A soil sample has a void ratio of 0.5. Its porosity (n) will be
- A25%
- B33.30%Correct
- C50%
- D66.60%
Solution
Concept
Porosity and void ratio phase relationship
Formula
n = e / (1 + e)
Step-by-step solution
1. The relationship between porosity (n) and void ratio (e) is given by n = e / (1 + e). 2. Given void ratio e = 0.5. 3. Substituting: n = 0.5 / (1 + 0.5) = 0.5 / 1.5 = 1/3. 4. Expressed as a percentage: n = (1/3) × 100% = 33.33% = 33.30%. Answer: B
Explanation
Porosity (n) is related to the void ratio (e) by the phase relationship n = e / (1 + e). For a void ratio of e = 0.5, the porosity is n = 0.5 / (1 + 0.5) = 0.5 / 1.5 = 1/3 = 0.333 or 33.30%.
Why the other options are wrong
A) 25% corresponds to e = 0.33. C) 50% corresponds to e = 1.0. D) 66.60% corresponds to e = 2.0.
Shortcut
n = e / (1 + e) => 0.5 / 1.5 = 1/3 = 33.33%.
Common mistake
Using the inverse formula e = n / (1 - n) incorrectly to compute porosity.
Correct answer: B) 33.30%