Settlement Calculator
Foundation Settlement · Primary Consolidation · Differential Settlement · Building Tilt
Settlement Calculator
Effective vertical stress at foundation level; typical 100–500 kPa
Deformation modulus; Sand: 10–50 MPa, Clay: 5–30 MPa, Rock: >100 MPa
Thickness of settlement zone (influence depth to bedrock or rigid layer)
Formulas & Fundamentals
Primary Settlement (Simplified Method):
s = (σ / E_s) · h
Settlement as product of stress ratio and layer thickness (linear-elastic soil mechanics)
s = (σ / E_s) · h
Settlement as product of stress ratio and layer thickness (linear-elastic soil mechanics)
Rearranged Formulas:
σ = (s · E_s) / h
E_s = (s · E_s) / h
h = (s · E_s) / σ
Calculate individual terms when others are known
σ = (s · E_s) / h
E_s = (s · E_s) / h
h = (s · E_s) / σ
Calculate individual terms when others are known
Differential Settlement & Building Tilt:
Δs = |s_B − s_A|
α = arctan(Δs / L) [rad]
α ≈ Δs / L [for small angles]
Tilt angle of structure due to unequal settlement
Δs = |s_B − s_A|
α = arctan(Δs / L) [rad]
α ≈ Δs / L [for small angles]
Tilt angle of structure due to unequal settlement
Symbol Table
| s | Foundation settlement [mm], [m] |
| σ | Effective vertical bearing stress [kPa] |
| E_s | Stiffness modulus (Deformation module) [kPa] |
| h | Thickness of settlement zone [m] |
| Δs | Differential settlement [mm] |
| α | Tilt angle [rad], [°] |
| L | Distance between foundations [m] |
Note: This calculation uses the linear-elastic model,
which assumes settlement proportional to stress. It provides a rough approximation.
For accurate forecasting, use settlement calculations per Edgeworth, Ménard, or numerical methods (FE).
Technical Background
Foundation Settlement
Settlement occurs when a foundation transmits load into the ground. Settlement is one of the most critical limit states for structures: it affects bearing capacity and serviceability. Unlike bearing capacity (failure), settlements are often reversible or permanent depending on soil type.
Types of Settlement
- Primary Settlement: Deformation from load-induced stress redistribution (dominant mechanism)
- Secondary Settlement: Time-dependent (creep); especially significant in clay
- Heave: Swelling from saturation (in cohesive soils); secondary effect
Stiffness Module E_s (Modulus of Elasticity)
| Soil Type | E_s [MPa] | Remark |
|---|---|---|
| Silt, soft material | 2–5 | Loosely compacted; large settlements expected |
| Clay, stiff | 5–15 | Overconsolidated; medium to high settlements |
| Sand, loose to medium dense | 10–30 | Depends on density and grain size |
| Gravel, compacted | 30–80 | High stiffness; good foundation material |
| Rock, unweathered | > 100 | Very stiff; minimal settlements |
Bearing Stress (Bearing Pressure)
Bearing stress is the effective normal stress under a foundation. It results from:
- σ = (Foundation Load) / (Foundation Area) − Buoyancy Effects
- Typical range: 100–500 kPa for building structures on massive foundations
- For deep foundations (piles): σ can be much higher (several MPa)
Allowable Settlement Limits
| Structure Type | s_allowable [mm] | Differential Δs [mm] | Tilt α [‰] |
|---|---|---|---|
| High-rise (Reinforced Concrete) | 50–100 | 10–20 | 5–10 |
| Machinery, Sensitive | 10–25 | 5–10 | 2–5 |
| Bridges | 25–75 | 10–30 | 5–10 |
| Roads / Pavements | 50–150 | 15–50 | 10–25 |
Disclaimer: This simplified calculation does not account for:
• Stress distribution in depth (Boussinesq, Westergaard)
• Time-dependent consolidation (primary vs. secondary)
• Nonlinear stiffness increase with depth
• Groundwater influence on effective stresses
For complex cases, use professional geotechnical software or consult a geotechnical engineer!
• Stress distribution in depth (Boussinesq, Westergaard)
• Time-dependent consolidation (primary vs. secondary)
• Nonlinear stiffness increase with depth
• Groundwater influence on effective stresses
For complex cases, use professional geotechnical software or consult a geotechnical engineer!