Bishop & Janbu Slope Stability Calculator – Limit Equilibrium Methods (FoS)

Bishop & Janbu Slope Stability Calculator

Bishop Simplified • Janbu method • Factor of safety (FoS) • Slice‑based analysis • 2D profile

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📐 1. Slope Stability – Bishop vs Janbu Methods

Limit equilibrium methods (LEM) are used to compute the factor of safety (FoS) of slopes. This tool implements:

Bishop Simplified: Assumes interslice forces are horizontal. FoS solved iteratively. Generally accurate for circular slip surfaces.
Janbu Method: Assumes interslice shear forces are zero. Uses correction factor f₀. Suitable for non‑circular slips.

FoS = Σ (c·Δl + W·tanφ·cosα) / Σ (W·sinα) for simplified approach with pore pressure effects. This tool computes FoS for a user‑defined slice model.

🚀 2. Slope Stability Calculator (Slice Method)

Slope height H (m)

Slope angle β (deg)

Soil cohesion c (kPa)

Soil friction angle φ (deg)

Unit weight γ (kN/m³)

Number of slices (5–15)

Pore pressure ratio r_u (0–0.5)

Batch CSV (H, β, c, φ, γ)

Get PDF Report via Email

CSV Template

📊 3. Slope Cross‑Section & Slices

📈 4. FoS vs Slope Angle & Design History

📘 5. How to Use the Calculator

Enter slope geometry (height, slope angle).
Provide soil parameters (c, φ, γ) and pore pressure ratio.
Select number of slices (more slices = higher accuracy).
Click "Compute FoS" – Bishop and Janbu factors of safety are displayed.
2D schematic shows slope profile and slice discretization.
Batch CSV: upload multiple designs for comparison.
PDF report includes all inputs, FoS values, and sketch.

❓ Frequently Asked Questions

❓ What is a safe factor of safety?

FoS ≥ 1.5 for normal conditions, ≥1.2 for seismic or temporary works. This tool marks FoS < 1.3 as unsafe.

❓ Why does Bishop give slightly higher FoS than Janbu?

Bishop considers interslice forces and is generally more accurate for circular slip surfaces. Janbu often underestimates FoS.

❓ How does pore pressure affect stability?

High pore pressure reduces effective stress, lowering shear strength and FoS. r_u = u / (γ·z) approximates this effect.

🌐 References

Bishop (1955) – Geotechnique | Janbu et al. (1956) | GeoSlope stability theory

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Bishop & Janbu Slope Stability Calculator – Limit Equilibrium Methods for Factor of Safety