Retaining & slopes · Slope stability
Slope stability: Janbu simplified (slices) calculator
Factor of safety for any (non-circular) slip surface entered as slices: width, mid-height, base inclination and pore-pressure ratio ru. Iterates the Janbu equation and applies the f0 correction.
Standard: Janbu simplified with f0 correction · non-circular
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 |
|---|---|---|
| Slices: b (m), h (m), α (°), ru | 2, 1.2, 42, 0 2, 2.8, 32, 0.1 2, 3.6, 22, 0.15 2, 3.4, 12, 0.15 2, 2.4, 4, 0.1 2, 1.0, -4, 0 | |
| Unit weight γ | 19 | kN/m³ |
| Cohesion c′ | 8 | kPa |
| Friction angle φ′ | 28 | ° |
| Depth of slip below chord, d | 1.8 | m |
| Chord length of slip, L | 12.5 | m |
| Required FS | 1.5 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| FS0 (uncorrected) | 2.010 | |
| Correction f0 | 1.057 | |
| FS = f0·FS0 | 2.126 | |
| Iterations | 7 | |
| Σ W tanα | 194.0 | kN/m |
- ✓ FS ≥ required — 2.13
Method, formulas and assumptions
- W = γbh; u = ru·γh
- FS0 = Σ[(c′b + (W − ub) tanφ′) / (cos²α (1 + tanα tanφ′/FS))] / Σ W tanα (iterated)
- f0 = 1 + b1[d/L − 1.4(d/L)²]; b1 = 0.5 (c′–φ′), 0.31 (φ′ only), 0.69 (c′ only)
- Spencer and Morgenstern–Price (full equilibrium) are not implemented. Janbu simplified satisfies force equilibrium only.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.