Mohr Coulomb Failure Criterion
The Mohr Coulomb criterion says soil and rock fail when shear stress on a plane overcomes friction plus cohesion, and it remains the workhorse strength model of geotechnics.
The equation
τ = c + σ´ tan φ
- τ is shear strength in kilopascals
- c is cohesion, φ the friction angle
- σ´ is effective normal stress on the failure plane
Worked example
A soil with cohesion 25 kilopascals and friction angle 28 degrees carrying 150 kilopascals effective normal stress resists 25 + 150 × 0.532 = 105 kilopascals of shear before failing.
When to use it
Use effective stress parameters with drainage, or undrained strength when loading outruns drainage in clay. The straight envelope overstates strength at very high stress, where real envelopes curve.
Related Calculators and Reference
- USCS Soil Classification Tool: classify soils from lab results.
- Slope Stability Risk Calculator: run stability with uncertainty included.
- ISSMGE: the international society for soil mechanics.