The Drucker–Prager failure criterion is a three-dimensional pressure-dependent model to estimate the stress state at which the rock reaches its ultimate strength. The criterion is based on the assumption that the octahedral shear stress at failure depends linearly on the octahedral normal stress through material constants. The Drucker–Prager failure criterion was established as a generalization of the Mohr–Coulomb criterion for soils (Drucker and Prager 1952). It can be expressed as: 1 $$ \sqrt {J_{2} } = \lambda I_{1}^{\prime } + \kappa $$ where λ and κ are material constants, J₂ is the second invariant of the stress deviator tensor and I′₁ is the first invariant of the stress tensor, and are defined as follows: