Availability of Data and Material
Data are provided in the Appendix.
References
Al-Ajmi AM, Zimmerman RW (2005) Relation between the Mogi and the Coulomb failure criteria. Int J Rock Mech Min Sci 42(2005):431–439
Baycan S (1996) Field performance of expansive anchors and piles in rock. Ph.D. thesis, Monash University, Melbourne, Australia
Besuelle P, Desrues J, Raynaud S (2000) Experimental characterisation of the localisation phenomenon inside a Vosges sandstone in a triaxial cell. Int J Rock Mech Min Sci 37(8):1223–1237
Brown ET (1981) Rock characterization, testing and monitoring: ISRM suggested methods. In: International society for rock mechanics
Carter BJ, Duncan EJS, Lajtai EZ (1991) Fitting strength criteria to intact rock. Geotech Geol Eng 9(1991):73–81
Chiu HK (1981) Geotechnical properties and numerical analysis for socketed pile design in weak rock. Ph.D. thesis, Monash University, Melbourne, Australia
Gowd TN, Rummel F (1980) Effect of confining pressure on the fracture behaviour of a porous rock. Int J Rock Mech Min Sci 17(4):225–229
Haimson B, Rudnicki JW (2010) The effect of the intermediate principal stress on fault formation and fault angle in siltstone. J Struct Geol 32(11):1701–1711
Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Eng Div 106(9):1013–1035
Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186
Hoek E, Brown ET (2019) The Hoek–Brown failure criterion and GSI—2018 edition. J Rock Mech Geotech Eng 11:445–463
Jaeger JC, Cook NG, Zimmerman RW (2007) Fundamentals of rock mechanics. Blackwell Publishing, Hoboken
Kovari K, Tisa A, Einstein HH, Franklin JA (1983) Suggested methods for determining the strength of rock materials in triaxial compression: revised version. Int J Rock Mech Min Sci 20(6):285–290
Labuz JF, Bridell JM (1993) Reducing frictional constraint in compression testing through lubrication. Int J Rock Mech Min Sci 30(4):451–455
Labuz JF, Dai ST, Papamichos E (1996) Plane-strain compression of rock-like materials. Int J Rock Mech Min Sci 33(6):573–584
Labuz JF, Zeng F, Makhnenko R, Li Y (2018) Brittle failure of rock: a review and general linear criterion. J Struct Geol 112(2018):7–28
Ma X, Haimson B (2016) Failure characteristics of two porous sandstones subjected to true triaxial stresses. J Geophys Res 122(4):2525–2540
Makhnenko R, Labuz JF (2014) Plane strain testing with passive restraint. Rock Mech Rock Eng 47:2021–2029
Meyer JP, Labuz JF (2013) Linear failure criteria with three principal stresses. Int J Rock Mech Min Sci 60:180–187
Mogi K (1971) Fracture and flow of rocks under high triaxial compression. J Geophys Res 76(5):1255–1269
Mogi K (2007) Experimental rock mechanics. CRC Press, Boca Raton
Mohr O (1900) Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materials? Zeitschrift des Vereines deutscher Ingenieure 44(45):1524–1530
Pan XD, Hudson JA (1988) A simplified three dimensional Hoek–Brown yield criterion. In: Paper presented at the ISRM international symposium, Madrid, Spain
Papamichos E, Tronvoll J, Vardoulakis I, Labuz JF, Skjvrstein A, Unander TE, Sulem J (2000) Constitutive testing of Red Wildmoor sandstone. Mech Cohesive Frict Mater 5(1):1–40
Paul B (1961) A modification of the Coulomb–Mohr theory of fracture. J Appl Mech 28(2):259–268
Paul B (1968) Generalized pyramidal fracture and yield criteria. Int J Solids Struct 4(2):175–196
Schwartz AE (1964) Failure of rock in the triaxial shear test. In: Proceedings of the 6th US symposium on rock mechanics (USRMS), Rolla, Missouri
Stavropoulou VG (1982) Behaviour of a brittle sandstone in plane-strain loading conditions. In: Proceedings of the 23rd US symposium on rock mechanics (USRMS), Berkeley, California
Tarokh A, Detournay E, Labuz JF (2018) Direct measurement of the unjacketed pore modulus of porous solids. Proc R Soc Lond A Math Phys Sci 474(2219)
Von Karman T (1911) Festigkeitsversuche unter all seitigem Druck. Z Verein Deut Ingr 55(17)
Wang B, Zhu JB, Wu AQ (2010) Experimental validation of nonlinear strength property of rock under high geostress. Chin J Rock Mech Eng 29(3):542–548
Williams AF (1980) The design and performance of piles into weak rock. Ph.D. thesis, Monash University, Melbourne, Australia
You M (2010) Three independent parameters to describe conventional triaxial compressive strength of intact rocks. J Rock Mech Geotech Eng 2(4):350–356
Zeng F, Folta BL, Labuz JF (2019) Strength testing of sandstone under multi-axial stress states. Geotech Geol Eng 37:4803–4814
Acknowledgements
Partial support for Pouyan Asem, with no endorsement of the approach, was provided by the J. S. Braun/Braun Intertec Visiting Chair at the Department of Civil, Environmental, and Geo-Engineering, University of Minnesota.
Funding
Pouyan Asem received funding from the Department of Civil, Environmental, and Geo-Engineering, University of Minnesota.
Author information
Authors and Affiliations
Contributions
PA, HF, and JFL: designed and analyzed the experiments, and contributed to the writing of the manuscript; PA and HF: conducted the experiments; PA: collected and analyzed the rock strength data.
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Asem, P., Fuselier, H. & Labuz, J.F. On a Four-Parameter Linear Failure Criterion. Rock Mech Rock Eng 54, 3369–3376 (2021). https://doi.org/10.1007/s00603-021-02451-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-021-02451-w