 # Settlement Calculation of Single Foundations According to DIN 4019 in RF-/FOUNDATION Pro

### Technical Article

For the serviceability limit state design according to Section 6.6 of Eurocode EN 1997-1, settlement has to be calculated for spread foundations. RF-/FOUNDATION Pro allows you to perform the settlement calculation for a single foundation. For this, you can select between elastic or solid foundation. By defining a soil profile, it is possible to consider several soil layers under the foundation base. The results of the settlement, foundation tilting, and vertical soil contact stress distribution are displayed graphically and in tables to provide a quick and clear overview of the calculation performed. In addition to the design of the foundation settlement in RF-/FOUNDATION Pro, the structural analysis determines the representative spring constants for the support and can be exported to the structural model of RFEM or RSTAB.

#### General

The total settlement s ges in the soil due to structural loads is composed of the components of the immediate settlement s 0 , the consolidation settlement s 1, and the time-dependent creep setting s 2 .

s ges = s 0 + s 1 + s 2 = s + s 2

According to DIN 4019  , the settlement "s" determined in the method described below includes the two settlement components from the immediate settlement and the consolidation settlement. Figure 1 shows the time-dependent settlement components graphically. Time t 0 represents the time until complete consolidation.

#### Settlement calculation using the vertical stresses in the soil

The settlement method described below is based on the model of the elastic, isotropic, homogeneous half-space. This calculation approach is also suitable for settling a subsoil with several layers.

To determine the settlement, the soil is divided into sub-layers and the vertical soil stresses below the foundation are determined. Based on the theory of elasticity, the specific settlements s i of the individual partial layers are then determined, which are then added together to form an overall settlement s.

$$\mathrm s\;=\;{\mathrm{Σs}}_\mathrm i\;=\;\mathrm\Sigma(\frac{{\mathrm{Δσ}}_{\mathrm z,\mathrm i}}{{\mathrm E}_{\mathrm S,\mathrm i}}\;\cdot\;{\mathrm{Δz}}_\mathrm i)\;\mathrm{nach}\;\mathrm{DIN}\;4019\;\lbrack2\rbrack$$
where
Δσ z, i = settling additional stress in sublayer i
E S, i = stiffness modulus of sublayer i
Δz i = thickness of partial layer i

#### Determination of vertical soil stresses

For the settlement calculation, the vertical soil stresses must first be determined. As a basis for the stress and settlement calculation, a model of the elastic-isotropic half-space is assumed. The respective stresses are differentiated according to their cause as follows:
σ z = stress due to structural load
σ z, i = stress due to structural load in partial layer i

The vertical soil stresses σ z due to the additional load in the depth z can be calculated on the basis of the approach of Boussinesq  and the superposition principle.

According to Boussinesq, the vertical stress in the soil is calculated as shown in Figure 2 due to a perpendicular single load V on the surface of the half-space.

The vertical soil stresses in the depth z below the corner point of a uniformly "flaccid" perpendicular rectangular stress σ z can be determined according to Figure 3.

The stress influence coefficient i R can also be taken from the corresponding nomograms, for example from DIN 4019 .

By using the methods mentioned above, a vertical soil stress distribution is created in the soil under the foundation, which is shown symbolically in Figure 4.

#### Depth of settlement influence

For the calculation of the settlement, the additional stresses due to soil loading up to the influence depth of the settlement, also called the limit depth, have to be considered. According to EN 1997-1  and DIN 4019 , it is allowed to assume the depth of influence of settlement at a depth z, where the vertical additional stresses from the settlement effective load amount to 20% of the effective vertical initial stresses in the soil.

#### Reference

  Eurocode 7 - Design, Calculation and Design in Geotechnical Engineering - Part 1: General rules; EN 1997-1: 2009  Soil - Settlement calculations; DIN 4019: 2015-05  Boussinesq, J .: Application of the potential according to the equilibrium et du mouvement des solid élastiques… Paris: Gauthier-Villars, 1885. 