Library / Civil / CIV-57
Civil
Secondary compression after primary consolidation
Settlement from creep after primary consolidation, growing with the logarithm of time.
- Ref
- CIV-57
- Rev
- v1
- Field
- Civil
- Result
- S2 [m]
After primary consolidation clay continues to compress slowly by creep, at a rate that is constant per logarithmic cycle of time. The secondary compression index Cα is the void ratio decrease per log₁₀ cycle, so the settlement between times t1 and t2 is S2 = Hp Cα log₁₀(t2/t1)/(1 + ep). Each tenfold increase in time adds the same increment.
Settlement from creep after primary consolidation, growing with the logarithm of time. Hp and ep are the layer thickness and void ratio at the start of secondary compression, Cα is the void-ratio decrease per log₁₀ cycle of time, and times t1 and t2 are in the same units with t2 > t1 > 0.
Calculator
- Number of log cycles, log₁₀(t₂/t₁)1
- Strain per log cycle, Cα/(1 + e)0.01
- Settlement per log cycle0.03 m
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.
- Creep adds 30 mm between 10 and 100; each further tenfold increase in time adds 30 mm.
- Because the rate falls as 1/t, most creep settlement is spread over the first few log cycles, but it never fully stops in soft clay and peat.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Hp Thickness at the start of creep | 0.5 to 30 m | 0.005 | 0.3 | 0.295 | +10% | +10 % |
| C_α Secondary compression index | 0.001 to 0.1 | 0.002 | 0.2 | 0.198 | +10% | +10 % |
| t1 Reference time | 1 to 50 days | 0.009031 | 0.06 | 0.05097 | +10% | −4.14 % |
| t2 Later time | 60 to 1,000 days | 0.02334 | 0.06 | 0.03666 | +10% | +4.14 % |
| ep Void ratio at the start of creep | 0.3 to 3 | 0.01125 | 0.03462 | 0.02337 | +10% | −3.23 % |
Sweep of Later time
| Later time (days) | Secondary settlement (m) |
|---|---|
| 60 | 0.02334 |
| 177.5 | 0.03748 |
| 295 | 0.04409 |
| 412.5 | 0.04846 |
| 530 | 0.05173 |
| 647.5 | 0.05434 |
| 765 | 0.05651 |
| 882.5 | 0.05837 |
| 1,000 | 0.06 |
Sweep one variable
Variables and how each one contributes
Secondary settlement
What the equation gives you. Everything else feeds it.
Thickness at the start of creep
The layer thickness at the start of secondary compression, in m. Scales the settlement in direct proportion. Raising it by 10 % (to 3.3) moves the result by +10 %, from 0.03 to 0.033 m.
Secondary compression index
The secondary compression index, void ratio change per log₁₀ cycle of time. Scales the settlement in direct proportion. Raising it by 10 % (to 0.0165) moves the result by +10 %, from 0.03 to 0.033 m.
Later time
The later time, in the same units as t₁. A later time raises the settlement logarithmically. Raising it by 10 % (to 110) moves the result by +4.14 %, from 0.03 to 0.03124 m.
Reference time
The reference time at the start of secondary compression, in the same units. A later start lowers the settlement for the same end time. Raising it by 10 % (to 11) moves the result by −4.14 %, from 0.03 to 0.02876 m.
Void ratio at the start of creep
The void ratio at the start of secondary compression. A larger e raises (1 + e) and lowers the strain. Raising it by 10 % (to 0.55) moves the result by −3.23 %, from 0.03 to 0.02903 m.
Worked example with the values above
- Log cycles: log₁₀(100/10) = 1.
- Strain per cycle: Cα/(1 + ep) = 0.015 / 1.5 = 0.01.
- S₂ = 3 × 0.01 × 1 = 0.03 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