# Relation Between Void Ratio, Water Content, Degree of Saturation & Specific Gravity

## Relation Between Void Ratio, Water Content, Degree of Saturation & Specific Gravity

In this article, we will make a formula or equation or relation between void ratio(e), water content(w), degree of saturation( $S_{r}$) and specific gravity(G).

Let,

• $W_{s}$ = Weight of soil solid in a given soil mass.
• $W_{w}$ = Weight of water.
• $V_{s}$ = Volume of soil solid in a given soil mass.
• $V_{w}$ = Volume of water present in the given soil mass.
• $\gamma_{s}$ = Unit weight of soil solids or density of solids.
• $\gamma_{w}$ = Unit weight of water or density of water.

By definition of water content, we can write, $w = \frac{W_{w}}{W_{s}}$

Or, $w = \frac{V_{w} \gamma_{w}}{V_{s}\gamma_{s} }$
[ We know, $G = \frac{\gamma_{s}}{\gamma_{w} }$ ]

Or, $w = \frac{V_{w}}{V_{s}G}$

Or, $w = \frac{1}{G}\times \frac{V_{v}}{V_{s}}\times \frac{V_{w}}{V_{v}}$
[ We know, $e = \frac{V_{v}}{V_{s}}$ and $S_{r}= \frac{V_{w}}{V_{v}}$ ]
So, $w = \frac{1}{G}. e.S_{r}$

Or, $w.G = e.S_{r}$

Alternative Method,

By the definition of void ratio, we have, $e = \frac{V_{v}}{V_{s}}$
Or, $e = \frac{V_{v}}{V_{w}}\times \frac{V_{w}}{V_{s}}$

Or, $e = \frac{V_{v}}{V_{w}}\times \frac{W_{w}/\gamma_{w} }{W_{s}/\gamma_{s} }$

Or, $e = \frac{V_{v}}{V_{w}}\times \frac{W_{w}}{W_{s}}\times\frac{\gamma_{s}}{\gamma_{w} }$

Or, $e = \frac{1}{S_{r}}\times w\times G$

Or, $w.G = e.S_{r}$