Question $3.(24$ marks$)$

The coordinates of two points on a virgin compression curve $($i$.$e$.,$ results

obtained from a consolidation test$)$ are as follows.

$e1=0\mathrm{.}80,{}_1^{\text{'}}=250k\frac{N}{m^2}$

$e2=0\mathrm{.}5o,{}_2^{\text{'}}=420k\frac{N}{m^2}$

$($i$)$ Determine the coefficient of volume compressibility, $m_v,$ for the pressure

range stated above,

$($ii$)$ Given the coefficient of consolidation, $c_v=0\mathrm{.}005c\frac{m^2}{sec},$ determine

the time it takes for a $15-mm-$thick of the specimen $($two$-$way drainage$)$ to

undergo $85\%$ consolidation in a laboratory test.

$($iii$)$ What would be the effective pressure corresponding to $e=0\mathrm{.}75?$