Correct Answer - Option 3 : 73 years
Case 1:
Consolidation of 4m thick clay covered with pervious sand on tope and impervious rock at bottom.
Case 2:
Consolidation test on an undisturbed specimen of clay from this deposit. We have two drainage in consolidation test in laboratory.
As per Terzaghi’s 1 D consolidation theory, the time factor, Tv is given as
\({T_v} = \;\frac{{{C_v}t}}{{{H^2}}}\)
Cv is coefficient of consolidation which depends on type of soil.
H = Length of drainage path
T = time required to have certain degree of consolidation
Tv depends on degree of consolidation.
In the given , the degree of consolidation is 90 % in both cases ⇒ Tv is constant
Further soil is clay in both cases ⇒ Cv is constant
∴ t ∝ H2
For Case 1: There will be one way drainage i.e. H1 = 4m and time required for 90 % consolidation is t.
For case 2: There will be two way drainage i.e. H2 = 20/2 = 10 mm (Since it is done in laboratory) and time required for 90% consolidation is 4 hours.
Now,
\(\frac{4}{{{{0.01}^2}}} = \frac{t}{{{4^2}}}\)
t = 64000 hours
∴ \(t = \frac{{640000}}{{365\: \times \:24}}\; = 73\;years\)