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Slope stability (Fellenius & Bishop)

Fellenius (ordinary/Swedish) and Simplified Bishop factor of safety for a circular slip surface defined by your slices.

Enter slices from heel to toe. α is positive toward the toe (slip surface dips toward toe). W is the total weight of each slice. The tool computes FS by both methods; Bishop is more accurate for circular arcs.

Inputs

c′kPa

φ′°

Slice	W [kN]	α [°]	l [m]	b [m]

Fellenius

FS—

Resist / Drive—

Simplified Bishop

FS—

Iterations—

Citations

FELLFS = Σ(c·l + N·tanφ) / Σ(W·sinα); Fellenius (1936). Conservative (no inter-slice forces).

BISHSimplified Bishop (1955): satisfies moment + vertical equilibrium; iterative; FS ≥ Fellenius.

VERIFYBishop FS ≥ Fellenius confirmed; unstable (FS<1) case verified; convergence in <20 iterations.

Preliminary calculation tool.