Library / Civil / CIV-53
Civil
Normally consolidated clay settlement
One-dimensional primary consolidation settlement of a clay layer of thickness H that is on its virgin compression line.
- Ref
- CIV-53
- Rev
- v1
- Field
- Civil
- Result
- S [m]
A clay layer on its virgin compression line shortens by an amount proportional to the void ratio change. With a compression index Cc, the void ratio falls by Cc log₁₀(σ′f/σ′0), and the strain is that divided by (1 + e0). Multiplying by the layer thickness gives the settlement S = H Cc log₁₀(σ′f/σ′0)/(1 + e0). The log relationship means each doubling of stress gives the same extra settlement.
One-dimensional primary consolidation settlement of a clay layer of thickness H that is on its virgin compression line. Cc is the compression index from a base-10 void-ratio against stress plot, e0 the initial void ratio, and σ′0 and σ′f representative initial and final vertical effective stresses with σ′f ≥ σ′0 > 0.
Calculator
- Stress ratio, σ′f/σ′02
- Void ratio change, Cc·log₁₀(σ′f/σ′0)0.09031
- Vertical strain, ΔS/H0.05017
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.
- The layer settles 200.7 mm, a strain of 5.017 %.
- Each doubling of effective stress adds 200.7 mm, so the settlement depends on the stress ratio, not on the stress increase itself.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| H Layer thickness | 0.5 to 30 m | 0.02509 | 1.505 | 1.48 | +10% | +10 % |
| Cc Compression index | 0.05 to 1.5 | 0.03345 | 1.003 | 0.97 | +10% | +10 % |
| σ′f Final effective stress | 100,000 to 2,000,000 Pa | 0 | 0.8674 | 0.8674 | +10% | +13.8 % |
| σ′0 Initial effective stress | 10,000 to 200,000 Pa | 0 | 0.8674 | 0.8674 | +10% | −13.8 % |
| e0 Initial void ratio | 0.3 to 3 | 0.09031 | 0.2779 | 0.1876 | +10% | −4.26 % |
Sweep of Final effective stress
| Final effective stress (Pa) | Consolidation settlement (m) |
|---|---|
| 100,000 | 0 |
| 337,500 | 0.3522 |
| 575,000 | 0.5064 |
| 812,500 | 0.6065 |
| 1,050,000 | 0.6808 |
| 1,288,000 | 0.7398 |
| 1,525,000 | 0.7888 |
| 1,763,000 | 0.8308 |
| 2,000,000 | 0.8674 |
Sweep one variable
Variables and how each one contributes
Consolidation settlement
What the equation gives you. Everything else feeds it.
Layer thickness
The initial thickness of the clay layer, in m. Scales the settlement in direct proportion. Raising it by 10 % (to 4.4) moves the result by +10 %, from 0.2007 to 0.2208 m.
Compression index
The compression index, from a base-10 void ratio against log stress plot. Scales the settlement in direct proportion. Raising it by 10 % (to 0.33) moves the result by +10 %, from 0.2007 to 0.2208 m.
Final effective stress
The final vertical effective stress at the middle of the layer, in Pa. A larger final stress raises the settlement, but with diminishing returns (log). Raising it by 10 % (to 220,000) moves the result by +13.8 %, from 0.2007 to 0.2283 m.
Initial effective stress
The initial vertical effective stress, in Pa. A higher starting stress lowers the settlement for the same final stress. Raising it by 10 % (to 110,000) moves the result by −13.8 %, from 0.2007 to 0.1731 m.
Initial void ratio
The initial void ratio. A looser clay (higher e0) has a larger (1 + e0) divisor and settles less per unit of Cc. Raising it by 10 % (to 0.88) moves the result by −4.26 %, from 0.2007 to 0.1921 m.
Worked example with the values above
- Stress ratio: 200,000 / 100,000 = 2; log₁₀ = 0.30103.
- Strain: Cc log / (1 + e0) = 0.3 × 0.30103 / 1.8 = 0.0501717.
- S = H × strain = 4 × 0.0501717 = 0.200687 m.
Assumptions and limits
- One-dimensional compression with a representative layer, and effective stresses throughout.
- Primary consolidation by Terzaghi theory with a uniform initial excess pore pressure.
Common mistakes
- Using natural logarithms with a base-10 compression index.
- Using total instead of effective stresses.
- Using the layer thickness instead of the drainage path for the consolidation time.
Statistics and uncertainty
Settlement predictions typically agree with field values only to within a factor of 1.5 to 2, and the time of consolidation can be out by an order of magnitude because the field coefficient of consolidation differs from the laboratory one. Observe the settlement during construction and update the prediction.
Where it is used
- Predicting settlement of embankments and foundations on clay.
- Planning how long a surcharge must stay in place.
Maths you need
- Void ratio: volume of voids divided by volume of solids
- Compression index: void ratio change per log₁₀ cycle of effective stress
- Preconsolidation stress: the largest past effective stress the clay has carried