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Finite and infinite slopes

Short answer

An infinite slope is very long with uniform soil, failure plane parallel to the surface, analyzed on a unit slice ignoring end effects. A finite slope has limited height with a curved or planar failure surface through the toe, analyzed by method of slices or Swedish circle.

Differentiate between finite and infinite slopes (explain finite slope and infinite slopes in regard to slope stability).

An infinite slope is a slope of very large extent whose length is much greater than the depth of the failure surface and which has uniform soil along its length. A finite slope has a limited height and length, with a definite top and toe.

PointInfinite slopeFinite slope
ExtentVery long; end effects ignoredLimited height HH, with a toe and crest
Failure surfacePlane, parallel to the slope surface (shallow)Curved (circular arc) or plane through the toe
SoilUsually uniform, often cohesionlessCohesive or cc-ϕ\phi soil
AnalysisA single slice of unit width; forces on its sides cancelMethod of slices, Swedish circle, Taylor's chart
Factor of safetyF=cγzsin⁡βcos⁡β+tan⁡ϕtan⁡βF = \dfrac{c}{\gamma z\sin\beta\cos\beta} + \dfrac{\tan\phi}{\tan\beta}Depends on geometry, e.g. F=cuLaRWxF = \dfrac{c_u L_a R}{W x} (ϕ=0\phi=0)
Depth of failureIndependent of slope heightRelated to slope height HH
ExamplesNatural hillside, long embankment surfaceEarth dam, road cutting, embankment

✓ Answer checked by Claude Opus 5.5 (high effort)

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