A Generalized Mogi–Coulomb Failure Criterion for Rocks
Publication: International Journal of Geomechanics
Volume 23, Issue 4
Abstract
A generalized failure criterion is proposed to describe the rock failure under polyaxial compression. The physical meaning of the new criterion is that rock failure will occur when the distortional strain energy of the material reaches some critical value that linearly increases with the effective mean stress σm,3 on the fracture plane striking in the σ2 direction. When w = 0.5, the new criterion reduced to the linear Mogi criterion. When w = 0 and 1, it reduced to two failure criteria corresponding to the upper bound and lower bound of the failure loci on the deviatoric plane, respectively. The linear Mogi criterion is an average of the upper and lower bounds. One new failure with w = 0 was convex on the deviatoric plane in contrast to the Mogi criterion with concave failure envelopes on the deviatoric plane. The new criterion was validated against polyaxial compression test data of eight different rock types at various stress states. The new criterion achieved a very good fit to the test data of each rock type and was better than the linear Mogi criterion.
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Acknowledgments
The opinions, findings, and conclusions do not reflect the views of the employer of the authors. The authors are grateful to use the rock test data provided by references as summarized in Tables S1–S8 for the validation work of our new criterion.
Notation
The following symbols are used in this paper:
- a, b
- material constants of the new criterion;
- c, φ
- cohesion strength and internal friction angle;
- I1
- first invariant of stress tensor;
- J2, J3
- second and third invariants of deviatoric stress tensor;
- k = ρt/ρc
- ratio of the tensile to compressive meridian radius;
- w
- weighting factor in the new criterion;
- δ
- percentage error;
- ξ, ρ, η
- Haigh–Westergaard coordinates;
- ρc, ρt
- compression and extension meridian radius on the deviatoric plane;
- σc, σt
- uniaxial compression and uniaxial tension strength;
- σe,
- equivalent tensile stress;
- σm
- mean stress;
- σm,2, σm,3
- effective mean stress;
- σ1, σ2, σ3
- principal stress at failure;
- ith calculated failure stress, ith test failure stress;
- τoct
- octahedral shear stress; and
- χ
- mean absolute percentage error.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 4 • April 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: May 9, 2022
Accepted: Oct 14, 2022
Published online: Jan 31, 2023
Published in print: Apr 1, 2023
Discussion open until: Jul 1, 2023
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