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Civil
Time to 90 percent average primary consolidation
Time for a clay layer to reach 90 % average primary consolidation by Terzaghi’s one-dimensional solution, for an instantaneous load with uniform initial excess pore pressure.
- Ref
- CIV-56
- Rev
- v1
- Field
- Civil
- Result
- t90 [s]
Terzaghi’s theory of one-dimensional consolidation gives the average degree of consolidation as a function of the time factor Tv = cv t/Hdr². Ninety per cent is reached at Tv = 0.848, so t90 = 0.848 Hdr²/cv. Doubling the drainage path quadruples the time. For drainage at both faces Hdr is half the layer thickness, and for one face it is the full thickness.
Time for a clay layer to reach 90 % average primary consolidation by Terzaghi’s one-dimensional solution, for an instantaneous load with uniform initial excess pore pressure. Hdr is the longest drainage path: half the thickness with drainage at both faces, the full thickness with one. cv is the coefficient of consolidation.
Calculator
- Time in days392.6 days
- Time in years1.075 years
- Time with the drainage path doubled4.299 years
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 reaches 90 % consolidation after 392.6 days (1.07 years).
- If drainage were only at one face the path would double and the time would rise fourfold to 4.3 years, so drains and sand layers can shorten construction greatly.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Hdr Longest drainage path | 0.1 to 20 m | 84,800 | 3.392e9 | 3.392e9 | +10% | +21 % |
| cv Coefficient of consolidation | 1e-9 to 1e-5 m²/s | 339,200 | 3.392e9 | 3.392e9 | +10% | −9.09 % |
Sweep of Coefficient of consolidation
| Coefficient of consolidation (m²/s) | Time to 90 % consolidation (s) |
|---|---|
| 1e-9 | 3.392e9 |
| 3.162e-9 | 1.073e9 |
| 1e-8 | 3.392e8 |
| 3.162e-8 | 1.073e8 |
| 1e-7 | 3.392e7 |
| 3.162e-7 | 1.073e7 |
| 1e-6 | 3,392,000 |
| 3.162e-6 | 1,073,000 |
| 1e-5 | 339,200 |
Sweep one variable
Variables and how each one contributes
Time to 90 % consolidation
What the equation gives you. Everything else feeds it.
Longest drainage path
The longest drainage path, in m. Raises the time with the square of the path length. Raising it by 10 % (to 2.2) moves the result by +21 %, from 3.392×107 to 4.104×107 s.
Coefficient of consolidation
The coefficient of consolidation, in m²/s. A higher cv gives faster consolidation, in inverse proportion. Raising it by 10 % (to 1.1×10−7) moves the result by −9.09 %, from 3.392×107 to 3.084×107 s.
Worked example with the values above
- Hdr² = 4 m².
- Time factor × Hdr² = 0.848 × 4 = 3.392 m².
- t90 = 3.392 / 1×10−7 = 3.392×107 s.
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 the full layer thickness as the drainage path when both faces drain.
- Using a laboratory cv for the field without allowing for sand lenses, which speed up drainage.
- Mixing units: cv in m²/s with times in days.
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