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Home/Biophysics, Fluids & Geoscience/Infinite Slope Stability

Infinite Slope Stability

Limit-equilibrium factor of safety for a shallow planar slide: slope angle, cohesion, friction, depth, and rainfall-driven pore pressure set the landslide threshold.

Infinite slope

32 deg
2.2 m
19 kN/m3
4 kPa
31 deg

Rainfall and pore pressure

0.15
28 mm/h
10 h
16 h

Rainfall raises a simple saturation index m, which increases pore pressure u = m γw z cos²θ. Higher u lowers effective normal stress and therefore frictional strength.

Measured values

Factor of safety0.98
saturation m0.39
pore pressure u6.0 kPa
driving shear τ18.8 kPa

This is the classic planar infinite-slope limit-equilibrium model. It is useful for rainfall-trigger intuition, but real landslides also depend on 3D geometry, roots, layering, suction, runoff, and transient seepage.

Live graphs

About this model

The infinite-slope model is a limit-equilibrium approximation for shallow translational landslides where a soil slab slides on a plane parallel to the ground surface. This simulator evaluates FS = [c′ + (γz cos²θ − u)tanφ′]/[γz sinθ cosθ]. Cohesion and friction resist downslope shear; slope angle, soil unit weight, and depth increase driving stress; rainfall raises a simple saturation index m and pore pressure u = mγwz cos²θ, reducing effective normal stress. The lower curve sweeps rainfall duration to show when FS crosses the threshold FS = 1. The page is a diagnostic teaching model, not a forecast: it omits 3D geometry, roots, suction, preferential flow, transient seepage, layered failures, and spatially variable rainfall.

Who it's for: Engineering geology, geomorphology, geotechnical engineering, or natural-hazards introductions.

Key terms

  • Factor of safety
  • Infinite slope
  • Pore pressure
  • Effective stress
  • Rainfall-triggered landslide

How it works

Infinite-slope factor of safety for a shallow translational slide: cohesion and friction resist downslope shear, while rainfall-driven pore pressure reduces effective normal stress.

Key equations

FS = [c′ + (γ z cos²θ − u) tanφ′] / [γ z sinθ cosθ]
u = m γw z cos²θ; FS < 1 marks limit-equilibrium failure

Frequently asked questions

What does FS below 1 mean?
In limit equilibrium it means the modeled resisting shear strength is smaller than the driving shear stress on the assumed plane. Real slopes may fail progressively or be stabilized by effects not included here.
Is rainfall infiltration solved physically?
No. Rainfall feeds a compact saturation index with a drainage response time. It is a transparent trigger control for pore pressure, not a Richards-equation infiltration model.