Saturated Slope FoS Calculator
Calculates the factor of safety of an infinite (planar) slope when the water table sits at the ground surface and seepage flows parallel to the face — the worst everyday case for a natural or cut soil slope. It also reports the dry, no-seepage factor of safety so you can see how much saturation costs you.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the effective shear-strength parameters c' (kPa) and φ' (°), the vertical depth z (m) to the slip plane parallel to the face, and the slope angle β (°).
- Enter the saturated unit weight γ_sat (kN/m³); leave γ_w at the default 9.81 kN/m³ unless you have a reason to change it.
- Read the saturated FoS (primary) and compare it with the dry FoS to gauge the effect of seepage.
How it works
For an infinite slope with a slip surface parallel to the face, the driving shear stress is γ_sat·z·sinβ·cosβ and the available strength is c' + σ'·tanφ'. With steady seepage parallel to the slope and full saturation, pore pressure reduces the effective normal stress so the frictional term becomes (γ_sat − γ_w)·z·cos²β·tanφ', giving FoS = [c' + (γ_sat − γ_w)·z·cos²β·tanφ'] / [γ_sat·z·sinβ·cosβ].
The dry case uses the full γ_sat in the frictional term. Because γ_sat is roughly twice γ_w for common soils, seepage nearly halves the frictional resistance. For a cohesionless soil (c' = 0) the expression collapses to FoS = [(γ_sat − γ_w)/γ_sat]·(tanφ'/tanβ), independent of depth.
Worked example
3 m deep slip plane in a 20° saturated slope. With c' = 5 kPa, φ' = 30°, z = 3 m, β = 20°, γ_sat = 20 kN/m³ and γ_w = 9.81 kN/m³: driving = 19.28 kPa; saturated frictional term = 15.30 kPa; saturated FoS = 1.07. The dry FoS is 1.85 — so seepage drops the factor of safety from 1.85 to a marginal 1.07.
Common mistakes
- Using total (moist) unit weight instead of the saturated unit weight γ_sat when the slope is fully saturated.
- Entering the slope length for z — z is the VERTICAL depth to the slip plane, measured down from the surface.
- Mixing total-stress strength (undrained cu) with this effective-stress equation; use effective c' and φ'.
Frequently asked questions
What does seepage parallel to the slope mean?
The standard steady-state case where the phreatic surface is at (or parallel to) the ground surface and water flows down-slope parallel to the face. It generates the pore pressure that reduces effective stress.
Why is the saturated factor of safety so much lower than the dry one?
Seepage replaces γ_sat with (γ_sat − γ_w) in the frictional term. For a typical soil where γ_sat ≈ 2·γ_w, that roughly halves the friction contribution.
What factor of safety is acceptable?
Long-term slopes are commonly designed to FoS ≥ 1.5, temporary works to ≥ 1.3, but the required value depends on the standard and consequence class. Treat this as a screening check.
Does this work for a cohesionless (sandy) slope?
Yes. Set c' = 0 and the result becomes FoS = [(γ_sat − γ_w)/γ_sat]·(tanφ'/tanβ), independent of depth — stable only while β is well below φ'.
Related tools
- Tension Crack Depth Calculator
- Drainage Effect on FoS Estimator
- Factor of Safety Calculator
- Bulk Density Calculator
- Piezometer Trend Calculator
- Piezometric Level Calculator
Explore more in Geology, Geotechnical & Ground Engineering.
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.