Question

For a soil sample having void ratio e, porosity n, water content w, degree of saturation \(S_r\), specific gravity of soil \(G\), Unit weight of water\( γ_w\), and saturated unit weight of water\( γ_{sat}\), which of the following expressions stands true?

• A. $e = \frac{n}{1-n}$
• B. $n = \frac{e}{1+e}$
• C. $S_r = \frac{w G}{e}$
• D. $\gamma_{\text{sat}} = \gamma_w G + e \gamma_w$

Hint:

Remember: Void ratio ($e$) and porosity ($n$) are related. Use $n = \frac{e}{1+e}$ for porosity when void ratio is given.

Answer 1

The Correct Option is B

Porosity $n$ and void ratio $e$ are related as follows:
\[n = \frac{V_v}{V_v + V_s}\]
Here:
$V_v$ represents the volume of voids.
$V_s$ represents the volume of solids.
Expressing $n$ in terms of $e$ yields the equation:
\[n = \frac{e}{1 + e}\]
Therefore, $n = \frac{e}{1+e}$ is the correct expression, confirming Option (B) as the valid answer.