Question

establish the relation between bulk unit weight, specific gravity, void ratio and degree of saturation ?​

Answer 1

Answer:

Explanation:

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}

Read More:

Relation Between Porosity and Void Ratio

Relation Between Dry unit Weight, Bulk unit Weight & Water Content