GATE 2026 CE (CE1) – Question 57
A circular pile of 600 mm diameter and 6 m length is embedded in a saturated clayey soil. Undrained cohesion of the soil is 80 kPa. Unit weight of the soil is 19.20 kN/m$^3$. The adhesion factor is 0.54. If the diameter of the pile is doubled to 1200 mm (keeping the length constant), the ratio of pile capacity of 1200 mm diameter pile to that of 600 mm diameter pile is ______ (*rounded off to two decimal places*).
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Correct answer: 2.64 to 2.66
Explanation
The pile capacity is the skin friction $\alpha c_u\pi DL$ plus the end bearing $(c_uN_c + \gamma L)\frac{\pi D^2}{4}$ with $N_c = 9$. For $D = 0.6$ m: friction $= 0.54 \times 80 \times \pi \times 0.6 \times 6 = 488.5$ kN, and end bearing $= (720 + 115.2) \times 0.2827 = 236.1$ kN, for a total of 724.6 kN. For $D = 1.2$ m: friction $= 977.0$ kN and end bearing $= 835.2 \times 1.131 = 944.6$ kN, for a total of 1921.6 kN. The ratio is $\frac{1921.6}{724.6} = 2.65$.