Void Ratio from Porosity

Easyphase relationshipsvoid ratio
A soil has porosity n = 0.40. What is its approximate void ratio e?
  1. A0.40
  2. B0.60
  3. C0.67
  4. D1.50
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Answer: C. 0.67

Equation: void ratio e = Vv/Vs, porosity n = Vv/V. Combining them gives e = n/(1 − n). Values: n = 0.40 is given, so the voids are 40% of the total volume V. The solids are the rest, Vs = 1 − 0.40 = 0.60 of V (the bottom 60% of the block). Step 1: take V = 1, so Vv = 0.40 and Vs = 0.60. Step 2: e = Vv/Vs = 0.40/0.60 = 0.67. Answering 0.40 confuses porosity with void ratio: porosity divides by the total volume, void ratio by the solids only. 1.50 inverts the ratio.
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