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GEO-12

Infinite-slope factor of safety

FS of an infinite c–φ slope with seepage parallel to the face.

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Slope stabilityTaylor 1948Eurocode 7

Governing equation

F=c+(γzcos⁡2β−u)tan⁡φγzsin⁡βcos⁡βF=\dfrac{c+(\gamma z\cos^2\beta-u)\tan\varphi}{\gamma z\sin\beta\cos\beta}

where

c
Cohesion (kPa)
\varphi
Friction angle (°)
\gamma
Unit weight (kN/m³)
z
Slice depth (m)
\beta
Slope angle (°)
u
Pore pressure (kPa)
F
Factor of safety (—)

Lecture brief

Historical brief

Soil mechanics became a quantitative laboratory after Karl von Terzaghi’s 1925–1943 work on effective stress, consolidation and bearing. These sheets still size shallow foundations, retaining walls, piles and drainage in SI. This sheet (GEO-12 — Infinite-slope factor of safety) is the form associated with Taylor 1948 · Eurocode 7. Working symbols: cc, φ\varphi, γ\gamma, zz, β\beta, uu →\rightarrow FF. Moment equilibrium on a slice of an infinite slope reduces to FS = (c + (γz cos²β − u) tanφ) / (γz sinβ cosβ).

Purpose

Purpose: compute FF from cc, φ\varphi, γ\gamma, zz, β\beta, uu in Geotechnical engineering via F=c+(γzcos⁡2β−u)tan⁡φγzsin⁡βcos⁡βF=\dfrac{c+(\gamma z\cos^2\beta-u)\tan\varphi}{\gamma z\sin\beta\cos\beta} FS of an infinite c–φ slope with seepage parallel to the face. Use it when a real geotechnical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given c=8.000 kPac = 8.000\,\mathrm{kPa}, φ=28.000 ∘\varphi = 28.000\,\mathrm{^{\circ}}, γ=19.000 kN/m3\gamma = 19.000\,\mathrm{kN/m^{3}}, z=3.000 mz = 3.000\,\mathrm{m}, β=25.000 ∘\beta = 25.000\,\mathrm{^{\circ}}, u=10.000 kPau = 10.000\,\mathrm{kPa}, the governing relation F=c+(γzcos⁡2β−u)tan⁡φγzsin⁡βcos⁡βF=\dfrac{c+(\gamma z\cos^2\beta-u)\tan\varphi}{\gamma z\sin\beta\cos\beta} yields F=1.263 —F = 1.263\,\mathrm{—}. Seepage parallel to slope: u = γw z cos²β if specified as ru = γw/γ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Factor of safety F1.263 —
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Narration of this film

Seepage parallel to slope: u = γw z cos²β if specified as ru = γw/γ.

Moment equilibrium on a slice of an infinite slope reduces to FS = (c + (γz cos²β − u) tanφ) / (γz sinβ cosβ).

Reading speed

Watch on YouTube