties of Single Foundations

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Documentation

Ground Failure

For the ground failure design, you can either specify user-defined values for the allowable soil stress or calculate the ground failure resistance according to EN 1997-1, taking into account the soil layers and soil properties.

User-Defined Values for Allowable Soil Stress

This type of design allows you to compare the existing soil pressure with the specified allowable soil stress.

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.