The GATE Grind

GATE 2021 CE (CE2) – Question 40

Geotechnical Engineering · Compaction and one-dimensional consolidation · 2 marks · Multiple choice

Clay thickness H has initial void ratio e₀ and stresses $p_0<p_c<p_0+\Delta p$. Compression and swelling indices are Cc and Cs. Which consolidation-settlement expression is correct?

  1. $\frac H{1+e_0}[C_c\log(p_c/p_0)+C_s\log((p_0+\Delta p)/p_c)]$
  2. $\frac H{1+e_0}[C_s\log(p_c/p_0)+C_c\log((p_0+\Delta p)/p_c)]$
  3. $\frac H{1+e_0}[C_c\log(p_0/p_c)+C_s\log((p_0+\Delta p)/p_c)]$
  4. $\frac H{1+e_0}[C_s\log(p_0/p_c)+C_c\log((p_0+\Delta p)/p_c)]$

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Correct answer: (B) $\frac H{1+e_0}[C_s\log(p_c/p_0)+C_c\log((p_0+\Delta p)/p_c)]$

Explanation

Loading first follows the recompression line from p₀ to pc, using Cs, then the virgin-compression line from pc to final stress, using Cc. Each logarithm must have its larger final stress over its initial stress. Summing the two strain contributions gives **B**.