GATE 2025 CE (CE1) – Question 56

Geotechnical Engineering · Shallow foundations: bearing capacity, combined footing, raft, settlement · 2 marks · Numerical answer

A 6 m × 6 m square footing constructed in clay is subjected to a vertical load of 2500 kN at its centre. The base of the footing is 2 m below the ground surface, as shown in the figure. The footing is made of 2 m thick concrete. The ground water table is at a great depth. Considering Terzaghi's bearing capacity theory, the factor of safety of footing against the bearing capacity failure is ____________ (*rounded off to 2 decimal places*).

Note:

Unit weight of concrete = 24 kN/m$^3$

Properties of clay: $c = 50$ kN/m$^2$, $\phi = 0°$, and $\gamma = 19$ kN/m$^3$

For $\phi = 0°$: $N_c = 5.7$, $N_q = 1$, $N_\gamma = 0$

A 6 m wide footing, 2 m thick, with its top at the ground surface and its base 2 m below it. A 2500 kN load acts at its centre.

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Correct answer: 3.46 to 3.50

Explanation

Terzaghi's equation for a square footing gives the ultimate bearing capacity $q_u = 1.3cN_c + \gamma D_fN_q + 0.4\gamma BN_\gamma = 1.3 \times 50 \times 5.7 + 19 \times 2 \times 1 + 0 = 370.5 + 38 = 408.5$ kN/m$^2$. The load on the soil includes the weight of the footing, $6 \times 6 \times 2 \times 24 = 1728$ kN, so the pressure at the base is $\frac{2500 + 1728}{36} = 117.4$ kN/m$^2$. The factor of safety is $\frac{408.5}{117.4} = 3.48$.