$2.($a$)$ A construction site over a large area is situated over a $8-$m thick clay deposit. The site is to be improved by preloading with sand fill. The groundwater table is located at the ground surface.

The clay deposit is originally normally consolidated and has an initial total unit weight $($ Y $)$ of $\backslash (16\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ The initial in$-$situ water content $($ w $)$ of the clay deposit is $\backslash (75\backslash \%\backslash )$ and its specific gravity $\backslash (\backslash$left$(\backslash$mathrm$\{$G$\}\_\{3\}\backslash$right$)\backslash )$ is $2\mathrm{.}7.$ The following information has been obtained from the results of oedometer tests carried out on a $20-$mm thick undisturbed sample obtained from the site:

Slope of the virgin compression line $\backslash (\backslash$quad$=0\mathrm{.}7\backslash )$

Time to reach $50\backslash \%$ degree of consolidation $\backslash (=10\backslash )$ minutes

The sand fill has a total unit weight of $\backslash (18\mathrm{.}5\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ The unit weight of water is $\backslash (10\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$

$($i$)$ Calculate the water content and degree of consolidation of the clay $2$ years after the placement of sand fill of $3$ m thick.

The compression of the sand is assumed to be negligible and the clay layer can be treated as one layer $($i$.$e$.,$ subdivisions are not required$).$ Ignore the buoyancy effect on the applied pressure from the sand fill in your calculation.

$($ii$)$ Due to a tight construction schedule, the duration of improvement needs to be accelerated. Calculate the minimum sand fill thickness required in order to achieve the same water content as computed in Q$2($a$)($i$)$ for the clay deposit within $6$ months' time with the same assumptions as in Q$2($a$)($i$).$

$($iii$)$ Explain the reason why a thicker sand fill is realistically required than that calculated in Q$2($a$)($ii$).$

$(15$ Marks$)$

$($b$)$ Explain briefly the differences between piezometer and tensiometer in terms of working principles, special design consideration and limitations$.$

$(5$ Marks$)$

$($c$)$ Explain the definition of soil pre$-$consolidation pressure and briefly describe the procedure to determine the pre$-$consolidation pressure from the oedometer test results.