Question

A soil has mass unit weight $\gamma$, water content 'w' (as ratio). The specific gravity of soil solids = G, unit weight of water =${\gamma }_w$. 'S' the degree of saturation of the soil is given by

• A. $S=\frac{1+w}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{G}}$
• B. $S=\frac{w}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{G}}$
• C. $S=\frac{(1+w)}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{G}}$
• D. $S=\frac{w}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{wG}}$
  

Answer 1

The correct option is B $S=\frac{w}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{G}}$

(b)

$\gamma =\frac{G(1+w)}{1+e}\gamma w$

$1+e=\frac{G(1+w)}{\gamma }\gamma w$

and Gw = se

$\frac{Gw}{S}=\frac{G(1+w)\gamma w}{\gamma }-1$

Dividing both sides by G, we get

$\Rightarrow \frac{w}{S}=(1+w)\frac{\gamma w}{\gamma }-\frac{1}{G}$

$S=\frac{w}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{G}}$