Failure Criterion of Rock with Multiple Friction Angles

Abstract:

The Paul-Mohr-Coulomb failure criterion is a linear function of the three principal stresses, and it can be written as Aσ_I + Bσ_II + Cσ_III = 1, where σ_I, σ_II, and σ_III are the major, intermediate, and minor principal stresses and A, B, and C are material parameters related to the friction angles in compression and extension and the (theoretical) uniform triaxial tensile strength. Conventional triaxial compression (σ_II = σ_III), extension (σ_I = σ_II), and plane strain (σ_I ≠ σ_II ≠ σ_III) experiments were performed on dry Indiana limestone, and the stress states at failure were represented in principal stress space.

Assuming isotropic behavior, a six-sided pyramidal failure surface was constructed by fitting a plane to the triaxial compression and extension data. The material parameters were determined, and the friction angle in extension was greater than the friction angle in compression, a sufficient condition for an intermediate stress effect. Multi-axial (plane strain) data were included and a twelve-sided failure surface with two different vertices was formed. The two vertices provide a change in the cross-section of the failure surface normal to the hydrostatic axis, which is often observed in failure of rock. The irregular dodecagon is associated with six parameters: two vertices and four friction angles.