What this calculator does
A slope stands or fails on one number: the factor of safety. The equation is short, but choosing the slip surface is the judgement, and this tool therefore uses the surface you describe rather than pretending to search for the critical one.
How to use it
- Describe the circular slip surface as vertical slices: weight, base length and pore pressure for each.
- Enter the effective cohesion and friction angle from your soil investigation — no soil table is held here.
- Enter the soil unit weight so slice heights can be derived consistently.
- Check which resistance is doing the work: a friction-dominated slope responds to drainage, a cohesion-dominated one does not.
Governing method
Governing Formula
FoS = Σ(c·L + N·tanφ) / Σ(W·sinα) Where:
-
= Effective cohesion, kPa -
= Effective friction angle, degrees -
= Slice weight, kN/m -
= Pore pressure on the base, kPa -
= Slip surface angle of the slice
Assumptions & limitations
- Only the slip surface you describe is analysed. This is not a search for the critical surface.
- The ordinary method ignores interslice forces, which makes it slightly unconservative for long slopes.
- Cohesion and friction angle are your inputs from your soil investigation; no soil table is held.
- No code acceptance criterion is applied. The 1.3 quoted in the verdict is a commonly used guidance figure, not a compliance claim.
Worked example — two slices, c = 5 kPa, φ = 30°
| Cohesion | 5 kPa |
|---|---|
| Friction angle | 30° |
| Soil unit weight | 20 kN/m³ |
| Slice 1 | 200 kN/m, 4 m base, 0 kPa pore |
| Slice 2 | 200 kN/m, 4 m base, 0 kPa pore |
Cohesion supplies 5 kPa over 8 m of base = 40 kN/m, and friction supplies the remainder from the normal force on each slice. Adding pore pressure lowers the normal force and raises the friction available, which is why drainage is usually the first lever on a marginal slope.