Consolidation Settlement Calculator
A 4 m normally consolidated clay layer (Cc = 0.3, e₀ = 0.9) loaded from 100 to 150 kPa settles 111.216 mm; with cv = 2 m²/yr and double drainage, half of it happens in about 0.39 years.
Skempton: Cc ≈ 0.009(LL − 10) for normally consolidated clay.
111.215532035167 mm
Full answer, then cut to fewer decimals (not rounded):
- 111.215532035167 mm
- 111.21553203516 mm
- 111.2155320351 mm
- 111.215532035 mm
- 111.21553203 mm
- 111.2155320 mm
- 111.215532 mm
- 111.21553 mm
- 111.2155 mm
- 111.215 mm
- 111.21 mm
- 111.2 mm
- Time factor Tv
- 0.1963495408
- Drainage path d
- 2 m
- Time to 50 % consolidation
- 0.3926990817 years
- In days
- 143.4333396 days
- Settlement at 50 %
- 55.60776602 mm
Step-by-step solution
- Sc = Cc H/(1 + e₀) log₁₀((σ′₀ + Δσ)/σ′₀) = 0.3 × 4 ÷ 1.9 × log₁₀(150/100) = 0.111215532 m
- Tv = (π/4)U² = (π/4) × 0.5² = 0.1963495408
- t = Tv d²/cv = 0.1963495408 × 2² ÷ 2 = 0.3926990817 years
Consolidation Settlement Formula
Sc = Cc H/(1 + e₀) log₁₀((σ′₀ + Δσ)/σ′₀), t = Tv d²/cv
Tv = (π/4)U² for U ≤ 60 %, else 1.781 − 0.933 log₁₀(100 − U%)
Worked Example
A 4 m doubly drained clay with Cc = 0.3, e₀ = 0.9, σ′₀ = 100 kPa and Δσ = 50 kPa:
- Sc = Cc H/(1 + e₀) log₁₀((σ′₀ + Δσ)/σ′₀) = 0.3 × 4 ÷ 1.9 × log₁₀(150/100) = 0.111215532 m
- Tv = (π/4)U² = (π/4) × 0.5² = 0.1963495408
- t = Tv d²/cv = 0.1963495408 × 2² ÷ 2 = 0.3926990817 years
Drainage path d: 2 m · Time to 50 % consolidation: 0.3926990817 years · In days: 143.4333396 days · Settlement at 50 %: 55.60776602 mm
GATE tip
Take σ′₀ and Δσ at the middle of the clay layer. For a thick layer, split it into sub-layers and add their settlements.
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Frequently asked questions
How does drainage change the time?
Time grows with the square of the drainage path: double drainage halves d and cuts the time to a quarter of single drainage.
What is Tv for 50 % and 90 % consolidation?
Tv = 0.197 for 50 % and 0.848 for 90 %, the two values most often used in GATE.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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Scientific Converters. (2026, October 15). Consolidation Settlement Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/consolidation-settlement-calculator/
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Scientific Converters, "Consolidation Settlement Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/consolidation-settlement-calculator/