# GATE Papers >> Civil >> 2019 >> Question No 165

Question No. 165

A square footing of 2 m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction $\mathrm\phi=25^\circ$, and unit weight $\mathrm\gamma=18$ kN/m3 . Terzaghi’s bearing capacity factors for $\mathrm\phi=25^\circ$ are Nc = 25.1, Nq = 12.7,${N}_{\gamma }=9.7,{N}_{c}^{\text{'}}=14.8,{N}_{q}^{\text{'}}=5.6,$ and ${\mathrm{N}}_{\mathrm{\gamma }}^{\text{'}}=3.2.$ The ultimate bearing capacity of the foundation (in kPa, round off to 2 decimal places) is _________

##### Answer : 350.00 to 355.00

Solution of Question No 165 of GATE 2019 Civil Paper

$\begin{array}{l}\mathrm\phi=25^\circ<29^\circ\Rightarrow\mathrm{Local}\;\mathrm{shear}\;\mathrm{failure}\\{\mathrm C}_{\mathrm m}=\frac23\mathrm C=\frac23\times24=16\mathrm{kPa}\end{array}$

As per Terraghi's theory

For square footing

$\begin{array}{l}\mathrm{Ultimate}\;\mathrm{bearing}\;\mathrm{capacity}\;\left({\mathrm q}_{\mathrm u}\right)=1.3{\mathrm C}_{\mathrm m}{\mathrm N}_{\mathrm C}+{\mathrm{γD}}_{\mathrm f}{\mathrm N}_{\mathrm q}+0.4\mathrm{γB}.{\mathrm N}_{\mathrm\gamma}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=1.3\times16\times14.8+0+0.4\times18\times2\times3.2\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=307.84+46.08=353.92\mathrm{kPa}\end{array}$

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