Consolidation Coefficient (Cv) Calculator
Compute the coefficient of consolidation Cv from a laboratory time-settlement curve using Cv = T·Hdr²/t. Cv controls how FAST a clay consolidates, feeding time-rate-of-settlement predictions for foundations and embankments.
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How to use this calculator
- Enter the Terzaghi time factor T for your fitting point — 0.197 for U = 50 % (Casagrande log-time) or 0.848 for U = 90 % (Taylor √time).
- Enter the elapsed time t (minutes) taken to reach that degree of consolidation in the oedometer test.
- Enter the drainage path length Hdr (m): half the specimen thickness for double drainage, the full thickness for single drainage.
How it works
Terzaghi's theory links the time factor T, the coefficient of consolidation Cv, the drainage path Hdr and elapsed time t by T = Cv·t / Hdr², which rearranges to Cv = T·Hdr² / t. By reading the time to a known degree of consolidation off the lab curve and inserting the standard T for that U, you recover Cv.
The two standard curve-fitting methods give fixed time factors: Casagrande's log-time construction locates U = 50 % (T = 0.197) and Taylor's square-root-time construction locates U = 90 % (T = 0.848). The drainage path Hdr is half the sample thickness when both faces drain, the full thickness when only one face drains. Results are given in m²/min, m²/year and mm²/s.
Worked example
U = 50 % reached in 10 minutes. For a double-drained 20 mm oedometer specimen, Hdr = 0.010 m. If U = 50 % (T = 0.197) is reached at t = 10 min, then Cv = 0.197 × (0.010)² / 10 = 1.97 × 10⁻⁶ m²/min, which is ≈ 1.04 m²/year, or about 0.033 mm²/s.
Common mistakes
- Using the full specimen thickness for Hdr when the sample is double-drained — Hdr is HALF the thickness for double drainage.
- Mismatching T and U: use T = 0.197 with the U = 50 % time and T = 0.848 with the U = 90 % time, not a mix.
- Forgetting to square Hdr — the formula is Cv = T·Hdr²/t, so a factor-of-two error in Hdr becomes a factor-of-four error in Cv.
Frequently asked questions
What is the drainage path length Hdr?
The longest distance pore water must travel to reach a drainage boundary. For DOUBLE drainage (water escapes both faces) Hdr is HALF the layer/specimen thickness; for SINGLE drainage (only one face drains) Hdr equals the full thickness.
Which time factor T should I use?
Use T = 0.197 with the time to 50 % consolidation from Casagrande's log-time method, or T = 0.848 with the time to 90 % consolidation from Taylor's square-root-time method.
What are typical Cv values?
Cv for clays commonly ranges from roughly 0.1 to 10 m²/year depending on plasticity and structure; silts are faster, high-plasticity clays slower.
How does Cv relate to settlement time?
Cv sets the rate, not the amount, of primary consolidation. The time to a given degree of consolidation is t = T·Hdr²/Cv, so larger Cv or shorter drainage paths mean faster settlement.
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