GATE Papers >> Civil >> 2018 >> Question No 20

Question No. 20 Civil | GATE 2018
The percent reduction in the bearing capacity of a strip footing resting on sand under flooding condition (water level at the base of the footing) when compared to the situation where the water level is at a depth much greater than the width of footing, is approximately

Answer : (C) 50

Solution of Question No 20 of GATE 2018 Civil Paper

Terzaghi's bearing capacity equation 

$\begin{array}{l}{\mathrm q}_\mathrm u={\mathrm{CN}}_\mathrm c+{\mathrm{qN}}_\mathrm q+\frac12B\gamma N_\mathrm\gamma\\\end{array}$

For cohensionless soil C = 0, Footing resting on sand surface so, Df = 0

When water level is at base of footing 

${\mathrm q}_{\mathrm u1}=\frac12{\mathrm{By}}_\mathrm{sub}{\mathrm N}_\mathrm\gamma$

When water level is at much greater depth

${\mathrm q}_{\mathrm u2}=\frac12{\mathrm{By}}_t{\mathrm N}_\mathrm\gamma$

Percentage reduction in bearing capacity

$\begin{array}{l}=\frac{{\mathrm q}_{{\mathrm u}_2}-{\mathrm q}_{{\mathrm u}_1}}{{\mathrm q}_{{\mathrm u}_1}}\times100\\=\frac{{\mathrm\gamma}_1-{\mathrm\gamma}_\mathrm{sub}}{{\mathrm\gamma}_\mathrm t}\times100\end{array}$

As ${\mathrm\gamma}_\mathrm{sub}\simeq0.5\;{\mathrm\gamma}_\mathrm t$

So, percentage reduction = 50%.

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