Slope Stability Calculator (Infinite Slope)
The factor of safety of a long, shallow soil slope against sliding — the infinite-slope method — with the dry-versus-seepage switch that shows why so many slopes fail after heavy rain.
When a Hillside Decides to Move
A slope stays put as long as the soil’s shear strength along a potential slip surface beats the gravity component trying to slide it downhill. The ratio of the two is the factor of safety. For a long, uniform slope where any failure plane runs parallel to the surface, the infinite-slope model captures that balance in a single equation.
The numerator is the soil’s strength — cohesion plus frictional resistance; the denominator is the driving shear stress from gravity. Notice the depth z appears in both terms only when there is cohesion: a purely frictional (cohesionless) slope has FS = tanφ′ / tanβ, independent of depth. That is why dry sand always rests at its angle of repose.
Why Slopes Fail After Rain
Add groundwater seeping parallel to the slope and the pore pressure cuts the effective stress that holds the soil together. The frictional strength term now uses the buoyant unit weight (γ minus the unit weight of water) instead of the full weight — roughly halving it. A cohesionless slope safe when dry at FS around 1.2 can drop below 1.0 fully saturated, which is exactly when hillsides let go.
Frequently Asked Questions
What factor of safety is acceptable?
Permanent slopes are usually designed for at least 1.5; temporary works may accept 1.3. Below 1.0 the model predicts failure. These are typical targets – the governing standard and risk decide the real requirement.
When is the infinite-slope model valid?
When the slope is long relative to the failure depth and the soil is reasonably uniform, so the slip surface is essentially planar and parallel to the surface. Short slopes and deep rotational failures need a circular (Bishop or Spencer) analysis.
What is the angle of repose?
For dry cohesionless soil, the steepest stable slope – where tan beta equals tan phi, so FS = 1. Pile dry sand and it settles to this angle on its own.
Related calculators
- Retaining Wall Calculator — holding back a slope that will not stand on its own.
- Excavation Calculator — cut volumes and batter for a stable face.
- Soil Bearing Capacity Calculator — how much load the ground can carry.
- Engineering Unit Converter — pressure and unit-weight units.