Which expression is correct for void ratio e in terms of porosity n?

• A. e = n/(1-n)
• B. e = (1-n)/n
• C. e = n^2/(1-n)
• D. e = n

Answer: (A)

Void ratio compares the amount of void (empty) space to solid material, while porosity compares the void space to the total volume. Start with Vv for void volume, Vs for solid volume, and Vt = Vs + Vv for total volume. Porosity is n = Vv / Vt, and void ratio is e = Vv / Vs.

From n = Vv / (Vs + Vv), multiply both sides by (Vs + Vv): nVs + nVv = Vv. Rearranging gives nVs = Vv(1 − n), so Vv = nVs / (1 − n). Then e = Vv / Vs = [nVs / (1 − n)] / Vs = n / (1 − n).

So the correct expression is e = n / (1 − n). For example, if n = 0.25, e = 0.25 / 0.75 ≈ 0.333.