Slope Stability Factor of Safety Calculator (Bishop Simplified Method)
Enter each slice of the trial slip circle from the back scarp (negative base angle) to the toe (positive base angle). Leave unused rows blank.
| Slice width b (ft) | Slice weight W (lb/ft run) | Base angle alpha (deg) | Pore pressure u (psf) |
|---|---|---|---|
Slope Stability Calculation (Bishop Simplified Method)
Generated by calculatgeek.com Slope Stability Factor of Safety Calculator
Slope stability analysis checks whether a soil mass is likely to slide along some trial failure surface, usually approximated as a circular arc. The result is a factor of safety, the ratio of forces resisting sliding to forces driving it along that surface. This calculator implements Bishop's simplified method of slices, one of the most widely used limit equilibrium methods in geotechnical practice, given the geometry and weight of each slice along a trial slip circle.
Method of slices
A trial slip circle is divided into a series of vertical slices. Each slice has a width b, a total weight W (soil plus any surcharge, per foot of slope length), a base angle alpha where the slip surface crosses that slice, and a pore water pressure u acting on its base. The soil's shear strength along the failure surface is described by effective cohesion c' and effective friction angle phi'.
Bishop's simplified equation
For each slice, the driving force is the component of weight acting along the slip direction, W sin(alpha). The resisting force draws on the Mohr-Coulomb strength of the soil along the slice base, adjusted by pore pressure and by a correction factor m-alpha that itself depends on the unknown factor of safety:
FS = sum[ (c' b + (W - u b) tan(phi')) / m-alpha ] / sum[ W sin(alpha) ]
m-alpha = cos(alpha) x (1 + tan(alpha) tan(phi') / FS)
Because FS appears on both sides of the equation through m-alpha, it is solved iteratively: start with a trial FS (this calculator starts at 1.0), compute a new FS from the equation, and repeat until the value stops changing. This normally converges within five to ten iterations, which is what the calculator does automatically and reports.
Worked example
For a trial circle divided into six 8 ft slices with weights ranging from 5,000 to 20,000 lb/ft and base angles from minus 10 to plus 45 degrees, using effective cohesion of 75 psf and effective friction angle of 18 degrees, the method converges to a factor of safety of about 1.42 after 5 iterations, generally acceptable for a temporary slope but worth a closer look for a permanent one.
Limitations
This calculator evaluates a single trial slip circle from the slice data supplied. A complete slope stability study searches many trial circles of different radius and center location to find the critical surface with the lowest factor of safety, and often uses dedicated slope stability software for that search. Use this tool to check a specific trial circle, verify hand calculations, or understand how changes in soil strength or pore pressure shift the result, not as a substitute for a full site-specific stability analysis.
Slope Stability Factor of Safety Calculator
Related Calculator and Reference
For earthwork volumes on the same site, see the Excavation Cut and Fill Calculator. Formula reference: Bishop's simplified method of slices, slope stability analysis.