GATE 2025 CE (CE1) – Question 58
A single pile with 450 mm diameter has been driven into a homogeneous clay layer, which has an undrained cohesion ($c_u$) of 20 kPa and unit weight of 18 kN/m$^3$. The ground water table is found to be at the surface of the clay layer. The adhesion factor ($\alpha$) of the soil is 0.95 and bearing capacity factor ($N_c$) is 9. The pile is supporting a column load of 144 kN with a factor of safety of 3.0 against ultimate axial pile capacity in compression.
The required embedment depth of the pile (in m) is ________________ (*rounded off to the nearest integer*).
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Correct answer: 15
Explanation
The ultimate capacity must be $3 \times 144 = 432$ kN. The base resistance is $N_cc_uA_b = 9 \times 20 \times \frac{\pi}{4}(0.45)^2 = 28.6$ kN. The shaft resistance is $\alpha c_u\pi DL = 0.95 \times 20 \times \pi \times 0.45 \times L = 26.86L$ kN. So $28.6 + 26.86L = 432$, which gives $L = 15.0$ m.