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Micro–macro modeling of brittle creep and progressive failure subjected to compressive loading in rock

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Abstract

A major challenge of rock mechanics is to link the time-dependent crack growth with macroscopic mechanical behavior. A new micro–macro method is presented to model the brittle creep and progressive failure of rock in compression. The Ashby’s microcrack model, Charles’ crack growth law and a new theoretical relation are incorporated into this method. This new relation is suggested to establish the linkage between microcrack growth and macroscopic strain based on the macroscopic and micromechanical definition of rock damage in this paper. The long-term strength of rock could also be calculated using this suggested micro–macro method. Rationality of the suggested method is verified through the theoretical and experimental results. Furthermore, effects of confining pressure on brittle creep and progressive failure of Sanxia granite is investigated. Theoretical corresponding relation between crack growth, damage and strain is investigated. And theoretical foundation of deep-buried construction design is also discussed in this paper.

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References

  • Ashby MF, Hallam SD (1986) The failure of brittle solids containing small cracks under compressive stress states. Acta Metall 34(3):497–510

    Article  Google Scholar 

  • Ashby MF, Sammis CG (1990) The damage mechanics of brittle solids in compression. Pure appl Geophys 133(3):489–521

    Article  Google Scholar 

  • Atkinson BK (1979) A fracture mechanics study of subcritical tensile cracking of quartz in wet environments. Pure appl Geophys 117(5):1011–1024

    Article  Google Scholar 

  • Atkinson BK (1984) Subcritical crack growth in geological materials. J Geophys Res 89(B6):4077–4114

    Article  Google Scholar 

  • Aubertin M, Li L, Simon R (2000) A multiaxial stress criterion for short- and long-term strength of isotropic rock media. Int J Rock Mech Min Sci 37(8):1169–1193

    Article  Google Scholar 

  • Bellenger E, Bussy P (2001) Phenomenological modeling and numerical simulation of different modes of creep damage evolution. Int J Solids Struct 38:577–604

    Article  Google Scholar 

  • Bhat HS, Sammis CG, Rosakis AJ (2011) The micromechanics of Westerly granite at large compressive loads. Pure appl Geophys 168(12):1–18

    Article  Google Scholar 

  • Brace WF, Paulding B, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71:3939–3953

    Article  Google Scholar 

  • Brantut N, Baud P, Heap MJ, Meredith PG (2012) Micromechanics of brittle creep in rocks. J Geophys Res 117:B08412

    Google Scholar 

  • Caia M, Kaisera PK, Tasakab 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 Sci 41:833–847

    Article  Google Scholar 

  • Challamel N, Lanos C, Casandjian C (2005) Creep damage modelling for quasi-brittle materials. Eur J Mech A-Solid 24:593–613

    Article  Google Scholar 

  • Chandler NA (2013) Quantifying long-term strength and rock damage properties from plots of shear strain versus volume strain. Int J Rock Mech Min Sci 59:105–110

    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 Sci 41:1069–1086

    Google Scholar 

  • Charles RJ (1958) Static fatigue of glass I. J Appl Phys 29(11):1549–1553

    Article  Google Scholar 

  • Chen ZH, Tang CA, Huang RQ (1997) A double rock sample model for rockbursts. Int J Rock Mech Min Sci 34(6):991–1000

    Article  Google Scholar 

  • Costin LS (1985) Damage mechanics in the post-failure regime. Mech Mater 4:149–160

    Article  Google Scholar 

  • Cruden DM (1970) A theory of brittle creep in rock under uniaxial compression. J Geophys Res 75(17):3431–3432

    Article  Google Scholar 

  • Deshpande VS, Evans AG (2008) Inelastic deformation and energy dissipation in ceramics: a mechanism-based constitutive model. J Mech Phys Solids 56(10):3077–3100

    Article  Google Scholar 

  • Diederichs MS, Kaiser PK, Eberhardt E (2004) Damage initiation and propagation in hard rock during tunneling and the influence of near-face stress rotation. Int J Rock Mech Min Sci 41:785–812

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Hou Z, Wundram L, Meyer R, Schmidt M, Schmitz S, Were P (2012) Development of a long-term wellbore sealing concept based on numerical simulations and in situ-testing in the Altmark natural gas field. Environ Earth Sci 67:395–409

    Article  Google Scholar 

  • Hudson JA and Fairhurst C (1969) Tensile strength, Weibull’s theory and a general statistical approach to rock failure. In: Proceedings of Civil Engineering Materials Conference, Southampton, pp 901–904

  • Jiang QQ, Li JT, Hu YF, Gui YL, Lai WM (2008) Effects of water on subcritical crack growth. Chin J Rock Soil Mech 29(9):2527–2530

    Google Scholar 

  • Kachanov LM (1986) Introduction to continuum damage mechanics. Martinus Nijhoff, Dordrecht

    Book  Google Scholar 

  • Krajcinovic D (1983) Constitutive equations for damaging materials. J Appl Mech 50:355–360

    Article  Google Scholar 

  • Kranz RL (1979) Crack growth and development during creep of Barre granite. Int J Rock Mech Mining Sci Geomech Abstr 16(1):23–35

    Article  Google Scholar 

  • Lajtai EZ, Scott Duncan EJ, Carter BJ (1991) The effect of strain rate on rock strength. Rock Mech Rock Eng 24(2):99–109

    Article  Google Scholar 

  • Lau JSO, Chandler NA (2004) Innovative laboratory testing. Int J Rock Mech Min Sci 41(8):1427–1445

    Article  Google Scholar 

  • Liu QS, Hu YH, Liu B (2009) Progressive damage constitutive models of granite based on experimental results. Chin J Rock Soil Mech 30(2):289–296

    Article  Google Scholar 

  • Ma L, Daemen JJK (2006) An experimental study on creep of welded tuff. Int J Rock Mech Min Sci 43(2):282–291

    Article  Google Scholar 

  • Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31(6):643–659

    Article  Google Scholar 

  • Miura K, Okui Y, Horii H (2003) Micromechanics-based prediction of creep failure of hard rock for long-term safety of high-level radioactive waste disposal system. Mech Mater 35(3):587–601

    Article  Google Scholar 

  • Munson DE (1997) Constitutive model of creep in rock salt applied to underground room closure. Int J Rock Mech Min Sci 34(2):233–247

    Article  Google Scholar 

  • Nara Y, Takada M, Mori D, Owada H, Yoneda T, Kaneko K (2010) Subcritical crack growth and long-term strength in rock and cementitious material. Int J Fract 164(1):57–71

    Article  Google Scholar 

  • Nara Y, Yamanaka H, Oe Y, Kaneko K (2013) Influence of temperature and water on subcritical crack growth parameters and long-term strength for igneous rock. Geophys J Int 193(1):47–60

    Article  Google Scholar 

  • Ohnaka M (1983) Acoustic emission during creep of brittle rock. Int J Rock Mech Min Sci Geomech Abstr 20(3):121–134

    Article  Google Scholar 

  • Park CH, Bobe A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77:2727–2748

    Article  Google Scholar 

  • Rice JR (1975) Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. Constitutive equations in plasticity. Massachusetts Institute of Technology Press, Cambridge, pp 23–79

    Google Scholar 

  • Sangha CM, Dhir RK (1972) Influence of time on the strength, deformation and fracture properties of a lower Devonian sandstone. Int J Rock Mech Min Sci 9:343–354

    Article  Google Scholar 

  • Schmidtke RH, Lajtai EZ (1985) The long-term strength of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 6(22):461–465

    Article  Google Scholar 

  • Scholz CH (1968) Mechanism of creep in brittle rock. J Geophys Res 73(10):3295–3302

    Article  Google Scholar 

  • Sun J, Ling JM (1997) On meso damage behaviour and long-term stability of high slope rock of the three gorges shiplocks. Chin J Rock Mech Eng 16(1):1–7

    Google Scholar 

  • Tang CA, Kou SQ (1998) Crack propagation and coalescence in brittle materials under compression. Eng Fract Mech 61:311–324

    Article  Google Scholar 

  • Tsai LS, Hsieh YM, Weng MC (2008) Time-dependent deformation behaviors of weak sandstones. Int J Rock Mech Min Sci 45(2):144–154

    Article  Google Scholar 

  • Wang TJ (1991) A continuum damage model for ductile fracture of weld heat affected zone. Eng Fract Mech 40(6):1075–1082

    Article  Google Scholar 

  • Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297

    Google Scholar 

  • Wu F, Liu JF, Wang J (2015) An improved Maxwell creep model for rock based on variable-order fractional derivatives. Environ Earth Sci 73(11):6965–6971

    Article  Google Scholar 

  • Xu T, Xu Q, Deng M, Ma T, Yang T, Tang CA (2014) A numerical analysis of rock creep-induced slide: a case study from Jiweishan Mountain, China. Environ Earth Sci 72:2111–2128

    Article  Google Scholar 

  • Zhang M, Li ZK, Su X (2005) Probabilistic volume element modeling in elastic damage analysis of quasi-brittle materials. Chin J Rock Mech Eng 24(23):4282–4288

    Google Scholar 

  • Zhu ZQ, Sheng Q, Leng XL, Zhang ZR (2007) Study on crack initiation mechanism of three gorges granite. Chin J Rock Mech Eng 26(12):2570–2575

    Google Scholar 

Download references

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Authors and Affiliations

  1. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    X. Z. Li & Z. S. Shao

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  1. X. Z. Li
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  2. Z. S. Shao
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Correspondence to Z. S. Shao.

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Li, X.Z., Shao, Z.S. Micro–macro modeling of brittle creep and progressive failure subjected to compressive loading in rock. Environ Earth Sci 75, 583 (2016). https://doi.org/10.1007/s12665-016-5365-3

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  • DOI: https://doi.org/10.1007/s12665-016-5365-3

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