What is the Ordinary (Fellenius) method?

The Ordinary method, also called the Fellenius or Swedish method, is a limit-equilibrium technique that assumes the interslice forces are parallel to the base of each slice. It satisfies moment equilibrium but not force equilibrium. It tends to give slightly conservative (lower) FS values compared to Bishop's simplified method.

How do I choose slice widths?

Divide the failure mass into equal-width slices, typically 8–15 for a hand calculation. More slices give a more accurate result. Each slice should be narrow enough that the base angle α is roughly constant within it.

What is the base angle α for a slice?

α is the angle between the horizontal and the tangent to the failure circle at the mid-base of each slice. With this calculator's sign convention, slices on the active (uphill) side typically have positive α, while slices on the passive (downhill) side have negative α.

How is pore water pressure included?

Enter the pore pressure u (in kPa) for each slice. It acts over the base length l = b/cosα, reducing effective normal stress. A common simplification uses a pore pressure ratio r_u = u/(γ·h).

What FS value is considered acceptable?

Most codes require FS ≥ 1.5 for permanent slopes, FS ≥ 1.3 for temporary cuts, and FS ≥ 1.2–1.4 for end-of-construction conditions. Values below 1.0 indicate predicted failure.

Does this tool account for tension cracks?

No. Tension crack effects, which reduce the effective arc length at the top of the slope, are not automatically applied. For slopes with tension cracks, reduce the number of slices at the crest accordingly or set c = 0 over the cracked zone.

Factor of Safety Slope Calculator

Compute the factor of safety for slope stability using the Ordinary (Fellenius) method of slices for a circular failure arc.

Soil Properties (Global)

Cohesion c (kPa)

0 for cohesionless soil.

Friction angle φ (°)

Unit weight γ (kN/m³)

Number of slices

Slice Parameters

α is positive for slices whose base dips toward the toe.

#	b (m)	h (m)	α (°)	u (kPa)

b = slice width, h = average height, α = base angle, u = pore pressure.

Fill in soil properties and slice data, then click Calculate.

Factor of Safety (Fellenius)

01.01.52.0+

Failure Marginal Safe

Force Totals

Total Resisting (Σ numerator)

kN/m

Total Driving (Σ W·sinα)

kN/m

Per-Slice Breakdown

#	W (kN/m)	l (m)	W·sinα	W·cosα	Resist.

W = slice weight, l = base arc length, Resist. = c·l + (W·cosα − u·l)·tanφ

Fellenius Formula

FS = Σ[c·l + (W·cosα − u·l)·tanφ] / Σ(W·sinα)

where l = b/cosα (arc length of each slice base)

Summary

The Ordinary (Fellenius) method of slices divides a potential circular failure mass into vertical slices and computes the factor of safety as the ratio of total resisting shear strength to total driving shear force along the arc. It is one of the foundational limit-equilibrium techniques in geotechnical engineering and applies Mohr-Coulomb failure criteria to each slice. This tool lets you define up to 10 slices with individual geometry and soil properties, then instantly calculates the global FS and per-slice contributions.

How it works

Enter the slice dimensions, base angles, unit weights, soil strengths, and pore pressures for the trial failure mass.
Enter the number of slices (up to 10) and the global soil properties: cohesion and friction angle.
For each slice, specify the slice width, average height, and the angle of the base of the slice to the horizontal.
The calculator applies the Fellenius formula: FS = Σ[c·l + (W·cosα − u·l)·tanφ] / Σ(W·sinα) for each slice.
Results show the overall factor of safety and a per-slice breakdown of resisting and driving forces.

Use cases

Preliminary stability check for embankments and earth dams.
Evaluate cut slopes in cohesive soils before excavation.
Compare dry vs. seepage-affected conditions for natural hillsides.
Teaching and learning limit-equilibrium slope stability concepts.
Screen failure arc candidates before running full software analysis.
Back-calculate soil shear strength from a known failure.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu