Failure envelope

The locus of critical combinations of normal stress and shear stress. Contact of a Mohr circle with this boundary identifies an ideal failure threshold; it does not by itself describe post-failure dynamics.

A frictional shear-strength approximation $|\tau |=c+{\sigma }_n^{\prime }\tan \phi$, with cohesion $c$ and internal friction angle $\phi$. Effective compression increases shear resistance. A separate tensile cutoff is generally needed at low confinement. The names refer to Christian Otto Mohr and Charles-Augustin de Coulomb.

The angle whose tangent gives the slope of a linear frictional failure envelope. It controls both the confinement dependence of strength and the optimum new shear-fracture orientation.

The shear-strength intercept $c$ at zero effective normal stress in a specified frictional failure envelope. It is a model parameter and is not automatically the tensile strength.