Which one of the following shows the time factor (approximate) for 50% degree of consolidation?

Asked in SSC JE 23/01/2018 (Morning)

Detailed Explanation

The time factor T_v is a dimensionless measure of time in Terzaghi's theory. For each average degree of consolidation U there is one value of T_v, regardless of the type of clay or the thickness of the layer.

For \(U \le 60\%\):

\[ T_v = \frac{\pi}{4}\,U^2 = \frac{\pi}{4} \times (0.5)^2 = 0.196 \approx 0.2 \]

For \(U > 60\%\): \(T_v = 1.781 - 0.933\log_{10}(100 - U\%)\).

Why “0.2” Is Correct

Using the standard relation, T₅₀ ≈ 0.197, which rounds to 0.2. This number is used all the time, for example to find c_v from the oedometer test with Casagrande's log-time method: c_v = 0.197 d²/t₅₀.

Average degree of consolidation U against time factor T_v (Terzaghi). Two values worth memorising: T_v ≈ 0.197 at U = 50% and T_v ≈ 0.848 at U = 90%.

Why the Other Options Are Wrong

B. 0.5: Tv = 0.5 corresponds to about U = 76%, not 50%.
C. 1: Tv = 1 corresponds to about U = 93%.
D. 2: At Tv = 2 consolidation is practically complete (U > 99%).

Key Point

Remember: T50 = 0.197 and T90 = 0.848.

Key Concepts for Students

Casagrande's log-time fitting method uses T50; Taylor's square-root-time method uses T90.
Time to reach a given U: t = Tv·d²/cv.
Doubling the drainage path d makes consolidation take four times as long.

Practice more: this is question 13 in Soil Consolidation MCQs – Part 1. Try the whole set and check every answer instantly.