Retaining & slopes · Slope stability
Slope stability (Bishop / Fellenius, grid search) calculator
Multi-layer slope with water table, crest surcharge and seismic coefficient. Searches a grid of centres for the critical circle and draws it with slices.
Standard: Bishop simplified (1955) · Fellenius OMS · circular grid search · pseudo-static kh
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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 height H | 8 | m |
| Slope angle β | 33.7 | ° |
| Layers top→down: bottom elevation (m, toe = 0), γ, c′, φ′ | 5, 18, 5, 28 -2, 19, 12, 24 -30, 20, 30, 30 | |
| Water table elevation (below toe = dry) | 2 | m |
| Crest surcharge q | 10 | kPa |
| Seismic coefficient kh | 0 | |
| Method | Bishop simplified | |
| Search grid (centres per side) | 12 | |
| Required FS | 1.5 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Critical FS (Bishop) | 1.290 | |
| Same circle, Fellenius | 1.200 | |
| Centre (x, y) | 10.47, 13.05 | m |
| Radius | 13.14 | m |
| Entry / exit x | -1.62 / 12.05 | m |
| Slices | 30 | |
| Total sliding weight | 679 | kN/m |
- ✗ FS ≥ 1.5
- ✓ Critical circle is not on the grid edge (else widen the search)
Method, formulas and assumptions
- Ground: crest at x ≤ 0, toe at x = H/tanβ; centres searched over a 12×12 grid with toe, tangent-depth and face-exit radii
- Fellenius: FS = Σ[c′l + (W cosα − ul)tanφ′] / Σ[W sinα + kh·W·a/R]
- Bishop: FS = Σ{[c′b + (W − ub)tanφ′]/mα} / Σ[W sinα + kh·W·a/R], mα = cosα + sinα·tanφ′/FS (iterated)
- u from a horizontal water table; ponded water above the toe is ignored (conservative for drawdown, unconservative for submerged toes)
- A screening tool: use dedicated software (e.g. GEO5, Slide) for design
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.