In consolidation, time factor is defined as:
Try it first: pick an option, then read the explanation.
Correct answer: A. Cᵥt / d²
Asked in SSC JE 2015
Detailed Explanation
Terzaghi's equation contains cv, time and depth. To make the solution apply to any clay layer, these are combined into a single dimensionless number, the time factor:
\[ T_v = \frac{c_v\,t}{d^2} \]
Why “Cᵥt / d²” Is Correct
cv has units of length²/time. Multiplying by time t gives length², and dividing by d² (length²) leaves a pure number. Only Cvt/d² is dimensionless, so it must be the time factor.
Why the Other Options Are Wrong
- B. Cᵥ²t / d: Cv²t/d has units of length³/time, so it cannot be dimensionless.
- C. Cᵥt² / d: Cv·t²/d has units of length × time.
- D. Cᵥt² / d²: Cv·t²/d² has units of time.
Key Point
Tv must be dimensionless: Tv = cv·t/d².
Key Concepts for Students
- Tv = 0.197 at U = 50% and 0.848 at U = 90%.
- For U ≤ 60%: Tv = (π/4)U².
- Because d is squared, halving the drainage path cuts consolidation time to a quarter.
Practice more: this is question 20 in Soil Consolidation MCQs – Part 2. Try the whole set and check every answer instantly.