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Experimental Study of Failure Differences in Hard Rock Under True Triaxial Compression

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Abstract

In view of a previous study of the intermediate principal stress effect at a limited σ2 range, a series of true triaxial tests, covering a full range of intermediate principal stresses that vary from the generalized triaxial compression stress state (σ2 = σ3) to the generalized triaxial tensile stress state (σ1 = σ2), was carried out on sandstone and granite samples. The experimental results revealed that the deformation, failure strength and failure mode have a significant dependence on the stress state. As an effect of the intermediate principal stress on crack evolution, the deformation difference known as stress-induced deformation anisotropy occurred and should be considered when developing the mechanical model. Moreover, a post-peak deformation with a step-shaped stress drop is observed and illustrates that there will be a multi-stage bearing capacity after the rock failure. The peak strength is non-symmetrical with the increasing σ2 and is closely related to the Lode angle. Based on the final fracture surface and SEM analysis under true triaxial compression, three failure modes and failure zones, including tension failure, shear failure and mixed failure, are delineated and discussed. Combining the failure mode and the strength under true triaxial compression, it is found that the strength variation exhibited a close relationship to the failure mechanism.

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Abbreviations

σ 1, σ 2, and σ 3 :

Maximum, intermediate, and minimum principal stresses

τ oct and σ oct :

Octahedral shear stress and octahedral normal stress

σ m,2 :

Mean effective normal stress

ε 1, ε 2, and ε 3 :

Maximum, intermediate, and minimum principal strains

ρ :

Unit weight

K 12 and K 13 :

Deformation moduli in the σ2 and σ3 directions

A:

Deformation anisotropy coefficient

µ :

Lode stress parameter

σ µ :

Peak strength under different Lode stress parameters

λ :

Strength-increasing coefficient

τ eff :

Effective shear stress

σ e :

Tensile stress

References

  • Benz T, Schwab R, Kauther RA, Vermeer PA (2008) A Hoek–Brown criterion with intrinsic material strength factorization. Int J Rock Mech Min Sci 45:210–222

    Article  Google Scholar 

  • Bruno MS (1994) Micromechanics of stress-induced permeability anisotropy and damage in sedimentary rock. Mech Mater 18:31–48

    Article  Google Scholar 

  • Cai M (2008) Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—insight from numerical modeling. Int J Rock Mech Min 45:763–772

    Article  Google Scholar 

  • Chang C, Haimson B (2012) A failure criterion for rocks based on true triaxial testing. Rock Mech Rock Eng 45:1007–1010

    Article  Google Scholar 

  • Colmenares LB, Zoback MD (2002) A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min 39:695–729

    Article  Google Scholar 

  • Feng X-T, Zhang X, Kong R, Wang G (2016) A novel mogi type true triaxial testing apparatus and its use to obtain complete stress–strain curves of hard rocks. Rock Mech Rock Eng 49:1649–1662

    Article  Google Scholar 

  • Feng X-T, Zhang X, Yang C et al (2017) Evaluation and reduction of the end friction effect in true triaxial tests on hard rocks. Int J Rock Mech Min 97:144–148

    Article  Google Scholar 

  • Fjær E, Ruistuen H (2002) Impact of the intermediate principal stress on the strength of heterogeneous rock. J Geophys Res Solid Earth 107:ECV 3-1

    Article  Google Scholar 

  • Haimson B (2006) True triaxial stresses and the brittle fracture of rock. Pure Appl Geophys 163:1101–1130

    Article  Google Scholar 

  • Ingraham MD (2012) Investigation of localization and failure behavior of Castlegate sandstone using true triaxial testing. Dissertation, Clarkson University

  • Jeager JC, Cook NGW, Zimmerman R (2007) Fundamentals of rock mechanics. Wiley-Blackwell, Singapore

    Google Scholar 

  • Jimenez R, Ma X (2013) A note on the strength symmetry imposed by Mogi’s true-triaxial criterion. Int J Rock Mech Min 64:17–21

    Article  Google Scholar 

  • Klein E, Baud P, Reuschlé T, Wong TF (2001) Mechanical behaviour and failure mode of Bentheim sandstone under triaxial compression. Phys Chem Earth Part A 26:21–25

    Article  Google Scholar 

  • Kong R, Feng X-T, Zhang X, Yang C (2018) Study on crack initiation and damage stress in sandstone under true triaxial compression. Int J Rock Mech Min 106:117–123

    Article  Google Scholar 

  • Kwasniewski M (2007) Mechanical behaviour of rocks under true triaxial compression conditions—volumetric strain and dilatancy. Arch Min Sci 52:409–435

    Google Scholar 

  • Kwaśniewski M (2012) Mechanical behavior of rocks under true triaxial compression conditions—a review. In: Kwasniewski M, Li X, Takahashi M (eds) True triaxial testing of rocks. CRC Press, Boca Raton, pp 99–138

    Chapter  Google Scholar 

  • Lode W (1926) Versuche über den Einfluß der mittleren Hauptspannung auf das Fließen der Metalle Eisen, Kupfer und Nickel. Z Für Phys 36:913–939

    Article  Google Scholar 

  • Ma X, Haimson BC (2016) Failure characteristics of two porous sandstones subjected to true triaxial stresses. J Geophys Res Solid Earth 121:6477–6498

    Article  Google Scholar 

  • Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. In: Proceedings of the Japan Society of Civil Engineers. vol 232, pp 59–70

  • Meyer JP, Labuz JF (2013) Linear failure criteria with three principal stresses. Int J Rock Mech Min 60:180–187

    Article  Google Scholar 

  • Mogi K (1967) Effect of the intermediate principal stress on rock failure. J Geophys Res 72:5117–5131

    Article  Google Scholar 

  • Mogi K (1971a) Effect of the triaxial stress system on the failure of dolomite and limestone. Tectonophysics 11:111–127

    Article  Google Scholar 

  • Mogi K (1971b) Fracture and flow of rocks under high triaxial compression. J Geophys Res 76:1255–1269

    Article  Google Scholar 

  • Mogi K (1977) Dilatancy of rocks under general triaxial stress states with special reference to earthquake precursors. J Phys Earth 25:S203–S217

    Article  Google Scholar 

  • Murrell SAF (1963) A criterion for brittle fracture of rocks and concrete under triaxial stress and the effect of pore pressure on the criterion. In: Fairhurst C (ed) Rock mechanics (Proc. 5th Symp. on Rock Mechanics, The University of Minnesota, Minneapolis, 1962). Pergamon Press, New York, pp. 563–577

    Google Scholar 

  • Pan P-Z, Feng X-T, Hudson JA (2012) The influence of the intermediate principal stress on rock failure behaviour: a numerical study. Eng Geol 124:109–118

    Article  Google Scholar 

  • Paterson MS, Wong TF (2005) Experimental rock deformation-the brittle field. Springer, The Netherlands

    Google Scholar 

  • Santarelli FJ, Brown ET (1989) Failure of three sedimentary rocks in triaxial and hollow cylinder compression tests. Int J Rock Mech Min Sci Geomech Abstr 26:401–413

    Article  Google Scholar 

  • Sayers CM, Van Munster JG, King MS (1990) Stress-induced ultrasonic anisotrophy in Berea sandstone. Int J Rock Mech Min Sci Geomech Abstr 27:429–436

    Article  Google Scholar 

  • Schöpfer MPJ, Childs C, Manzocchi T (2013) Three-dimensional failure envelopes and the brittle-ductile transition. J Geophys Res Solid Earth 118:1378–1392

    Article  Google Scholar 

  • Singh M, Raj A, Singh B (2011) Modified Mohr–Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks. Int J Rock Mech Min 48:546–555

    Article  Google Scholar 

  • Wawersik WR, Fairhurst C (1970) A study of brittle rock fracture in laboratory compression experiments. Int J Rock Mech Min Sci Geomech Abstr 7:561–575

    Article  Google Scholar 

  • Wu B, Hudson JA (1991) Stress-induced anisotropy in rock and its influence on wellbore stability. In: Roegiers (ed) Rock Mechanics as a Multidisciplinary Science: Proceedings of the 32nd U.S. Symposium. Balkema, Rotterdam, pp 941–950

  • Xu YH, Cai M, Zhang XW, Feng XT (2017) Influence of end effect on rock strength in true triaxial compression test. Can Geotech J 54:862–880

    Article  Google Scholar 

  • You M (2009) True-triaxial strength criteria for rock. Int J Rock Mech Min 46:115–127

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the financial supports of the 111 Project under Grant No. B17009, the National Natural Science Foundation of China under Grant No. 11572083 and the State Key Research and Development Program of China under Grant No. 2016YFC0600707.

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Authors and Affiliations

  1. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, 110819, China

    Xia-Ting Feng, Rui Kong, Xiwei Zhang & Chengxiang Yang

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  1. Xia-Ting Feng
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  2. Rui Kong
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Correspondence to Xia-Ting Feng.

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Feng, XT., Kong, R., Zhang, X. et al. Experimental Study of Failure Differences in Hard Rock Under True Triaxial Compression. Rock Mech Rock Eng 52, 2109–2122 (2019). https://doi.org/10.1007/s00603-018-1700-1

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  • DOI: https://doi.org/10.1007/s00603-018-1700-1

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