GATE 2025 CE (CE2) – Question 57
A $4 \times 4$ group pile, with each pile 20 m long and 500 mm in diameter, is installed in a square pattern in a clayey soil, as shown in the figure. The average unconfined compressive strength of the soil is 100 kN/m$^2$, and the adhesion factor is 0.8. Neglect the bearing at the tip of the piles. For a group efficiency factor of 1.0, the centre to centre spacing ($s$) of the piles (in m) would be ________ (round off to two decimal places).
Figure: a group of piles in clay, each 20 m long, with the plan of the 4 × 4 square pattern with the spacing s between neighbouring piles.
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Correct answer: 1.50 to 1.52
Explanation
The undrained cohesion is $c_u = \frac{q_u}{2} = 50$ kPa. The capacity of one pile is $\alpha c_u\pi dL = 0.8 \times 50 \times \pi \times 0.5 \times 20 = 1256.6$ kN, so the 16 piles acting individually carry $16 \times 1256.6 = 20106$ kN. The group efficiency is the ratio of the capacity of the block of piles to the sum of the individual capacities. With the block of width $B = 3s + 0.5$ the skin friction of the block is $c_u \times 4B \times L = 50 \times 4(3s + 0.5) \times 20 = 4000(3s + 0.5)$. Setting the efficiency to 1: $4000(3s + 0.5) = 20106$, so $3s + 0.5 = 5.027$ and $s = 1.51$ m.