Civil Engineering > GATE 2026 SET-1 > Pile Foundation
A group of 25 circular piles is arranged in 5 × 5 uniform pattern in a soft clay soil with equal spacing in both the directions. These are friction piles with negligible end bearing.
Consider the following details:
Diameter of each pile = 1 m
Length of each pile = 15 m
Cohesion of the soil = 20 kN/m2
Unit weight of the soil = 16 kN/m3
Adhesion factor = 0.75
Considering the efficiency of the pile group as unity, the optimum value of the ratio of the pile spacing to pile diameter is __________________ (rounded off to one decimal place).
Consider the following details:
Diameter of each pile = 1 m
Length of each pile = 15 m
Cohesion of the soil = 20 kN/m2
Unit weight of the soil = 16 kN/m3
Adhesion factor = 0.75
Considering the efficiency of the pile group as unity, the optimum value of the ratio of the pile spacing to pile diameter is __________________ (rounded off to one decimal place).
Correct : 2.0
The optimum s/d ratio is found by equating the group block failure capacity to the sum of individual pile capacities (efficiency = 1).
Individual pile capacity (25 piles):
Qsingle = α × c × π × d × L = 0.75 × 20 × π × 1 × 15 = 706.86 kN
Qtotal = 25 × 706.86 = 17671.5 kN
Group block capacity:
Block side Bg = (5−1)s + d = 4s + 1
Qgroup = c × (perimeter × L) + Nc × c × Bg²
= 20 × 4(4s+1) × 15 + 5.14 × 20 × (4s+1)²
= 1200(4s+1) + 102.8(4s+1)²
Setting Qgroup = Qtotal:
Let x = 4s+1:
102.8x² + 1200x = 17671.5
Solving: x ≈ 8.51 → s ≈ 1.878 m → s/d ≈ 1.9 ≈ 2.0 (rounded to one decimal place)
Correct answer: 2.0 ✓
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