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Degree of Consolidation Calculator

Q: When do I use Cr vs Cc?

Cr (recompression index) is used when the soil remains below σ'ₚ. Cc (compression index) is used when stress exceeds σ'ₚ. Typical Cr = Cc/5 to Cc/10.

Q: What is the Casagrande method for t50/t90?

Casagrande's log-time method uses t50 (0.197×d²/Cv) to find the coefficient of consolidation. The √time method uses t90 (0.848×d²/Cv). Both are standard oedometer interpretation methods.

Q: What is a typical time for 90% consolidation?

For a 5m clay layer with double drainage and Cv=5 m²/yr: t90 = 0.848 × (2.5)² / 5 = 1.06 years. For single drainage with same clay: t90 = 0.848 × (5)² / 5 = 4.24 years.

Q: Is secondary compression included?

No — this calculator covers primary consolidation only (Terzaghi 1D theory). Secondary compression (creep) occurs after primary consolidation and is not included.

Calculate degree of consolidation, settlement at time t, and final consolidation settlement per Terzaghi 1D theory. Supports NC and OC clay with Casagrande time estimates.

Soil Mechanics Geotechnical engineers, foundation engineers Commercial Intent: HIGH

Engineering Formulas

Drainage Path Length

d = H (single drainage)
d = H/2 (double drainage)

d: Maximum drainage path length (m)

H: Clay layer thickness (m)

Time Factor Tv

Tv = Cv × t / d²

Tv: Dimensionless time factor

Cv: Coefficient of consolidation (m²/yr)

t: Time (years)

Degree of Consolidation U

U = √(4×Tv/π) for Tv ≤ 0.2
U = 1 − (8/π²)×exp(−π²×Tv/4) for Tv > 0.2

U: Degree of consolidation (%)

Tv: Time factor

Final Settlement (NC Clay)

Sc = H × Cc/(1+e₀) × log₁₀((σ'₀+Δσ)/σ'₀)

Sc: Final consolidation settlement (mm)

Cc: Compression index

e₀: Initial void ratio

Settlement at Time t

St = U × Sc_final

St: Settlement at time t (mm)

U: Degree of consolidation (decimal)

Time for 50% and 90% Consolidation

t₅₀ = 0.197 × d² / Cv
t₉₀ = 0.848 × d² / Cv

t₅₀: Time for 50% consolidation

t₉₀: Time for 90% consolidation

Worked Example

Consolidation of 5m Clay Layer (Double Drainage)

h: 5drainage: doublecv: 5cvUnit: m2yeart: 365tUnit: daysdeltaSigma: 100sigma0: 80cc: 0.25e0: 0.9sigmaP: 150cr: 0.05

Drainage Path

d = 5/2 = 2.5 m (double drainage)

Time Factor

Tv = 5 × 1 / 2.5² = 0.8000

Degree of U

U = 1 − (8/π²)×exp(−π²×0.8/4) = 82.5%

NC/OC Check

σ'₀=80 < σ'ₚ=150, σ'avg=180 > 150 → transition

Final Settlement

Sc = 5×0.05/1.9×log(150/80) + 5×0.25/1.9×log(180/150) = 0.082 + 0.046 = 0.128 m = 128 mm

Settlement at t

St = 0.825 × 128 = 105.6 mm

Result: U = 82.5%, St = 105.6 mm, Sc = 128 mm, t50 = 95 days, t90 = 410 days

Engineering Notes

Double drainage halves consolidation time compared to single drainage.

Preconsolidation stress σ'ₚ is determined from oedometer tests using Casagrande's construction.

Settlement at 50% consolidation = 0.5 × Sc_final regardless of soil properties.

For staged construction, use superposition to sum settlements from each load increment.

Vertical drains (PVDs) can significantly reduce consolidation time by shortening drainage path.

Assumptions

• Terzaghi 1D consolidation theory applies

• Soil is homogeneous and saturated

• Darcy's law is valid

• Constant Cv throughout the stress range

• No secondary compression (creep)

• Instantaneous loading

Common Mistakes

✕ Using single drainage path when both top and bottom are pervious (should be double)

✕ Confusing Cc and Cr — using Cc for OC range overestimates settlement

✕ Forgetting to convert time units consistently (years vs days)

✕ Using total stress instead of effective stress in settlement formula

✕ Ignoring preconsolidation stress and treating all clay as NC

Frequently Asked Questions

What is the degree of consolidation?

The degree of consolidation (U%) represents the percentage of total expected settlement that has occurred at a given time. U=50% means half of final settlement has occurred.

What is the difference between single and double drainage?

Single drainage: water escapes through one boundary (clay on impervious rock). Double drainage: water escapes through both top and bottom (sandwich between sand layers). Double drainage gives half the drainage path length.

What is a typical Cv value for clay?

Typical Cv: soft clay 1-4 m²/yr, medium clay 4-10 m²/yr, stiff clay 10-100 m²/yr. From oedometer tests, Cv varies with stress level.

What is NC vs OC clay?

NC (normally consolidated): current stress = max past stress (σ'₀ = σ'ₚ). OC (overconsolidated): current stress < max past stress (σ'₀ < σ'ₚ). OC clays have higher stiffness.

When do I use Cr vs Cc?

Cr (recompression index) is used when the soil remains below σ'ₚ. Cc (compression index) is used when stress exceeds σ'ₚ. Typical Cr = Cc/5 to Cc/10.

What is the Casagrande method for t50/t90?

Casagrande's log-time method uses t50 (0.197×d²/Cv) to find the coefficient of consolidation. The √time method uses t90 (0.848×d²/Cv). Both are standard oedometer interpretation methods.

What is a typical time for 90% consolidation?

For a 5m clay layer with double drainage and Cv=5 m²/yr: t90 = 0.848 × (2.5)² / 5 = 1.06 years. For single drainage with same clay: t90 = 0.848 × (5)² / 5 = 4.24 years.

Is secondary compression included?

No — this calculator covers primary consolidation only (Terzaghi 1D theory). Secondary compression (creep) occurs after primary consolidation and is not included.

References & Standards

ASTM D2435IS 2720 Part 15BS 1377-5Terzaghi 1D Theory

ASTM D2435

Standard Test Method for One-Dimensional Consolidation of Soils

IS 2720 Part 15

Determination of Consolidation Properties

BS 1377-5

Consolidation by Oedometer Method

Terzaghi, Peck & Mesri (1996)

Soil Mechanics in Engineering Practice

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