If the porosity of a soil sample is 20%, the void ratio is
- A0.25Correct
- B0.2
- C0.5
- D1
Solution
Concept
Relationship between soil porosity and void ratio
Formula
e = n / (1 - n)
Step-by-step solution
1. Porosity n = 20% = 0.20. 2. The relationship between void ratio (e) and porosity (n) is e = n / (1 - n). 3. Substituting values: e = 0.20 / (1 - 0.20) = 0.20 / 0.80 = 0.25. Answer: A
Explanation
The void ratio of a soil sample is calculated using the formula e = n / (1 - n), where n represents porosity. Substituting a porosity of 0.20 yields e = 0.20 / (1 - 0.20), which simplifies to 0.20 / 0.80 = 0.25. Therefore, a soil with 20% porosity has a void ratio of 0.25.
Why the other options are wrong
B) 0.2 is equal to the porosity value itself, not the calculated void ratio. C) 0.5 corresponds to a porosity of 33.3%, not 20%. D) 1 corresponds to a porosity of 50%, which does not match the given 20%.
Shortcut
e = n / (1 - n) -> e = 0.2 / (1 - 0.2) = 0.25.
Common mistake
Equating void ratio directly to porosity instead of using the relationship e = n / (1 - n).
Correct answer: A) 0.25