Online Manuals RFEM 6 / RSTAB 9 | Concrete Foundation

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Ann-Kathrin Dannwerth, B.Sc.

2024-07-11

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Overview

Add-on Concrete Foundation

Theoretical Principles

Design Specifications

Design Properties of Single Foundations

Design

Results

Documentation

Load Capacity of Soil

The bearing capacity of the subsoil can be verified in different ways depending on the standard. In the Eurocode, the verification is carried out by comparing design values of actions and resistances (bearing resistance design), while North American standards often use allowable soil pressures. Both approaches describe the same structural behavior of the subsoil but differ in terms of safety concept and design format.

EN 1997-1: Bearing resistance design

In the bearing resistance design according to EN 1997-1, the resistance can be determined either via specified allowable soil pressures or by calculating the bearing resistance considering the soil layers and soil parameters.

Verification with specified allowable soil pressure

In this verification type, the existing soil pressure is compared with the specified allowable soil pressure. The value of the allowable bearing capacity σ_a is defined in the Geotechnical Design Configurations of the "Concrete Foundations" add-on in the "Allowable Soil Pressure" section.

Determination of stresses in the soil joint and the 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 at the center of the foundation base 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 the effective foundation area

In the bearing resistance design, only a part of the actual base area is considered – the part where the resulting axial force is applied at 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

Verification

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

Verification with calculated bearing resistance (Annex D)

In the bearing resistance design according to EN 1997-1 [1], a comparison is made between the actions perpendicular to the foundation base and the design values of the resistances. A computational method according to [1] 6.5.2.2 is used. Annex D of the standard provides an informative example for the analytical determination of the bearing resistance.

Determination of the bearing resistance for drained conditions

The characteristic value of the bearing resistance can be determined according to [1] Annex D, Equation (D.2) for drained 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 factors (N_c, N_q, N_γ): These factors are calculated considering the soil conditions and the angle of friction.

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 factors (s_c, s_q, s_γ): These consider the geometry of the foundation, such as rectangular or square base areas.

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

Base inclination factors (b_c, b_q, b_γ): The base inclination factors consider the inclination of the foundation base α and are generally calculated for the bearing resistance 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): These consider the influences 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 the bearing resistance for undrained conditions

In the case of undrained 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)

Verification

The design value of the bearing 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 (Actions A), soil parameters (Material M), and the resistances (Resistance R) shall be reduced using the partial safety factors 𝛾 according to [1] A.3.

IBC 2021 / ACI 318-19 (ASD): Soil pressure

Purpose of the verification

The soil pressure verification checks whether the contact stresses transferred from the foundation to the subsoil do not exceed the allowable soil pressure. The stress distribution under the foundation is assumed to be linear in the case of combined stresses from axial force and bending moment.

Stress distribution

The soil contact stresses are determined from the axial force and the bending moment at the foundation base:

q_{u} = \frac{P_{z}}{A} \pm \frac{M}{S}

P_z	entire vertical load on the foundation [kip]
A	Foundation area [ft²]
M	bending moment at the foundation base [kipft]
S	Section modulus of the foundation area [ft³]

Soil pressure

Verification

The resulting soil contact stresses must not exceed the allowable soil pressure. The allowable soil pressure σ_a can be defined in the geotechnical design configuration of the Concrete Foundations add-on.

Utilization ratio

η = \frac{q_{u}}{σ_{a}}

Utilization - Soil pressure

Software configuration

The allowable soil pressure σ_a is defined in the geotechnical design configuration of the Concrete Foundations add-on. All vertical loads acting on the foundation are adopted from the defined load cases.

Parent Chapter

External stability - Geotechnical design