Slope Stability Calculator (Infinite Slope Method)
Calculate the factor of safety against sliding for a soil slope using the infinite slope method, based on cohesion, friction angle, unit weight, slope angle, and groundwater condition. Enter your soil parameters to get a factor of safety in US units and compare it against standard minimum values. For OSHA excavation slope limits, see the trench calculator.
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Infinite Slope Method | Factor of Safety | Groundwater Condition
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View Chart →OSHA Maximum Slope Angle by Soil Type (Excavation Safety)
This table is a separate worker-safety standard for temporary excavations, not the engineering factor of safety this calculator produces. Use it as a quick sanity check for excavation slopes, and use the calculator above for the actual stability factor of safety.
| Soil Type | Max Slope (H:V) | Slope Angle | Benching Permitted? |
|---|---|---|---|
| Stable Rock | Vertical | 90° | N/A |
| Type A | 3/4:1 | 53° | Yes, max 4 ft bench height |
| Type B | 1:1 | 45° | Yes, max 4 ft bench height |
| Type C | 1 1/2:1 | 34° | Not permitted |
Source: OSHA 29 CFR 1926, Subpart P, Appendix B, Table B-1. Applies to excavations 20 ft deep or less.
Calculation Method
Define Geometry
Slope angle (or H:V ratio) and depth to the failure plane set up the driving force geometry for the infinite slope equation.
Apply Soil Strength
Cohesion and friction angle define the resisting shear strength along the assumed failure plane, per the Mohr-Coulomb failure criterion.
Adjust for Water
The pore pressure ratio ru reduces effective normal stress, reflecting how saturation weakens the soil's frictional resistance.
Compare to Target
The resulting factor of safety is compared against standard minimums for permanent, temporary, or seismic conditions.
Why the Infinite Slope Method Has Limits
The infinite slope method assumes the potential failure surface runs parallel to the ground surface at a constant depth, extending far enough in both directions that edge effects do not matter. This assumption holds reasonably well for a long, uniform fill embankment or a shallow soil layer over a much stronger material like bedrock, where failure genuinely tends to occur as a shallow, planar slide parallel to the slope face.
It does not hold for many real slopes, especially taller cuts and fills where failure surfaces curve, rotating along something closer to a circular arc rather than a flat plane. For those cases, engineers use methods such as Bishop's Simplified Method of Slices, which divides the slope into vertical slices along an assumed circular surface and iterates to find both the factor of safety and the critical (lowest-FS) failure circle among many candidates. That analysis requires dedicated software and is outside what a simplified web calculator can honestly provide.
Why Cohesion and Friction Contribute Differently
Cohesion contributes a constant resisting force regardless of the normal stress on the failure plane, which is why the cohesion term in the FS equation does not scale with depth the same way the friction term does. Friction resistance depends on effective normal stress, which increases with depth and decreases with pore water pressure. This is why deep slopes in cohesionless (c = 0) soil reduce to the simple check FS = tan(phi) / tan(beta): without cohesion, only the ratio between friction angle and slope angle matters.
💡 Tip - The Cohesionless Dry Slope Check Is a Fast Sanity Test
If you know a soil is essentially cohesionless (clean sand or gravel) and dry, the slope is stable at a given angle only if the friction angle exceeds the slope angle. A 30° friction angle sand slope at 34° is unstable by this simple check alone, before any water or cohesion is even considered.
Example: Same Slope, Dry vs. Saturated
Case 1: Dry Slope
2:1 slope (26.57°), H = 15 ft, c = 200 psf, φ = 28°, γ = 120 pcf, ru = 0
FS = 0.34 + 1.00 = 1.34
Below the 1.5 minimum for a permanent slope, so this dry slope alone would not meet standard practice.
Case 2: Same Slope, Saturated (ru = 0.3)
Identical geometry and soil, but with pore pressure ratio ru = 0.3
FS = 1.02
Adding realistic pore pressure dropped FS from 1.34 to 1.02, a 24% reduction, illustrating why slope failures cluster around wet seasons.
Common Mistake: Ignoring Cohesionless Simplification
Same slope geometry, but soil is clean sand (c = 0), φ = 25°
Since friction angle (25°) is less than slope angle (26.57°), this slope is inherently unstable in cohesionless soil regardless of depth, a case some quick estimates miss by not checking phi against beta directly.
Common Slope Stability Calculation Mistakes
⚠ Errors That Change the Result
- Applying the infinite slope method to a tall, curved failure: This method assumes a planar failure parallel to the surface. Taller slopes with likely circular failure surfaces need Bishop's or Janbu's method, not the infinite slope equation.
- Ignoring pore water pressure entirely: Using dry-condition parameters for a slope that saturates seasonally overstates the actual factor of safety, sometimes significantly, as shown in the worked example above.
- Confusing OSHA excavation slope limits with engineering factor of safety: OSHA Table B-1 sets a maximum temporary excavation slope for worker safety. It does not represent a calculated long-term factor of safety and should not be treated as an engineering design value for permanent slopes.
- Using peak strength parameters for a slope with prior movement: A slope that has already experienced some sliding may have strength closer to residual (post-peak) values, which are lower than peak cohesion and friction angle from an intact sample.
- Mixing units between psf and psi, or degrees and radians: The infinite slope formula is sensitive to consistent units. Confirm cohesion and unit weight are in compatible units (psf and pcf) and that angles are in the same unit used throughout the calculation.
Using Slope Stability Results for Site Planning
For cut and fill slopes on a residential or light commercial site, a factor of safety check is often part of the grading permit process, especially in areas with a history of slope failures, expansive soil, or hillside development. Combine this check with the cut and fill calculator for earthwork volume and the soil compaction calculator to confirm placed fill meets the density assumed in this stability check, since loosely placed fill has lower strength than the compacted parameters typically used in design.
If a slope supports or sits near a structure, retaining wall, or property line, the retaining wall calculator and a full geotechnical investigation become necessary rather than optional. Slopes failing this check, or any slope over 4 feet supporting a structure, typically require a licensed geotechnical or structural engineer's review before construction proceeds, consistent with IBC 2024 Section 1804.
Frequently Asked Questions
The infinite slope method gives factor of safety as FS = [c + (1 - ru) x gamma x H x cos^2(beta) x tan(phi)] / (gamma x H x sin(beta) x cos(beta)), where c is soil cohesion, phi is the friction angle, gamma is unit weight, H is the depth to the failure plane, beta is the slope angle from horizontal, and ru is the pore water pressure ratio. For a dry, cohesionless slope this simplifies to FS = tan(phi) / tan(beta).
A minimum factor of safety of 1.5 is standard US engineering practice for permanent slopes under static loading, consistent with AASHTO, FHWA, and USACE guidelines. Temporary slopes during construction sometimes use 1.25 to 1.3, and seismic (pseudo-static) checks often accept 1.1 to 1.2, reflecting the short-duration nature of earthquake loading.
The infinite slope method assumes a failure plane parallel to the ground surface at a constant depth, appropriate for slopes that are long relative to the depth of the potential failure surface, such as shallow soil over bedrock or a uniform fill embankment. It is not appropriate for slopes with a distinct circular or rotational failure surface, which require slope-specific slip circle analysis such as Bishop's or Janbu's method.
Water increases pore pressure within the soil, which reduces the effective normal stress holding soil particles together along the potential failure plane. This is represented by the pore pressure ratio ru in the infinite slope equation. A saturated slope with ru around 0.4 to 0.5 can have a factor of safety 30 to 50 percent lower than the same slope when dry, which is why most slope failures happen during or after heavy rain.
Per OSHA 29 CFR 1926, Subpart P, Appendix B, Table B-1, the maximum allowable slope for excavations 20 feet deep or less is 3/4:1 (53 degrees) for Type A soil, 1:1 (45 degrees) for Type B soil, and 1 1/2:1 (34 degrees) for Type C soil. This OSHA requirement is a worker safety standard for temporary excavations, separate from the long-term factor of safety used for permanent slope design.
No. This calculator uses the infinite slope method, which assumes a planar failure surface parallel to the slope face at a fixed depth. Circular or rotational failures, which are common in taller cut and fill slopes, require methods such as Bishop's Simplified Method of Slices that search many candidate slip circles to find the critical (lowest factor of safety) surface. That analysis requires geotechnical software or a licensed engineer and is beyond the scope of this tool.
No. This calculator provides a simplified infinite slope estimate for planning purposes using soil parameters you enter. Actual slope design, including soil investigation, circular failure analysis, and seismic checks, must be performed by a licensed geotechnical engineer, particularly for any slope near a structure, roadway, or property line, per IBC 2024 Section 1804.
Sources and Methodology
- USACE EM 1110-2-1902, "Slope Stability," US Army Corps of Engineers, Appendix C (Factor of Safety definitions).
- Infinite slope method formula (Skempton and DeLory, 1957), as presented in standard geotechnical engineering references and MIT OpenCourseWare course materials.
- OSHA 29 CFR 1926, Subpart P, Appendix B, Table B-1 (Maximum Allowable Slopes).
- Minimum factor of safety guidance for permanent, temporary, and seismic slope conditions: consistent with AASHTO, FHWA, and USACE published design practice.
- Typical soil unit weight, cohesion, and friction angle ranges: standard published geotechnical engineering reference values.
- IBC 2024, Section 1804 (Excavation, Grading and Fill) and Section 1604 (General Design Requirements, licensed design professional review).
Last reviewed: September 2026. Reviewed by site author.
Disclaimer
This calculator provides estimates for planning purposes. For permitted structural work, foundations, multi-story construction, retaining walls over 4 feet, and commercial projects, calculations must be verified by a licensed structural engineer per IBC 2024 Section 1604. ConcreteCalculate.com is not liable for structural decisions made from these estimates.
Slope stability decisions, including soil parameter selection, failure surface geometry, and acceptable factor of safety, must be made by a licensed geotechnical engineer based on actual site investigation data. This calculator's infinite slope method does not replace a circular failure analysis or full geotechnical evaluation for slopes supporting structures, roads, or located near property lines.
Built by Muhammad Ramzan Babar, physics researcher (PhD candidate). Reviewed by site author.
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