GATE AG 2009 • Q32 MCQ • 1 Mark

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Engineering properties of soils

Question Statement:

The intensity of active earth pressure in kPa at a depth of 10 m in dry cohesionless sand with an angle of internal friction of 25° and specific weight of 15 kN m⁻³ is

Options:

  • (A) 39
  • (B) 61
  • (C) 79
  • (D) 129

Official Answer Key:

B

Step-by-Step Solution & Explanation

Rankine's active earth pressure coefficient: Ka = (1−sinφ)/(1+sinφ) = (1−0.4226)/(1+0.4226) = 0.5774/1.4226 = 0.4059. For cohesionless soil, active pressure at depth z: pa = Ka·γ·z = 0.4059 × 15 × 10 = 60.9 kPa ≈ 61 kPa, matching option (B).

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