Slope stability checks whether a hillside or embankment could slide along a slip surface—and whether a safe margin exists.

Scope (slope stability)

This page covers stability of soil and rock slopes: factor of safety against sliding along slip surfaces, infinite-slope and method-of-slices idealisations, and the role of pore pressure and seismic actions. In South Africa, geotechnical limit states for slopes and earthworks are framed in SANS 10160-5; roads and dams may reference additional project standards (e.g. COLTO, dam safety). Groundwater and drainage assumptions must match the investigation.

Limit equilibrium (concept)

  1. Define soil strength (c′, φ′ or undrained su) and pore pressure along potential slip surfaces.
  2. Choose an analysis type: infinite slope for long uniform slopes; slices (Bishop, Spencer, etc.) for general slip circles or blocks.
  3. Compute factor of safety F = resisting / driving; compare to project criteria (often F > 1.25–1.5 for permanent slopes).
  4. Use the calculator below for a dry infinite-slope illustration; use software for Bishop/Spencer searches and water flow.

Geotechnical Engineering — Slope Stability

Evaluate factor of safety against sliding along potential slip surfaces in natural slopes and embankments.

Introduction

Slope failure occurs when shear stress along a potential slip surface exceeds available strength (effective stress analysis). Engineers use limit equilibrium (Fellenius, Bishop, Janbu, Spencer) or finite-element strength reduction for complex geometry and layering.

The infinite slope model is a closed-form check for long slopes with parallel seepage; real cuts and embankments usually need searched critical surfaces.

Slope divided into vertical slices for method of slices stability analysis
Method of slices: dividing a slip mass for limit equilibrium. See licence on Wikimedia Commons
Two-dimensional slope profile for stability analysis
2D slope idealisation (schematic). See licence on Wikimedia Commons

What slope-stability analysis produces

  • Factor of safety for assumed or searched failure mechanisms.
  • Critical slip surface geometry (circle, non-circular, wedge) when using search methods.
  • Sensitivity to groundwater, material strength, and surcharge or seismic coefficients.
  • Support for stabilisation options (benching, drains, nails, anchors).

Standards (South Africa)

Geotechnical design basis: SANS 10160-5. Soil strength testing: SANS 3001. Road cuttings and embankments may follow national road authority guidance. Always tie parameters to the ground model and monitoring where required.

Infinite slope (dry, parallel base):   F = (c + γ H cos²β tan φ) / (γ H sin β cos β)   (consistent units).

Notation (common)

  • F — factor of safety (shear strength / mobilised stress).
  • β — slope angle; H — depth of sliding mass normal to slope (model-dependent).
  • c, φ — cohesion and friction angle (effective stress parameters when using c′, φ′).
  • ru — pore-pressure ratio in advanced analyses.

Examples in practice

  • Road cut in residual soil: circular slip search with design groundwater.
  • Tailings dam embankment: staged construction and undrained/drained stages.
  • Natural hillside: debris-flow and deep-seated mechanisms may control design.
  • Reinforced slope: include nail or geogrid forces in limit equilibrium.

Calculator — infinite slope (dry)

Illustrative dry infinite slope with cohesion and friction; all inputs positive. Matches the script’s ratio of resisting to driving terms along a planar slip parallel to the surface.

Factor of safety

Factor of safety for a dry infinite slope from c, φ, γ, slope angle β, and depth H.

Key terms

Factor of safety (F)
Ratio of available shear strength to mobilized shear stress on the slip surface.

Software and slope stability

Commercial tools perform slip surface searches, groundwater integration, and seismic pseudo-static factors. Examples (official sites):

  • GeoStudio — Slope/W and related limit-equilibrium / FE slope tools.
  • Rocscience — Slide2 and other 2D slope stability products.
  • PLAXIS — FE strength reduction and deformation.
  • gINT — subsurface data for parameter selection.

No product endorsement—verify pore pressures and material models against investigation data. The infinite-slope calculator is not a substitute for site-specific limit equilibrium or FE analysis.

Diagram sources

Educational schematics. Files in Images/slope-stability/ were downloaded from Wikimedia Commons into this repo (not copied from other topic folders). Confirm licence on each Commons file page before reuse.