Slope Stability
Watch one factor-of-safety marker walk down as rain, a toe excavation and a rapid drawdown each take their share.
Skip to the animationA slope's factor of safety is the ratio of resisting to driving moments on the most critical slip surface — and rain, toe excavation and rapid drawdown each reduce it without changing the slope's geometry or the soil in it.
What reduces the factor of safety
| Cause | Mechanism | Timescale |
|---|---|---|
| Rainfall | Pore pressure rises, σ′ falls, strength falls | Days to weeks |
| Toe excavation | Removes soil with the longest lever arm | Immediate |
| Crest loading | Increases the driving moment | Immediate |
| Rapid drawdown | External water support removed, internal pore pressure remains | Hours |
| Long-term equilibration | Pore pressures in a cutting rise toward steady state | Years |
Most landslides occur during or shortly after prolonged rain, and none of these causes changes the slope's geometry or the soil in it — only the pore pressure and the loading.
Why the toe matters most
Soil at the toe resists rotation with the longest lever arm, so removing it costs more stability than removing the same volume anywhere else. A road cutting, a river undercutting a bank, or a trench along the base all do exactly that.
Rapid drawdown
Reservoir water presses on the upstream face and helps hold it up. Empty it faster than the fill can drain and that support vanishes in hours while the internal pore pressure remains for weeks. It is usually the governing case for an embankment dam, and drawdown rates are limited by licence for that reason.
The method of slices
Strength depends on normal stress, which varies along a curved slip surface — so the mass is divided into slices, each with its own weight, normal stress and pore pressure. Summing moments gives F for one trial circle, and the analysis then searches many circles for the worst.
Bishop's simplified method assumes horizontal interslice forces and is accurate to a few per cent. For undrained clay with φ_u = 0, strength is c_u everywhere on the arc and the problem reduces to Taylor's stability number charts.
Residual strength
Once a slip surface has formed, only the residual strength remains on it — which in a stiff plastic clay can be under half the peak. That is why an old landslip reactivates at an angle that a fresh analysis using peak strength would call comfortably safe.
Remedies, in order of cost-effectiveness
- Drainage — raises effective stress along the whole slip surface and needs no structure. Cheapest by a wide margin.
- Flatten or bench — reduces the driving moment.
- Toe weighting — a berm restoring the lever arm that was removed.
- Piles or anchors — expensive, and dependent on the slip surface being where the analysis said it was.
The numbers you will be asked for
- Factor of safety
F = resisting moment / driving moment
- Infinite slope, dry
F = tan φ′ / tan β
- Infinite slope, seepage parallel
F = (γ′/γ_sat)·(tan φ′/tan β)
- Bishop simplified
F = Σ[(c′b + (W − ub)tan φ′)/m_α] / Σ W sin α
- Taylor stability number
N = c_u / (F γ H)
Watch it work
Check yourself
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One question at a time. Pick an answer to see why it is right or wrong, then move on — there is no score to keep and nothing is saved.