# Settlements (Retaining Wall)

# General

If the settlement module is available settlements is calculated for all load cases according to [5] 2.6 and 3.53.

Calculations of settlements shall include both immediate and delayed settlements.

The depth of the compressible soil layer to be considered may normally be taken as the depth at which the effective vertical stress due to the foundation load is 20% of the effective overburden stress.

If the ratio between the bearing capacity of the ground to the applied serviceability loading is less than 2 the calculations should also take account of creep:

S_{d} > R_{d} / 2

# Cohesionless soil

For cohesionless soil the calculation can be performed with regard to peak pressure sounding where the characteristic peak pressure q_{ck} is obtained or with regard to estimated modules or dilatometer results. If the latter method is used for settlement calculations of small footings relatively the soil depth the elasticity modulus E is recommended as it includes the effect of lateral extension while in other cases the compression modulus M can be used. The safety factor γ_{R,d} will consider uncertainties in the calculation model.

**Peak pressure sounding**

The settlement s is according to De Beer (1965) calculated layer wise as:

- s = γ
_{R,s}Σ 2.3 / C_{d}log ((σ_{0d}' + Δσ_{d}') / σ_{od}') Δ z - C
_{d}= 1,5 q_{cd}/σ_{od}' - q
_{d}is the peak pressure q_{d}= q_{k}/ γ_{M} - σ
_{od}' is the effective pressure at the middle of each layer, - σ
_{od}' = γ (d + z) above ground water level, - σ
_{od}' = γ (d + h) + γ'(z – h) below ground water level, - Δσ
_{d}' is the vertical stress increase and is calculated with the 2:1 method, - Δσ
_{d}' = Δ q / ((1 + z / B') (1 + z / L')) - Δq is the load at ground level.

**Estimated modules**

The settlement s is calculated layer wise as:

- s = γ
_{R,s}(Δ σ_{d}' / Ε_{d}) Δ z - Δ σ
_{d}´ is the vertical stress increase and is calculated with the 2:1 method - Δσ
_{d}´ = Δq / ((1 + z / B') (1 + z / L')) - Δq is the load at ground level
- E
_{d}is the E-modulus E_{d}= E_{k}/ γ_{M}or the compression modulus M_{d}= M_{k}/ γ_{M}.

# Cohesive soil

For cohesive soil the calculation can be performed with regard to soil conditions based on laboratory tests where consolidation pressure and compression properties are evaluated.

The safety factor γ_{R,ds} will consider uncertainties in the calculation model.

The settlement s is calculated with regard to the compression modulus M.

Until the consolidation pressure reaches σ_{c}' the compression modulus is constant with the value M_{o}. The compression modulus will then fall to a lower value M_{L} which will be constant until the pressure reached σ_{L}'. If the load is further increased the compression modulus M will also increase as seen above.

The settlement s is calculated layerwise as:

- s = γ
_{R,s}Σ (Δσ'/ Μ) Δz - 0 < σ
_{d}'< σ_{cd}' - s = γ
_{R,s}Σ (σ_{d}' - σ_{od}') / Μ_{o}Δz - σ
_{cd}' < σ_{d}' < σ_{Ld}' - s = γ
_{R,s}Σ [(σ_{cd}' - σ_{od}') / M_{o}+ (σ_{d}' - σ_{cd}') / Μ_{L}] Δz - σ
_{d}' > σ_{Ld}' - s = γ
_{R,s}Σ [(σ_{cd}'-σ_{od}')/M_{o}+(σ_{Ld}'-σ_{cd}')/Μ_{L}+1/M' ln ((σ_{d}'-σ_{Ld}') M'/M_{L}+1)] Δz - σ
_{d}' = σ_{0d}'+ Δσ_{d}' = σ_{0d}'+ Δq / ((1 + z / B') (1 + z / L'))- σ
_{od}' is the effective pressure at the middle of each layer - σ
_{od}' = γ (d + z) above ground water level - σ
_{od}' = γ (d + h) + γ'(z – h) below ground water level - Δσ
_{d}' is the vertical stress increase and is calculated with the 2:1 method - Δq is the load at ground level

- σ

# Medium soil

With medium soil means soil types where both un drained and drained analysis has to be made e.g. silt and clay moraine. The settlement is calculated with regard to estimated modules or dilatometer results. For settlement calculations of small footings relatively the soil depth the elasticity modulus E is recommended as it includes the effect of lateral extension while in other cases the compression modulus M can be used.

The safety factor γ_{R,s} will consider uncertainties in the calculation model.

The settlement s is calculated layerwise as:

- s = γ
_{R,s}((σ_{d}' - σ_{od}') / Μ_{d}) Δz - Δ σ
_{d}' is the vertical stress increase and is calculated with the 2:1 method - σ
_{d}' = σ_{0d}' + Δ σ_{d}'= σ_{0d}' + Δq /((1 + z / B') (1 + z / L')) - Δq is the load at ground level
- σ
_{od}' is the effective pressure at the middle of each layer as above - M
_{d}is the compression modulus M_{d}= M_{k}/ γ_{M}or the E-modulus E_{d}= E_{k}/ γ_{M}