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Energy evolution analysis and related failure criterion for layered rocks

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Abstract

Energy accumulation and energy release are typical characteristics during the whole deformation process of layered rocks. To reveal the characteristics of the energy evolution and failure mechanism of layered rocks, uniaxial compression tests are carried out on layered shale samples. The anisotropic properties of layered rocks are studied. The energy indexes, namely, the elastic energy, dissipated energy, and total input energy of the specimens, are further investigated, revealing the energy damage evolution mechanism of the layered rocks. The experimental results show that the mechanical properties and failure modes of layered rocks are obviously anisotropic. The failure modes of layered rocks can be divided into three types, and the uniaxial compression strength typically shows “U” shaped with the increasing orientation of bedding planes. The energy reserve of the layered rock mass is also anisotropic due to the influence of bedding planes. Before the peak strength, the energy evolution of the layered rock samples is nearly similar, dominated by energy accumulation. The energy dissipation and energy release predominated after the peak strength. In the postpeak stress stage, the elastic strain energy (Ue) is released suddenly, while the dissipated energy (Ud) increases significantly. After that, the elastic-dissipated energy ratio (Ud/Ue) of the layered rocks is studied. The elastic-dissipated energy ratio slowly decreases with strain in the elastic stage, while it increases significantly in the postpeak fracture stage, which has a mutation point. The mutation point is defined as the critical elastic-dissipated energy ratio (Kc), which also shows a typical “U” shape with the orientation of bedding planes. Therefore, the strength failure criterion according to the energy mutation is proposed, which does not need to consider the tensile or shear failure mode of the layered rocks. The failure criterion is validated by the experimental results of other layered rock samples made of similar materials in the laboratory. The criterion is useful for the strength prediction of layered rocks under uniaxial compression.

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References

  • Amadei B (1983) Rock anisotropy and the theory of stress measurements Lecture Notes in Engineering Series. Springer, New York

    Book  Google Scholar 

  • Amadei B (1996) Importance of anisotropy when estimation and measuring in situ stresses in rock. Int J Rock Mech Min Sci Geomech Abstr 33(3):293–326

    Article  Google Scholar 

  • Bieniawski ZT (1967) Mechanism of brittle fracture of rock: part I—theory of the fracture process. Int J Rock Mech Min Sci Geomech Abstr 4(4):395–406

    Article  Google Scholar 

  • Bieniawski ZT (1968) Fracture dynamics of rock. Int J Fract Mech 4(4):415–430

    Article  Google Scholar 

  • Cazacu O, Cristescu ND (1999) A paraboloid failure surface for transversely isotropic materials. Mech Mater 31:381–393

    Article  Google Scholar 

  • Chen X, Yang Q, Qiu KB, Feng JL (2008) An anisotropic strength criterion for jointed rock masses and its application in wellbore stability analyses. Int J Numer Anal Methods Geomech 32:607–631

    Article  Google Scholar 

  • Chen YF, Wei K, Liu W, Hu SH, Hu R, Zhou CB (2016) Experimental characterization and micromechanical modelling of anisotropic slates. Rock Mech Rock Eng 49:3541–3557

    Article  Google Scholar 

  • Cho JW, Kim H, Joen SK, Min KB (2012) Deformation and strength anisotropy of Asan gneiss, Boryeong shale, and Yeoncheon schist. Int J Rock Mech Min Sci 50:158–169

    Article  Google Scholar 

  • Debecker B, Vervoort A (2009) Experimental observation of fracture patterns in layered slate. Int J Fract 159(1):51–62

    Article  Google Scholar 

  • Donath FA (1961) Experimental study of shear failure in anisotropic rocks. Geol Soc Am Bull 72(6):985–989

    Article  Google Scholar 

  • Duveau G, Shao JF (1998) A modified single discontinuity theory for the failure of highly stratified rocks. Int J Rock Mech Min Sci 35(6):807–813

    Article  Google Scholar 

  • Gholami R, Rasouli V (2014) Mechanical and elastic properties of transversely isotropic slate. Rock Mech Rock Eng 47:1763–1773

    Article  Google Scholar 

  • He MC, Sousa LRE, Miranda T, Zhu GL (2015) Rockbust laboratory tests databasedapplication of data mining techniques. Eng Geol 185:116–130

    Article  Google Scholar 

  • Jaeger JC (1960) Shear failure of anisotropic rocks. Geol Mag 97(1):65–72

    Article  Google Scholar 

  • Lai YS, Wang CY, Tien YM (1999) Modified Mohr-Coulomb-type micromechanical failure criteria for layered rocks. Int J Numer Anal Methods Geomech 23(5):451–460

    Article  Google Scholar 

  • Li ZY, Wu G, Huang TZ, Liu Y (2018) Variation of energy and criteria for strength failure of shale under triaxial cyclic loading. Chin J Rock Mech Eng 37(3):662–670 (in Chinese)

    Google Scholar 

  • McLamore R, Gray KE (1967) The mechanical behavior of anisotropic sedimentary rocks. J Eng Ind 89(1):62–73

    Article  Google Scholar 

  • Meng QB, Zhang MW, Zhang ZZ, Han LJ, Pu H (2018) Experimental research on rock energy evolution under uniaxial cyclic loading and unloading compression. Geotech Test J 41(4):717–729

    Article  Google Scholar 

  • Nasseri MHB, Rao KS, Ramamurthy T (2003) Anisotropic strength and deformation behavior of Himalayan schists. Int J Rock Mech Min Sci 40:3–23

    Article  Google Scholar 

  • Niandou H, Shao JF, Henry JP, Fourmaintraux D (1997) Laboratory investigation of the mechanical behavior of Tournemire shale. Int J Rock Mech Min Sci 34(1):3–16

    Article  Google Scholar 

  • Saroglou H, Tsiambaos G (2008) A modified Hoek-Brown failure criterion for anisotropic intact rock. Int J Rock Mech Min Sci 45:223–234

    Article  Google Scholar 

  • Shi XC, Yang X, Meng YF, Li G (2016) An anisotropic strength model for layered rocks considering planes of weakness. Rock Mech Rock Eng 49:3783–3792

    Article  Google Scholar 

  • Singh M, Samadhiya NK, Kumar A, Kumar V, Singh B (2015) A nonlinear criterion for triaxial strength of inherently anisotropic rocks. Rock Mech Rock Eng 48(4):1387–1405

    Article  Google Scholar 

  • Solecki R, Conant RJ (2003) Advanced Mechanics of Materials. Oxford University Press, London

    Google Scholar 

  • Tan X, Konietzky H, Fruhwirt T, Dan DQ (2014) Brazilian tests on transversely isotropic rock. Rock Mech Rock Eng 48(4):1341–1351

    Article  Google Scholar 

  • Tien YM, Kuo MC (2001) A failure criterion for transversely isotropic rocks. Int J Rock Mech Min Sci 38:399–412

    Article  Google Scholar 

  • Tien YM, Kuo MC, Juang CH (2006) An experimental investigation of the failure mechanism of simulated transversely isotropic rocks. Int J Rock Mech Min Sci 43:1163–1181

    Article  Google Scholar 

  • Tien YM, Tsao PF (2000) Preparation and mechanical properties of artificial transversely isotropic rock. Int J Rock Mech Min Sci 37:1001–1012

    Article  Google Scholar 

  • Wang GL, Zhang L, Xu M, Liang ZY, Rang LB (2019) Energy damage evolution mechanism of non-across jointed rock mass under uniaxial compression. Chin J Geotech Eng 41(4):639–647 (in Chinese)

    Google Scholar 

  • Wang MM, Li P, Wu XW, Chen HR (2016) A study on the brittleness and progressive failure process of anisotropic shale. Environ Earth Sci 75(10):866

    Article  Google Scholar 

  • **e HP, Ju Y, Li LY (2005b) Criteria for strength and structural failure of rocks based on energy dissipation and release principles. Chin J Rock Mech Eng 24(17):3003–3010 (in Chinese)

    Google Scholar 

  • **e HP, Ju Y, Li LY, Peng RD (2008) Energy mechanism of deformation and failure of rock masses. Chin J Rock Mech Eng 27(9):1729–1740 (in Chinese)

    Google Scholar 

  • **e HP, Li LY, Ju Y, Peng RD, Yang YM (2011) Energy analysis for damage and catastrophic failure of rocks. Sci China Technol Sci 54(S1):199–209

    Article  Google Scholar 

  • **e HP, Li LY, Peng RD, Ju Y (2009) Energy analysis and criteria for structure failure of rocks. J Rock Mech Geotech Eng 1(1):11–20

    Article  Google Scholar 

  • **e HP, Peng RD, Ju Y, Zhou HW (2005a) On energy analysis of rock failure. Chin J Rock Mech Eng 24(15):2603–2608 (in Chinese)

    Google Scholar 

  • Yang YR, **e HQ, **ao ML, Liu JF, He JD (2017) Deformation failure and energy characteristics of transversely-isotropic rock under unloading of high confining pressure. Rock Soil Mech 36(8):1999–2006 (in Chinese)

    Google Scholar 

  • Zhang P, Yang CH, Wang H, Guo YT, Xu F, Hou ZK (2018) Stress-strain characteristics and anisotropy energy of shale under uniaxial compression. Rock Soil Mech 39(6):2106–2114 (in Chinese)

    Google Scholar 

  • Zhou YY, Feng XT, Xu DP, Fan QX (2017) An enhanced equivalent continuum model for layered rock mass incorporating bedding structure and stress dependence. Int J Rock Mech Min Sci 97:75–98

    Article  Google Scholar 

Download references

Funding

The authors appreciate the financial support by the Natural Science Research Project of Anhui Educational Committee (2022AH050798), Anhui Provincial Natural Science Foundation (2108085QE208), China Postdoctoral Science Foundation (2021M700753), the University Synergy Innovation Program of Anhui Province (GXXT-2022-20). The authors wish to acknowledge these supports.

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Authors and Affiliations

  1. Engineering Research Center of Underground Mine Construction, Ministry of Education, Anhui University of Science and Technology, Huainan, 232001, China

    Min Gao, Qinghe Zhang & Jiuqun Zou

  2. Institute of Unconventional Oil & Gas, Northeast Petroleum University, Daqing, 163318, China

    Min Gao & Shanpo Jia

  3. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Zhengzhao Liang

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  1. Min Gao
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  2. Zhengzhao Liang
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  4. Qinghe Zhang
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  5. Jiuqun Zou
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Correspondence to Zhengzhao Liang.

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Gao, M., Liang, Z., Jia, S. et al. Energy evolution analysis and related failure criterion for layered rocks. Bull Eng Geol Environ 82, 439 (2023). https://doi.org/10.1007/s10064-023-03445-4

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