Infinite Slope Equation

Reference

For a long uniform slope failing parallel to its surface, stability collapses to one line of algebra, and it explains most shallow landslides.

The equation

FoS = tan φ / tan β (dry, no cohesion)
  • φ is the friction angle of the soil
  • β is the slope angle
  • Seepage parallel to the slope multiplies the result by roughly half

Worked example

A dry sandy slope at 25 degrees with a friction angle of 35 degrees has FoS = 0.700/0.466 = 1.50. Fill the slope with parallel seepage to the surface and the effective weight halves, dragging the factor to about 0.75: the same slope fails in a wet season.

When to use it

The model behind rainfall triggered landslide warnings. It suits shallow planar slides over rockhead or compacted layers, not deep rotational failures, and it shows why nature rarely holds wet sandy slopes much above thirty degrees.

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