## Mohr-Coulomb Failure Criterion

### Fundamental :

Mohr's theory of failure postulates that rupture begins at a point in a material when the shear stress on the failure plane depends only on the normal stress, i.e., τ = f ( σ ) %tau=f( %sigma ) .

The corresponding curve is called the intrinsic curve. The Mohr-Coulomb failure criterion (shear strength of a soil) is expressed as:

τ = c ' + σ ' tan ϕ ' %tau=c'+%sigma'tan %phi'

Where:

- c ' c' : Cohesion (shear strength under zero normal stress).

- ϕ ' %phi' : Angle of internal friction.

- H = c ' / tan ϕ H=c'/tan%phi : Soil tensile strength.

Mohr-Coulomb failure criterion

### Note :

The failure envelope curve is the envelope of all Mohr circles drawn for failure under different loading conditions.

failure curve as the envelope of Mohr's Circles