### Abstract

We have shown that linear Mogi criterion does a good job in representing rock failure under polyaxial stress states. When σ_{2} = σ_{3} the linear version of Mogi's triaxial failure criterion reduces exactly to the Coulomb criterion. Hence, the linear Mogi criterion can be thought of as a natural extension of the Coulomb criterion into three dimensions (i.e., polyaxial stress space). As Mohr's extension of the Coulomb criterion into three dimensions is often referred to as the Mohr-Coulomb criterion, we propose that the linear version of the Mogi criterion be known as the "Mogi-Coulomb" failure criterion. The classical Coulomb failure criterion can therefore be thought of as a special case, which applies only when σ_{2} = σ_{3} of the more general linear Mogi failure criterion. Furthermore, we found that the numerical values of the parameters that appear in the Mogi-Coulomb criterion can be estimated from conventional triaxial test data. Thus, this polyaxial failure criterion can be applied even in the absence of polyaxial (true triaxial) data. This offers a great advantage, as most laboratories are equipped to conduct only traditional σ_{2} = σ_{3} tests. Finally, we showed that if the linear form of the Mogi criterion is used, the parameters that appear in it can be unambiguously related to the traditional parameters appearing in the Coulomb failure law. The lack of such a relationship for the parameters appearing in the power-law Mogi criterion has been cited in [8] as a major drawback to the use of that model.

Original language | English |
---|---|

Pages (from-to) | 431-439 |

Number of pages | 9 |

Journal | International Journal of Rock Mechanics and Mining Sciences |

Volume | 42 |

Issue number | 3 |

DOIs | |

Publication status | Published - Apr 2005 |

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### ASJC Scopus subject areas

- Geotechnical Engineering and Engineering Geology

### Cite this

*International Journal of Rock Mechanics and Mining Sciences*,

*42*(3), 431-439. https://doi.org/10.1016/j.ijrmms.2004.11.004

**Relation between the Mogi and the Coulomb failure criteria.** / Al-Ajmi, Adel M.; Zimmerman, Robert W.

Research output: Contribution to journal › Article

*International Journal of Rock Mechanics and Mining Sciences*, vol. 42, no. 3, pp. 431-439. https://doi.org/10.1016/j.ijrmms.2004.11.004

}

TY - JOUR

T1 - Relation between the Mogi and the Coulomb failure criteria

AU - Al-Ajmi, Adel M.

AU - Zimmerman, Robert W.

PY - 2005/4

Y1 - 2005/4

N2 - We have shown that linear Mogi criterion does a good job in representing rock failure under polyaxial stress states. When σ2 = σ3 the linear version of Mogi's triaxial failure criterion reduces exactly to the Coulomb criterion. Hence, the linear Mogi criterion can be thought of as a natural extension of the Coulomb criterion into three dimensions (i.e., polyaxial stress space). As Mohr's extension of the Coulomb criterion into three dimensions is often referred to as the Mohr-Coulomb criterion, we propose that the linear version of the Mogi criterion be known as the "Mogi-Coulomb" failure criterion. The classical Coulomb failure criterion can therefore be thought of as a special case, which applies only when σ2 = σ3 of the more general linear Mogi failure criterion. Furthermore, we found that the numerical values of the parameters that appear in the Mogi-Coulomb criterion can be estimated from conventional triaxial test data. Thus, this polyaxial failure criterion can be applied even in the absence of polyaxial (true triaxial) data. This offers a great advantage, as most laboratories are equipped to conduct only traditional σ2 = σ3 tests. Finally, we showed that if the linear form of the Mogi criterion is used, the parameters that appear in it can be unambiguously related to the traditional parameters appearing in the Coulomb failure law. The lack of such a relationship for the parameters appearing in the power-law Mogi criterion has been cited in [8] as a major drawback to the use of that model.

AB - We have shown that linear Mogi criterion does a good job in representing rock failure under polyaxial stress states. When σ2 = σ3 the linear version of Mogi's triaxial failure criterion reduces exactly to the Coulomb criterion. Hence, the linear Mogi criterion can be thought of as a natural extension of the Coulomb criterion into three dimensions (i.e., polyaxial stress space). As Mohr's extension of the Coulomb criterion into three dimensions is often referred to as the Mohr-Coulomb criterion, we propose that the linear version of the Mogi criterion be known as the "Mogi-Coulomb" failure criterion. The classical Coulomb failure criterion can therefore be thought of as a special case, which applies only when σ2 = σ3 of the more general linear Mogi failure criterion. Furthermore, we found that the numerical values of the parameters that appear in the Mogi-Coulomb criterion can be estimated from conventional triaxial test data. Thus, this polyaxial failure criterion can be applied even in the absence of polyaxial (true triaxial) data. This offers a great advantage, as most laboratories are equipped to conduct only traditional σ2 = σ3 tests. Finally, we showed that if the linear form of the Mogi criterion is used, the parameters that appear in it can be unambiguously related to the traditional parameters appearing in the Coulomb failure law. The lack of such a relationship for the parameters appearing in the power-law Mogi criterion has been cited in [8] as a major drawback to the use of that model.

UR - http://www.scopus.com/inward/record.url?scp=15544382269&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=15544382269&partnerID=8YFLogxK

U2 - 10.1016/j.ijrmms.2004.11.004

DO - 10.1016/j.ijrmms.2004.11.004

M3 - Article

AN - SCOPUS:15544382269

VL - 42

SP - 431

EP - 439

JO - International Journal of Rock Mechanics and Minings Sciences

JF - International Journal of Rock Mechanics and Minings Sciences

SN - 1365-1609

IS - 3

ER -