Porosity of a well-sorted sand is 0.35. The volume of the voids is 15 in^3. What is the void ratio e?

• A. 0.75
• B. 0.35
• C. 0.54
• D. 0.25

Answer: (C)

Understanding how porosity and void ratio relate is key. Porosity (n) is the fraction of the total volume that is void, while the void ratio (e) is the ratio of void volume to solid volume. They are connected by e = n/(1 − n) (equivalently, n = e/(1 + e)).

With porosity 0.35, the void ratio is e = 0.35 / (1 − 0.35) = 0.35 / 0.65 ≈ 0.5385, about 0.54.

You can also check using the given void volume: Vv = 15 in^3. Total volume Vt = Vv / n = 15 / 0.35 ≈ 42.86 in^3, so Vs = Vt − Vv ≈ 27.86 in^3. Then e = Vv / Vs ≈ 15 / 27.86 ≈ 0.5385, again about 0.54.

So the void ratio is approximately 0.54.