Slope Stability Calculator
Compute the factor of safety against sliding failure on an infinite slope using soil strength and groundwater parameters. Used by geotechnical engineers assessing embankments, hillside cuts, and natural slopes.
About this calculator
The infinite slope model is the simplest analytical method for evaluating slope stability where the failure surface runs parallel to the ground surface at shallow depth. The factor of safety FS is: FS = [c′ + γ·z·(1 − m)·cos α · tan φ′] / [γ·z·sin α], where c′ is effective cohesion (kN/m²), γ is soil unit weight (kN/m³), z is the depth to the failure plane (m), α is the slope angle (°), φ′ is the internal friction angle (°), and m is the water-table ratio (0 = dry, 1 = fully saturated). A FS above 1.5 is generally considered safe, 1.0–1.5 is marginal, and below 1.0 indicates failure. Pore-water pressure from a high water table significantly reduces effective stress and, consequently, the resisting force.
How to use
Given: slope angle α = 30°, cohesion c′ = 5 kN/m², friction angle φ′ = 25°, unit weight γ = 18 kN/m³, failure depth z = 3 m, water table condition m = 0 (dry). Step 1 — Numerator: 5 + (18 × 3 × 1 × cos 30° × tan 25°) = 5 + (54 × 0.866 × 0.466) = 5 + 21.79 = 26.79. Step 2 — Denominator: 18 × 3 × sin 30° = 54 × 0.5 = 27.0. Step 3 — FS = 26.79 / 27.0 ≈ 0.99. This result is just below 1.0, indicating the slope is at the verge of failure — steepening or saturating it would trigger sliding.
Frequently asked questions
What factor of safety is considered acceptable for slope stability in geotechnical engineering?
Most geotechnical codes and standards require a minimum factor of safety of 1.5 for permanent slopes under static loading. For temporary construction slopes a FS of 1.25 is sometimes accepted. Critical infrastructure such as dams or highway embankments may demand FS ≥ 2.0. When dynamic loads such as earthquakes are included in the analysis, lower values around 1.1–1.2 may be tolerated because seismic events are transient. Always consult local building codes and a licensed geotechnical engineer for site-specific decisions.
How does a rising water table affect slope stability and factor of safety?
A rising water table increases pore-water pressure within the soil, which reduces effective normal stress on the failure plane. Since shear strength (the resisting force) depends on effective stress, higher pore pressure directly lowers the factor of safety. In the infinite slope formula, the term (1 − m) shows this effect: when m = 1 (fully saturated), the cohesion-independent friction contribution is eliminated entirely. This is why many slope failures occur during or immediately after heavy rainfall events that raise the water table.
When is the infinite slope method appropriate versus more advanced stability analyses?
The infinite slope method is appropriate when the failure surface is long relative to the depth — typically a depth-to-length ratio less than about 0.1 — and runs parallel to the slope surface. It works well for shallow translational failures in uniform soils, such as debris slides or shallow cut slopes. For deeper rotational failures, irregular geometry, layered soils, or complex pore-pressure distributions, methods such as Bishop's Simplified, Janbu, or Spencer's method — or finite-element analysis — are more appropriate and accurate.