Paul-Mohr-Coulomb failure surface of rock in the brittle regime

Roman Y. Makhnenko, Justice Harvieux, Joseph F. Labuz

Research output: Contribution to journalArticlepeer-review


The Paul-Mohr-Coulomb failure criterion includes the intermediate principal stress σII and friction angles at the limiting stress states of σII = σIII and σII = σI, where σI and σIII are major and minor principal stresses. Conventional triaxial compression (σII = σIII), extension (σII = σI), and plane strain (σI ≠ σII ≠ σIII) experiments were performed on dry rock. The failure data were plotted in principal stress space, and material parameters were determined in the context of two internal friction angles and the theoretical uniform triaxial (all-around equal) tensile strength. Assuming isotropy, the triaxial compression and extension results were used to construct a six-sided pyramidal failure surface, and the extension friction angle was larger than the compression friction angle, a sufficient but not necessary condition of the intermediate stress effect. To capture the behavior of the rock in multiaxial loading, the Paul-Mohr-Coulomb criterion was extended to form a 12-sided pyramid with best fit planes.

Original languageEnglish (US)
Pages (from-to)6975-6981
Number of pages7
JournalGeophysical Research Letters
Issue number17
StatePublished - Sep 16 2015
Externally publishedYes


  • failure criterion
  • intermediate stress effect
  • plane strain test
  • rock mechanics
  • triaxial compression test
  • triaxial extension test

ASJC Scopus subject areas

  • Geophysics
  • General Earth and Planetary Sciences


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