Question

What is the void ratio of a soil sample if its porosity is 25%?

• A. 0.25
• B. 0.33
• C. 0.50
• D. 0.75

Hint:

Remember: $e = \frac{n}{1-n}$.

Answer 1

The Correct Option is B

Concept: Porosity ($n$) and void ratio ($e$) are related soil parameters.
Step 1: Relation between porosity and void ratio.
\[ n = \frac{e}{1+e} \]
Step 2: Given value.
\[ n = 25% = 0.25 \]
Step 3: Substitute and solve.
\[ 0.25 = \frac{e}{1+e} \] \[ 0.25(1+e) = e \] \[ 0.25 + 0.25e = e \] \[ 0.25 = e - 0.25e = 0.75e \] \[ e = \frac{0.25}{0.75} = \frac{1}{3} \approx 0.33 \]
Step 4: Evaluating the options.

• 0.25 $\rightarrow$ Incorrect
• 0.33 $\rightarrow$ Correct
• 0.50 $\rightarrow$ Incorrect
• 0.75 $\rightarrow$ Incorrect

Step 5: Conclusion.
Thus, the void ratio is approximately 0.33.