SSC JE Civil Engineering 30-Oct-2020 Shift 2 Paper

Concept:
Bulk Unit weight $\left({\mathit{\gamma }}_{\mathit{b}}\right)$:
It is defined as the ratio of the total weight of soil to the total volume of the soil mass.
${\mathrm{\gamma }}_{\mathit{b}}$ = $\frac{\mathrm{W}}{\mathrm{V}}$ = $\frac{{\mathrm{W}}_{\mathit{s}}+{\mathrm{W}}_{\mathit{w}}}{{\mathrm{V}}_{\mathit{s}}+{\mathrm{V}}_{\mathit{w}}+{\mathrm{V}}_{\mathit{a}}}$
Water Content (w):​Water content or moisture content of a soil mass is defined as the ratio of the weight of water to the weight of solids (dry weight) of the soil mass.
W = $\frac{{\mathrm{W}}_{\mathit{w}}}{{\mathrm{W}}_{\mathit{s}}}$ ; w ≥ 0
It is denoted by the w and is commonly expressed as a percentage. The minimum value for water content is 0. There is no upper limit for water content.
Dry Unit Weight $\left({\mathrm{\gamma }}_{\mathit{d}}\mathit{­}\right)$:-​
Dry unit weight is defined as the weight of soil solids per unit volume of soil. It is denoted by the letter symbol γd it has the unit of kN/ ${\mathrm{m}}_3$ .
$\left({\mathit{\gamma }}_{\mathit{d}}\right)=\frac{{\mathrm{W}}_{\mathrm{s}}}{\mathrm{V}}=\frac{{\mathrm{W}}_{\mathrm{d}}}{\mathrm{V}}$
It is used as a measure of the denseness of soil. A high value of dry unit weight indicates that more solids are packed in a unit volume of soil hence a more compact soil.
Specific gravity of solids (G):-​
The specific gravity of solids is defined as the ratio of the unit weight of solids to the unit weight of water. It is denoted by the letter G and is a unitless quantity.
G = $\frac{{\mathrm{\gamma }}_{\mathit{s}}}{{\mathrm{\gamma }}_{\mathit{w}}}$
Explanation:
${\mathrm{\gamma }}_{\mathrm{d}}=\frac{\mathit{\gamma }}{1+\mathrm{w}}=\frac{20}{1+0.17}$ $=17.094\mathrm{kN}∕{\mathrm{m}}^3$
If void ratio 'e' remains unchanged during drying, $\frac{\mathrm{\gamma }}{\mathit{d}}$ also remains unchanged.
${\mathrm{\gamma }}_{\mathrm{d}}=\frac{\mathit{\gamma }}{1+\mathit{w}}$
$17.094=\frac{19}{1+\mathrm{w}}$
$\mathrm{w}=0.11=11\%$