Modulus of Subgrade Reaction (k)
The modulus of subgrade reaction is one of the most important parameters in foundation engineering and pavement design. It represents the soil stiffness and indicates how much settlement occurs under a given pressure.
General Formula
Where:
- k = Modulus of subgrade reaction (kN/m³)
- q = Soil pressure (kN/m²)
- δ = Settlement (m)
Methods for Determination of Modulus of Subgrade Reaction
| Method | Description |
|---|---|
| Plate Load Test Method | Determined directly from plate load test results |
| Elastic Settlement Method | Calculated using elastic theory |
| Correlation with CBR | Estimated using California Bearing Ratio |
| Empirical Correlations | Based on soil type and field experience |
| Winkler Spring Model | Used in beam and raft foundation analysis |
1. Plate Load Test Method
Plate Load Test Calculator
2. Elastic Settlement Method
Using elastic theory:
Where:
- Es = Modulus of elasticity of soil
- B = Width of footing
- μ = Poisson’s ratio
Elastic Settlement Calculator
3. Correlation with CBR Method
For pavement and subgrade design, modulus of subgrade reaction can be approximately estimated from CBR value.
CBR Correlation Calculator
4. Empirical Correlation Method
Approximate values of modulus of subgrade reaction based on soil type are given below:
| Soil Type | Approximate k (MN/m³) |
|---|---|
| Soft Clay | 5 – 15 |
| Medium Clay | 15 – 40 |
| Dense Sand | 40 – 120 |
| Gravel | 80 – 200 |
Empirical Soil Type Calculator
5. Winkler Spring Model
In Winkler’s idealization, soil is represented as independent springs. The pressure at any point is proportional to settlement at that point.
Where:
- p = Soil reaction pressure
- k = Modulus of subgrade reaction
- y = Deflection
Winkler Model Calculator
Engineering Applications
- Raft foundation design
- Flexible pavement analysis
- Machine foundation design
- Beam on elastic foundation analysis
- Settlement analysis
- Tank foundation design
Important Notes
- k is not a constant soil property.
- It depends on footing size and shape.
- Values obtained from small plates must be corrected for actual foundation size.
- Layered soils significantly affect the modulus value.
- Field tests provide more reliable values than empirical correlations.
Disclaimer
This calculator and article are prepared for educational and informational purposes only. The formulas and empirical correlations used are approximate and may vary depending upon soil conditions, testing procedures, and applicable design standards. Users should consult relevant codes, laboratory investigations, and professional engineers before practical implementation in real projects.
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