GATE 2025 CE (CE2) – Question 56
A designer used plate load test to obtain the value of the bearing capacity factor $N_\gamma$. A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is 16.66 kN/m$^3$. The plate is loaded to failure at a pressure of 1500 kPa.
Considering Terzaghi's bearing capacity theory, the bearing capacity factor $N_\gamma$ is ______ (round off to the nearest integer).
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Correct answer: 300
Explanation
For a circular footing Terzaghi's equation is $q_u = 1.3cN_c + \gamma D_fN_q + 0.3\gamma BN_\gamma$. For dry sand $c = 0$ and the plate is on the surface, $D_f = 0$, so $q_u = 0.3\gamma BN_\gamma$. Then $N_\gamma = \frac{1500}{0.3 \times 16.66 \times 1} = 300$.