Input Data
Enter screening inputs below. The calculator posts back to the same page and places the result block directly below the header area.
Example Data Table
| Case | c′ (kPa) | φ′ (°) | β (°) | γ (kN/m³) | z (m) | q (kPa) | m | kh | FS |
|---|---|---|---|---|---|---|---|---|---|
| Dry cut slope | 20 | 30 | 26 | 18 | 2.5 | 10 | 0.20 | 0.00 | 2.001 |
| Loaded embankment | 25 | 34 | 28 | 18 | 3.0 | 25 | 0.40 | 0.05 | 1.645 |
| Wet seismic slope | 15 | 28 | 35 | 19 | 4.0 | 15 | 0.70 | 0.08 | 0.753 |
Formula Used
This page applies an infinite slope effective stress screening model. It is useful for fast preliminary review of shallow translational failure surfaces in soil slopes.
Overburden load: W = γz + q
Normal stress: σn = W cos2β
Pore pressure: u = m γw z cos2β
Driving shear: τ = W sinβ cosβ + khW
Resisting shear: s = c′ + (σn - u) tanφ′
Factor of Safety: FS = s / τ
- c′ is effective cohesion along the slip surface.
- φ′ is the effective friction angle.
- m represents the saturated thickness ratio over the failure depth.
- kh adds a simplified horizontal seismic demand term.
- The method is intended for screening. Final design should include a full geotechnical stability analysis.
How to Use This Calculator
- Enter soil strength inputs: effective cohesion and internal friction angle.
- Enter geometry and loading values: slope angle, failure depth, soil unit weight, and surcharge.
- Set seepage conditions using the water ratio and water unit weight.
- Add a horizontal seismic coefficient if a pseudo-static screening check is required.
- Choose a target safety factor to compare current performance with a project requirement.
- Press Calculate Safety Factor to render the results directly below the header area.
- Use the export buttons to download the current result summary as CSV or PDF.
Engineering Notes
Why Screening Matters
Slope safety factor screening helps engineers compare available shear resistance with driving demand before modelling begins. On embankments and cut slopes, preliminary acceptance often starts near 1.30 to 1.50, depending on consequence class, groundwater uncertainty, and seismic exposure. A quick calculator shortens option testing, highlights weak combinations, and supports better planning for drainage, reinforcement, and construction.
Strength Inputs Drive Capacity
Effective cohesion and friction angle strongly influence resistance. For the loaded embankment example, c′ = 25 kPa and φ′ = 34° generate resisting shear of about 78.35 kPa against driving shear near 47.64 kPa, producing FS ≈ 1.64. Small reductions in laboratory-derived parameters can materially lower reserve, so teams should review disturbance, strain compatibility, and whether peak or residual strength fits movement.
Water Pressure Changes Stability Fast
Groundwater commonly causes the sharpest stability loss because pore pressure directly reduces effective normal stress. In the wet seismic example, a water ratio of 0.70 combined with depth of 4 m raises pore pressure enough to pull FS down to about 0.75. That result shows why drains and runoff control often deliver more benefit than flattening geometry after rainfall problems appear.
Surcharge and Geometry Must Be Balanced
Additional crest loading from traffic, stockpiles, retaining structures, or temporary equipment increases normal stress and driving shear together, but not always favorably. Steeper slope angles amplify the downslope component rapidly through sinβ cosβ. In practical reviews, moving surcharge back from the crest or reducing local angle by several degrees can improve stability more economically than adding blanket reinforcement across the slope face.
Seismic Checks Need Clear Assumptions
Pseudo-static screening adds horizontal inertia through kh, making demand rise immediately. Even a moderate coefficient such as 0.05 can reduce reserve when seepage is already high. Because this method is simplified, engineers should document seismic coefficients, expected deformation tolerance, and whether post-earthquake residual strengths are relevant. Where consequences are severe, limit-equilibrium or numerical analyses should follow the calculator’s findings rather than replace them.
Using Output for Decisions
Useful outputs are not only FS, but also normal stress, pore pressure, effective stress, required cohesion, and required friction angle needed to reach a target. Those values help teams decide whether drainage, soil improvement, nails, geogrids, or slope flattening will close the gap efficiently. Used carefully, the calculator becomes a communication tool linking field conditions, laboratory data, and practical stabilization choices in one transparent workflow.
FAQs
Is this calculator suitable for final design?
No. It is a preliminary screening tool based on an infinite slope approach. Final design should use site-specific investigation, groundwater assessment, and detailed stability analysis by a qualified geotechnical engineer.
Why does water ratio reduce the factor of safety so much?
A higher water ratio increases pore pressure along the potential slip plane. That lowers effective normal stress, reduces frictional resistance, and usually decreases the safety factor quickly.
What factor of safety should I target?
Target values depend on project standards, consequence level, soil variability, and loading uncertainty. Many screening reviews look around 1.30 to 1.50, but your governing code or engineer should set the requirement.
Does surcharge always make the slope less safe?
Usually yes, because extra loading raises driving shear. However, the exact effect depends on slope angle, strength parameters, water conditions, and how the load is represented in the chosen model.
Can I use seismic coefficient for earthquake screening?
Yes. The horizontal seismic coefficient provides a simplified pseudo-static check. It is useful for rapid comparison, but important slopes usually need deformation-based or more detailed seismic stability evaluation.
What if my result is below 1.0?
A value below 1.0 means resisting shear is lower than driving shear in this screening model. Recheck inputs, review groundwater conditions, and assess mitigation such as drainage, flattening, or reinforcement.