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Hedi Boukraa, M.Sc.

2024-07-11

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Bearing Resistance According to EN 1997-1, Annex D

In the 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 considering 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): They take into account the geometry of the foundation, such as rectangular or quadratic ground 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 inclination of the foundation base α and are always calculated for the ground failure design.

b_{q} = (1 - α \cdot \tan (φ_{d}^{'}))^{2}

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

b_{γ} = b_{q}

Base Coefficients

Slope coefficients (i_c, i_q, i_γ): They take into account the effects of inclined loads.

m_{B} = (2 + B^{'} / L^{'}) / (1 + B^{'} / L^{'})

m_{L} = (2 + L^{'} / B^{'}) / (1 + L^{'} / B^{'})

m = m_{L} \cdot \cos^{2} (ω) + m_{B} \cdot \sin^{2} (ω)

i_{q} = (1 - H_{d} / (V_{d} + A^{'} \cdot c_{d}^{'} \cdot \cot (φ_{d}^{'})))^{m}

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

i_{γ} = (1 - H_{d} / (V_{d} + A^{'} \cdot c_{d}^{'} \cdot \cot (φ_{d}^{'})))^{m + 1})

Slope Coefficients

Force Inclination Angle and Geometric Relations for Determining Slope Coefficients

Determination of Bearing Resistance for Undrained Soil Conditions

In the case of undrained soil conditions, the following formula is used:

R_{k} / A^{'} = (π + 2) \cdot c_{u} \cdot b_{c} \cdot s_{c} \cdot i_{c} + q

Characteristic Value of Bearing Resistance According to EN 1997-1 Annex D (Undrained)

Design

The design value of the ground failure action is compared with the design value of the bearing resistance:

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

Design Criterion of Ground Failure

Info

The actions (A), soil parameters (Material M), and resistances (Resistance R) need to be reduced by the partial safety factors 𝛾 according to [1] A.3.

References

European Committee for Standardization (CEN). (2014). Eurocode 7: Geotechnical Design – Part 1: General Rules, EN 1997-1:2014-03. Berlin: Beuth Verlag GmbH.

Parent Chapter

Ground Failure