GATE AG 2007 • Q49 MCQ • 1 Mark

Section 4: Soil and Water Conservation Engineering

Soil and Water Erosion

Subtopic: Earthen dams

Question Statement:

A drop spillway is subjected to horizontal and vertical forces of 40.8 kN and 36.5 kN respectively. The area of plane of sliding is 10 m². Angle of internal friction and cohesive resistance of foundation material are 25° and 4.9 kPa respectively. The factor of safety against sliding is

Options:

  • (A) 0.53
  • (B) 0.61
  • (C) 1.62
  • (D) 1.86

Official Answer Key:

C

Step-by-Step Solution & Explanation

Resisting force = cohesion×area + (vertical force)×tan φ = 4.9×10 + 36.5×tan25° = 49.0+17.02 = 66.02 kN. Driving (horizontal) force = 40.8 kN. FS = resisting/driving = 66.02/40.8 = 1.62.

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