Coefficient of consolidation is used for calculating:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2015
Detailed Explanation
Two separate questions are asked in any settlement problem: how much will the structure settle, and how fast? Each is answered by a different soil parameter.
\[ c_v = \frac{k}{m_v\,\gamma_w} \qquad t = \frac{T_v\,d^2}{c_v} \]
Why “time rate of settlement” Is Correct
The coefficient of consolidation cv appears in Terzaghi's time equation. Given cv, the drainage path and the degree of consolidation required, it tells you how long the settlement will take. So it is used for the time rate of settlement. Its units are area per time (for example cm²/s or m²/year).
| Question | Parameter used | Typical formula |
|---|---|---|
| How much settlement? | Cc (or mv) | ΔH = CcH log(σ′f/σ′0)/(1 + e0) |
| How fast? | cv | t = Tvd²/cv |
| Stress history? | σ′c, OCR | Casagrande construction |
Why the Other Options Are Wrong
- B. total settlement: Total (final) settlement is calculated with Cc or mv, not cv.
- C. preconsolidation pressure: Preconsolidation pressure is found graphically from the e – log σ′ curve.
- D. stress in soil: Stresses in soil are found from overburden and Boussinesq/Westergaard theory.
Key Point
cv → time. Cc / mv → magnitude.
Key Concepts for Students
- cv is found from the oedometer test using the log-time (T50) or square-root-time (T90) method.
- Higher permeability → higher cv → faster consolidation.
- Sand drains shorten the drainage path d and so speed up consolidation without changing cv.
Practice more: this is question 18 in Soil Consolidation MCQs – Part 2. Try the whole set and check every answer instantly.