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

The relationship between void ratio $e$ and porosity $n$ is derived as:
\[n = \frac{V_v}{V_v + V_s}\]
where:
$V_v$ is the volume of voids.
$V_s$ is the volume of solids
Rewriting $n$ in terms of $e$, the equation becomes:
\[n = \frac{e}{1 + e}\]
Hence, $n = \frac{e}{1+e}$ is the correct expression, making Option (B) the valid answer.