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Slope Stability / Factor of Safety Calculator

Calculate factor of safety for slope stability using infinite slope, planar failure, Fellenius, and Bishop simplified methods. Supports pore pressure, tension cracks, surcharge, and seismic loads.

Soil Mechanics Geotechnical engineers, civil engineers, mining engineers Commercial Intent: HIGH

Engineering Formulas

Infinite Slope (Dry)

FS = (c + γ × H × cos²β × tanφ) / (γ × H × sinβ × cosβ)
c: Cohesion (kPa)
γ: Unit weight (kN/m³)
H: Slope height (m)
β: Slope angle (°)
φ: Friction angle (°)

Infinite Slope (with Seepage)

FS = (c + (γsat — γw) × H × cos²β × tanφ) / (γsat × H × sinβ × cosβ)
γ_sat: Saturated unit weight (kN/m³)
γ_w: Water unit weight (9.81 kN/m³)

Planar Failure

FS = (c × L + W × cosβ × tanφ) / (W × sinβ) L = H / sinβ W = 0.5 × γ × H² / tanβ
L: Length of failure plane (m)
W: Weight of failure wedge (kN/m)

Fellenius (Swedish) Method

FS = Σ(c×lᵢ + (Wᵢ×cosαᵢ — uᵢ×lᵢ)×tanφ) / Σ(Wᵢ×sinαᵢ)
lᵢ: Slice base length (m)
αᵢ: Slice base angle (°)
Wᵢ: Slice weight (kN/m)
uᵢ: Pore pressure at slice base (kPa)

Bishop Simplified

FS = Σ((c×lᵢ + (Wᵢ — uᵢ×lᵢ)×tanφ) / mα) / Σ(Wᵢ×sinαᵢ) mα = cosαᵢ + sinαᵢ × tanφ / FS (iterative)
mα: Bishop coefficient (depends on FS, solved iteratively)

Worked Example

Infinite Slope in Sandy Soil

analysisType: infiniteslopeAngle: 30slopeHeight: 10unitWeight: 18cohesion: 5frictionAngle: 32seepage: falsesurcharge: 0seismicCoeff: 0porePressureRatio: 0tensionCrack: 0
Parameters
β = 30°, H = 10 m, γ = 18 kN/m³, c = 5 kPa, φ = 32°
Denominator
γ × H × sinβ × cosβ = 18 × 10 × 0.5 × 0.866 = 77.94
Numerator
c + γ × H × cos²β × tanφ = 5 + 18 × 10 × 0.75 × 0.625 = 5 + 84.38 = 89.38
FS
FS = 89.38 / 77.94 = 1.15
Result: FS = 1.15 — Unstable (FS < 1.2). Consider flattening slope, adding drainage, or installing retaining structure.

Engineering Notes

Always analyze both short-term (end-of-construction) and long-term (steady-state) conditions.
For cuts in clay, short-term undrained analysis using φ = 0, su is critical.
For fills, long-term drained analysis with effective stress parameters governs.
Seismic analysis should be performed for slopes in seismic zones (IS 1893).
Three-dimensional effects can increase FS by 10–30% compared to 2D analysis.

Assumptions

• Soil is homogeneous and isotropic
• Mohr-Coulomb failure criterion applies
• Plane strain conditions (infinite slope / 2D slice methods)
• Circular slip surface for Fellenius and Bishop methods
• No three-dimensional effects considered

Common Mistakes

✕ Using total stress parameters for long-term (drained) analysis
✕ Forgetting to convert degrees to radians in trigonometric functions
✕ Not considering the effect of tension cracks on failure surface length
✕ Ignoring pore water pressure in fine-grained slopes during rainy season
✕ Using too few slices for Fellenius or Bishop methods (need at least 4–6)

Frequently Asked Questions

What is a minimum acceptable factor of safety?

For permanent slopes: FS ≥ 1.5 (static), ≥ 1.2 (seismic). For temporary slopes: FS ≥ 1.3 (static). For dams: FS ≥ 1.5 for end-of-construction, ≥ 1.4 for steady seepage.

What is the difference between infinite and finite slope analysis?

Infinite slope analysis assumes the failure plane is parallel to the slope surface with depth << length — suitable for long, shallow slopes. Finite slope analysis (Fellenius, Bishop) considers circular or planar failure surfaces in a limited soil mass.

What is the Fellenius method?

The Fellenius (Swedish) method divides the slope into vertical slices and calculates FS as the ratio of resisting to driving moments. It is the simplest slice method but can underestimate FS for high pore pressures.

What is the Bishop simplified method?

Bishop simplified also uses vertical slices but considers interslice normal forces (ignoring shear). It is more accurate than Fellenius and is widely used. FS is found iteratively.

How does pore water pressure affect stability?

Pore water pressure reduces effective stress, which reduces shear strength. Higher pore pressure = lower FS. The ratio r_u = pore pressure / overburden stress is a common parameter.

What is pseudostatic analysis?

Pseudostatic analysis adds a horizontal seismic force (k_h × W) to the driving side to simulate earthquake loading. Typical k_h values: 0.05–0.15 for low to moderate seismicity, 0.15–0.30 for high seismicity.

How many slices are needed for slice methods?

At least 4–6 slices for preliminary analysis, 10–15 for detailed analysis. More slices = better accuracy but diminishing returns beyond 20 slices.

What is a tension crack?

A tension crack forms at the crest of a cohesive slope due to tensile stress. It reduces the length of the failure surface and can collect water, increasing pore pressure in the crack.

References & Standards

IS 7894Eurocode 7 (EN 1997-1)USACE EM 1110-2-1902Duncan & Wright (2005)
IS 7894
Code of Practice for Stability Analysis of Earth Dams
Eurocode 7 (EN 1997-1)
Geotechnical Design — Slope Stability Requirements
USACE EM 1110-2-1902
US Army Corps of Engineers — Slope Stability Manual
Duncan & Wright (2005)
Soil Strength and Slope Stability — definitive reference

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