Question

A clay sample in laboratory test has 24mm thickness. It is tested with single drainage and consolidated 50%. The clay layer from which sample was obtained is 4m thick. Find the time to consolidate 50% with single drainage.

(a) 386 days

(b) 390 days

(c) 404 days

(d) 175 days

This question was addressed to me in unit test.

My question comes from Consolidation Problems topic in portion One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

Right answer is (a) 386 days

To explain I would say: Given, single drainage for both the sample and for the field layer,

t1=20 min

d1=24 mm= 2.4 cm

d2 =4 m = 400cm

Since, for same degree of consolidation of 50%, Tv is same,

\(t∝\frac{d^2}{C_r}\)

Therefore, \(\frac{t_2}{t_1} =(\frac{d_2}{d_1} )^2\)

So, \(t_2=t_1 (\frac{d_2}{d_1})^2=20(\frac{400}{2.4})^2=386 \,days.\)