GATE 2024 CE (CE2) – Question 53
A homogeneous earth dam has a maximum water head difference of 15 m between the upstream and downstream sides. A flownet was drawn with the number of potential drops as 10 and the average length of the element as 3 m. Specific gravity of the soil is 2.65. For a factor of safety of 2.0 against piping failure, void ratio of the soil is ______________ (rounded off to 2 decimal places).
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Correct answer: 0.64 to 0.66
Explanation
The head loss per drop is $\frac{15}{10} = 1.5$ m and the exit gradient is $i_e = \frac{1.5}{3} = 0.5$. The factor of safety against piping is $\frac{i_c}{i_e} = 2$, so $i_c = 1.0$. The critical gradient is $i_c = \frac{G_s - 1}{1 + e} = \frac{1.65}{1 + e} = 1$, so $e = 0.65$.