Relation Between Submerged Unit Weight, Specific Gravity, Void Ratio and Unit Weight of Water

Relation Between Submerged Unit Weight, Specific Gravity, Void Ratio and Unit Weight of Water

In this article, we shall make a formula or relation between the submerged unit weight({\gamma }'), specific gravity(G), void ratio(e) and unit weight of water/ density of water(\gamma_{w} ).

We know,

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\gamma _{sat} = \frac{W_{sat}}{V_{sat}}
Or, \gamma _{sat} = \frac{W_{s} + W_{w}}{V_{s}+V_{v}}

Or, \gamma _{sat} = \frac{G \gamma_{w} + e\gamma_{w} }{1+e}

Or, \gamma _{sat} = \left (\frac{G + e}{1 + e} \right )\gamma_{w}

From the definition of submerged unit weight, we have,

 {\gamma }' = \gamma_{sat} - \gamma_{w}

Or,  {\gamma }' = \left (\frac{G + e}{1 + e} \right )\gamma_{w} - \gamma _{w}

Or,  {\gamma }' = \left (\frac{G - 1}{1 + e} \right )\gamma_{w}

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