GATE 2019 CE (CE1) – Question 65
A square footing of side 4 m at depth 1 m in dry sand has ultimate bearing capacity 600 kPa. Sand unit weight is 15 kN/m³; take $d_c=d_q=d_\gamma=1.0$ and $N_\gamma=18.75$. If the footing is placed at depth 2 m in the same soil, find safe bearing capacity (kPa) with safety factor 3 using Terzaghi’s theory.
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Correct answer: 240 to 240 OR 250 to 250 OR 270 to 270
Explanation
Terzaghi’s square-footing sand term is $0.4\gamma BN_\gamma=0.4(15)(4)(18.75)=450$ kPa. At 1 m depth, $600-450=15(1)N_q$, so Nq = 10. At 2 m, gross ultimate is $450+15(2)(10)=750$ kPa and net ultimate is 720 kPa. Net safe is **720/3 = 240 kPa**; gross safe is **240 + 30 = 270 kPa**; dividing gross ultimate directly gives **750/3 = 250 kPa**. The official key explicitly accepts all three conventions.