Mass$-$volume Relationship

Q$.1$ A sand sample has a total volume of $1\mathrm{.}5m^3,$ a total mass of $2850kg$ and a dry

mass of $2478kg.$ The specific gravity of the soil solids is $2\mathrm{.}65.$ The maximum

and minimum void ratios are $0\mathrm{.}8$ and $0\mathrm{.}4$ respectively. Compute the following:

the mass of water

the water content

the volume of the soil solid

the volume of the water

the volume of air

the void ratio

the porosity

the air void ratio

the degree of saturation

the bulk density

the dry density

the saturated density

the submerged density

the corresponding water content if the soil is fully saturated

the relative density of the sand sample

Q$.2$ A natural soil sample had a mass of $0\mathrm{.}183kg$ and a volume of $86\mathrm{.}2{10}^{-6}$

$m^3.$ After being completely dried in an oven, the dry density ${}_{\text{d}\text{r}\text{y}}$ of the soil

sample was found to be $1830k\frac{g}{m^3}.$ The specific gravity of the soil grains

was $2\mathrm{.}72.$

Determine the following physical properties for this natural soil sample:

$($i$)$ bulk density, ${}_{\text{b}\text{u}\text{l}\text{k}}$

$($ii$)$ moisture content, $m$ or $w$

$($iii$)$ void ratio, e

$($iv$)$ porosity, $n.$

$($v$)$ degree of saturation, $S_r$

$($vi$)$ saturated density, ${}_{\text{s}\text{a}\text{t}}$