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

## 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]

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.]

Or, $1 - n_{a} = \frac{W_{s}/G\gamma_{w}}{V} + \frac{W_{w}/\gamma _{w}}{V}$

[We know, Density of solids$(\gamma_{d}) = \frac{W_{s}}{V}$]

Or, $1 - n_{a} = \frac{\gamma_{d}}{G\gamma_{w} } + \frac{wW_{s}/\gamma _{w}}{V}$

Or, $1 - n_{a} = \frac{\gamma_{d}}{G\gamma_{w} } + \frac{w\gamma_{d} }{\gamma_{w} }$

Or, $1 - n_{a} = \frac{\gamma_{d}}{\gamma_{w} }\left [ w + \frac{1}{G} \right ]$
$\gamma_{d} = \frac{(1 - n_{a})G \gamma_{w}}{1 + wG}$