GATE 2026 AG – Question 57
A homogeneous earthen embankment retains water 12 m deep. Crest width is 3 m, upstream/downstream slopes are 2H:1V and 2.5H:1V, and freeboard is 2 m. Permeability is $2.5\times10^{-5}$ m/s. A horizontal filter extends 20 m inward from the downstream toe. If seepage per unit length is $n\times10^{-5}\,\mathrm{m^3/(s\,m)}$,find n, to two decimals.
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Correct answer: 5.91 to 5.95
Explanation
Total dam height is $H=12+2=14$ m, so base width is $B=2(14)+3+2.5(14)=66$ m. The upstream waterline meets the slope 24 m from the upstream toe, and the filter begins at $66-20=46$ m. Their horizontal separation is 22 m. Casagrande’s entry correction adds $.3(24)=7.2$ m, giving $d=29.2$ m. For the base parabola,$y_0=\sqrt{d^2+h^2}-d=\sqrt{29.2^2+12^2}-29.2=2.3696$ m. Seepage $q=ky_0\approx5.924\times10^{-5}$,so **n=5.92** (about 5.93 depending on intermediate rounding).