Last reviewed 16 Sept 2026 · 6 min read
Slopes and failures
A slope may be natural (hillsides, river banks) or man-made (cuttings, embankments, earth dams). Gravity and seepage tend to move soil downhill; shear strength resists. When shear stress along a surface exceeds shear strength, a slope failure (landslide) occurs.
| Failure type | Description |
|---|---|
| Translational | Movement along a plane nearly parallel to the surface — long (infinite) slopes, shallow weathered layers over rock |
| Rotational | Movement along a curved (circular or non-circular) surface — typical of homogeneous clay slopes |
| — Face (slope) failure | Slip surface meets the slope above the toe |
| — Toe failure | Slip surface passes through the toe (most common in steep slopes) |
| — Base failure | Slip surface passes below the toe (flat slopes over soft clay with a firm layer at depth) |
| Compound / wedge | Combination influenced by weak layers |
| Flow slides, falls, topples | Liquefied or very weak material; rock falls |
Factor of safety
Variants: factor of safety with respect to cohesion , with respect to friction , or with respect to height . Typical minimum values for design: about 1.3–1.5 for permanent slopes (lower for temporary works; codes for earth dams specify values for each loading case).
Infinite slopes
A slope is "infinite" when its extent is large compared with the depth of the potential slip surface, which is parallel to the ground surface.
Dry or moist cohesionless soil:
The slope is stable as long as ; at , = angle of repose. Independent of depth.
Submerged cohesionless slope (no seepage): also (γ′ cancels).
Cohesionless slope with seepage parallel to the surface (water table at the surface):
c–φ soil, slip at depth z:
The depth at which is the critical depth (for ).
Finite slopes
Culmann's method (plane failure through the toe)
Assumes a plane slip surface through the toe. For a vertical cut in cohesive soil it gives the critical height (with = 0). Reasonable for steep slopes; unconservative for flatter ones.
Swedish circle method — φ = 0 analysis
For saturated clays under undrained (short-term) conditions. Take a trial circular slip surface of radius and arc length ; the weight of the sliding mass acts at a horizontal distance from the centre:
Many trial circles are analysed; the minimum gives the critical circle. A tension crack reduces the arc length (and may fill with water, adding a disturbing force).
Method of slices
The sliding mass is divided into vertical slices. For slice with base length , weight , base inclination and pore pressure :
Ignores inter-slice forces; conservative (lower F), especially with high pore pressures.
= slice width. Includes horizontal inter-slice forces; appears on both sides, so it is solved by iteration. More accurate than Fellenius; widely used.
Other methods: Janbu (non-circular), Morgenstern–Price and Spencer (rigorous), finite element strength reduction.
Friction circle method
For c–φ soils: the resultant reaction on the slip surface is tangent to a friction circle of radius ; forces (weight, cohesion resultant, reaction) are combined graphically to find the mobilised cohesion and .
Taylor's stability number
For simple homogeneous slopes, Taylor produced charts of the stability number:
Given slope angle, and depth factor, read from the chart, then . For and a deep firm stratum (base failure governs for flatter slopes), approaches 0.181.