Correct Answer - Option 4 : 11%

**Concept:**

Bulk Unit weight (γ_{b}):

It is defined as the ratio of the total weight of soil to the total volume of the soil mass.

\({γ _b} = \frac{W}{V} = \frac{{{W_s} + {W_w}}}{{{V_s} + {V_w} + {V_a}}}\)

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.

\({\rm{w = }}\frac{{{{\rm{W}}_{\rm{w}}}}}{{{{\rm{W}}_{\rm{s}}}}};{\rm{w}} \ge 0\)

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 (γd):-

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/m3.

\({{\rm{γ }}_{\rm{d}}}{\rm{ = }}\frac{{{{\rm{W}}_{\rm{s}}}}}{{\rm{V}}}{\rm{ = }}\frac{{{{\rm{W}}_{\rm{d}}}}}{{\rm{V}}}\)

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.

\({\rm{G = }}\frac{{{{\rm{γ }}_{\rm{s}}}}}{{{{\rm{γ }}_{\rm{w}}}}}\)

**Explanation:**

\(\begin{array}{l} {γ_d} = \frac{γ}{{1 + w}} = \frac{{20}}{{1 + 0.17}} = 17.094\; kN/{m^3}\\ {γ_d} = \frac{{{γ_w}.G}}{{1 + e}} \end{array}\)

If void ratio 'e' remains unchanged during drying, \(γ_d\) also remains unchanged.

\(\begin{array}{l} {γ_d} = \frac{γ}{{1 + w}}\\ 17.094 = \frac{{19}}{{1 + w}} \end{array}\)

w = 0.11 = 11 %

Air content:

Air content is defined as the ratio of the volume of air to the volume of voids. It is denoted by ac.

\({{\bf{a}}_{\bf{c}}} = \frac{{{{\bf{V}}_{\bf{a}}}}}{{{{\bf{V}}_{\bf{v}}}}} = \frac{{{\bf{Volume\ of\ air}}}}{{{\bf{Volume\ of\ voids}}}}\)

Porosity:

Porosity is defined as the ratio of the volume of voids to the total volume of soil. It is denoted by n. It varies between 0 and 1.

\({\bf{n}} = \frac{{{{\bf{V}}_{\bf{v}}}}}{{\bf{V}}} = \frac{{{\bf{Volume\ of\ voids}}}}{{{\bf{Total\ volume}}}}\)

Percentage air voids:

Percentage air voids are defined as the ratio of the volume of air to the total volume of soil. It is denoted by na.

\({{\bf{n}}_{\bf{a}}} = \frac{{{{\bf{V}}_{\bf{a}}}}}{{\bf{V}}} \times 100 = \frac{{{\bf{Volume\ of\ air}}}}{{{\bf{Total\ volume}}}} \times 100\)

**Degree of Saturation:**

Degree of Saturation of a soil mass is defined as the ratio of the volume of water in the voids to the volume of voids. It is denoted by S.

\(S = \frac{{{V_w}}}{{{V_v}}} \times 100\;\;;0 \le S \le 100\)

- For a fully saturated soil mass Vv = Vw, hence S = 100%
- For fully dry soil mass Vw = 0, hence S = 0%