Slope Stability

Slopes fail when driving forces exceed soil strength along a slip surface. Learn failure types, factor of safety, infinite-slope analysis (dry, with seepage, cohesive), circular slip and the method of slices (Fellenius, Bishop), and stabilisation measures.

Landslides kill thousands of people every year and cut roads and railways. Cuttings, embankments, dams and natural hillsides must all be checked for stability — especially after heavy rain, when pore pressures rise.

Slope stability compares the shear strength available along a potential slip surface with the shear stress needed for equilibrium.

An analogy

A book on a tilting table stays put until the tilt exceeds its friction angle. Wet the table and it slides sooner — water does the same to slopes.

Types of slope failure

Translational (shallow slabs parallel to the surface, common in residual soils), rotational (circular slips in clays), wedge and planar failures in rock, flows (debris and mudflows), and falls/topples in rock faces.

Infinite slope analysis

For long, shallow slides: dry sand is stable if β < φ. Seepage parallel to the slope roughly halves FS for sand because pore pressures reduce effective normal stress — which is why slopes fail after rain.

Circular slips and slices

For clays, trial circular slip surfaces are analysed by dividing the sliding mass into vertical slices and summing resisting and driving moments. Fellenius (ordinary) is conservative; Bishop's simplified method is standard; Spencer and Morgenstern–Price satisfy all equilibrium conditions. Software searches thousands of circles for the minimum FS.

Stabilisation and monitoring

Flatten or bench the slope, unload the crest, add toe berms, drain (horizontal drains, trench drains), reinforce (soil nails, anchors, piles, geogrids), vegetate against erosion. Monitor with inclinometers, piezometers and InSAR. Rapid drawdown (reservoirs) and earthquakes are critical design cases.

Formulas

• Infinite slope, dry, c = 0: FS = tan φ / tan β
• With parallel seepage (WT at surface): FS = (γ′/γ_sat) · tan φ / tan β
• Cohesive infinite slope: FS = c/(γ z sin β cos β) + tan φ / tan β
• Circular slip (φ = 0): FS = c_u L_arc R / (W x)
• Fellenius slices: FS = Σ[c′l + (W cos α − u l) tan φ′] / Σ W sin α

Worked example: Dry sand slope

Given: φ = 32°, β = 25°

Find: FS.

• FS = tan 32°/tan 25° = 0.625/0.466 = 1.34

Answer: 1.34

Worked example: Same slope saturated with seepage

Given: γ_sat = 20 kN/m³

Find: FS.

• γ′/γ_sat = 10.19/20 = 0.51
• FS = 0.51 × 1.34 = 0.68 < 1 → failure

Answer: 0.68 — slope fails

Common mistakes

• Wrong: Checking only dry conditions. — Right: Consider worst credible pore pressures — rain, seepage, drawdown.
• Wrong: Assuming one trial circle is critical. — Right: Search many surfaces (software) for the minimum FS.

Applications

• Highway & rail cuttings: Design slopes, benches and drainage; soil nailing for steep cuts.
• Dams & embankments: Steady seepage, rapid drawdown and seismic stability cases.
• Hillside development & mining: Landslide hazard assessment and pit-slope design.

Key takeaways

• FS = available strength / required strength.
• Infinite slope: tan φ/tan β (dry), ≈ half with seepage.
• Circular slips: method of slices, search for minimum.
• Drainage is the cheapest stabiliser.

Going further

• Probabilistic analysis: Variability in c′, φ′ and pore pressure expressed as probability of failure.
• FE strength reduction: Reduce strength until non-convergence to find FS without assuming slip shapes.
• Early warning: Rainfall thresholds and real-time monitoring trigger evacuation for landslide-prone areas.