Retaining & slopes · Slope stability
Infinite slope (static & pseudo-static) calculator
Factor of safety for a long translational slide with seepage, seismic coefficient and the yield acceleration ky.
Standard: Infinite slope · Mohr–Coulomb · yield acceleration
Open the live calculator → All retaining & slopes calculators
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Slope angle β | 26 | ° |
| Depth of slip plane z | 2.5 | m |
| Soil γ | 19 | kN/m³ |
| c′ | 4 | kPa |
| φ′ | 32 | ° |
| Water ratio m (water height / z) | 0.5 | |
| Seismic coefficient kh | 0.1 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| FS static | 1.164 | |
| FS pseudo-static | 0.914 | |
| Yield coefficient ky (FS = 1) | 0.061 | g |
- ✗ Static FS ≥ 1.5
- ✗ Pseudo-static FS ≥ 1.1
Method, formulas and assumptions
- σn = γz(cos²β − kh sinβ cosβ); τ = γz(sinβ cosβ + kh cos²β)
- u = m·γw·z·cos²β (seepage parallel to slope)
- FS = [c′ + (σn − u)tanφ′]/τ
- ky by bisection where FS = 1
Related retaining & slopes calculators
- Slope stability (Bishop / Fellenius, grid search) — Multi-layer slope with water table, crest surcharge and seismic coefficient. Searches a grid of centres for…
- Slope stability: Janbu simplified (slices) — Factor of safety for any (non-circular) slip surface entered as slices: width, mid-height, base inclination…
- Slope stability: Spencer & Morgenstern–Price with reinforcement and earthquake — Layered slope with a phreatic line, crest surcharge and a horizontal seismic coefficient. Finds the critical…
- Planar failure with tension crack (Hoek & Bray) — Factor of safety of a planar slide with a water-filled tension crack, uplift on the plane and optional…
- Anti-slide (stabilising) piles in a slope — Force each pile must provide to raise the slope factor of safety, the moment and shear at the slip surface…
- Lateral earth pressure — Active, passive or at-rest pressure diagram with water table, surcharge and cohesion.
For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.