Bishop Simplified Method for Slope Stability

Reference

The Bishop simplified method sums forces on vertical slices around a circular slip surface, and remains the default check for most soil slopes.

The equation

FoS = Σ[(c b + W tan φ) / mα] / Σ(W sin α)
  • Each slice contributes weight W, base angle α, and width b
  • mα contains the factor of safety itself, so the solution iterates
  • FoS below 1.0 means the driving moments win

Worked example

For a 10 meter cut in clay with cohesion 20 kilopascals and friction angle 25 degrees, the search over circles typically lands near a factor of safety of 1.28, with the critical circle exiting just beyond the toe. Two or three iterations settle the answer to three figures.

When to use it

Sound for circular failures in soils without strong layering. Translational slides along a weak seam need wedge or Morgenstern Price methods, and pore pressure assumptions matter more than the method chosen.

Related Calculators and Reference