Mohr–Coulomb Failure Criterion



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 σII being neglected. MC can be written as a function of (1) major σI and minor σIII 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 σI and σIII, 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).

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Mohr–Coulomb Failure Criterion