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A bed consists of compressible clay of 4 m thickness with pervious sand on top and impervious rock at the bottom. In a consolidation test on an undisturbed specimen of clay from this deposit 90% settlement was reached in 4 hours. The specimen was 20 mm thick. The time for the building founded over this deposit to reach 90% of its final settlement will be
1. 91 years
2. 82 years
3. 73 years
4. 64 years

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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

∴ \(t = \frac{{640000}}{{365\: \times \:24}}\; = 73\;years\)

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