Infinite-Slope Factor of Safety

F S = \frac{c ^{'}}{γ H sin β cos β} + \frac{tan ϕ ^{'}}{tan β} (seepage parallel: use γ^{'} / γ_{b} form)

Long planar failure parallel to the slope (residual soil, shale). Dry cohesionless: FS=tanφ/tanβ. Seepage parallel to slope replaces γ with γ' in the tanφ term (worst). Need FS≥1.3–1.5 typically.

$β$: Slope angle
$H$: Depth of the failure plane
$c^{'}, φ^{'}$: Effective strength

Step-by-step solved example

Sand c'=0, φ'=32°, β=20°, dry. FS?

Infinite slope: failure plane at depth H, angle β.

1. Ratio
tan32/tan20=0.625/0.364=1.72.
2. Verdict
>1.5, generally OK for a dry sand slope this flat.

Answer: FS = 1.72

10 practice questions

0/10 correct

1.If β=φ and c=0, dry FS=

2.Seepage parallel (worst) for cohesionless uses

3.c'>0 helps more when H is

4.φ=30°, β=15°, c=0 dry: FS=

5.Method of slices (Bishop) is for

6.Rapid drawdown is dangerous because

7.A tension crack at the crest is often

8.γ=20 kN/m³, H=1.5 m, β=30°, c=5 kPa, φ=0: FS from cohesion term

9.Vegetation roots mainly add

10.If β>φ and c=0 the dry infinite slope