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Hedi Boukraa, B.Sc.

2024-07-11

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Overview

Add-on Concrete Foundations

Theory Bases

External Stability - Geotechnical Checks
Internal Stability - Reinforced Concrete Checks
- Determination of the design moments
- Definition of reinforcement areas and design strips

Design Specifications

Types for Foundations
Concrete Foundations
Design properties of single foundations
- Foundation plate
  
  Main
  
  Geometry
  
  Reinforcement
  
  Concrete Cover
  
  Slab Reinforcement
  
  Mats
  
  Reinforcing Bars
  
  Mesh and rebars
  
  Soil Properties
  
  Geotechnical Configuration
  
  Concrete Configuration
Additional foundation loads

Design

Results

Documentation

Bearing resistance according to EN 1997-1 Annex D

In the ground failure design according to EN 1997-1 [1], the actions normal to the foundation base and the design values of the resistances are compared. Es kommt ein rechnerisches Verfahren gemäß [1] 6.5.2.2 zum Einsatz. In Anhang D der Norm findet sich ein informatives Beispiel für die analytische Ermittlung des Grundbruchwiderstandes.

Bestimmung des Grundbruchwiderstandes für konsolidierte Verhältnisse

Der charakteristische Wert des Grundbruchwiderstandes lässt sich nach [1] Anhang D, Gleichung (D.2) für konsolidierte Verhältnisse bestimmen zu:

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}^{'}) if φ^{'} / 2 (rough base area)

Bearing Capacity Coefficients

Formbeiwerte (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 relationships for determining inclination coefficients

Force Inclination Angle and Geometric Relationships for Determining Slope Coefficients

Bestimmung des Grundbruchwiderstandes für unkonsolidierten Verhältnisse

Im Fall von unkonsolidierten Verhältnissen wird folgende Formel verwendet:

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 check

Der Bemessungswert der Grundbrucheinwirkung wird mit dem Bemessungswert des Grundbruchwiderstands verglichen:

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

Design Criterion of Ground Failure

Info

Die Einwirkungen (Actions A), Bodenkenngrößen (Material M) und die Widerstände (Resistance R) sind mit den Teilsicherheitsbeiwerten 𝛾 gemäß [1] A.3 abzumindern.

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