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GATE 2017 CE (CE2) – Question 47

Geotechnical Engineering · Stability of slopes · 2 marks · Multiple choice

At A on the potential slip surface of the highway cut shown, shear stress is 50 kPa. Soil parameters are $c^\prime=20$ kPa, $\phi^\prime=18^\circ$, $s_u=80$ kPa; unit weights above/below groundwater are 18/20 kN/m³. Take water unit weight 9.81 kN/m³. Factors of safety for undrained and drained conditions, respectively, are ______.

Diagram for GATE 2017 CE (CE2) question 47
  1. 1.6 and 0.9
  2. 0.9 and 1.6
  3. 0.6 and 1.2
  4. 1.2 and 0.6

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Show answer and explanation

Correct answer: (A) 1.6 and 0.9

Explanation

Undrained safety factor is $s_u/\tau=80/50=1.6$. At A, total normal stress is $18(2)+20(4)=116$ kPa and pore pressure is $9.81(4)=39.24$ kPa. Drained strength is $20+(116-39.24)\tan18^\circ=44.94$ kPa, giving $F=44.94/50\approx0.9$. Answer A.