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

Step 1: Understanding the Concept:
The relationship between void ratio (\(e\)) and porosity (\(n\)) is a basic volume-mass relationship in soil mechanics.
Void ratio is defined as the volume of voids divided by the volume of solids.
Porosity is defined as the volume of voids divided by the total volume of the soil.
Step 2: Key Formula or Approach:
The mathematical relationship used to convert porosity to void ratio is:
\[ e = \frac{n}{1 - n} \] Where \(n\) is expressed as a decimal value (not a percentage).
Step 3: Detailed Explanation:
Given the porosity \(n = 25% = 0.25\).
Substitute the value of \(n\) into the conversion formula:
\[ e = \frac{0.25}{1 - 0.25} \] \[ e = \frac{0.25}{0.75} \] \[ e = \frac{1}{3} \] \[ e \approx 0.3333 \] Rounding to two decimal places, we get \(e = 0.33\).
Step 4: Final Answer:
The void ratio of the soil sample is 0.33.