Abstract
This paper reviews the efforts made in the last 100 years to characterize the effect of the intermediate principal stress σ 2 on brittle fracture of rocks, and on their strength criteria. The most common theories of failure in geomechanics, such as those of Coulomb, and Mohr, disregard σ 2 and are typically based on triaxial testing of cylindrical rock samples subjected to equal minimum and intermediate principal stresses (σ 3=σ 2). However, as early as 1915 Böker conducted conventional triaxial extension tests (σ 1=σ 2) on the same Carrara marble tested earlier in conventional triaxial compression by von Kármán that showed a different strength behavior. Efforts to incorporate the effect of σ 2 on rock strength continued in the second half of the last century through the work of Nadai, Drucker and Prager, Murrell, Handin, Wiebols and Cook, and others. In 1971 Mogi designed a high-capacity true triaxial testing machine, and was the first to obtain complete true triaxial strength criteria for several rocks based on experimental data. Following his pioneering work, several other laboratories developed equipment and conducted true triaxial tests revealing the extent of σ 2 effect on rock strength (e.g., Takahashi and Koide, Michelis, Smart, Wawersik). Testing equipment emulating Mogi’s but considerably more compact was developed at the University of Wisconsin and used for true triaxial testing of some very strong crystalline rocks. Test results revealed three distinct compressive failure mechanisms, depending on loading mode and rock type: shear faulting resulting from extensile microcrack localization, multiple splitting along the σ 1 axis, and nondilatant shear failure. The true triaxial strength criterion for the KTB amphibolite derived from such tests was used in conjunction with logged breakout dimensions to estimate the maximum horizontal in situ stress in the KTB ultra deep scientific hole.
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References
Atkinson, R.H., and Ko, H.Y. (1973), A fluid cushion, multiaxial cell for testing cubical rock specimens, Intl. J. Rock Mech. and Mining Sci. 10, 351–361.
Böker, R. (1915), Die Mechanik der bleibenden Formanderung in kristallinisch aufgebauten Körpern, Verhandl. Deut. Ingr. Mitt. Forsch. 175, 1–51.
Brace, W.F., Pauling, B.W., and Scholz, C.H. (1966), Dilatancy in the fracture of crystalline rocks, J. Geophys. Res. 71, 3939–3953.
Bresler, B. and Pister, K.S. (1957), failure of plane concrete under combined stresses, Trans. Am. Soc. Civ. Engrs. 122, 1049–1068.
Brudy, M., Zoback, M.D., Fuchs, K., Rummel, F., and Baumgärtner, J. (1997), Estimation of the complete stress tensor to 8 km depth in the KTB scientific drill holes: implications for crustal strength, J. Geophys. Res. 102, 18,453–18,475.
Chang, C. and Haimson, B.C. (2000), True triaxial strength and deformability of the KTB deep hole amphibolite, J. Geophys. Res. 105, 18,999–19,014.
Chang, C. and Haimson, B.C. (2005), Nondilatant deformation and failure mechanism in two long valley caldera rocks under true triaxial compression, Intl. J. Rock Mech. and Mining Sci. 42, 402–414.
Crawford, B.R., Smart, B.G.D., Main, I.G., and Liakopoulou-Morris, F. (1995), Strength characteristics and shear acoustic anisotropy of rock core subjected to true triaxial compression. Int. J. Rock Mech. and Min. Sci. 32, 189–200.
Desai, C.S., Janardahonan, R., and Sture, S. (1982), High capacity multiaxial testing device, Geotech. Testing J. 5, 26–33.
Drucker, D.C., and Prager, W. (1952), Soil mechanics and plastic analysis or limit design, Quart. Appl. Math. 10, 157–165.
Emmermann, R., and Lauterjung, J. (1997), The german continental deep drilling program KTB: Overview and major results, J. Geophys. Res. 102, 18,179–18,201.
Escartin, J., Hirth, G., and Evans, B. (1997), Nondilatant brittle deformation of serpentinites: Implications for Mohr-Coulomb theory and the strength of faults. J. Geophys. Res. 102, 2897–2913.
Ewy, R.T., Wellbore stability predictions using a modified lade criterion. In Rock Mechanics in Petroleum Engineering, vol. 1, Proc. Eurock 98 (Society of Petroleum Engineers, 1998), pp. 247–254..
Freudenthal, A., The inelastic behavior and failure of concrete. In Proc. I (ASME, New York, 1951), pp. 641–646.
Haimson, B., and Chang, C. (2000), A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of westerly granite, Int. J. Rock Mech. Min. Sci. 37, 285–296.
Haimson, B., and Chang, C. (2002), True triaxial strength of the KTB amphibolite under borehole wall conditions and its use to estimate the maximum horizontal in situ stress, J. Geophys. Res. 107(B10), ETG 15-1 to 14.
Handin, J., Heard, H.C., and. Magouirk, J.N. (1967), Effect of the intermediate principal stress on the failure of limestone, dolomite, and glass at different temperature and strain rate, J. Geophys. Res. 72, 611–640.
Jaeger, J.C., and Cook, N.G.W., Fundamentals of Rock Mechanics, 3rd ed., (Chapman and Hall, London 1979) 593 pp.
Jaeger, J.C., and Hoskins, E.R. (1966), Rock failure under the combined Brazilian test, J. Geophys. Res. 71, 2651–2659.
Katz, O. and Reches, Z. (2000), micro-and macro-structural analysis of small faults in a quartz-syenite intrusion: Faulting of a brittle rock without microcracking? EOS Transactions, AGU 81, F1121.
Ko, H.Y. and Scott, R. F. (1967), A new soil testing apparatus, Geotechnique 17, 40–57.
Lade, P.V. and Duncan, J.M. (1973), Cubical triaxial tests on cohesionless soil, J. Soil Mech. and Foundation Div., ASCE 99, 793–812.
Michelis, P. (1985), A true triaxial cell for low and high-pressure experiments. Int. J. Rock Mech. Min. Sci. 22, 183–188.
Mogi, K. (1966), Some precise measurements of fracture strength of rocks under uniform compressive strength, Rock Mech. Engin. Geology 4, 51–55.
Mogi, K. (1967), Effect of the intermediate principal stress on rock failure, J. Geopys. Res. 72, 5117–5131.
Mogi, K. (1971). Fracture and flow of rocks under high triaxial compression, J. Geophys. Res. 76, 1255–1269.
Murrell, S.A.F., A criterion for brittle fracture of rocks and concrete under triaxial stress, and the effect of pore pressure on the criterion. In Proc. Fifth Symp. on. Rock Mechanics, (Pergamon Press, 1963), pp. 563–577.
Nadai, A., Theory of Flow and Fracture of Solids, vol. 1 (McGraw-Hill, New York, 1950).
Smart, B.G.D. (1995), A true triaxial cell for testing cylindrical rock specimens, Int. J. Rock Mech. and Min. Sci. 32, 269–275.
Sture, S., and Desai, C.S. (1979), Fluid cushion truly triaxial or multiaxial testing device, Geotech. Testing J. 2, 20–33.
Takahashi, M., and Koide, H., Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m, In Rock at Great Depth (eds. V. Maury and D. Fourmaintraux) (Balkema, Rotterdam, 1989), pp. 19–26.
Vernik, L., and Zoback, M.D. (1992), Estimation of maximum horizontal principal stress magnitude from stress-induced well bore breakouts in the cajon pass scientific research borehole, J. Geophys. Res. 97, 5109–5119.
von Karman, T. (1911), Festigkeitsversuche unter all seitigem Druck, Z. Verein Deut. Ingr. 55, 1749–1759.
Wawersik, W.R., Carlson, L.W., Holcomb, D.J., and Williams, R.J. (1997), New method for true-triaxial rock testing, Int. J. Rock Mech. and Min. Sci. 34, Paper no. 330.
Wiebols, G.A. and Cook, N.G.W. (1968), An energy criterion for the strength of rock in polyaxial compression, Int. J. Rock Mech. Min. Sci. 5, 529–549.
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Haimson, B. (2006). True Triaxial Stresses and the Brittle Fracture of Rock. In: Dresen, G., Zang, A., Stephansson, O. (eds) Rock Damage and Fluid Transport, Part I. Pageoph Topical Volumes. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7712-7_12
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