Under a given load a clay layer attains 30% degree of consolidation in 100 days. The time taken by the same clay layer to attain 60% degree of consolidation will be?

Question

Answer

Explanation:

Definition: Degree of consolidation is a measure of the rate at which a soil layer consolidates under load.

Formula: Degree of consolidation (U) = (e_o - e)/(e_o - e_r)

e_o: Initial void ratio

e: Void ratio at any time t

e_r: Void ratio of the soil particle

Given: U₃₀ = 0.3, t₃₀ = 100 days

To find: t₆₀

Solution:

Using the formula of degree of consolidation, we can write: U₃₀ = (e_o - e₃₀)/(e_o - e_r) = 0.3

Similarly, at U₆₀, we can write: U₆₀ = (e_o - e₆₀)/(e_o - e_r) = 0.6

Dividing the above two equations, we get: (e_o - e₆₀)/(e_o - e_r) / (e_o - e₃₀)/(e_o - e_r) = 0.6/0.3

Cancelling out e_r, we get: (e_o - e₆₀)/(e_o - e₃₀) = 2

Further simplifying, we get: e₆₀ = 2e₃₀ - e_o

Now, we can use the time factor to determine the relation between e_o, e₃₀ and e₆₀

For a given soil, the time factor (T_v) can be defined as the time required for 50% consolidation to occur

Using the formula for time factor, we get: T_v = (t₃₀/t₆₀)log[(1-U₃₀)/(1-U₆₀)] = 1

Answer

200days

Similar GATE Doubts

A 3 m thick clay layer is subjected to an initial uniform pore pressure of 145 kPa as shown in the figure.For the given ground conditions, the time(in days, rounded to the nearest integer)required for 90%consolidation would be ________ Correct answer is '1770.833'. Can you explain this answer?

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