SLOPE STABILITY
SIMPLIFIED BISHOP · CIRCULAR SURFACE · EN 1997
to obtain the FOS and the stability diagram
Tool information
What this page computes
The calculator checks the stability of a slope (an earth slope) against sliding on a circular failure surface, and returns the factor of safety \(F_s\) — the ratio of the moment resisting sliding to the moment causing it:
\(F_s = \frac{\text{resisting moment}}{\text{driving moment}}\)
The circular failure surface
A slope fails by the sliding of a soil mass on a curved surface, approximated by a circular arc. The sliding mass tends to rotate about the circle centre: its weight produces a driving moment, and the shear resistance mobilised along the arc opposes it.
The shear resistance of the soil follows the Mohr-Coulomb criterion, \(\tau = c + \sigma' \tan\varphi\) — so the cohesion \(c\) and the friction angle \(\varphi\) are the parameters that hold the slope in place. The calculator searches for the most unfavourable circle (with minimum \(F_s\)) over a grid of centres and radii.
How to read the factor of safety
The usual practice criterion:
- \(F_s \ge 1.5\) — stable
- \(1.0 \le F_s < 1.5\) — marginal
- \(F_s < 1.0\) — unstable (the slope slides)
Important for Eurocode design: EN 1997 does not work with a global factor of safety but with partial factors on the soil parameters (for example Design Approach 3: \(\gamma_{\varphi'} = \gamma_{c'} = 1.25\) applied to \(\tan\varphi\) and \(c\)). The global \(F_s\) here is useful for quick assessment and comparison; the code check is done with the reduced design parameters.
Input data
- Slope geometry — the height and the inclination of the slope.
- Soil parameters — the unit weight \(\gamma\), the cohesion \(c\), the friction angle \(\varphi\).
- Failure circle geometry — the centre and radius, or an automatic search for the critical one.
Assumptions and limitations
- Circular failure surface and homogeneous soil (a single layer). Stratification and non-circular surfaces require a more general method.
- The analysis is in plane strain (a 2D section per unit length).
- Pore water pressure is not treated unless entered explicitly; seepage pressures can reduce \(F_s\) significantly.
- Progressive failure, seismic effects and time-dependent consolidation are not covered.
- The calculation runs on an external analysis engine.
Related calculations
- Earth pressure — the active pressure on a retaining wall
- Stress bulb — the stress distribution in the ground
- Winkler pressures — the contact pressures at footings