Question

Which one of the following relation gives the value of degree of saturation S, in terms of unit weight $\gamma$ water content w (as ratio) and specific gravity of soil solids $G_s,{\gamma }_w$ is unit weight of water?

• A. $S=\frac{W}{\left(\gamma /{\gamma }_w\right)(1+W)-1/G_s}$
• B. $S=\frac{W}{\left(\gamma /{\gamma }_w\right)(1+W)+1/G_s}$
• C. $S=\frac{W}{\left({\gamma }_w/\gamma \right)(1+W)+1/G_s}$
• D. $S=\frac{W}{\left({\gamma }_w/\gamma \right)(1+W)-1/G_s}$

Answer 1

The correct option is D

$S=\frac{W}{\left({\gamma }_w/\gamma \right)(1+W)-1/G_s}$

(d)
Unit weight

$\gamma =\frac{G_s(1+W)}{(1+e)}{\gamma }_w$

$1+e=\frac{G_s(1+W){\gamma }_w}{\gamma }$

Using $G_{s}w=Se$

$1+\frac{G_{s}w}{S}=\frac{G_s(1+W){\gamma }_w}{\gamma }$

Divinding both sides by$G_s$ and rearranging, we get

$S=\frac{W}{\left({\gamma }_w/\gamma \right)(1+W)-1/G_s}$