---
title: "Factor of safety"
subject: "Engineering Geology II"
chapter: 6
key: "semester_4/engineering_geology_ii:factor-of-safety"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/factor-of-safety
site: BCT Engineering
---

# Factor of safety

Engineering Geology II · Chapter 6: Measurement, analysis and interpretation of structural geological data

- Asked in: 2072 Asoj, 2 marks
- Video: [Slope stability: failure definition and factor of safety](https://www.youtube.com/watch?v=lfrRzlPlv-I) — GEOTECH VIDEOS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/factor-of-safety
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-6

## Question

What is factor of safety?

## Short answer

Factor of safety is the ratio of resisting force/shear strength to driving force/shear stress along a failure surface. FS >1 is stable, FS=1 is limiting equilibrium, FS<1 fails. Design values are usually 1.3–1.5 for permanent slopes and 1.2–1.3 for temporary slopes; water and earthquakes reduce FS.

## Answer

The **factor of safety (FS)** of a slope is the ratio of the forces (or shear strength) resisting failure to the forces (or shear stress) driving failure along the potential failure surface.

$$
FS = \frac{\text{resisting force (shear strength)}}{\text{driving force (shear stress)}}
$$

For plane failure of a block of weight $W$ on a plane of dip $\psi_p$, area $A$, cohesion $c$ and friction angle $\phi$ (dry):
$$
FS = \frac{cA + W\cos\psi_p\tan\phi}{W\sin\psi_p}
$$

- $FS > 1$: stable; $FS = 1$: limiting equilibrium; $FS < 1$: failure.
- Design values are usually $FS \geq 1.3$ to $1.5$ for permanent slopes and about $1.2$ to $1.3$ for temporary slopes. Water and earthquake loads reduce the factor of safety.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is FS?
   A. Driving force / resisting force
   B. Resisting force (shear strength) / driving force (shear stress)
   C. Weight / area
   D. Cohesion / friction
   Answer: B. FS is resistance over driving effect. (Key point: Definition)

2. What does FS = 1 mean?
   A. Stable
   B. Failed
   C. Limiting equilibrium
   D. Overdesigned
   Answer: C. FS > 1 stable, = 1 limiting equilibrium, < 1 failure. (Key point: Meaning of values)

3. Dry plane FS equals which?
   A. (cA + W sin psi tan phi) / (W cos psi)
   B. (cA + W cos psi tan phi) / (W sin psi)
   C. W sin psi / cA
   D. tan psi / tan phi only
   Answer: B. Resisting = cA + W cos psi tan phi; driving = W sin psi. (Key point: Plane formula)

## Related in other subjects

- [Short note: Factor of safety](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Ashort-note-factor-of-safety) — Engineering Geology I, chapter 6, asked 2×
- [Factor of safety and partial safety factor](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Afactor-safety-partial-safety) — Design of Steel and Timber Structure, chapter 3, asked 2×
- [Gumbel design flood, safety factor, confidence limits](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agumbel-20yr-life35-rel87) — Engineering Hydrology, chapter 6
- [Gumbel design flood, factor of safety 1.3, 45-year life](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agumbel-25yr-life45-fos1-3) — Engineering Hydrology, chapter 6