Layered slope stability
The Bishop search assumes one homogeneous soil and a circular surface. Neither holds on a real site: a residual soil over weathered rock over fresh rock is three different strengths, and the critical surface usually follows the weak layer rather than a circle. Janbu’s method works on any surface, so it is the natural choice once the geometry stops being a single wedge.
| Layer | c’ (kPa) | φ’ (°) | γ (kN/m³) |
|---|---|---|---|
| Layer 1 — 5.0 m | 5 | 20 | 18.0 |
| Layer 2 — 5.0 m | 15 | 25 | 19.0 |
| Layer 3 — 10.0 m | 50 | 30 | 20.0 |
| Slope height | 10.0 m | — | — |
| Slope angle | 30° | — | — |
| Pore pressure ratio | 0.20 | — | — |
| Raw Janbu F | 1.31 | — | — |
| Correction f₀ | 1.08 | — | — |
| Corrected F | 1.42 | Stable | — |
The critical surface runs to 9.9 m below the crest, mostly in layer 2. Janbu's correction raises the raw 1.31 to 1.42, which is stable.
F = Σ[c b + (W−ub)tanφ]/n_α ÷ Σ W tanα · Any surface.
cos²α(1 + tanα tanφ/F) · Implicit in F.
f₀ = 1 + 0.69[(d/L) − 1.4(d/L)²] · Janbu 1973.
by elevation at the slice base · Strength varies.
A clear path from inputs to results.
The Bishop search assumes one homogeneous soil and a circular surface. Neither holds on a real site: a residual soil over weathered rock is three different strengths, and the critical surface usually follows the weak layer.
How to use
- Enter the slope height and angle.
- Set the thickness and strength of each layer.
- Add the pore pressure ratio.
- Read the corrected factor of safety and the critical layer.
The formula
Reference: Janbu simplified method with the f₀ correction (Janbu 1973), on a non-circular surface.
Worked example
A 10 m slope over three layers
- 10 m at 30°, three layers: 5 m at c’ 5/φ’ 20, 5 m at 15/25, then 50/30.
- Pore pressure ratio 0.2.
- 1
The surface is searched as two segments through the toe and the crest.
- 2
Each slice takes the strength of the layer at its base.
- 3
Janbu iterates on F because n_α depends on it.
- 4
The raw factor is multiplied by f₀ = 1 + 0.69[(d/L) − 1.4(d/L)²].
- 5
The corrected result identifies which layer the surface runs deepest into.
A corrected factor of safety with the critical layer identified.
Interpreting the result
The layer boundaries matter more than the averages. A thin weak seam will pull the critical surface to it however strong the material above and below, which is why a site investigation that samples only the bulk soil can miss the mechanism entirely.
Assumptions & limitations
- Up to three layers, defined by elevation.
- A two-segment non-circular surface.
- Each slice takes the strength of the layer at its base.
- No reinforcement, no seismic load and no external surcharge.
Frequently asked questions
Why Janbu rather than Bishop?
Because Bishop requires a circular surface. Once the profile is layered the critical surface follows the weak layer and is generally not circular, so a method that accepts any shape is needed.
How accurate is the correction?
Within about 5% for a typical slope, which is well inside the uncertainty in the strength parameters.
What if the surface crosses a thin seam?
That is exactly the case this page is for. Set the seam as one of the layers and the search will find whether the surface prefers to run along it.
Why is the raw answer lower?
Janbu ignores the interslice forces that Bishop partly accounts for, so it is less accurate. The f₀ correction brings it back into line with more rigorous methods.
Can I have more than three layers?
The method generalises to any number; three covers most profiles and keeps the interface readable.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.