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Linear failure criterion for estimating the compressive strength of brittle foliated rocks in response to the loading direction

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Abstract

In this study, a failure criterion is proposed for describing the strength variation of foliated rocks that possess inherently anisotropic properties due to the existence of macro weak planes (MWPs). These rocks are typically characterized by the clustering and directional arrangement of needle-flaky minerals, a quasi-interlayered structure composed of weak and strong layers, and a directional arrangement of microcracks. The compressive failure mode of foliated rocks subjected to confining pressure is heavily dependent on the loading direction, which can be divided into two types within a certain range of confining pressures: shear-slip failure along the MWP and macro shear failure oblique to the MWP. From the perspective of the failure mechanism related to rock fabric and macrofailure characteristics, the linear failure criteria available for the two modes are proposed based on fracture mechanics theory, the Mohr–Coulomb criterion and the maximum axial strain criterion. The criteria involve 6 parameters that can be simply determined by a small amount of test data. Among them, the friction coefficient f is closely related to the loading direction corresponding to the minimum compressive strength, and the transversely isotropic parameter n controls the variation form of anisotropic strength with the loading direction. The predicted values of several kinds of exemplary foliated rocks agree well with their measured compressive strengths depending on the confining pressure and loading direction, suggesting a high prediction accuracy for the new criterion. The analysis reveals that the new criterion is suitable for describing the failure of brittle foliated rocks within a certain range of confining pressures.

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References

  • Asadi M, Bagheripour MH (2015) Modified criteria for sliding and non-sliding failure of anisotropic jointed rocks. Int J Rock Mech Min Sci 73:95–101

    Article  Google Scholar 

  • Attewell PB, Sandford MR (1974) Intrinsic shear strength of a brittle, anisotropic rock—I. Int J Rock Mech Min Sci Geomech Abst 11:423–430

    Article  Google Scholar 

  • Attewell PB, Taylor RK (1969) A microtextural interpretation of a welsh slate. Int J Rock Mech Min Sci Geomech Abstr 6(5):425–438

    Article  Google Scholar 

  • Bagheripour MH, Rahgozar R, Pashnesaz H, Malekinejad M (2011) A complement to Hoek-Brown failure criterion for strength prediction in anisotropic rock. Geomech Eng 3(1):61–81

    Article  Google Scholar 

  • Barton N (1976) The shear strength of rock and rock joints. Int J Rock Mech Min Sci Geomech Abstr 13(9):255–279

    Article  Google Scholar 

  • Behrestaghi M, Rao KS, Ramamurthy T (1996) Engineering geological and geotechnical responses of schistose rocks from dam project areas in India. Eng Geol 44(1):183–201

    Article  Google Scholar 

  • Bobet A, Einstein HH (1998) Fracture coalescence in rock-type material under uniaxial and biaxial compressions. Int J Rock Mech Min Sci 35(7):863–888

    Article  Google Scholar 

  • Boehler JP (1987) Anisotropic linear elasticity. Springer, Vienna

    Book  Google Scholar 

  • Chen LL, Liu C, Zhao WC, Liu LC (2018) An isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution. Comput Methods Appl Mech Eng 336:507–532

    Article  Google Scholar 

  • Cho JW, Kim H, Jeon S, 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 

  • Deng HF, Wang W, Li JL, Zhang YC, Zhang XJ (2018) Experimental study on anisotropic mechanical properties of layered sandstone. Chin J Rock Mech Eng 37(1):112–120

    Google Scholar 

  • Donath FA (1964) Strength variation and deformational behavior in anisotropic rock. In: Judd WR (ed) State of stress in the Earth’s crust. Elsevier, New York, pp 281–297

    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 

  • Duveau G, Shao JF, Henry JP (1998) Assessment of some failure criteria for strongly anisotropic geomaterials. Mech Cohes Frict Mater Int J Exp Model Comput Mater Struct 3(1):1–26

    Article  Google Scholar 

  • Fereidooni D, Khanlari GR, Heidari M, Sepahigero AA, Kolahi AP (2016) Assessment of inherent anisotropy and confining pressure influences on mechanical behavior of anisotropic foliated rocks under triaxial compression. Rock Mech Rock Eng 49(6):2155–2163

    Article  Google Scholar 

  • Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Eng Div 106(15715):1013–1035

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kwasniewski MA (1993) Mechanical behavior of anisotropic rocks. In: Hudson JA (ed) Comprehensive rock engineering, vol 1. Pergamon, Oxford, pp 285–312

    Google Scholar 

  • Li LQ, Zhang CS, Wang W (2018) A modified Hoek-Brown failure criterion for anisotropic rock mass. Chin J Rock Mech Eng 37(Supp. 1):3239–3246

    Google Scholar 

  • Li SY (2010) Introduction of rock fracture mechanics. University of Science & Technology China press, Hefei

    Google Scholar 

  • Martin CD (1997) The effect of cohesion loss and stress path on brittle rock strength. Can Geotech J 34(5):698–725

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Nasseri MH, Rao KS, Ramamurthy T (1997) Failure mechanism in schistose rocks. Int J Rock Mech Min Sci 34(3–4):219–234

    Google Scholar 

  • Nasseri MH, Rao KS, Ramamurthy T (2003) Transversely isotropic strength and deformational 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 behaviour of Tournemire shale. Int J Rock Mech Min Sci 34(1):3–16

    Article  Google Scholar 

  • Ohtsu M, Isoda T, Tomoda Y (2007) Acoustic emission techniques standardized for concrete structures. J Acoust Emiss 25:21–32

    Google Scholar 

  • Pariseau WG (1968) Plasticity theory for anisotropic rocks and soils. In: The 10th U.S. Symposium on Rock Mechanics, Austin, Texas

  • Ramamurthy T (1993) Strength and modulus responses of anisotropic rocks. In: Hudson JA (ed) Comprehensive rock engineering, vol 1. Pergamon, Oxford, pp 313–329

    Google Scholar 

  • Ramamurthy T (2004) A geo-engineering classification for rocks and rock masses. Int J Rock Mech Min Sci 41(1):89–101

    Article  Google Scholar 

  • Ramamurthy T, Rao GV, Singh J (1988) A strength criterion for anisotropic rocks. In: Proc. 5th Australia-New Zealand Conference on Geomechanics, Sydney

  • Ramamurthy T, Rao GV, Singh J (1993) Engineering behaviour of phyllites. Eng Geol 33(3):209–225

    Article  Google Scholar 

  • Rawling GC, Baud P, Tengfong W (2002) Dilatancy, brittle strength, and anisotropy of foliated rocks: experimental deformation and micromechanical modeling. J Geophys Res 107(B10):2234–2247

    Google Scholar 

  • Saeidi O, Rasouli V, Vaneghi RG, Gholami R, Torabi SR (2014) A modified failure criterion for transversely isotropic rocks. Geosci Front 5(2):215–225

    Article  Google Scholar 

  • Sagong M, Bobet A (2002) Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min Sci 39(2):229–241

    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(2):223–234

    Article  Google Scholar 

  • Shi XC, Yang X, Meng YF, Li G (2016) Modified Hoek-Brown failure criterion for anisotropic rocks. Environ Earth Sci 75(11):1–11

    Article  Google Scholar 

  • Singh J, Ramamurthy T, Rao GV (1989) Strength anisotropies in rocks. Indian Geotech J 19(2):147–166

    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 

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

    Article  Google Scholar 

  • Tsai SW, Wu EM (1971) A general theory of strength of anisotropic materials. J Compos Mater 5(1):58–80

    Article  Google Scholar 

  • Walsh JB, Brace WF (1964) A fracture criterion for brittle anisotropic rock. J Geophys Res 69(16):3449–3456

    Article  Google Scholar 

  • Wang CL, Hou XL, Li HT, Zhang SJ, Tao ZG (2019) Experimental investigation on dynamic evolution characteristics of micro-cracks for sandstone samples under uniaxial compression. Bull Disaster Prevent Res Inst Kyoto Univ 41(11):2120–2125

    Google Scholar 

  • Wu YS, Tan ZS, Yu XB, Yu Y, Li L, Guo XL (2001) Comparative tests on strength and deformation of phyllite of northern tunnels of Longmen Mountains. Chin J Geotech Eng 38:399–412

    Google Scholar 

  • Zhang XP, Wong L, Wang SJ et al (2011) Engineering properties of quartz mica schist. Eng Geol 121(3–4):135–149

    Article  Google Scholar 

  • Zhou Y, Su SR, Li P, Ma HS, Zhang XD (2019) Microstructure and mechanical properties of broken phyllite. J Jilin Univ (earth Sci Ed) 49(2):504–513

    Google Scholar 

  • Yin XM, Yan EC, Wang LN, Liu LC, Feng B, Wang PZ (2020) Anisotropy of quartz mica schist based on quantitative extraction of fabric information. Bull Eng Geol Env 79(5):2439–2456

    Article  Google Scholar 

  • Yin XM, Zhang X, Lei YJ, Wang LN (2021) Response characteristics and mechanism of the strength and energy of schist to the schistosity orientation and water. Bull Eng Geol Env 80(9):7029–7049

    Article  Google Scholar 

Download references

Funding

This research is financially supported by the Natural Science Foundation of China (Grant no. 41807240) and the Nanhu Scholars Program of Xinyang Normal University. The author gratefully acknowledges the financial support provided by them.

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Authors and Affiliations

  1. College of Intelligent Construction, Wuchang University of Technology, Wuhan, 430223, China

    Xiaomeng Yin

  2. College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang, 464000, China

    Xiaomeng Yin & Yage Zhang

  3. School of Education, Hubei University of Arts and Science, Xiangyang, 441053, China

    Yuju Lei

  4. School of Civil Engineering, Liaoning Petrochemical University, Fushun, 113001, China

    Lunan Wang

Authors
  1. Xiaomeng Yin
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  2. Yage Zhang
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  3. Yuju Lei
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  4. Lunan Wang
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Correspondence to Yuju Lei.

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Yin, X., Zhang, Y., Lei, Y. et al. Linear failure criterion for estimating the compressive strength of brittle foliated rocks in response to the loading direction. Bull Eng Geol Environ 81, 189 (2022). https://doi.org/10.1007/s10064-022-02681-4

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  • DOI: https://doi.org/10.1007/s10064-022-02681-4

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