If an infinite slope in sand has slope angle of 35 degree and angle of internal friction is 32 degree, then the FOS against sliding is expected to be
- A1
- B>1
- C<1Correct
- D>2
Solution
Concept
Factor of Safety for Infinite Slope in Cohesionless Soil
Formula
FOS = tan(φ) / tan(β)
Step-by-step solution
1. Identify given values: φ = 32° and β = 35°. 2. Apply the formula: FOS = tan(32°) / tan(35°). 3. Compare angles: Since φ \< β (32° \< 35°), tan(32°) \< tan(35°). 4. Conclude: FOS \< 1.
Explanation
For a dry, infinite slope of cohesionless soil (sand), the Factor of Safety (FOS) against sliding is calculated as the ratio of the tangent of the friction angle (φ) to the tangent of the slope angle (β): FOS = tan(φ) / tan(β) Here, the slope angle (β = 35°) is greater than the internal friction angle (φ = 32°). Because the tangent function increases with higher angles, tan(32°) is smaller than tan(35°). Dividing a smaller number by a larger number gives a value less than 1 (FOS < 1), which means option C is correct.
Shortcut
If friction angle (φ) is less than slope angle (β), FOS is less than 1. If φ > β, FOS > 1. Since 32° < 35°, FOS < 1.
Common mistake
Students often invert the Factor of Safety formula as tan(slope angle)/tan(friction angle) instead of tan(φ)/tan(β), leading them to select >1 (Option B) instead of <1 (Option C).
Correct answer: C) <1