GATE 2016 CE (CE2) – Question 54

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

A 4 m wide strip footing lies 1.5 m below ground in c–φ soil. The water table is 5.5 m below ground. Soil properties: $c\prime=35$ kN/m$^2$, $\phi\prime=28.63^\circ$, $\gamma_{sat}=19$, $\gamma_{bulk}=17$, $\gamma_w=9.81$ kN/m$^3$. Using Terzaghi and safety factor 2.5, the net safe bearing capacity for local shear failure is ______ kN/m$^2$.

Bearing factors (φ′: Nc, Nq, Nγ): 15°: 12.9, 4.4, 2.5; 20°: 17.7, 7.4, 5.0; 25°: 25.1, 12.7, 9.7; 30°: 37.2, 22.5, 19.7.

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Correct answer: 298 to 300

Explanation

For local shear use c*=2c/3=23.333kPa and tanφ*=2tan28.63°/3, giving φ*≈20°. The table supplies Nc17.7,Nq7.4,Nγ5.0. Water table lies one footing width below the base, so use bulk γ17kN/m³. Net ultimate pressure=c*Nc+γDf(Nq−1)+0.5γBNγ=746.2kPa; divide by2.5 to obtain **298.48kPa**.