Question

A saturated clay stratum draining both at the top and bottom undergoes 50% consolidation in 16 years under an applied load. If an additional drainage layer was present at the middle of the clay stratum, 50% consolidation would occur in

• A. 2 year
• B. 4 year
• C. 8 year
• D. 16 year

Answer 1

The correct option is B 4 year

$T_v=\frac{C_{v}t}{H^2}$

For the same soil and same degree of consolidation $T_{v}and{C}_v$ remains same

$t\alpha H^2$

$t_1\alpha H_1^2$

When additional drainage layer is present at the middle of clay layer, length of drainage path will be reduced to $H_1/2,$

$t_2\alpha {\left(\frac{H_1}{2}\right)}^2$

$\Rightarrow \frac{t_1}{t_2}=\frac{(H_1{)}^2}{{\left(\frac{H_1}{2}\right)}^2}=4$

$Given{t}_1=16years$

$t_2=\frac{t_1}{4}=4years$