Slope Stability Calculator

Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

Saturated Unit Weight Conditional: About this input

The unit weight of the soil below the water table, in kilonewtons per cubic metre, used where seepage makes the soil saturated.

Unit kN/m3 Default 20 Range At least 0
Pore Condition: About this input

The groundwater state on the slip surface, such as dry, or seepage parallel to the slope. Seepage raises pore pressure and lowers the factor of safety.

Default Dry Allowed Dry, Seepage
Water Unit Weight Conditional: About this input

The unit weight of water, in kilonewtons per cubic metre, used to compute pore pressure on the failure plane. It is close to 9.81.

Unit kN/m3 Default 9.81 Range At least 0
Slope Angle: About this input

The inclination of the slope surface above horizontal, in degrees and below 90. A steeper slope increases the driving shear and lowers the factor of safety.

Unit deg Default 20 Range 0.1 to 89.9
Depth To Failure Plane: About this input

The vertical depth from the slope surface to the assumed failure plane, in metres, for the infinite slope analysis.

Unit m Default 3 Range At least 0
Cohesion: About this input

The effective cohesion of the soil along the failure plane, in kilopascals, the strength that does not depend on normal stress.

Unit kPa Default 5 Range At least 0
Moist Unit Weight Conditional: About this input

The unit weight of the soil above the water table, in kilonewtons per cubic metre, in its moist but unsaturated state.

Unit kN/m3 Default 18 Range At least 0
Friction Angle Phi: About this input

The effective angle of internal friction of the soil, in degrees and below 90, the strength that grows with effective normal stress.

Unit deg Default 30 Range 0 to 89.9

Outputs

Pore Pressure: About this output

The pore water pressure on the failure plane, in kilopascals, set by the groundwater condition.

Unit kPa
Resisting Shear Stress: About this output

The available shear strength along the failure plane, in kilopascals, from cohesion plus the effective normal stress times the tangent of the friction angle.

Unit kPa
Total Normal Stress On Plane: About this output

The total stress acting perpendicular to the failure plane, in kilopascals, from the weight of soil above.

Unit kPa
Model Status: About this output

The overall check on your entries, shown above the results. It reads OK when the inputs are usable, NOT VALID with a reason when an entry makes the model meaningless, or CHECK with a reason when a result is valid but worth a second look. Read it before you trust the numbers below.

No unit declared
Driving Shear Stress: About this output

The shear stress driving movement along the failure plane, in kilopascals, the destabilising component of the soil weight.

Unit kPa
Effective Normal Stress: About this output

The normal stress carried by the soil skeleton on the failure plane, in kilopascals: total normal stress minus pore pressure. It governs the frictional strength.

Unit kPa
Factor Of Safety: About this output

The ratio of resisting to driving shear stress along the failure plane, dimensionless. A value below 1 indicates instability; the tool reports this ratio and is not a design or a check of one, so slope design must be performed and sealed by a licensed engineer.

No unit declared

What it is

The Slope Stability Calculator computes the factor of safety of a long, uniform slope by the infinite-slope method. It resolves the weight of a soil block on a failure plane parallel to the slope surface into the shear stress driving movement and the normal stress holding it, applies the Mohr-Coulomb strength criterion, and reports the ratio between resisting and driving shear.

It handles a dry slope and one with seepage parallel to the slope surface, which is the condition that most often triggers failure.

It works in SI units: degrees for angles, metres for depth, kilonewtons per cubic metre for unit weights, and kilopascals for stresses and cohesion.

Use it for a first-pass check on a shallow translational slide in a long uniform slope. It is the right model for exactly that geometry and the wrong one for most others.

Methodology

Purpose and model boundary

This model evaluates the factor of safety of an idealized infinite slope for dry or seepage conditions. It resolves the soil weight into normal and downslope shear stresses on a plane parallel to the ground surface and compares Mohr-Coulomb resistance with the driving stress. It does not analyze finite slopes or search for a critical circular failure surface.

The spreadsheet is the calculation authority. The page sends its named inputs to the calculation service and presents the returned factor, stresses, chart and status.

Inputs and units

Input	Meaning and unit
Slope angle `β`	Ground and assumed failure-plane inclination, degrees.
Failure depth `z`	Vertical depth to the infinite failure plane, m.
Cohesion `c'`	Effective cohesion, kPa.
Friction angle `φ'`	Effective friction angle, degrees.
Pore condition	Dry or seepage.
Unit weights	Moist and saturated soil unit weights plus water unit weight, kN/m³.

Governing relationships

For the unit weight active in the selected pore condition, the infinite-slope stress components are

σn = γ z cos²β and τ = γ z sinβ cosβ.

Dry conditions use u = 0. The seepage branch calculates pore pressure from the entered water unit weight and failure depth using the workbook's plane-parallel seepage assumption. Effective normal stress is σ'n = σn − u. Mohr-Coulomb resistance is τr = c' + σ'n tan φ', and the reported factor of safety is FS = τr / τ.

For a dry cohesionless slope, the equations reduce to FS = tan φ' / tan β; consequently FS = 1 when β = φ'.

Calculation sequence

Validate slope angle, friction angle, depth and applicable unit weights.
Select the dry or seepage unit-weight and pore-pressure branch.
Resolve total normal and driving shear stresses on the failure plane.
Subtract pore pressure and calculate available shear resistance.
Divide resistance by driving stress and create the factor-of-safety sweep against slope angle.
Apply the workbook's status precedence.

Outputs and interpretation

The stress outputs expose each term of the stability ratio. Factor of safety below 1 means the idealized plane is unstable under the model. A larger value represents more modeled resistance relative to demand, but does not establish an acceptable design factor for a particular consequence class or code.

Validation and status logic

Condition	Returned status
Depth or the applicable soil unit weight is nonpositive	`NOT VALID: depth and unit weight must be positive`
Slope angle is not strictly between 0° and 90°	`NOT VALID: slope angle must be between 0 and 90 degrees`
Friction angle is negative or reaches 90°	`NOT VALID: friction angle must be at least 0 and below 90 degrees`
In seepage mode, saturated unit weight is at or below water unit weight	`CHECK: saturated unit weight at or below the water unit weight is inconsistent`
Factor of safety is below 1	`CHECK: factor of safety below 1; the slope is unstable`
Factor of safety is between 1 and the workbook's usual 1.5 reference	`CHECK: factor of safety below the usual minimum of about 1.5`
None of the preceding branches applies	`OK`

Assumptions and limitations

The slope and failure plane are infinitely long and parallel, with uniform depth and soil properties.
The selected dry or plane-parallel seepage condition is uniform.
Soil strength is fully represented by constant effective c' and φ' values.
Finite geometry, layered soils, tension cracks, rainfall infiltration, transient pore pressure, reinforcement, seismic loading, progressive failure and three-dimensional effects are omitted.
The model does not locate a critical surface or replace a method-of-slices analysis.

Restrictions and non-computing states

Mode-specific unit weights are used only when applicable. This calculator enforces declared bounds, while the workbook explicitly refuses singular 90° angle states. Numerical residues produced by trigonometric formulas at invalid endpoints must be ignored when status is NOT VALID.

Errors and warnings

A rejected entry means the request did not satisfy the published input rules. NOT VALID prevents a stability interpretation. CHECK indicates a computed but unstable, low-margin or internally inconsistent state. A calculation-service error is an availability problem, not a factor of safety.

References

The workbook derives its relations rather than reproducing any table, chart or figure from a specification, standard or agency publication. The analysis is the standard infinite-slope limit equilibrium with the Mohr-Coulomb strength criterion.

United States Army Corps of Engineers. Slope Stability, EM 1110-2-1902. https://www.publications.usace.army.mil/Portals/76/Publications/EngineerManuals/EM_1110-2-1902.pdf
Wikipedia. Slope stability analysis, for the range of methods and where the infinite-slope model sits among them. https://en.wikipedia.org/wiki/Slope_stability_analysis
Wikipedia. Mohr-Coulomb theory, for the strength criterion. https://en.wikipedia.org/wiki/Mohr%E2%80%93Coulomb_theory

Minimum acceptable factors of safety come from the code or standard adopted where the work is built and depend on the consequence of failure and on how well the parameters are known. This tool applies no threshold and takes no view on what value is adequate.

Effective cohesion, effective friction angle and the pore pressure condition must come from laboratory testing and piezometric data for the site. The values shipped with the workbook are illustrative and carry no authority.

Additional source notes migrated from Methodology

The workbook implements the conventional Mohr-Coulomb infinite-slope relationship for dry and seepage cases. Site investigation, pore-pressure assessment, the governing standard and review by a licensed geotechnical engineer control real slope analysis.

Frequently asked questions

When is the infinite-slope method the right model?

When the potential failure surface is roughly parallel to the ground surface and shallow relative to the slope's length: a translational slide in a uniform mantle of soil over firmer ground, which is the classic shallow landslide. It is not appropriate for a rotational or circular slip, a wedge sliding on a discontinuity, a finite slope where the crest and toe matter, or a layered profile with strength varying by depth. Using it on those geometries gives a number, but not a meaningful one.

Why does seepage reduce the factor of safety so much?

Because it reduces effective stress, and the frictional part of soil strength depends on effective stress rather than total. Pore water on the failure plane pushes the grains apart and less of the overburden is carried by grain-to-grain contact, so the `tan(phi)` term shrinks while the driving shear stays the same. For a cohesionless slope, full seepage parallel to the surface roughly halves the factor of safety. It is why slopes stable through a dry season fail after prolonged rain: the soil did not change, the water did.

Does the failure depth affect the answer?

It depends on the soil. In a purely frictional soil, depth cancels out of the factor of safety entirely and only the slope angle against the friction angle matters. With cohesion in the mix, the cohesive contribution is fixed while the frictional part grows with depth, so shallow surfaces are relatively more stable and cohesive slopes tend to fail deeper. The tool analyses the depth you specify; it does not search for the critical one, so trying several is worthwhile.

The factor of safety is above 1. Is the slope safe?

Not on that basis alone. A factor of safety above 1 means stable by this model, for this geometry, at this depth, under this pore pressure condition, with these strength parameters. Every one of those is an assumption. What value is adequate depends on the consequence of failure and on how confident you are in the parameters (codes commonly require substantially more than 1), and this tool applies no threshold and offers no opinion.

Why is a slope angle of 90 degrees or more refused?

Because the infinite-slope geometry stops meaning anything: at 90 degrees the failure plane is vertical, the resolved stresses degenerate, and the trigonometric expressions are being evaluated outside the domain where they describe a slope. Rather than return a number from a formula operating outside its range, the tool refuses the entry.

Can I model a reinforced slope, or one with a surcharge at the crest?

No. The method models the self-weight of a soil block on a plane and nothing else. Surcharge or structural loading at the crest, soil nails, anchors, geogrid, retaining structures, seismic acceleration and tension cracks are all outside it. So is root cohesion from vegetation, which can be a meaningful part of shallow slope stability and is sometimes the thing removed just before a failure.

Found a problem, or have an idea?

Tell us if a result looks wrong, a label is unclear, or something is missing. We read every message.

This page is provided by LogicCommons for informational purposes only. Results are analysis outputs computed from the inputs you supply and are not engineering advice, a design, or a substitute for review by a licensed professional under the codes adopted where the work is built. Verify all inputs and results independently.

LogicCommons is in beta. If a result, label, or reference looks wrong, tell us here; we read every message.