GATE 2019 CE (CE2) – Question 65
A square footing of side 2 m rests at the surface of homogeneous soil with c = 24 kPa, φ = 25° and γ = 18 kN/m³. Terzaghi factors are $N_c=25.1$, $N_q=12.7$, $N_\gamma=9.7$ and $N_c^\prime=14.8$, $N_q^\prime=5.6$, $N_\gamma^\prime=3.2$. Find ultimate bearing capacity (kPa), to two decimal places.
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Correct answer: 920 to 925 OR 350 to 356
Explanation
For general shear at a surface square footing, $$q_u=1.3cN_c+0.4\gamma BN_\gamma=1.3(24)(25.1)+0.4(18)(2)(9.7)=922.80\ \mathrm{kPa}.$$ Local shear uses reduced cohesion $2c/3=16$ kPa and primed factors: $1.3(16)(14.8)+0.4(18)(2)(3.2)=353.92$ kPa. The official key accepts both regimes, with ranges around **922.8 and 354.0 kPa**. There is no surcharge term at the ground surface.