GATE 2025 CE (CE2) – Question 31
From a flow-net diagram drawn under a concrete dam, following information are obtained: (i) The head difference between upstream and downstream side of the dam is 9 m. (ii) The total number of equipotential drops between upstream and downstream side of the dam is 10. (iii) The length of the field nearest to the toe of the dam in the downstream side is 1 m.
If the soil below the dam is having a saturated unit weight of 21 kN/m$^3$ and unit weight of water is 9.81 kN/m$^3$, then the factor of safety against the quick condition will be ______ (round off to two decimal places).
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Correct answer: 1.26 to 1.28
Explanation
The head lost in each drop is $\frac{9}{10} = 0.9$ m. The exit gradient is the head loss in the last field divided by its length, $i_e = \frac{0.9}{1} = 0.9$. The critical gradient is $i_c = \frac{\gamma_{sat} - \gamma_w}{\gamma_w} = \frac{21 - 9.81}{9.81} = 1.141$. The factor of safety is $\frac{i_c}{i_e} = \frac{1.141}{0.9} = 1.27$.