Hong Life CalculatorsUnderstanding the consolidation settlement calculator — concept and principle
When a saturated clay layer is loaded by a building, embankment or fill, water is slowly squeezed out of its pores and the ground sinks. This calculator estimates the final primary consolidation settlement of a normally consolidated clay layer and the time needed to reach 90% of that settlement. It is used early in design to judge whether preloading, drains or deep foundations may be needed.
How it is calculated
- Final settlement: S = Cc·H/(1 + e₀)·log₁₀((σ′₀ + Δσ)/σ′₀), shown in mm.
- Time to 90%: t₉₀ = 0.848·H_dr²/c_v, where H_dr = H/2 for double drainage and H_dr = H for single drainage.
Cc is the compression index, e₀ the initial void ratio, H the layer thickness (m), σ′₀ the initial effective stress at mid-layer (kPa), Δσ the added stress (kPa) and c_v the coefficient of consolidation (m²/year).
The principle
In a normally consolidated clay, the void ratio falls in a straight line when plotted against the logarithm of effective stress; the slope of that line is Cc. The drop in void ratio is Δe = Cc·log(σ′₁/σ′₀), and because a soil element of height H contains solids of height H/(1 + e₀), the change in height is H·Δe/(1 + e₀). Timing comes from Terzaghi's one-dimensional theory, in which excess pore pressure dissipates like heat diffusing out of a slab; 90% average consolidation corresponds to time factor T_v = 0.848. Because time scales with the square of the drainage path, halving H_dr cuts the time by a factor of four.
Worked example
- Inputs: Cc = 0.3, e₀ = 0.9, H = 4 m, σ′₀ = 80 kPa, Δσ = 50 kPa, c_v = 2 m²/year, double drainage.
- Cc·H/(1 + e₀) = 0.3 × 4 / 1.9 = 0.6316 m.
- log₁₀(130/80) = log₁₀(1.625) = 0.2109.
- S = 0.6316 × 0.2109 = 0.1332 m, so final settlement ≈ 133.17 mm.
- H_dr = 4/2 = 2 m, so t₉₀ = 0.848 × 2² / 2 = 1.696 years.
| Initial effective stress (kPa) | Final settlement (mm) |
|---|---|
| 20 | 343.6219227 |
| 40 | 222.4310641 |
| 60 | 166.2577483 |
| 80 | 133.1705465 |
| 100 | 111.215532 |
| 120 | 95.53747916 |
| 160 | 74.58903921 |
How to read the result
The settlement is the long-term value after excess pore pressure has fully dissipated; about 90% of it is reached at t₉₀. For structures, differential settlement between supports usually matters more than the total. A result above about 100 mm, as here, usually prompts a look at ground improvement.
Common mistakes
- Using σ′₀ at the top of the layer instead of mid-depth, or using total stress instead of effective stress.
- Applying the Cc formula to overconsolidated clay; below the preconsolidation pressure the smaller recompression index Cr governs.
Frequently asked questions
Where do Cc and e₀ come from?
From an oedometer (one-dimensional consolidation) test on an undisturbed sample.
What is the time to 50% consolidation?
Use T_v = 0.197 instead of 0.848; for the example that gives about 0.39 years.
Does settlement stop after t₉₀?
No. Secondary compression (creep) continues and is estimated with the index Cα.
Sources: K. Terzaghi, Theoretical Soil Mechanics, Wiley, 1943 · B. M. Das, Principles of Geotechnical Engineering, Cengage Learning · ASTM D2435, Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading