$($a$)$ A $2\mathrm{.}5$ kg rammer compaction test was carried out in a $105$ mm diameter mould of volume $1000c{m}^3$ and mass $1125$ g $.$ The results obtained are presented in Table Q$2$a below.

$($i$)$ Determine the optimum moisture content and maximum dry density of the soil from a plot of dry density against moisture content.

$($ii$)$ Add the $0\%$ air void line to the plot, assuming the particle density of the material is $2\mathrm{.}7\frac{g}{c}{m}^3.$

$[6$ marks$]$

$[6$ marks$]$

$($iii$)$ The contractor is proposing to use a smoothed wheeled roller of mass per metre width $3500$ kg and Method $2$ as specified in the Specification for Highway Works to compact the soil. Table $\frac{6}{4}$ from the Specification for Highway Works can be found at the end of this paper. What depth of soil layer and number of passes should be used to meet the specification?

$[3$ marks$]$

Table Q$2$a

$\backslash$table$[[$Moisture Content $(\%),10\mathrm{.}0,11\mathrm{.}0,12\mathrm{.}0,13\mathrm{.}0,14\mathrm{.}0],[$Mass of wet soil and mould $($g$),3168,3300,3334,3350,3320]]$