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GATE 2018 CE (CE2) – Question 18

Geotechnical Engineering · Permeability and seepage: flow nets, uplift pressure, piping, capillarity · 1 mark · Multiple choice

A flow net below a dam has 24 equipotential drops and 7 flow channels. Upstream-to-downstream head difference is 6 m. The flow-line length adjacent to the toe at exit is 1 m. Soil specific gravity and void ratio are 2.70 and 0.70. The piping factor of safety is ______.

  1. 1.67
  2. 2.5
  3. 3.4
  4. 4

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Correct answer: (D) 4

Explanation

Head loss per drop is $6/24=0.25$ m, giving exit gradient $i_e=0.25/1=0.25$. Critical gradient is $i_c=(G_s-1)/(1+e)=(2.70-1)/(1+0.70)=1$. Thus piping safety factor is $i_c/i_e=4$ (D).