Nonetheless, Mohr’s criterion allows for a curved shape of the failure envelope, and this nonlinear behavior is exhibited by many rock types (Jaeger and Cook 1979). However, the additional claim that the point of tangency of the critical stress circle with the failure envelope, as constructed on the Mohr diagram, represents the normal and shear stresses (σ, τ) f on the failure plane with normal inclined to σ I at an angle α f is not always observed in experiments. ( 2), Coulomb’s criterion is equivalent to the assumption of a linear Mohr envelope.Ĭoulomb’s and Mohr’s criteria are notable in that an effect of σ m, the mean stress in the σ I, σ III plane, is considered, which is important for materials such as rock and soil i.e., experiments on geomaterials demonstrate that τ m at failure increases with σ m. 1), and failure occurs if the stress state at failure, the circle of diameter (σ I − σ III), is tangent to the failure envelope, τ = g(σ). ( 3), the Mohr envelope can be constructed on the σ, τ plane (Fig. A linear failure criterion with an intermediate stress effect was described by Paul ( 1968) and implemented by Meyer and Labuz ( 2012). 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).
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). The MC criterion can be considered as a contribution from Mohr and Coulomb (Nadai 1950). 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. 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. 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).
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.
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