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Slope stability

A slope is stable when the strength of the soil is greater than the forces trying to make it slide. The ratio is called the factor of safety. For a long, dry sand slope it depends only on the friction angle and the inclination.

F=resistancedriving forceF = \frac{\text{resistance}}{\text{driving force}}factor of safety
F=tan⁡φtan⁡βF = \frac{\tan\varphi}{\tan\beta}infinite dry sand slope

Symbols

FFfactor of safety
φ\varphifriction angle°
β\betaslope inclination°

Example

φ=35∘\varphi = 35^\circ and β=25∘\beta = 25^\circ:

F=0.700/0.466≈1.5F = 0.700/0.466 \approx 1.5.

F below 1 means the slope will slide. Water in the slope lowers F sharply.
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Part of Geotechnical Engineering: Earth pressure, bearing capacity and stability.