Q$.3($a$)$ The results below were obtained in a Standard Proctor compaction test on

a soil sample with a specific gravity $(G_s)$ of $2\mathrm{.}7.$

Table Q$\mathrm{.}3($a$)$: Results from a standard proctor compaction test.

$($i$)$ Plot the curve of dry density against moisture content.

$($ii$)$ Determine the maximum dry density and the optimal moisture

content for this compaction test.

$($iii$)$ Calculate the air$-$void ratio $(A_v),$ void ratio $($e$),$ and degree of

saturation $(S_r)$ of the soil at the optimum moisture content.

$($iv$)$ Under filled compaction conditions, the air$-$void ratio and optimum

moisture content may both vary up to $+-2\%.$ Calculate, therefore,

the lower field limit of dry density that you will specify.