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A potential stress indicator for failure prediction of laboratory-scale rock samples

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Abstract

Based on the two-dimensional renormalization group model, which can consider the stress transfer mechanism, in the present paper, the theoretical quantitative correlation between the threshold of the crack damage stress (σ cd ) and the uniaxial compressive strength (σ ucs ) was constructed. The results indicate that the normalized quantity σ cd /σ ucs decreases as the shape parameter m increases, and that it gradually tends towards a constant horizontal asymptote that is ~0.82. In addition, the experimental results of σ cd /σ ucs obtained in previous studies using different rock types were analyzed. From this analysis, it was found that the overall average and the standard deviation of σ cd /σ ucs for low-porosity rock samples is ~0.80 (±0.10), which would appear to be approximately consistent with the theoretical solution. This preliminary study indicates that the normalized quantity σ cd ucs might be an intrinsic property of low-porosity rocks and thus could be regarded as a potential indicator for the failure prediction of laboratory-scale rock samples.

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References

  • Abdusalam HA (2001) Renormalization group method and Julia sets. Chaos, Solitons Fractals 12(2):423–428. doi:10.1016/S0960-0779(00)00008-4

    Article  Google Scholar 

  • Allegre C, Le Mouel J, Provost A (1982) Scaling rules in rock fracture and possible implications for earthquake prediction. Nature 297:47–49. doi:10.1038/297047a0

    Article  Google Scholar 

  • Amann F, Button EA, Evans KF, Gischig VS, Blumel M (2011) Experimental study of the brittle behavior of clay shale in rapid unconfined compression. Rock Mech Rock Eng 44(4):415–430. doi:10.1007/s00603-011-0156-3

    Article  Google Scholar 

  • Andersson JC, Martin CD, Stille H (2009) The Äspö pillar stability experiment: part II—rock mass response to coupled excavation-induced and thermal-induced stresses. Int J Rock Mech Min 46(5):879–895. doi:10.1016/j.ijrmms.2009.03.002

    Article  Google Scholar 

  • Bieniawski ZT (1967a) Mechanism of brittle fracture of rock: part I—theory of the fracture process. Int J Rock Mech Min 4(4):395–406. doi:10.1016/0148-9062(67)90030-7

    Article  Google Scholar 

  • Bieniawski ZT (1967b) Mechanism of brittle fracture of rock: part II—experimental studies. Int J Rock Mech Min 4(4):407–423. doi:10.1016/0148-9062(67)90031-9

    Article  Google Scholar 

  • Borri-Brunetto M, Carpinteri A, Chiaia B (2004) The effect of scale and criticality in rock slope stability. Rock Mech Rock Eng 37(2):117–126. doi:10.1007/s00603-003-0004-1

    Article  Google Scholar 

  • Brace WF, Paulding BW, Scholz CH (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71(16):3939–3953. doi:10.1029/JZ071i016p03939

    Article  Google Scholar 

  • Cai M, Kaiser P, Tasaka Y, Maejima T, Morioka H, Minami M (2004) Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min 41(5):833–847. doi:10.1016/j.ijrmms.2004.02.001

    Article  Google Scholar 

  • Carpinteri A, Chiaia B, Cornetti P (2001) Static–kinematic duality and the principle of virtual work in the mechanics of fractal media. Comput Method Appl Mech Eng 191(1):3–19. doi:10.1016/S0045-7825(01)00241-9

    Article  Google Scholar 

  • Carpinteri A, Chiaia B, Invernizzi S (2002) Applications of fractal geometry and renormalization group to the Italian seismic activity. Chaos, Solitons Fractals 14(6):917–928. doi:10.1016/S0960-0779(02)00081-4

    Article  Google Scholar 

  • Carpinteri A, Corrado M, Lacidogna G (2012) Three different approaches for damage domain characterization in disordered materials: fractal energy density, b-value statistics, renormalization group theory. Mech Mater 53:15–28. doi:10.1016/j.mechmat.2012.05.004

    Article  Google Scholar 

  • Chang SH, Lee CI (2004) Estimation of cracking and damage mechanisms in rock under triaxial compression by moment tensor analysis of acoustic emission. Int J Rock Mech Min 41(7):1069–1086. doi:10.1016/j.ijrmms.2004.04.006

    Google Scholar 

  • Chen GY, Lin YM (2004) Stress–strain–electrical resistance effects and associated state equations for uniaxial rock compression. Int J Rock Mech Min 41(2):223–236. doi:10.1016/S1365-1609(03)00092-3

    Article  Google Scholar 

  • Chen Z, Tham L, Yeung M, Tsui Y, Lee P (2002) A study on the peak strength of brittle rocks. Rock Mech Rock Eng 35(4):255–270. doi:10.1007/s00603-002-0029-x

    Article  Google Scholar 

  • Chen ZH, Tham LG, Yeung MR, Xie H (2006) Confinement effects for damage and failure of brittle rocks. Int J Rock Mech Min 43(8):1262–1269. doi:10.1016/j.ijrmms.2006.03.015

    Article  Google Scholar 

  • Chen YF, Li DQ, Jiang QH, Zhou CB (2012) Micromechanical analysis of anisotropic damage and its influence on effective thermal conductivity in brittle rocks. Int J Rock Mech Min 50:102–116. doi:10.1016/j.ijrmms.2011.11.003

    Article  Google Scholar 

  • Diederichs MS, Kaiser PK, Eberhardt E (2004) Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation. Int J Rock Mech Min 41(5):785–812. doi:10.1016/j.ijrmms.2004.02.003

    Article  Google Scholar 

  • Eberhardt E, Stead D, Stimpson B, Read R (1997) Changes in acoustic event properties with progressive fracture damage. Int J Rock Mech Min 34(3–4):71. e71–71. e12. doi:10.1016/S1365-1609(97)00062-2

    Google Scholar 

  • Eberhardt E, Stead D, Stimpson B, Read R (1998) Identifying crack initiation and propagation thresholds in brittle rock. Can Geotech J 35(2):222–233

    Article  Google Scholar 

  • Eberhardt E, Stead D, Stimpson B (1999) Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression. Int J Rock Mech Min 36(3):361–380. doi:10.1016/S0148-9062(99)00019-4

    Article  Google Scholar 

  • Eslami J, Hoxha D, Grgic D (2012) Estimation of the damage of a porous limestone using continuous wave velocity measurements during uniaxial creep tests. Mech Mater 49:51–65. doi:10.1016/j.mechmat.2012.02.003

    Article  Google Scholar 

  • Gatelier N, Pellet F, Loret B (2002) Mechanical damage of an anisotropic porous rock in cyclic triaxial tests. Int J Rock Mech Min 39(3):335–354. doi:10.1016/S1365-1609(02)00029-1

    Article  Google Scholar 

  • Hansen A, Roux SR, Aharony A, Feder J, Jøssang T, Hardy HH (1997) Real-space renormalization estimates for two-phase flow in porous media. Transport Porous Media 29(3):247–279. doi:10.1023/A:1006593820928

    Article  Google Scholar 

  • Hatzor YH, Zur A, Mimran Y (1997) Microstructure effects on microcracking and brittle failure of dolomites. Tectonophysics 281(3):141–161. doi:10.1016/S0040-1951(97)00073-5

    Article  Google Scholar 

  • Hidalgo KP, Nordlund E (2013) Comparison between stress and strain quantities of the failure–deformation process of Fennoscandian hard rocks using geological information. Rock Mech Rock Eng 46(1):41–51. doi:10.1007/s00603-012-0242-1

    Article  Google Scholar 

  • Huang D, Huang RQ, Zhang YX (2012) Experimental investigations on static loading rate effects on mechanical properties and energy mechanism of coarse crystal grain marble under uniaxial compression. China J Rock Mech Eng 31(2):245–255 (in Chinese)

    Google Scholar 

  • Iwashita Y, Nakanishi I (2005) Scaling laws of earthquakes derived by renormalization group method. Chaos, Solitons Fractals 24(2):511–518. doi:10.1016/j.chaos.2004.08.002

    Article  Google Scholar 

  • Jiang YD, Xian XF, Xiong DG, Zhou FC (2005) Study on creep behaviour of sandstone and its mechanical models. Chin Journal Geotech Eng 27(12):1478–1481 (in Chinese)

    Google Scholar 

  • Katz O, Reches Z (2002) Pre-failure damage, time-dependent creep and strength variations of a brittle granite. In: Proceedings, 5th international conference on analysis of discontinuous deformation, Ben-Gurion University, Balkema, Rotterdam

  • Lajtai EZ, Lajtai VN (1974) The evolution of brittle fracture in rocks. J Geol Soc Lond 130(1):1–16. doi:10.1144/gsjgs.130.1.0001

    Article  Google Scholar 

  • Li X, Cao WG, Su YH (2012) A statistical damage constitutive model for softening behavior of rocks. Eng Geol 143:1–17. doi:10.1016/j.enggeo.2012.05.005

    Article  Google Scholar 

  • Liang WG, Zhao YS, Xu SG, Dusseault MB (2011) Effect of strain rate on the mechanical properties of salt rock. Int J Rock Mech Min 48(1):161–167. doi:10.1016/j.ijrmms.2010.06.012

    Article  Google Scholar 

  • Liang CY, Li X, Wang SX, Li SD, He JM, Ma CF (2012) Experimental investigations on rate-dependent stress–strain characteristics and energy mechanism of rock under uniaixal compression. China J Rock Mech Eng 31(9):1830–1838 (in Chinese)

    Google Scholar 

  • Lin QX, Liu YM, Tham LG, Tang CA, Lee PKK, Wang J (2009) Time-dependent strength degradation of granite. Int J Rock Mech Min 46(7):1103–1114. doi:10.1016/j.ijrmms.2009.07.005

    Article  Google Scholar 

  • Madden TR (1983) Microcrack connectivity in rocks: a renormalization group approach to the critical phenomena of conduction and failure in crystalline rocks. J Geophys Res: Solid Earth (1978–2012) 88(B1):585–592. doi:10.1029/JB088iB01p00585

    Article  Google Scholar 

  • Martin CD (1993) The strength of massive Lac du Bonnet granite around underground openings. University of Manitoba, Winnipeg

    Google Scholar 

  • Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Geomech Abstr 31(6):643–659. doi:10.1016/0148-9062(94)90005-1

    Article  Google Scholar 

  • Matsuba I (2002) Renormalization group approach to earthquake scaling. Chaos, Solitons Fractals 13(6):1281–1294. doi:10.1016/S0960-0779(01)00134-5

    Article  Google Scholar 

  • Meng XR, Gao ZN, Wang XQ (2009) Study on critical conditions for rock failure by means of group renormalization. J Coal Sci Eng (China) 15(1):50–54

    Article  Google Scholar 

  • Palchik V, Hatzor YH (2002) Crack damage stress as a composite function of porosity and elastic matrix stiffness in dolomites and limestones. Eng Geol 63(3):233–245. doi:10.1016/S0013-7952(01)00084-9

    Article  Google Scholar 

  • Qin SQ, Jiao JJ, Tang CA, Li ZG (2006) Instability leading to coal bumps and nonlinear evolutionary mechanisms for a coal-pillar-and-roof system. Int J Solids Struct 43(25–26):7407–7423. doi:10.1016/j.ijsolstr.2005.06.087

    Article  Google Scholar 

  • Ranjith PG, Jasinge D, Choi SK, Mehic M, Shannon B (2010) The effect of CO2 saturation on mechanical properties of Australian black coal using acoustic emission. Fuel 89(8):2110–2117. doi:10.1016/j.fuel.2010.03.025

    Article  Google Scholar 

  • Saleur H, Sammis CG, Sornette D (1996) Renormalization group theory of earthquakes. Nonlinear Proc Geophys 3(2):102–109. doi:10.5194/npg-3-102-1996

    Article  Google Scholar 

  • Schulze O, Popp T, Kern H (2001) Development of damage and permeability in deforming rock salt. Eng Geol 61(2):163–180. doi:10.1016/S0013-7952(01)00051-5

    Article  Google Scholar 

  • Smalley RF, Turcotte DL, Solla SA (1985) A renormalization group approach to the stick-slip behavior of faults. J Geophys Res: Solid Earth (1978–2012) 90(B2):1894–1900. doi:10.1029/JB090iB02p01894

    Article  Google Scholar 

  • Souley M, Homand F, Pepa S, Hoxha D (2001) Damage-induced permeability changes in granite: a case example at the URL in Canada. Int J Rock Mech Min 38(2):297–310. doi:10.1016/S1365-1609(01)00002-8

    Article  Google Scholar 

  • Sun Q, Zhu S, Xue L (2014) Electrical resistivity variation in uniaxial rock compression. Arab J Geosci 1–12. doi:10.1007/s12517-014-1381-3

  • Takarli M, Prince W, Siddique R (2008) Damage in granite under heating/cooling cycles and water freeze-thaw condition. Int J Rock Mech Min 45(7):1164–1175. doi:10.1016/j.ijrmms.2008.01.002

    Article  Google Scholar 

  • Tang C, Liu H, Lee P, Tsui Y, Tham L (2000) Numerical studies of the influence of microstructure on rock failure in uniaxial compression—part I: effect of heterogeneity. Int J Rock Mech Min 37(4):555–569. doi:10.1016/S1365-1609(99)00121-5

    Article  Google Scholar 

  • Wong TF, Wong RH, Chau K, Tang C (2006) Microcrack statistics, Weibull distribution and micromechanical modeling of compressive failure in rock. Mech Mater 38(7):664–681. doi:10.1016/j.mechmat.2005.12.002

    Article  Google Scholar 

  • Xu NC, Yang XY, Qin J (2012) Relationship between rock’s bulk strain and long-term strength under uniaxial compression. J Liaoning Tech Univ 31(3):358–361 (in Chinese)

    Google Scholar 

  • Xue L, Qin SQ, Sun Q, Wang YY, Lee LM, Li WC (2013) A study on crack damage stress thresholds of different rock types based on uniaxial compression tests. Rock Mech Rock Eng 1–13. doi:10.1007/s00603-013-0479-3

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 41302233 and 41030750), the Project funded by China Postdoctoral Science Foundation (No. 2012M520376), the Science Foundation of Key Laboratory of Engineering Geomechanics, Institute of Geology and Geophysics, Chinese Academy of Sciences (No. KLEG201106) and the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDB10030302.

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Xue, L. A potential stress indicator for failure prediction of laboratory-scale rock samples. Arab J Geosci 8, 3441–3449 (2015). https://doi.org/10.1007/s12517-014-1456-1

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