Question

A soil has a void ratio of 0.50. Then its porosity is:

• A. 3
• B. \( \frac{1}{3} \)
• C. 2
• D. \( \frac{1}{2} \)

Hint:

Use the formula: \( n = \frac{e}{1 + e} \) where \( e \) is the void ratio.

Answer 1

The Correct Option is B

To determine the porosity of a soil with a given void ratio, we use the fundamental relationship between these two soil properties.

1. Understanding Key Definitions:
- Void ratio (e): Ratio of volume of voids to volume of solids (e = V_v/V_s)
- Porosity (n): Ratio of volume of voids to total volume (n = V_v/V)

2. The Relationship Formula:
The porosity can be calculated from void ratio using:
n = e / (1 + e)

3. Calculation:
Given e = 0.50:
n = 0.50 / (1 + 0.50) = 0.50 / 1.50 = 1/3

4. Verification:
- For e = 0.50, the correct porosity is exactly 1/3 (≈0.333)
- This matches standard geotechnical engineering references
- The other options (3, 2, 1/2) would violate physical limits of porosity (0 ≤ n ≤ 1)

5. Practical Significance:
A porosity of 1/3 indicates:
- Moderate water holding capacity
- Typical for many sandy or loamy soils
- Good balance between drainage and retention

Conclusion:
The correct porosity for a soil with void ratio 0.50 is 1/3.

Final Answer:
The correct option is: \( \frac{1}{3} \).