Slope Stability — Infinite Slope FoS
Factor of safety against translational failure on a planar slip surface parallel to the ground. Cohesionless slopes (sand), cohesive slopes (clay), and c-φ slopes with steady-state seepage. Standard infinite-slope analysis.
Defaults: 20° slope, 10 ft to slip plane, dense sand-clay (γ = 120 pcf, c = 200 psf, φ = 28°), dry. Use ru = 0.4–0.5 for steady-state seepage along the slope, or for short-term saturated conditions.
When the infinite-slope assumption applies
Infinite-slope analysis is valid when slope length is much greater than depth to slip plane (L >> H), the failure surface is roughly parallel to ground surface, and end effects can be neglected. This describes shallow translational landslides — typical for veneer failures over bedrock, soil slopes draped over hardpan, and saturated colluvial slopes after intense rainfall.
For deep-seated rotational failures, use the Bishop or Spencer method of slices. Geotechnical software (Slide, GeoStudio, GeoSuite) handles these with iteration over many trial circles.
Design FoS targets
- Permanent slopes, long-term: FoS ≥ 1.5 (under operating loads, drained strength)
- Permanent slopes, seismic: FoS ≥ 1.1 (pseudo-static analysis)
- Construction (temporary cuts): FoS ≥ 1.25
- Earth dam, end of construction: FoS ≥ 1.3
- Earth dam, steady seepage: FoS ≥ 1.5
- Earth dam, rapid drawdown: FoS ≥ 1.1–1.2
Pore pressure ratio ru
ru = u / (γ H) on the slip surface. Typical values:
- Dry slope, dry season: ru = 0
- Phreatic surface at half-depth, parallel to slope: ru ≈ 0.25
- Phreatic surface at ground surface, parallel seepage: ru = 0.5
- Saturated colluvium, intense rainfall: ru = 0.5–0.7
For seepage parallel to the slope, hydrostatic on the slip plane, u = γw z cos²β, where z is depth to slip plane below the phreatic surface. For seepage from the top down (artesian), u can exceed γw z.
Sand slope (c = 0)
For pure sand (cohesionless), the equation simplifies to FoS = (1 - ru sec² β) × tan φ / tan β. A dry sand slope is stable when β < φ (the angle of repose). With seepage parallel to slope, the maximum stable angle drops to about half of φ — saturated sand slopes can collapse at angles much shallower than dry sand.
Clay slope (φ = 0, undrained)
For saturated clay analyzed undrained (φ = 0): FoS = cu / (γ H sin β cos β). This is the short-term stability check immediately after construction or after rapid loading. Long-term stability uses drained c' and φ' parameters and gives different FoS.
Reference: Duncan, J.M., Wright, S.G. (2005). Soil Strength and Slope Stability, Wiley. Das, B.M. (2014). Principles of Geotechnical Engineering, 8th ed., Cengage, ch. 15.