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GATE 2023 CE (CE1) – Question 17

Geotechnical Engineering · Deep foundations: piles and pile groups · 1 mark · Multiple choice

A group of 9 friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter 300 mm and length 7 m. Assume that the soil is cohesionless with effective friction angle $\phi' = 32°$. What is the center-to-center spacing of the piles (in m) for the pile group efficiency of 60%?

  1. 0.582
  2. 0.486
  3. 0.391
  4. 0.677

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Correct answer: (A) 0.582

Explanation

Use the Converse-Labarre formula for the group efficiency, $\eta = 1 - \frac{\theta}{90°}\cdot\frac{(n - 1)m + (m - 1)n}{mn}$ with $m = n = 3$ and $\theta = \tan^{-1}\frac{d}{s}$. The factor is $\frac{2 \times 3 + 2 \times 3}{9} = 1.333$. Setting $0.6 = 1 - \frac{\theta}{90} \times 1.333$ gives $\theta = 27°$, so $s = \frac{0.3}{\tan 27°} = 0.589$ m, closest to 0.582 m.