Mohr–Coulomb Failure Criterion

Excerpt

The Mohr–Coulomb (MC) failure criterion is a set of linear equations in principal stress space describing the conditions for which an isotropic material will fail, with any effect from the intermediate principal stress σ_II being neglected. MC can be written as a function of (1) major σ_I and minor σ_III principal stresses, or (2) normal stress σ and shear stress τ on the failure plane (Jaeger and Cook 1979). When all principal stresses are compressive, experiments demonstrate that the criterion applies reasonably well to rock, where the uniaxial compressive strength C ₀ is much greater than the uniaxial tensile strength T, e.g. C ₀/T > 10; some modification is needed when tensile stresses act, because the (theoretical) uniaxial tensile strength T ₀ predicted from MC is not measured in experiments. The MC criterion can be considered as a contribution from Mohr and Coulomb (Nadai 1950). Mohr’s condition is based on the assumption that failure depends only on σ_I and σ_III, and the shape of the failure envelope, the loci of σ, τ acting on a failure plane, can be linear or nonlinear (Mohr 1900). Coulomb’s condition is based on a linear failure envelope to determine the critical combination of σ, τ that will cause failure on some plane (Coulomb 1776). A linear failure criterion with an intermediate stress effect was described by Paul (1968) and implemented by Meyer and Labuz (2012). …