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Calculation methods (LEM)

Slope NX uses the limit equilibrium method (LEM): the potentially unstable mass is divided into vertical slices and the factor of safety (FoS) is sought as the ratio between the available shear strength and the mobilized one along the slip surface.

\[ FoS = \frac{\tau_{f}}{\tau} = \frac{c' + (\sigma - u)\tan\varphi'}{\tau_{mob}} \]

The five methods

Method Equilibrium Inter-slice forces Surfaces
Fellenius (ordinary) Moments Neglected Circular
Bishop simplified Moments Horizontal only Circular
Janbu Forces Horizontal only Any
Spencer Forces + moments Constant inclination Any
Morgenstern-Price (GLE) Forces + moments Function f(x) Any
  • Fellenius is the most conservative (it neglects inter-slice forces): useful as a quick estimate and a code reference.
  • Bishop simplified is the standard for circular surfaces: accurate and stable, valid when the base does not assume the lever arm = R.
  • Janbu, Spencer, Morgenstern-Price satisfy more equilibrium equations and are valid for general (non-circular) surfaces too. Bishop and Fellenius are allowed for circles only.

Analysis condition

In drained (effective stress) the strength uses c′ and φ′ and the pore pressure u is subtracted at the base. In undrained (total stress) the strength is cu with φ = 0 and u is not subtracted (cu already incorporates it). If you choose undrained, make sure the materials have cu > 0.

Surface shape

  • Circular — the search examines circles centred on the nodes of the grid of centres; several radii are tried per centre. Auto-place grid puts the grid above the slope's critical zone.
  • General — a surface of any shape defined by points, or found by a global search (evolutionary algorithm) that explores the whole domain.

Admissible surfaces

A surface is discarded if it is not kinematically valid: if it emerges above the profile (it would split the mass in two), if it crosses a retaining structure, or if it drops below the bedrock. If the search finds nothing, the actionable panel explains why.

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