State Mohr-Coulomb failure criterion

Mohr-Coulomb failure criterion: a soil fails when the shear stress on any plane reaches the shear strength, which is a linear function of the normal stress on that plane:

$$\tau_f = c + \sigma\tan\phi$$

In terms of effective stress, $\tau_f = c' + \sigma'\tan\phi'$. Here $c$ is the cohesion intercept and $\phi$ is the angle of shearing resistance (internal friction).

• If the Mohr circle for a stress state lies wholly below the failure line, the soil is stable.
• If the circle touches the line, the soil is on the point of failure.
• A circle cannot extend above the line.

Failure occurs on a plane inclined at $45^\circ+\phi/2$ to the major principal plane.