Settlement verification

The combination used for settlement check is ULS101 +1x[1 G]+0.3x[2 Q].

Appendix F recommends two methods for the calculation of the total settlement (based on the elasticity theory):

Simplified adjusted elasticity method

Vertical strains integration method

Simplified adjusted elasticity method

One layer soil (under the footing base level)

one layer soil

The settlement verification is done according to the simplified adjusted elasticity method defined in Annex F of EN1997-1.

SLS

According to EN 1997-1 §F.2(1), the total settlement of a foundation on cohesive or non-cohesive soil may be evaluated using elasticity theory and an equation of the form:

s = p x B x f/E_m

where:

E_m = the design value of the modulus of elasticity.

According to EN 1997-1 §F.2(3), If no useful settlement results, measured on neighboring similar structures in similar conditions are available, the design drained modulus E_m of the deforming stratum for drained conditions may be estimated from the results of laboratory or in-situ tests.

Note: The EC7 does not specify a method for determining the f coefficient, leaving the choice of the method to the engineers. The existing literature describes many methods, but they are all similar. Below is the method by ref 2.

f = the settlement coefficient

According to EN 1997-1 §F.2(2), The value of the settlement coefficient f depends on the shape and dimensions of the foundation area, the variation of stiffness with depth, the thickness of the compressible formation, Poisson's ratio, the distribution of the bearing pressure, and the point for which the settlement is calculated.

ν = Poisson’s ratio of soil

ν = 0.25

ω = shape and rigidity factor; for a rigid foundation the factor can be approximated by the equation:

B = footing width [m]

L = footing length [m]

Note: The above equation is valid for square, perpendicular, and continuous foundations. For circular foundations, ω = 0.79.

p = the bearing pressure, linearly distributed on the base of the foundation.

V = the characteristic vertical load (with foundation weight) [kN]

B, L = footing’s dimensions [m]

Allowable settlement s_max = 5 cm

s = 5.07 cm ≤ s_max = 5 cm

The condition is not satisfied.

Multi-layer soil

Multilayer soil

s = p × B × f/ E_m

where:

E_m = an average value of modulus of elasticity of the soil under the foundation, calculated for soil layers to level z_max

E_i = modulus of elasticity of layer “i”

h_i = “i” layer height

D_f = foundation bottom level

B = foundation width

z_max = 500 + 2.5 × 1500

z_max = 4250 mm

ν = an arithmetic average value of Poisson’s ratio of soil, calculated for soil layers to level z_max

ν_i – Poisson’s ratio of layer “i”

ν = 0.4

Allowable settlement s_max = 5 cm

s = 1.4 cm ≤ s_max = 5 cm

The condition is satisfied.

Vertical strains integration method

The settlement verification is done according to the vertical strains integration method, according to the statements from article 6.6.1 and appendix F of EN1997-1-1.

sls

The general approach draws on subdividing the subsoil bellow the footing bottom into layers of a different thickness. Vertical deformation of each layer is then computed – the settlement is then defined as a sum of partial settlements of individual layers within the influence zone (to the depth where the limit value of additional stresses (of effective overburden stress) is less than 20% [6.6.2 (6)]. Deformations below the influence zone are either zero or neglected.

where

S = total settlement

Δ_si = settlement of the ith layer

h_i = the thickness of the sublayer

M_i = The original (without relaxation effects taken into account), oedometric (obtained in the three-axial compression apparatus) compressibility modulus of the soil

σ_i = the average settlement in the middle height of each sublayer

Required data (Soil Profile dialog):

top ground level: 0.00m

foundation bottom level: 0.50 m

Required data

soil properties parameters:

- γ = unit weight of the soil

- ν = Poisson’s ratio of the soil

- E = modulus of elasticity of the soil

- M = oedometric compressibility modulus of the soil

Note 1: There is a relationship between the Young modulus and the oedometric compressibility modulus. It is expressed by the formula:

M E

Note 2: The unit weight of the soil is calculated taking into account the water level (buoyancy effect).

the footing geometry (width B and L, where B <= L)

the characteristic load acting on the bottom of the foundation

V₀ = V_k (external load) + V_f (weight of the foundation) + V_s (weight of the soil above foundation) = 247.59 kN

Stress calculation

To calculate settlement, i is required to calculate the vertical stress below the center of a rectangular area in many levels.

There are many theories on how to calculate the vertical stress (at level z) below the center of a rectangular area. Below is the relationship according to Ref 2, Braja M. Das; Principles of Foundation Engineering; Seventh Edition; Global Engineering 2011, p 230.

Where:

z = level, where z = 0 is at the bottom of foundation level

q = uniform distributed stress at the level of foundation base

q = q₀ if the stress is calculated from the external load

q = q_0s if the stress is calculated from soil existing before soil excavation

Note: To easily verify the above equations, an alternative simplified “2:1” method to obtain stress in the soil at level z may be used.

Steps:

Step 1. Divide the soil under foundation into sublayers; the height of each sublayer h_i should be not greater than:

0.5 * B (B is the smaller dimension of a foundation)

0.5 m

thickness of a soil layer

Step 2. Assign soil parameters for each sublayer:

Step 3. Calculate

Step 4. Calculate the stress at the level of foundation base caused by soil existing before excavation (as a sum of weight from each soil layer calculated from top ground level to bottom of foundation level).

Step 5. Calculate at the bottom of each sublayer the original stress induced by the soil (starting from the top ground level), and the limit value for that sublayer.

step 5

Step 6. Calculate at the center and at the bottom height of each sublayer the average vertical stresses caused by external loads (by using the equations described in the Stress calculation paragraph).

σ_bp = stress at the bottom of the sublayer

q = q₀

z = sublayer bottom

σ_mp = stress at the middle height of the sublayer

q = q0

z = sublayer middle height

Step 7. Calculate at the center and the bottom height of each sublayer the average vertical stress caused by the soil existing before excavation (by using the equations described in the "Stress calculation" paragraph).

σ_bs = stress at the bottom of the sublayer

q = q0s

z = sublayer bottom

σ_ms = stress at the middle height of the sublayer

q = q0s

z = sublayer middle height

Step 8. Calculate the additional stresses of the soil sublayer, as a difference between the stresses caused by the external load and the original stresses.

σ_mi = max (σ_mp– σ_ms; 0)

σ_bi = max (σ_bp– σ_bs; 0)

Step 9. Calculations performed on the basis of the soil properties

Step 10. Calculations of the influence zone (the depth z_max where the value of additional stress is equal to 20% of original soil stress)

z_max is a level, where σ_lim= σ_bi

Note: The limit layer is a layer where the limit value of additional stress σ_lim is equal to or bigger than the additional stress σ_bi.

Step 11. Calculation of the total settlement of the soil as a sum of the settlement values of sublayer, started from the bottom of the foundation to the layer for which the bottom level is = z_max.

step 11

The table below shows how the software calculates the total settlement using the vertical strains integration method:

Verification

According to Eurocode 7, 2.4.8 (1): E_d ≤ C_d

Therefore, for settlement, it takes the form: S ≤ S_max

where:

S = total settlement

S_max = the limit value

41.75 mm ≤ 50 mm

Related topics

Theoretical background

Calculations

Errors and warning