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Viscosity of rock mass at different structural levels

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Abstract

This paper examines viscosity of rock mass at different structural hierarchies. The study shows that viscosity and characteristic strain rate of rock mass vary at different structural levels. There exists one-to-one correspondence between characteristic scale level and strain rate. High viscosity with low characteristic strain rate occurs under macro-level, while meso- and micro-levels are characterized by low viscosity with high characteristic strain rate. Generally, with the increase in strain rate, deformation and fracture take place at decreasing scale levels, and viscosity gradually decreases. With high characteristic strain rate at meso- and micro-levels, viscosity is inversely proportional to strain rate at these levels. Based on the analysis on viscosity at different structural levels, a unified description of viscosity is suggested and applied to the description of the strength–strain rate sensitivity of rock mass.

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References

  1. Anderson O, Grew P (1977) Stress corrosion theory of crack propagation with application to geophysics. Rev Geophys Space Phys 15:77–104

    Article  Google Scholar 

  2. Ando R, Yamashita T (2007) Effects of mesoscopic-scale fault structure on earthquake ruptures: dynamic formation of geometrical complexity of earthquake faults. J Geophys Res 112:B09303. doi:10.1029/2006JB004612

    Article  Google Scholar 

  3. Altshuler LV, Doronin GS, Kim GKh (1987) Viscosity of shock compressed liquids. App Mech Tech Phys 28(6):110–118

    Google Scholar 

  4. Atkinson B (1984) Subcritical crack growth in geological materials. J Geophys Res 89:4077–4114

    Article  Google Scholar 

  5. Atkinson B, Meredith P (1987) The theory of subcritical crack growth with application to minerals and rocks. In: Atkinson BK (ed) Fracture mechanics of rock. Academy Press, New York, pp 111–166

  6. Barton CC (1995) Fractal analysis of scaling and spatial clustering of fractures. In: Barton CC, Lapointe PR (eds) Fractal in the earth science. Plenum Press, New York, pp 141–178

    Chapter  Google Scholar 

  7. Belinsky IV, Khristoforov BD (1968) Viscosity of NaCl under shock compression. Appl Mech Tech Phys 9(1):150–151

    Google Scholar 

  8. Belinsky IV, Mikhaliuk AV, Khristoforov BD (1975) Viscosity of rock mass in deformation processes. Phys Solid Earth 11(8):80–84

    Google Scholar 

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

    Article  Google Scholar 

  10. Bird RB, Armstrong RC and Hassager O (1987) Dynamics of polymeric liquid, vol. 2, 2-nd ed. Wiley, New York

  11. Broberg KB (1999) Cracks and Fracture. Academic Press, San Diego

    Google Scholar 

  12. CEB (1993) CEB-FIP model code 1990. Committee Euro-International Du Beton, Redwood Books, Trowbridge, Wiltshire

    Google Scholar 

  13. Chekunaev NI, Kaplan AM (2009) Limiting speed of crack propagation in elastic materials. J Appl Mech Tech Phys 50(4):677–683

    Article  MATH  Google Scholar 

  14. Chow TS (2000) Mesoscopic physics of complex materials. Springer, New York

    Book  MATH  Google Scholar 

  15. Dove PM (1995) Geochemical controls on the kinetics of quartz fracture at subcritical tensile stresses. J Geophys Res 100:22349–22359

    Article  Google Scholar 

  16. Dulaney EN, Brace WF (1960) Speed behavior of a growing crack. J Appl Phys 31(12):2233–2236

    Article  Google Scholar 

  17. Faulkner D, Jackson CAL, Lunn RJ, Schlische RW, Shiptone ZK, Wibberley CAJ, Withjack MO (2010) A review of recent developments concerning the structure, mechanics and fluid flow properties of fault zones. J Struct Geol 32(11):1557–1575

    Article  Google Scholar 

  18. Field JE (1971) Brittle fracture: its study and application. Comtemp Phys 12(1):1–31

    Article  Google Scholar 

  19. Fineberg J, Marder M (1999) Instability in dynamic fracture. Phys Rep 313:101–108

    Article  MathSciNet  Google Scholar 

  20. Finkel VM (1962) Investigation on crack growth under dynamic fracture of glass. Phys Solid State 4(6):1412–1418

    Google Scholar 

  21. Freiman S (1984) Effects of chemical environments on slow crack growth in glasses and ceramics. J Geophys Res 89:4072–4076

    Article  Google Scholar 

  22. Freund LB (1990) Dynamic fracture mechanics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  23. Grady DE (1996) Shock wave properties of brittle solids. In: Schmidt Steve (ed) Shock compression of condensed matters, 9–20. AIP Press, New York

    Google Scholar 

  24. Grady DE (2008) Fragment size distribution from the dynamic fragmentation of brittle solids. Int J Impact Eng 35(12):1557–1562

    Article  Google Scholar 

  25. Grady DE (2010) Length scale and size distribution in dynamic fragmentation. Int J Fract 63:85–99

    Article  MATH  Google Scholar 

  26. Grady DE, Hollebach RE, Schuler KW, Callender JF (1977) Strain rate dependence in Dolomite inferred from impact and static compression rests. J Geophs Res 82:1325–1333

    Article  Google Scholar 

  27. Hadley K (1976) Comparison of computed and observed crack densities and seismic velocities in Westerly granite. J Geophys Res 81:3484–3494

    Article  Google Scholar 

  28. Hong L, Li XB, Ma C, Yin TB, Ye ZY, Liao GY (2008) Study on size effect of rock dynamic strength and strain rate sensitivity. Chin J Rock Mech Eng 27(3):526–533

    Google Scholar 

  29. Horie Y, Yano K (2002) Non-equilibrium fluctuations in shock compression of polycrystalline α-iron. In: Furnish MD (ed) Shock compression of condensed matter-2001. AIP, New York, pp 553–556

    Google Scholar 

  30. Housen KR, Holsapple KA (1999) Scale effects in strength-dominated collisions of rocky asteroids. Icarus 142:21–33

    Article  Google Scholar 

  31. Kipp ME, Grady DE (1985) Dynamic fracture growth and interaction in one dimension. J Mech Phys Solids 33(4):399–415

    Article  Google Scholar 

  32. Kipp ME, Grady DE, Chen EP (1980) Strain-rate dependent fracture initiation. Int J Fract 16:471–478

    Article  Google Scholar 

  33. Kocharyan GG (2014) Scale effect in seismotectonics. Geodyn Tectonophys 5(2):353–385. doi:10.5800/GT2014520133

    Article  Google Scholar 

  34. Kocharyan GG, Kulyukin AA, Markov VK, Markov DV, Pavlov DV (2005) Small disturbances and stress-strain state of the Earth’s crust. Phys Mesomech 8(1):23–36

    Google Scholar 

  35. Kuksenko VS (1987) Physical and methodological fundament for prediction of rock-bursts. J Min Sci 23(1):9–22

    Google Scholar 

  36. Kurlenia MV, Oparin VN (1996) Scale factor of phenomenon of zonal disintegration of rock and canonical series of atomic and ionic radii. J Min Sci 32(2):81–90

    Article  Google Scholar 

  37. Kurlenia MV, Oparin VN, Eremenko AA (1993) Relation of linear block dimensions of rock to crack opening in the structural hierarchy of masses. J Min Sci 29(3):197–203

    Article  Google Scholar 

  38. Landau LD, Lifshitz EM (1959) Theory of elasticity. Pergamon, London

    MATH  Google Scholar 

  39. Lawn BR, Wilshaw TR (1975) Fracture of brittle solids. Cambridge University Press, Cambridge

    Google Scholar 

  40. Lee J (2002) The universal role of turbulence in the propagation of strong shocks and detonation waves. In: Horie Y (ed) High-pressure shock and compression of solids VI. Springer, Berlin, pp 121–148

    Google Scholar 

  41. Lindholm US, Yeakley LM, Nagy A (1974) The dynamic strength and fracture properties of Dresser basalt. Int J Rock Mech Min Sci Geomech Abstr 11(5):181–191. doi:10.1016/0148-9062(74)90885-7

    Article  Google Scholar 

  42. Lockner DA, Moore RM, Reches Z (1992) Microcrack interaction leading to shear failure. In: Tillerson JR, Wawersik WR (eds) Rock Mechanics, Proceedings of the 33rd US Symposium. Balkema, The Netherland, pp 807–817

    Google Scholar 

  43. Lysak SV, Levi KG (1992) Continental rift zone patterns and their geophysical fields. In: Logatchev NA (ed) Faulting in lithosphere, extensional zones. Nauka, Siberian Branch, Novosibirsk, pp 6–21

    Google Scholar 

  44. Moore RM, Lockner DA (1995) The role of microcracking in shear fracture propagation in granite. J Struct Geol 17:95–114

    Article  Google Scholar 

  45. Mott NF (1948) Brittle fracture in mild steel plates. Engineering 165:16–18

    Google Scholar 

  46. Oparin VN, Yushkin VF, Akinin AA, Balmashnov EG (1998) A new scale of hierarchically structured representations as a characteristic for ranking entities in a geomedium. J Min Sci 34(5):387–401

    Article  Google Scholar 

  47. Ožbolt J, Rah KK, Mestrović D (2006) Influence of loading rate on concrete cone failure. Int J Frac 139:239–252

    Article  Google Scholar 

  48. Panin VE (1998) Physical mesomechanics of heterogeneous media and computer-aided design of materials. Cambridge Int Sci Pub, Cambridge

    Google Scholar 

  49. Petrov VA (1984) Lifetime of solids under low loads-nonfracturing stresses. Phys Solid State 26(7):2116–2119

    Google Scholar 

  50. Perzyna P (1998) Constitutive modeling of dissipative solid for localization and fracture. localization and fracture phenomena in inelastic solids. Springer, Wien, New York, pp 99–241

    Chapter  Google Scholar 

  51. Piggot AR (1997) Fractal relations for the diameter and trace length of disc-shaped fractures. J Geophys Res 102:18121–18125

    Article  Google Scholar 

  52. Popov VL, Kröner E (2001) Theory of elastoplastic media with mesostructure. Theo App Fra Mech 37(1–3):299–310

    Article  Google Scholar 

  53. Qi CZ, Qian QH (2003) Physical mechanism of brittle material strength-strain rate sensitivity. Chin J Rock Mech Eng 21(2):177–181

    Google Scholar 

  54. Qi CZ, Qian QH (2009) Basic problems of dynamic deformation and fracture of rock mass. Science Press, Beijing

    Google Scholar 

  55. Qi CZ, Wang MY, Bai JP, Li KR (2014) Mechanism underlying dynamic size effect on rock mass strength. Int J Impact Eng 68:1–7

    Article  Google Scholar 

  56. Chengzhi Qi, Mingyang Wang, Qihu Qian, Jianjie Chen (2008) Structural hierarchy of rock masses and the mechanisms of its formation. Moscow University Mech Bull 63(5):113–121. doi:10.3103/S0027133008050026

    Article  Google Scholar 

  57. Radionov VN, Sizov IA, Tsvetkov VM (1986) Fundamental of geomechanics. Nedra, Moscow

    Google Scholar 

  58. Rahiman TIH, Pettinga JR (2009) Fracture lineaments, fault mesh formation and seismicity: towards a seismotectonic model for Viti Levu, Fiji. Bull New Zealand Soc Earth Eng 42(1):63–72

    Google Scholar 

  59. Roberts DK, Wells AA (1954) The speed of brittle fracture. Engineering 24:820–821

    Google Scholar 

  60. Rosakis AJ, Samudrala O, Coker D (1999) Cracks faster than the shear wave speed. Science 284:1337–1340

    Article  Google Scholar 

  61. Rouleau A, Gale JE (1985) Statistical characterization of the fracture system in the Stripa granite. Int J Rock Mech Min Sci Geomech Abstr 22:353–367

    Article  Google Scholar 

  62. Sadovsky MA, Bolkhovitinov LG, Pisarenko VF (1987) Deformation of geophysical medium and seismic process. Publishing house “Nauka”, Moscow (In Russian)

  63. Sadovsky MA, Pisarenko VF (1983) On dependence of preparation time of earthquake on its energy. Rep Acad Sci USSR 271(2):330–333

    Google Scholar 

  64. Sadovsky MA, Pisarenko VF, Shteinberg VV (1983) On dependence of energy of earthquake on earthquake source volume. Rep Acad Sci USSR 271(3):598–602

    Google Scholar 

  65. Salganik R, Rapoport L, Gotlib VA (1997) Effect of structure on environmentally assisted subcritical crack growth in brittle materials. Int J Fract 87:21–46

    Article  Google Scholar 

  66. Savage HM, Brodsky EE (2011) Collateral damage: Evolution with displacement of fracture distribution and secondary fault strands in fault damage zones. J Geophys Res 116(B3):B03405

    Article  Google Scholar 

  67. Scholz CH, Dawers NH, Yu JZ, Anders MH, Cowie PA (1993) Fault growth and scaling laws: preliminary results. J Geophys Res 98:21951–21961

    Article  Google Scholar 

  68. Senseny PE, Hansen FD, Russell JE, Carter NL, Hardin JW (1992) Mechanical behavior of rock salt: Phenomenology and micro-mechanism. Int J Rock Mech Min Sci Geomech Abstr 29(4):363–378

    Article  Google Scholar 

  69. Sherman SI (1992) The relationships between quantitative parameters of faults. In: Logatchev NA (ed) Faulting in lithosphere, extensional zones. Nauka, Siberian Branch, Novosibirsk, pp 78–102

    Google Scholar 

  70. Sherman SI (2012) Destruction of the lithosphere: fault-block divisibility and its tectonophysical regularities. Geophys Tectonophys 3(4):315–344

    Article  Google Scholar 

  71. Shibi T, Kamei T (2008) Investigation of the mechanism of fault formation using bifurcation analysis. In: Proceedings of the eighteenth international offshore and polar engineering conference, 654–659. Vancouver, BC, Canada, July 6–11

  72. Sih GC (2008) Birth of mesomechanics arising from segmentation and multiscaling: nano-micro-macro. Phys Mesomech 11(3–4):128–140

    Google Scholar 

  73. Spahn F, Neto EV, Guimaraes AHF, Gorban AN, Brilliantov NV (2011) A statistical model of aggregates fragmentation. Eprint arXiv: 1106.2721lvl [cond-mat-stat-mech] 14 Jun 2011

  74. Stepanov GV, Kharchenko VV (1984) Relation between stress and strain in metals under impulsive action. Probl Strength 11:32–37

    Google Scholar 

  75. Steverding B, Lehnigk SH (1970) Response of cracks to impact. J Appl Phys 41(5):2096–2099

    Article  Google Scholar 

  76. Tyapkin KF, Kiveliuk TT (1982) Investigation of fault structure by geological-geophysical methods. Nedra, Moscow

    Google Scholar 

  77. Wang TM (2006) Control of cracking in engineering structures. China Architecture & Building Press, Beijing

    Google Scholar 

  78. Yavari A, Khezrzadeh H (2010) Estimating terminal speed of rough cracks in the framework of discrete fractal fracture mechanics. Eng Fra Mech 77(10):1516–1526

    Article  Google Scholar 

  79. Yoffe EH (1951) The moving Griffith crack. Phil Mag 42:739–750

    Article  MathSciNet  MATH  Google Scholar 

  80. Zhurkov SN (1965) Kinetic concept of the strength of solids. Int J Fract 1(4):311–322

    Google Scholar 

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Acknowledgments

The study was financially supported in part by the National Natural Science Foundation of China (Nos. 51174012 and 51478027), the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality (No. IDHT20130512), the “973” Key State Research Program (Grant No. 2015CB0578005), Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51021001), as well as Development of High-Caliber Talents Project of Beijing Municipal Institutions granted to Dr. Jilin Qi (No. CIT&TCD20150101).

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Authors and Affiliations

  1. Beijing High Institution Research Center for Engineering Structures and New Materials, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China

    Chengzhi Qi, Chen Haoxiang & Jilin Qi

  2. Faculty of Computing, Engineering and Science, University of South Wales, Pontypridd, CF37 1DL, UK

    Jiping Bai

  3. School of Civil Engineering, PLA University of Science and Technology, Nanjing, 210007, China

    Kairui Li

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  1. Chengzhi Qi
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Correspondence to Chengzhi Qi.

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Qi, C., Haoxiang, C., Bai, J. et al. Viscosity of rock mass at different structural levels. Acta Geotech. 12, 305–320 (2017). https://doi.org/10.1007/s11440-016-0449-5

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