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Civil
Effective stress in saturated soil
Stress carried by the soil grains after pore-water pressure is subtracted.
- Ref
- CIV-06
- Rev
- v1
- Field
- Civil
- Result
- σ′ [kPa]
σ′ effective stress, σ total normal stress, u pore-water pressure, ρ_w = 1000 kg/m³ water density, h the depth below the water table. Compression is positive.
In wet soil, the water carries some of the load. The grains only feel the total stress minus the water pressure, and it is this effective stress that controls the soil’s strength and settlement.
Calculator
- Pore-water pressure u49.03 kPa
- Effective ÷ total stress67.31 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Raising the water table lowers the effective stress and the soil’s shear strength. This is a leading cause of landslides and foundation failures after heavy rain.
- When pore pressure rises to equal the total stress, the effective stress is zero and the soil behaves like a liquid.
- The water pressure part is the same hydrostatic ρgh used for any still liquid.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| σ Total stress | 50 to 600 kPa | 0.9667 | 551 | 550 | +10% | +14.9 % |
| h Depth below the water table | 0.5 to 20 m | −46.13 | 145.1 | 191.2 | +10% | −4.86 % |
Sweep of Depth below the water table
| Depth below the water table (m) | Effective stress (kPa) |
|---|---|
| 0.5 | 145.1 |
| 2.938 | 121.2 |
| 5.375 | 97.29 |
| 7.813 | 73.39 |
| 10.25 | 49.48 |
| 12.69 | 25.58 |
| 15.13 | 1.674 |
| 17.56 | −22.23 |
| 20 | −46.13 |
Sweep one variable
Variables and how each one contributes
Effective stress
What the equation gives you. Everything else feeds it.
Total stress
Total vertical stress at the depth considered (soil weight plus surface loads). Directly adds to the effective stress.
Depth below the water table
Vertical distance from the water table down to the point. Raises pore pressure by about 9.8 kPa per metre, lowering the effective stress.
Worked example with the values above
- Pore pressure: u = ρwgh = 1000 × 9.80665 × 5 = 49,030 Pa = 49.03 kPa.
- Subtract from the total stress: 150 − 49.03.
- σ′ = 101 kPa.
Assumptions and limits
- Fully saturated soil with a hydrostatic water table (no seepage).
- Compression positive.
- Constant water density.
Common mistakes
- Forgetting to subtract pore pressure.
- Measuring depth from the surface instead of from the water table.
- Using this above the water table in unsaturated soil.
Statistics and uncertainty
The result is a difference between two similar-sized stresses, so errors in each are magnified. If u is 40% of σ, a 5% error in each term gives roughly a 9% error in σ′. Water table position is often the greatest uncertainty.
Where it is used
- Foundation and retaining-wall design.
- Slope stability.
- Trafficability and track design on wet ground.
Maths you need
- Hydrostatic pressure: u = ρgh
- Stress: force per unit area