Page 14 - CBT 2018

Ncσ - (Nc- Ne)σII - (Ne+1)σIII = V0
, N =―1-sinΦe e 2sinΦe
N =―1-sinΦc c 2sinΦc
12
Paul-Mohr-Coulomb Failure Criterion
Any failure criterion can be represented as a surface in principal stress space σ1, σ2, σ3 (with no order implied), and the shape of that surface depends on its functional form. For isotropic rock that exhibits a pressure dependence on strength, the simplest failure criterion
is Mohr-Coulomb, which is linear in principal stresses and independent
of the intermediate principal stress.
The Paul-Mohr-Coulomb (PMC) failure criterion is also linear but with three principal stresses, and it is formulated with three identifiable material constants: Vo, the vertex on the tension side of the hydrostatic axis, and friction angles for compression Φc and extension Φe. The advantages of PMC are many, including a convenient approximation to the nonlinear nature of the failure surface by fitting two planes with six parameters to form a 12-sided pyramid over a range of mean stress. [10–12]