Slope Stability Infinite Slope Calculator
Calculate the factor of safety of an infinite (planar) slope from slope angle, failure depth, cohesion, friction angle, unit weight and groundwater level. Includes the critical slope angle and how the factor of safety drops as the soil saturates.
Input
Vertical depth of the potential slip surface (m in SI, ft in US customary).
kPa in SI, psf in US customary. Use 0 for sand and gravel.
Total unit weight: kN/m³ in SI (typically 16–21), lb/ft³ in US customary (100–130).
Fraction of the depth to the failure plane that sits below a water table parallel to the slope. 0 = dry, 1 = water at the surface.
Output
| Property | Value |
|---|---|
| No data yet | |
| Water table ratio (m) | Factor of safety | Assessment |
|---|---|---|
| No data yet | ||
Same slope with the water table at different heights.
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/slope-stability-infinite-slope-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"unitSystem": "si",
"slopeAngle": "25",
"depth": "3",
"cohesion": "5",
"frictionAngle": "30",
"unitWeight": "18",
"saturation": "0"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `slope-stability-infinite-slope-calculator` tool (Slope Stability Infinite Slope Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
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| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
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Guides
This calculator estimates the factor of safety (FS) of a long, uniform slope against shallow planar failure using the infinite slope method. Enter the slope angle, depth to the failure plane, soil strength and unit weight, plus how high the groundwater sits, and it returns the factor of safety, the stresses acting on the failure plane and the critical slope angle at which FS drops to 1. A second table shows how the factor of safety falls as the soil saturates.
How to use it
- Choose SI or US customary units.
- Enter the slope angle (β), depth to the failure plane (z), effective cohesion (c') and effective friction angle (φ').
- Enter the soil unit weight (γ) and the water table height ratio (m): 0 for a dry slope, 1 when groundwater reaches the surface.
The equation
With seepage parallel to the slope, the factor of safety is:
FS = [ c' + (γ·z·cos²β − u)·tanφ' ] / ( γ·z·sinβ·cosβ )
u = m·γw·z·cos²βThe numerator is the shear strength along the failure plane; the denominator is the driving shear stress. For dry cohesionless soil this reduces to FS = tanφ' / tanβ.
How to read the result
FS below 1.0 means the slope is predicted to fail. Between 1.0 and 1.3 it is marginal, 1.3–1.5 is often accepted for temporary works, and 1.5 or more is the usual target for permanent slopes. Rising groundwater is the most common trigger of shallow landslides, which is why the table shows FS at five water table levels.
Limitations
The infinite slope model assumes the failure surface is long and shallow compared with its depth, the soil is homogeneous, and seepage runs parallel to the surface. It is not suited to deep rotational failures or slopes with toe or crest effects — use a limit-equilibrium method for those. This is a screening estimate, not a substitute for a geotechnical engineer's design.
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