GATE 2026 CE (CE2) – Question 57
The ultimate bearing capacity of a 1 m wide strip footing is 532.80 kPa, when it is embedded at 1 m depth in dry cohesionless soil. The soil has a unit weight of 18 kN/m$^3$. The ultimate bearing capacity is 864 kPa when the depth of embedment becomes 2 m.
Neglecting the effect of the depth factor, the bearing capacity factor $N_q$ is ______ (*rounded off to one decimal place*).
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Show answer and explanation
Correct answer: 18.31 to 18.49
Explanation
For a cohesionless soil $q_u = \gamma D_f N_q + \frac{1}{2}\gamma B N_\gamma$. The second term does not change with depth, so subtracting the two cases gives $864 - 532.8 = \gamma\,(2 - 1)\,N_q = 18\,N_q$. So $N_q = \frac{331.2}{18} = 18.4$.