GATE 2023 CE (CE2) – Question 59
A circular pile of diameter 0.6 m and length 8 m was constructed in a cohesive soil stratum having the following properties: bulk unit weight = 19 kN/m$^3$; angle of internal friction = 0° and cohesion = 25 kPa. The allowable load the pile can carry with a factor of safety of 3 is ______ kN (round off to one decimal place). [Adopt: Adhesion factor, α = 1.0 and Bearing capacity factor, $N_c=9.0$]
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 146.17 to 147.63
Explanation
**Step 1: shaft (skin friction) resistance** in a cohesive soil with $\alpha=1$, $c=25$ kPa:
$$Q_s=\alpha c\,(\pi DL)=1.0\times25\times\pi(0.6)(8)=377.0\text{ kN}.$$
**Step 2: end-bearing (tip) resistance.** The tip area is $A_b=\dfrac{\pi}{4}(0.6)^2=0.2827$ m², so
$$Q_b=N_c\,c\,A_b=9.0\times25\times0.2827=63.6\text{ kN}.$$
**Step 3: ultimate capacity.**
$$Q_u=Q_s+Q_b=377.0+63.6=440.6\text{ kN}.$$
**Step 4: allowable load** with $FS=3$:
$$Q_{all}=\frac{440.6}{3}=\mathbf{146.9\ kN}.$$