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GATE 2017 CE (CE2) – Question 14

Geotechnical Engineering · Compaction and one-dimensional consolidation · 1 mark · Multiple choice

Let G be soil-solids specific gravity, w water content, $\gamma_w$ unit weight of water and $\gamma_d$ dry unit weight of soil. The zero-air-voids line in a compaction plot is ______.

  1. $\gamma_d=G\gamma_w/(1+Gw)$
  2. $\gamma_d=G\gamma_w/(Gw)$
  3. $\gamma_d=Gw/(1+\gamma_w)$
  4. $\gamma_d=Gw/(1-\gamma_w)$

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Correct answer: (A) $\gamma_d=G\gamma_w/(1+Gw)$

Explanation

Zero air voids means saturation $S=1$. From $Se=wG$, the void ratio is $e=wG$. Therefore $\gamma_d=G\gamma_w/(1+e)=G\gamma_w/(1+wG)$ (A). Use w as a decimal mass ratio.