Question

Consolidation test was conducted on two soils A and B respectively. The soil A is 1.5 times more compressible than soil B. The thickness of A was 2 times that of B. If the time required for 50% consolidation was three times longer for soil A than for soil B, the ratio of coefficient of permeability of A to that of B is ?

• A. $0.5$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

$(m_v{)}_A=1.5(m_v{)}_B$
$d_A=2d_B$
$t_A=3t_B$
We know, $T_v=\frac{C_v.t}{d^2}$
$\frac{C_v.t}{d^2}=constant$
$C_v=\frac{K}{m_v{\gamma }_w}$
$\left(\frac{K_A}{K_B}\right)\times \left(\frac{(m_v{)}_B}{(m_v{)}_A}\right)\times \frac{t_A}{t_B}={\left(\frac{d_A}{d_B}\right)}^2$
$\left(\frac{K_A}{K_B}\right)\times \frac{2}{3}\times 3={\left(2\right)}^2$
$\frac{K_A}{K_B}=2$