Relation between the Mogi and the Coulomb failure criteria

Al-Ajmi, A.; Zimmerman, Robert W.

doi:10.1016/j.ijrmms.2004.11.004

Cited by 434 publications

(116 citation statements)

References 7 publications

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“…2b (Meyer and Labuz 2012). Various researchers (Mogi 1971(Mogi , 1974Takahashi and Koide 1989;Chang and Haimson 2000;Al-Ajmi and Zimmerman 2005) have performed true triaxial testing, and the intermediate stress effect appears to depend on rock type, although anisotropy and experimental conditions may also influence the results. In fact, anisotropy can cause a reserve intermediate-stress effect, where the friction angle appears larger in compression than extension (Dehler and Labuz 2007).…”

Section: Experimental Datamentioning

confidence: 99%

Mohr–Coulomb Failure Criterion

2012

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List of SymbolsThe Mohr-Coulomb (MC) failure criterion is a set of linear equations in principal stress space describing the conditions for which an isotropic material will fail, with any effect from the intermediate principal stress r II being neglected. MC can be written as a function of (1) major r I and minor r III principal stresses, or (2) normal stress r and shear stress s on the failure plane (Jaeger and Cook 1979). When all principal stresses are compressive, experiments demonstrate that the criterion applies reasonably well to rock, where the uniaxial compressive strength C 0 is much greater than the uniaxial tensile strength T, e.g. C 0 /T [ 10; some modification is needed when tensile stresses act, because the (theoretical) uniaxial tensile strength T 0 predicted from MC is not measured in experiments. The MC criterion can be considered as a contribution from Mohr and Coulomb (Nadai 1950). Mohr's condition is based on the assumption that failure depends only on r I and r III , and the shape of the failure envelope, the loci of r, s acting on a failure plane, can be linear or nonlinear (Mohr 1900). Coulomb's condition is based on a linear failure envelope to determine the critical combination of r, s that will cause failure on some plane (Coulomb 1776). A linear failure criterion with an intermediate stress effect was described by Paul (1968) and implemented by Meyer and Labuz (2012). BackgroundCoulomb, in his investigations of retaining walls (Heyman 1972), proposed the relationshipwhere S 0 is the inherent shear strength, also known as

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Section: Experimental Datamentioning

confidence: 99%

Mohr–Coulomb Failure Criterion

2012

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“…In this paper, it is assumed that the creep failure of rocks is due to the presence of penny-shaped microcracks and there is abundant evidence for the existence of microcracks in rocks [13][14]. Therefore, this model is physically plausible and the following assumptions are made: (i) penny-shaped microcracks are assumed to be randomly distributed in Burgers viscoelastic rock matrix; (ii) the interaction between penny-shaped microcracks is neglected before the coalescence of microcracks.…”

Section: The Analytical Modelmentioning

confidence: 99%

An innovative micromechanics-based three-dimensional long-term strength criterion for fracture assessment of rock materials

Zhou

Huang

Berto

2018

Frattura Ed Integrità Strutturale

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ABSTRACT. Rocks may exhibit time-dependent behaviors. Long-term strength criterion significantly dominates creep failure of rocks. Rocks contain many microcracks, which lead to degrade of long-term strength. In this paper, it is assumed that there exist three-dimensional penny-shaped microcracks in rocks. The mode II stress intensity factors at tips of three-dimensional pennyshaped microcracks in Burgers viscoelastic rock matrix is derived. A novel micromechanics-based three-dimensional long-term strength criterion is established to consider the effects of time and the intermediate principal stress on creep failure of rocks. By comparison with the previous experimental data, it is found that the novel micromechanics-based threedimensional long-term strength criterion is in good agreement with the experimental data. KEYWORDS.Micromechanics-based three-dimensional long-term strength criterion; Burgers viscoelastic rock matrix; three-dimensional penny-shaped creep microcracks; Stress intensity factor; The intermediate principal stress.Citation: Zhou, X.-P., Huang, X.-C., Berto, F., An innovative micromechanics-based three-dimensional long-term strength criterion for fracture assessment of rock materials, Frattura ed Integrità Strutturale, 44 (2018) 64-81.

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“…25). Moreover, Al-Ajmi and Zimmerman (2005) showed that for an axisymmetric state of stresses (σ 2 = σ 3 ), the linear Mogi criterion (11) reduces to the Coulomb criterion (2) or (3) with parameters a and b equal, respectively, to: …”

Section: Summary and Final Remarksmentioning

confidence: 99%

Recent Advances in Studies of the Strength of Rocks Under True Triaxial Compression Conditions / Postępy W Badaniach Nad Wytrzymałością Skał W Warunkach Prawdziwego Trójosiowego Ściskania

Kwaśniewski

2013

Archives of Mining Sciences

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The results of true triaxial compression tests carried out by K. Mogi at the University of Tokyo, M. Takahashi at the Geological Survey of Japan and B. Haimson at the University of Wisconsin are summarized and the effect of the intermediate principal stress on the ultimate strength of rocks is discussed in the first part of the paper. Then, the Huber-Mises-Hencky failure theory, which was generalized by Nádai and further modified by Mogi to explain the stress-dependency of both the brittle fracturing and the ductile flow of rocks, is revisited. In the main part of the paper, the results of recent experimental studies carried out on samples of a Coal-Measure sandstone from the strata of the Upper Silesian Coal Basin under true triaxial compression conditions are presented. The studies focused on the effect of, independently, confining pressure, intermediate principal stress and minimum principal stress on the ultimate strength of this rock. The paper closes with a presentation and discussion of a general failure criterion that is capable of predicting the ultimate strength of rocks under both axisymmetric and true triaxial (asymmetric) compressive stress conditions.

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Relation between the Mogi and the Coulomb failure criteria

Cited by 434 publications

References 7 publications

Mohr–Coulomb Failure Criterion

Mohr–Coulomb Failure Criterion

An innovative micromechanics-based three-dimensional long-term strength criterion for fracture assessment of rock materials

Recent Advances in Studies of the Strength of Rocks Under True Triaxial Compression Conditions / Postępy W Badaniach Nad Wytrzymałością Skał W Warunkach Prawdziwego Trójosiowego Ściskania

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