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001920

2024-11-26

Calculating Bearing Resistance According to EN 1997-1: Methods, Formulas, & Examples

The Concrete Foundations add-on for RFEM 6 allows you to perform geotechnical design checks according to EN 1997-1. In particular, this includes the ground failure design, which analyzes the allowable soil pressures on the basis of drained conditions according to Annex D.4 of the standard. In the add-on, the calculation takes into account the soil parameters, foundation geometry, and loads.

Entering Basic Data

The ground failure design is based on the specification of a soil profile that describes the governing layers and their properties. These include:

Specific weight γ_k

Angle of internal friction φ^'_k

Cohesion c^'_k

These data are taken from a stored soil library, but can also be defined manually. The data are entered in the corresponding window that allows for a clear separation between the different soil layers.

Based on the input data, the program automatically calculates the design values that are used in the design:

Specific weight γ_d = γ_k/γ_γ

Angle of internal friction φ^'_d = arctan(tan(φ^'[sub>k) / γ^'_φ)

Cohesion c^‘_d = c^‘_k / γ^‘_c

These values are used as a basis for further calculations in the design.

Foundation Dimensions and Loads

The design loads, including additional foundation loads, are calculated automatically:

Vertical load V_z,+add (corresponds to V_d)

Horizontal load H_x,+add and H_y,+add

Bending moment at the support M_x,+add,SA and M_y,+add,SA

Based on these design loads, RFEM 6 determines the resulting eccentricities e_x and e_y of the actions.

Info

In Method 2*, the eccentricities are not calculated on the basis of the design loads, but with the corresponding characteristic actions (including the additional foundation loads).

The eccentricities are calculated as follows:

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

Based on the entered foundation dimensions w_x, w_y, and t, the program calculates the effective soil length L^', soil width B^', and base area A^':

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'

Visualisierung der rechnerischen Sohllänge und -Breite für Geotechnik

Visualisierung der rechnerischen Sohllänge, -Breite und Fläche

Calculation of Parameters for Ground Failure Resistance

Based on the entered soil parameters and the foundation dimensions, the program determines the following parameters for the calculation of the bearing resistance:

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): Thus, the geometry of the foundation (such as rectangular or square floor plans) is taken into account.

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

The program assumes a horizontal foundation base with α = 0°, whereby the slope coefficients of the foundation base are set to b_q = b_c = b_γ = 1 by default.

This simplifies the calculations and covers the typical applications for horizontal foundation bases.

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

In this, H_d is the resulting horizontal action of the XY plane.

Info

In Method 2*, the slope coefficients are not calculated on the basis of the design loads (H_d and V_d), but with the corresponding characteristic actions (including the additional foundation loads).

Calculation of Bearing Resistance

The characteristic ground failure resistance is calculated according to the general equation described in EN 1997‑1, Annex D:

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)

where q^' = γ₁ ⋅ d

The soil parameters are calculated in drained form, taking into account the relevant safety factors. The results are shown in an output window and can be checked and adjusted.

Allowable Soil Pressure

The calculation of the design value of the ground failure resistance is carried out by applying a partial safety factor γ_R,v that is specified according to the selected National Annex:

\frac{R_{d}}{A^{'}} = \frac{R_{k} / A^{'}}{γ_{R, v}}

Design Value of Allowable Soil Pressure

Design check

The add-on compares the existing soil pressure with the allowable design value. The result is output as a design criterion so that it is immediately clear whether the design check has been fulfilled.

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

Design Criterion of Ground Failure

The design is performed exclusively using the design actions and resistances.

Info

The partial safety factors to be applied are strongly dependent on the methods and can have a considerable impact on the design ratio μ. See the Knowledge Base article:

KB | Design Methods for Determining Ground Failure Resistance According to Eurocode 7 (EN 1997-1)

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