Janbu Methods

The Janbu method computes the factor of safety from horizontal force equilibrium, without an empirical correction factor.

Choose Janbu Corrected to apply Janbu's empirical correction for surface shape and soil strength. Each method searches for its own minimum and can be selected alongside Bishop, Spencer and GLE.

Theory summary

• Equilibrium satisfied: horizontal force equilibrium of the sliding mass, and vertical force equilibrium of each slice. Moment equilibrium is not satisfied.
• Interslice forces: the simplified Janbu assumption sets the interslice shear force to zero (interslice forces are taken as horizontal). Only the interslice normal force is implied.
• Surface type: circular or non-circular. Unlike Bishop, the force-equilibrium formulation does not rely on a circular geometry, so Janbu is applicable to non-circular surfaces.

Like Bishop, the method is iterative: the slice normal force depends on the mobilized shear, which depends on the factor of safety. JSlope solves the same implicit slice normal force, then updates the factor of safety from a horizontal force balance:

numerator   = sum( available_resistance * cos(alpha) )
denominator = sum( normal_force * sin(alpha) + horizontal_driving )
F_next      = numerator / denominator

Iteration converges when successive factors of safety differ by 1e-4, with a hard limit of 100 iterations. For circular surfaces the iteration is seeded with the Ordinary (Fellenius) method; otherwise it starts from 1.5. Steffensen acceleration (default on) speeds up convergence without changing the result.

Janbu Corrected

The corrected method multiplies the converged Simplified factor by an empirical factor:

F_corrected = f0 * F_simplified
f0 = 1 + b1 * (d/L - 1.4 * (d/L)^2)

L is the chord joining the slip-surface endpoints. d is the greatest perpendicular depth of the slice bases below that chord. The soil coefficient b1 is 0.69 for cohesion-only soil, 0.31 for friction-only soil and 0.50 for soil with both strength components or a mixture of soil types. Nonlinear strength uses the equivalent cohesion and friction at the calculated base stress. This follows Rocscience's Janbu Corrected definition.

The correction is applied during search and refinement as well as final evaluation. It approximately accounts for neglected interslice shear; it does not solve moment equilibrium. The displayed slice forces are those of the uncorrected Janbu equilibrium calculation. A planar surface has d=0 and receives no correction.

Applicability

• A useful, fast force-equilibrium check, available for both circular and non-circular surfaces.
• Often run alongside Bishop and a rigorous method to bracket the factor of safety.

Conservatism notes

• Without the f0 correction, expect Janbu values to sit below corrected Janbu and usually below the rigorous methods for the same surface.
• Treat the uncorrected Janbu factor of safety as a conservative lower-bound style indicator rather than a best estimate. For a defensible result on a non-circular surface, use Spencer or GLE / Morgenstern-Price, which satisfy full equilibrium.