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Overconsolidated clay settlement through preconsolidation stress
Settlement of a clay layer whose preconsolidation stress σ′c lies between the initial σ′0 and final σ′f effective stresses: recompression (index Cr) up to σ′c, then virgin compression (index Cc) beyond it.
- Ref
- CIV-54
- Rev
- v1
- Field
- Civil
- Result
- S [m]
Overconsolidated clay is stiff up to its preconsolidation stress σ′c, the largest stress it has previously carried. Below σ′c it follows the recompression line (index Cr, small); beyond it, the virgin line (index Cc, larger). The settlement is the sum of the two parts, each as H/(1 + e0) × C × log₁₀ of its stress ratio. If loading ends below σ′c, only the recompression term applies, ending at σ′f.
Settlement of a clay layer whose preconsolidation stress σ′c lies between the initial σ′0 and final σ′f effective stresses: recompression (index Cr) up to σ′c, then virgin compression (index Cc) beyond it. If loading ends below σ′c use only the recompression term with σ′f as its endpoint.
Calculator
- Recompression part, H·Cr·log(σ′c/σ′0)/(1 + e0)0.0258 m
- Virgin-compression part, H·Cc·log(σ′f/σ′c)/(1 + e0)0.1548 m
- Overconsolidation ratio, σ′c/σ′02
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 settlement is 180.6 mm: 14.29 % from recompression and 85.71 % from virgin compression.
- Using the virgin line for the whole range would give 309.6 mm, 1.71 times too much.
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 | 0.0301 | 1.806 | 1.776 | +10% | +10 % |
| Cc Compression index | 0.05 to 1.5 | 0.05161 | 0.7999 | 0.7483 | +10% | +8.57 % |
| σ′f Final effective stress | 100,000 to 1,000,000 Pa | 0.0258 | 0.5401 | 0.5143 | +10% | +11.8 % |
| σ′c Preconsolidation stress | 50,000 to 200,000 Pa | 0.05161 | 0.3096 | 0.258 | +10% | −9.82 % |
| e0 Initial void ratio | 0.3 to 3 | 0.07902 | 0.2431 | 0.1641 | +10% | −4.11 % |
| Cr Recompression index | 0.005 to 0.3 | 0.1574 | 0.3096 | 0.1522 | +10% | +1.43 % |
| σ′0 Initial effective stress | 10,000 to 100,000 Pa | 0.1548 | 0.2405 | 0.08571 | +10% | −1.96 % |
Sweep of Preconsolidation stress
| Preconsolidation stress (Pa) | Consolidation settlement (m) |
|---|---|
| 50,000 | 0.3096 |
| 68,750 | 0.2504 |
| 87,500 | 0.2055 |
| 106,300 | 0.1693 |
| 125,000 | 0.1391 |
| 143,800 | 0.1131 |
| 162,500 | 0.09025 |
| 181,300 | 0.06993 |
| 200,000 | 0.05161 |
Sweep one variable
Variables and how each one contributes
Consolidation settlement
What the equation gives you. Everything else feeds it.
Layer thickness
The initial layer thickness, in m. Scales the settlement in direct proportion. Raising it by 10 % (to 3.3) moves the result by +10 %, from 0.1806 to 0.1987 m.
Recompression index
The recompression index, usually 0.1 to 0.2 of Cc. Scales the recompression part of the settlement. Raising it by 10 % (to 0.055) moves the result by +1.43 %, from 0.1806 to 0.1832 m.
Compression index
The compression index along the virgin line. Scales the virgin-compression part of the settlement. Raising it by 10 % (to 0.33) moves the result by +8.57 %, from 0.1806 to 0.1961 m.
Initial effective stress
The initial vertical effective stress, in Pa. A higher value lowers the recompression part. Raising it by 10 % (to 55,000) moves the result by −1.96 %, from 0.1806 to 0.1771 m.
Preconsolidation stress
The preconsolidation stress, in Pa (between σ′0 and σ′f). A higher preconsolidation stress moves the break point and shifts settlement to the cheaper recompression branch. Raising it by 10 % (to 110,000) moves the result by −9.82 %, from 0.1806 to 0.1629 m.
Final effective stress
The final vertical effective stress, in Pa. A higher final stress raises the virgin-compression part. Raising it by 10 % (to 220,000) moves the result by +11.8 %, from 0.1806 to 0.2019 m.
Initial void ratio
The initial void ratio. A larger e0 lowers the strain through the 1 + e0 divisor. Raising it by 10 % (to 0.825) moves the result by −4.11 %, from 0.1806 to 0.1732 m.
Worked example with the values above
- Recompression: H Cr log₁₀(σ′c/σ′0)/(1 + e0) = 3 × 0.05 × 0.30103 / 1.75 = 0.0258026 m.
- Virgin: H Cc log₁₀(σ′f/σ′c)/(1 + e0) = 3 × 0.3 × 0.30103 / 1.75 = 0.154815 m.
- S = 0.180618 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