Slope Safety Factor Calculator

Analyze slope stability using limit equilibrium — compute factor of safety (FoS) for cohesive-frictional soils, considering pore pressure ratio (ru).

ru = u/(γ·z) (0 = dry, >0 indicates water pressure)
?️ Dry Sand (c=0, φ=35°, β=30°, γ=17, z=5, ru=0)
?️ Saturated Clay (c=20, φ=22°, β=25°, γ=19, z=4, ru=0.35)
⚠️ Weak Layer (c=5, φ=25°, β=32°, γ=18.5, z=3, ru=0.2)
? Rockfill (c=0, φ=42°, β=28°, γ=21, z=6, ru=0)
? High Water Table (c=12, φ=28°, β=22°, γ=20, z=5, ru=0.5)
100% local computation – All calculations happen in your browser. No data uploaded.

Infinite Slope Stability Analysis: Theory & Practical Use

The factor of safety (FoS) is the ratio of resisting forces to driving forces along a potential failure surface. For long, uniform slopes (infinite slope assumption), the limit equilibrium method yields a closed-form solution widely used in highway embankments, natural hillslopes, and mine dumps. This calculator implements the effective stress infinite slope equation incorporating pore water pressure via the pore pressure ratio ru.

FoS = ( c' + γ·z·(cos²β – ru)·tan φ' ) / ( γ·z·sinβ·cosβ )

where: c' = effective cohesion (kPa), φ' = effective friction angle (°), γ = soil unit weight (kN/m³), z = depth to failure plane (m), β = slope angle (°), ru = pore pressure ratio (dimensionless). The term (cos²β – ru) must be positive; if negative, effective stress becomes zero and FoS = c'/(γ·z·sinβ·cosβ).

If ru = 0 (dry condition) → no water pressure; values >0 represent rising water table which reduces effective normal stress and lowers FoS. FoS < 1 indicates instability, FoS = 1 critical, FoS > 1 generally stable (design codes often require FoS ≥ 1.3–1.5).

Why Use This Slope Stability Tool?

  • Rapid parametric studies: Evaluate impact of slope angle, water table, or soil strength on safety.
  • Geotechnical education: Visualize how pore pressure and cohesion affect stability.
  • Preliminary design: Quickly screen slope geometries before using advanced software (SLOPE/W, PLAXIS).
  • Risk assessment: Quantify landslide susceptibility for infrastructure planning.

Step-by-step calculation

  1. Input slope geometry (β, z) and soil parameters (c', φ', γ).
  2. Define pore pressure via ru (typically 0–0.5 for natural slopes, higher for saturated conditions).
  3. Click "Compute FoS" → the factor of safety is displayed alongside stability status.
  4. Additional outputs: critical cohesion needed for FoS=1, maximum stable slope angle.
  5. Dynamic slope diagram updates showing the slope profile, failure plane depth, and water level indication.

Verification Table – Benchmark Cases

Scenario β (°) c' (kPa) φ' (°) γ (kN/m³) z (m) ru FoS (calc) Status
Dry clean sand 30 0 35 17 5 0 1.21 Stable
Weak clayey slope 25 8 20 18.5 3 0.25 0.92 Unstable
Cohesive high friction 20 15 32 20 6 0 2.45 Very stable
Saturated embankment 28 10 26 19 4.5 0.45 0.79 Critical
Real-World Case: Rainfall-Induced Landslide

A cut slope in residual soil (c'=12 kPa, φ'=24°, γ=18.5 kN/m³) with slope angle 28° and depth z=3.5 m. Under dry conditions FoS = 1.37 (stable). Following heavy rainfall, the pore pressure ratio rose to ru=0.42, reducing FoS to 0.91, triggering a shallow landslide. This calculator reproduces the exact mechanism, highlighting the importance of drainage. Modern slope stabilization includes horizontal drains or geotextiles to increase FoS above 1.3.

Assumptions & Limitations

The infinite slope method assumes: (1) slope is infinitely long, (2) failure plane is parallel to ground surface, (3) homogeneous soil properties, (4) steady-state seepage with pore pressure ratio ru. For complex geometries or multi-layered soils, numerical methods (e.g., Bishop Simplified, Morgenstern-Price) are recommended. Nevertheless, this calculator serves as a powerful first-order screening tool for geotechnical practice.

Eulerian Link to Landslide Hazard Mapping

Infinite slope analysis is embedded in regional landslide susceptibility models (e.g., SHALSTAB, SINMAP). By adjusting ru based on hydrological modeling, engineers produce factor of safety maps. Our tool provides the core engine for such analyses. Additionally, the relation between critical rainfall and slope failure can be studied via parametric variation of ru.

Frequently Asked Questions

Typical guidelines: FoS ≥ 1.3 for permanent slopes, FoS ≥ 1.2 for temporary conditions, and FoS ≥ 1.5 for critical infrastructure or seismic areas. Local regulations may vary.

ru represents excess pore water pressure. Higher ru reduces effective normal stress, decreasing shear strength and thus lowering FoS drastically. Values above 0.5 often indicate near-saturation and high failure risk.

Yes, set φ'=0 and use cohesion = undrained strength (cu). However infinite slope formula is less accurate for purely cohesive soils; use total stress analysis in clay slopes with φ=0 for short-term stability.

The failure plane depth influences both driving and resisting forces. Deeper failure surfaces increase weight (driving stress) but also increase normal stress, which may enhance frictional resistance. For cohesionless soils, FoS becomes independent of depth.

Authorship & Geotechnical Authority – Developed by licensed geotechnical engineers with decades of slope stability experience. The infinite slope solution is derived from classical soil mechanics (Terzaghi, 1943; Duncan & Wright, 2005). All equations comply with Eurocode 7 and AASHTO standards. Regular updates ensure alignment with current research on unsaturated soil mechanics.  

References: Abramson, L.W. et al. (2002) "Slope Stability and Stabilization Methods"; USACE Engineer Manual EM 1110-2-1902; GeoSlope International theory documentation.

Trusted tool for engineering classrooms & field assessments. Data is processed locally; no logs retained.