Q$.3$ In an oedometer test on a specimen of saturated soil subjected to a pressure change from $150$ kPa to $300$ kPa with $2-$way drainage, the following dial gauge readings were recorded. The changes of thickness $($mm$)$ vs$.$ time were plotted as in Figure Q$.3$ on page $13.$

Table Q$\mathrm{.}3$: Results of an oedometer test.

By interpolating suitable lines on Figure Q$\mathrm{.}3,$ determine the following:

$($a$)$ The coefficient of consolidation, $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$mathrm$\{$v$\}\}\backslash )(\backslash (\backslash$mathrm$\{$m$\}^\{2\}/\backslash )$ year$)$ of the soil by using the Root$-$Time method. $($Consider one year is $365$ days.$)$

$(15$ marks$)$

$($b$)$ The coefficient of compressibility, $\backslash (\backslash$mathrm$\{$m$\}\_\{\backslash$mathrm$\{$v$\}\}\backslash$left$(\backslash$mathrm$\{$m$\}^\{2\}/\backslash$mathrm$\{$kN$\}\backslash$right$)\backslash ).$

$(5$ marks$)$

$($c$)$ The permeability, $\backslash (\backslash$mathrm$\{$k$\}(\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\})\backslash ).$

$(5$ marks$)$

Note: Submit Figure Q$.3$ with your answer booklet.