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

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

6th March 2020 0 By Malay Sautya

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}

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