$($a$)$ Draw a labelled phase diagram for a soil sample and use it to define the following quantities: water content, bulk density, dry density, void ratio, degree of saturation and air content.

$[4]$

$($b$)$ In its natural condition, a soil sample has a mass of $2290$ g and a volume of $1\mathrm{.}15{10}^{-3}{m}^3.$ After being completely dried in an oven, the mass of the sample is $2035$ g $.$ The value of $G_s$ for the soil is $2\mathrm{.}68.$ Calculate all of the quantities in $($a$)$ above.

$[9]$

$($c$)$ Using neat sketches to support your answer, distinguish between pinned, roller and fixed supports as used in structures, and show what reactions are relevant to each support.

$[3]$

$($d$)$ Calculate the support reactions generated at support A for the beam shown in Figure Q$3$

$[4]$

Figure Q$3$