GATE AG 2021 • Q28 NAT • 1 Mark

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Stability of slopes

Question Statement:

Cohesionless soil is naturally deposited and makes a slope of infinite extent having slope angle of 25°. If the effective angle of internal friction of this soil is 30°, the factor of safety of slope is ______. [round off to 2 decimal places]

Official Answer Key:

1.22 to 1.25

Step-by-Step Solution & Explanation

For an infinite slope in cohesionless (c′ = 0) soil, Factor of Safety FS = tan(φ′)/tan(β), where β is the slope angle. FS = tan(30°)/tan(25°) = 0.5774/0.4663 = 1.24.

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