Calculate slope factor of safety using the simplified infinite slope method. Enter slope height, angle, cohesion, friction angle, and unit weight. Pass/fail at FS 1.5. For preliminary assessment only — licensed geotechnical engineer required for design.
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Shop Express Tools →The infinite slope factor of safety formula assumes a failure plane parallel to the slope surface. It separates the resisting force into a cohesion term and a friction term:
The cohesion term decreases as slope height increases — taller slopes are harder to stabilize with cohesion alone. The friction term depends only on the ratio of friction angle to slope angle, not on height. This is why purely granular slopes (c = 0) have a maximum stable angle equal to the friction angle, regardless of height — the infinite slope condition.
| Soil Type | Cohesion (psf) | Friction Angle | Unit Weight (pcf) |
|---|---|---|---|
| Loose Sand | 0 | 28–32° | 95–105 |
| Dense Sand | 0 | 35–40° | 110–125 |
| Gravel | 0 | 35–45° | 115–130 |
| Soft Clay | 100–300 | 15–20° | 95–110 |
| Stiff Clay | 300–800 | 20–25° | 110–125 |
| Silty Sand | 0–100 | 28–34° | 100–115 |
Values are representative ranges. Site-specific parameters must be determined by geotechnical investigation and laboratory testing.
The infinite slope method is suitable for shallow, planar failure analysis in uniform soil. It does not account for: circular or non-planar failure surfaces (common in deep clay slopes), heterogeneous soil layers, seismic loading, pore water pressure from rainfall infiltration, surcharge loads from buildings, roads, or equipment near the crest, and progressive failure in sensitive clays.
For final design, a licensed geotechnical engineer performs rigorous stability analysis using software such as SLOPE/W, SLIDE, or ReSSA — applying Bishop, Spencer, or Morgenstern-Price limit equilibrium methods with site-specific soil profiles from boring logs and laboratory test results.
The factor of safety (FS) for slope stability is the ratio of resisting forces to driving forces on a potential failure surface. FS = 1.0 means the slope is at the point of failure. FS = 1.5 is the minimum typically required for new construction. FS = 2.0 or higher may be required for critical slopes near structures, utilities, or where failure consequences are severe. A FS below 1.5 requires redesigning the slope angle, adding drainage, installing ground reinforcement, or geotechnical engineering review.
The infinite slope method is a simplified stability analysis that assumes failure occurs along a plane parallel to the slope surface, at a depth small relative to slope length. It works well for shallow planar failures in uniform soil, granular slopes, and slopes where the failure surface can be approximated as planar. It does not account for circular slip surfaces, heterogeneous soil profiles, seepage forces, or surcharge loading. More complete methods (Bishop, Spencer, Morgenstern-Price) are used for final design.
Cohesion is the component of soil shear strength that exists independent of normal stress — it represents the "stickiness" of clay particles. Cohesive soils (clay, silt) can maintain near-vertical excavation faces in the short term because cohesion provides shear resistance. However, cohesion in clay decreases over time as water infiltrates (long-term drained conditions). For slope stability analysis, use short-term undrained cohesion for rapid loading and long-term drained cohesion (often lower) for permanent slopes. Sandy and gravelly soils have essentially zero cohesion.
The internal friction angle (phi, or φ) represents the frictional component of soil shear strength. It controls how much shear resistance the soil develops per unit of normal stress. Higher friction angles produce more stable slopes. Typical values: loose sand 28–32°, dense sand 35–40°, gravel 35–45°, soft clay 15–20°, stiff clay 20–28°. Friction angle is determined by laboratory direct shear or triaxial tests on undisturbed samples, or estimated from SPT N-values and CPT tip resistance.
Soil unit weight (γ) ranges from about 95 to 130 pcf depending on soil type and moisture content. Typical values: loose sand 100–110 pcf, dense sand 115–125 pcf, gravel 115–130 pcf, soft clay 95–110 pcf, stiff clay 110–125 pcf, saturated clay 120–130 pcf. The default in this calculator is 110 pcf, which is a reasonable estimate for many natural soils. Site-specific unit weight should be measured from undisturbed samples for accurate analysis.
Slope stability analysis is required whenever a cut or fill slope is created that could fail and cause injury, property damage, or project risk. This includes highway cut and fill slopes, embankment dams, retaining structure backfills, excavation sidewalls, landfill sideslopes, and river or stream bank modifications. OSHA requires a competent person to evaluate excavation stability. For permanent slopes, a licensed geotechnical engineer must perform stability analysis as part of the geotechnical report.