Relation Between Dry Unit Weight, Specific Gravity, Percentage of Air Voids and Water Content

In this article, we shall make the formula or relation between the dry unit weight( $\gamma _{d}$ ), specific gravity(G), percentage of air voids and water content(w).

[Note: Dry unit weight means dry density]

Relation Between Dry Unit Weight, Specific Gravity, Percentage of Air Voids and Water Content

Soil three-phase diagram is shown in the above picture. From this diagram, we can write,

Total Volume = Volume of solids ( $V_{s}$ )+ Volume of water ( $V_{w}$ ) + Volume of air ( $V_{a}$ )

$V = V_{s} + V_{w} + V_{a}$
[Both sides divided by V]
Or, $\frac{V}{V}= \frac{V_{s}}{V} + \frac{V_{w}}{V} + \frac{V_{a}}{V}$

[We know, $\frac{V_{a}}{V} = n_{a}$ ]

Or, $1 = \frac{V_{s}}{V} + \frac{V_{w}}{V} + n_{a}$
Or, $1 - n_{a} = \frac{V_{s}}{V} + \frac{V_{w}}{V}$

[ We know, $\gamma_{s} = \frac{W_{s}}{V_{s}}$ , and Specific Gravity(G) $= \frac{\gamma_{s}}{\gamma_{w} } = \frac{W_{s}}{V_{s}\gamma_{w} }$ ]

[From this equation, $G = \frac{W_{s}}{V_{s}\gamma_{w} }$ , we can write $V_{s} = \frac{W_{s}}{G\gamma _{w}}$ . Now, place the value of $V_{s}$ in the above equation.]