Janbu Simplified
The Janbu Simplified method of slices.
The Janbu Simplified method computes the factor of safety from horizontal force equilibrium. In JW Slope it is labeled Janbu Simplified (Uncorrected) to make explicit that no empirical correction factor is applied.
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. JW Slope 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 / denominatorIteration 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.
No correction factor (f0)
The classical Janbu Simplified procedure multiplies the computed factor of safety by an empirical correction factor f0 that approximately accounts for the neglected interslice shear. JW Slope does not apply any such correction. The reported value is the raw, uncorrected force-equilibrium factor of safety. Because the correction factor is greater than one for most geometries, the uncorrected result is typically lower (more conservative) than a corrected Janbu value.
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.