Question

A saturated clay layer with double drainage taken 5 years to attain 90% degree of consolidation under a structure. If the same layer were to be single drained, what would be time (in years) required to attain the same consolidation under the same loading conditions?
1. 10
2. 15
3. 20
4. 25

Answer 1

Correct Answer - Option 3 : 20

Concept:

Time factor (T_v):

(i) This is a non-dimensional parameter, which directly proportional to time elapsed t for a particular soil and inversely proportional to the square of length of drainage path. this is given by

\({T_v} = \frac{{{C_v}.t}}{{{d^2}}}\)

Where, C_v = Coefficient of consolidation, d = Length of drainage path

d = H/2, for two way drainage

d = H, for one way drainage

Taylor gives the following approximate relationship between T_v and U which are widely adopted

(i) T_v = π/4 × U², When U ≤ 0.6

(ii) T _v = 1.781 - 0.933 log ₁₀ (100 - U%)

Calculation:

Case 1: d₁ = H/2, t₁ = 5 year, %U = 90

\({T_v} = \frac{{{C_v}.{t_1}}}{{d_1^2}}\) ...................(i)

Case 2: d₂ = h, t₂ = ?, %U = 90

\({T_v} = \frac{{{C_v}.{t_2}}}{{d_2^2}}\)...................(ii)

Since degree of consolidation in both the case is same , so time factor is same for both case

\(\frac{{{C_v}.{t_1}}}{{d_1^2}} = \frac{{{C_v}.{t_2}}}{{d_2^2}}\) ⇒ \(\frac{{{t_1}}}{{d_1^2}} = \frac{{{t_2}}}{{d_2^2}}\)

\(\frac{5}{{{{\left( {\frac{H}{2}} \right)}^2}}} = \frac{{{t_2}}}{{{H^2}}}\)

t₂ = 20 year