The Factor of Safety (FOS) against the sliding of an Earthen Slope is defined as the ratio of
- ADriving force to Resisting force.
- BMaximum shear strength to the mobilized shear stress along the failure surface.Correct
- CTotal weight of the slope to the pore water pressure.
- DHeight of the slope to the depth of the hard strata.
Solution
Concept
Factor of Safety in Slope Stability
Formula
FOS = Shear Strength / Mobilized Shear Stress
Step-by-step solution
1. Review the question regarding the definition of Factor of Safety (FOS) against the sliding of an earthen slope. 2. Recall the formula for FOS in slope stability: FOS = Maximum Shear Strength / Mobilized Shear Stress. 3. Compare this definition with the options and select Option (b) as the correct choice.
Explanation
Option B correctly defines the Factor of Safety as the ratio between the maximum shear strength (the total resisting capacity of the soil) and the mobilized shear stress (the actual stress acting along the sliding surface due to loads and gravity). If the available strength exceeds the stress trying to slide the slope, the factor of safety is greater than 1, indicating a stable slope.
Shortcut
To remember the Factor of Safety (FOS) in slope stability, use the rule "Resisting over Driving" (Strength over Stress): - Resisting (Strength): Maximum shear strength available goes on top (Numerator) - Driving (Stress): Actual mobilized shear stress causing sliding goes on bottom (Denominator) - Safety Rule: Ratio must be greater than 1 for a stable slope (Strength \> Stress)
Common mistake
A common mistake is selecting option A by incorrectly reversing the ratio as driving force to resisting force. In reality, the Factor of Safety is the ratio of resisting force (or shear strength) to driving force (or mobilized shear stress), meaning the resisting capacity must be in the numerator for FOS to be greater than 1 for a stable slope.
Correct answer: B) Maximum shear strength to the mobilized shear stress along the failure surface.