Question

When a stress of 180 kPa is applied on a saturated clay layer drained at both ends, 40% consolidation occurs in 16 years. If an additional drainage layer is assumed to be present at the middle of the clay layer, 40% consolidation could occur in years.

• A. 4 years
• B. 8 years
• C. 16 years
• D. 64 years

Answer 1

The correct option is A 4 years

$T_v=\frac{C_v\cdot t}{d^2}$
For same degrees of consolidation, $T_v$ is constant
$\therefore t\propto d^2$
$\frac{t_1}{t_2}={\left(\frac{d_1}{d_2}\right)}^2$
when a middle drainage layer is introduced, drainage path reduce to half
$d_2=\frac{d_1}{2}$
$\therefore t_2=t_1\times {\left(\frac{d_2}{d_1}\right)}^2$
$=\frac{t_1}{4}$

$=\frac{16}{4}=4years$