Rock Mechanics and Rock Engineering

, Volume 49, Issue 7, pp 2569–2580 | Cite as

Time-Dependent Behaviors of Granite: Loading-Rate Dependence, Creep, and Relaxation

Original Paper


To assess the long-term stability of underground structures, it is important to understand the time-dependent behaviors of rocks, such as their loading-rate dependence, creep, and relaxation. However, there have been fewer studies on crystalline rocks than on tuff, mudstone, and rock salt, because the high strength of crystalline rocks makes the detection of their time-dependent behaviors much more difficult. Moreover, studies on the relaxation, temporal change of stress and strain (TCSS) conditions, and relations between various time-dependent behaviors are scarce for not only granites, but also other rocks. In this study, previous reports on the time-dependent behaviors of granites were reviewed and various laboratory tests were conducted using Toki granite. These tests included an alternating-loading-rate test, creep test, relaxation test, and TCSS test. The results showed that the degree of time dependence of Toki granite is similar to other granites, and that the TCSS resembles the stress-relaxation curve and creep-strain curve. A viscoelastic constitutive model, proposed in a previous study, was modified to investigate the relations between the time-dependent behaviors in the pre- and post-peak regions. The modified model reproduced the stress–strain curve, creep, relaxation, and the results of the TCSS test. Based on a comparison of the results of the laboratory tests and numerical simulations, close relations between the time-dependent behaviors were revealed quantitatively.


Time-dependent behavior Loading-rate dependence Creep Relaxation Constitutive model 


  1. Brace WF, Jones AH (1971) Comparison of uniaxial deformation in shock and static loading of three rocks. J Geophys Res 76:4913–4921CrossRefGoogle Scholar
  2. Brace WF, Martin RJ III (1968) A test of the law of effective stress for crystalline rocks of low porosity. Int J Rock Mech Min Sci 5:415–426CrossRefGoogle Scholar
  3. Carlson SR, Nishizawa O, Satoh T, Kusunose K (1998) Pore pressure transients, strain and acoustic emission activity during creep in Inada granite. Int J Rock Mech Min Sci 35:135–146CrossRefGoogle Scholar
  4. Cho SH, Ogata Y, Kaneko K (2003) Strain-rate dependency of the dynamic tensile strength of rock. Int J Rock Mech Min Sci 40:763–777CrossRefGoogle Scholar
  5. Choi JH, Faisal Anwar AHM, Ichikawa Y (2008) Observation of time-dependent local deformation of crystalline rocks using a confocal laser scanning microscope. Int J Rock Mech Min Sci 45:431–441CrossRefGoogle Scholar
  6. Chugh YP (1974) Viscoelastic behavior of geologic materials under tensile stress. Trans Soc Min Eng AIME 256:259–264Google Scholar
  7. Coates DF, Parsons RC (1966) Experimental criteria for classification of rock substances. Int J Rock Mech Min Sci 3:181–189CrossRefGoogle Scholar
  8. Fujii Y, Kiyama T, Ishijima Y, Kodama J (1999) Circumferential strain behavior during creep tests of brittle rocks. Int J Rock Mech Min Sci 36:323–337CrossRefGoogle Scholar
  9. Goldsmith W, Sackman JL, Ewert C (1976) Static and dynamic fracture strength of Barre granite. Int J Rock Mech Min Sci Geomech Abstr 13:303–309CrossRefGoogle Scholar
  10. Hashiba K, Fukui K (2015) Index of loading-rate dependency of rock strength. Rock Mech Rock Eng 48:859–865CrossRefGoogle Scholar
  11. Hashiba K, Okubo S, Fukui K (2004): Creep of granite at low stress level. In: Proceedings of the ISRM regional symposium Eurock 2004 and 53rd geomechanics colloquy, pp 471–474Google Scholar
  12. Hashiba K, Okubo S, Fukui K (2006) A new testing method for investigating the loading rate dependency of peak and residual rock strength. Int J Rock Mech Min Sci 43:894–904CrossRefGoogle Scholar
  13. Ito H (1979) Rheology of the crust based on long-term creep tests of rocks. Tectonophysics 52:629–641CrossRefGoogle Scholar
  14. Ito H, Kumagai N (1994) A creep experiment on a large granite beam started in 1980. Int J Rock Mech Min Sci Geomech Abstr 31:359–367CrossRefGoogle Scholar
  15. Ito H, Sasajima S (1980) Long-term creep experiment on some rocks observed over three years. Tectonophysics 62:219–232CrossRefGoogle Scholar
  16. Ito H, Sasajima S (1987) A ten year creep experiment on small rock specimens. Int J Rock Mech Min Sci Geomech Abstr 24:113–121CrossRefGoogle Scholar
  17. JNC (2000) H12: project to establish the scientific and technical basis for HLW disposal in Japan, Supporting report 2 repository design and engineering technology. Japan Nuclear Cycle Development Institute (JNC), Ibaraki, Appendix D.2.1Google Scholar
  18. Koyama T, Ishibashi K, Suzuki Y, Minami M, Okubo S, Fukui K (2006): Prediction of long-term behavior for a large underground cavern. In: Proceedings of the International symposium of the International Society for Rock Mechanics, EUROCK 2006, pp 325–330Google Scholar
  19. Kranz RL (1979) Crack growth and development during creep of Barre granite. Int J Rock Mech Min Sci Geomech Abstr 16:23–35CrossRefGoogle Scholar
  20. Kranz RL (1980) The effects of confining pressure and stress difference on static fatigue of granite. J Geophys Res 85:1854–1866CrossRefGoogle Scholar
  21. Kranz RL, Scholz CH (1977) Critical dilatant volume of rocks at the onset of tertiary creep. J Geophys Res 82:4893–4898CrossRefGoogle Scholar
  22. Kumar A (1968) The effect of stress rate and temperature on the strength of basalt and granite. Geophysics 33:501–510CrossRefGoogle Scholar
  23. Lajtai EZ, Bielus LP (1986) Stress corrosion cracking of Lac du Bonnet granite in tension and compression. Rock Mech Rock Eng 19:71–87CrossRefGoogle Scholar
  24. Lajtai EZ, Schmidtke RH (1986) Delayed failure in rock loaded in uniaxial compression. Rock Mech Rock Eng 19:11–25CrossRefGoogle Scholar
  25. Lajtai EZ, Schmidtke RH, Bielus LP (1987) The effect of water on the time-dependent deformation and fracture of a granite. Int J Rock Mech Min Sci Geomech Abstr 24:247–255CrossRefGoogle Scholar
  26. Lajtai EZ, Scott Duncan EJ, Carter BJ (1991) The effect of strain rate on rock strength. Rock Mech Rock Eng 24:99–109CrossRefGoogle Scholar
  27. Lanaro F, Sato T, Nakama S (2009) Depth variability of compressive strength test results of Toki granite from Shobasama and Mizunami construction sites, Japan. Rock Mech Rock Eng 42:611–629CrossRefGoogle Scholar
  28. Lau JSO, Chandler NA (2004) Innovative laboratory testing. Int J Rock Mech Min Sci 41:1427–1445CrossRefGoogle Scholar
  29. Li HB, Zhao J, Li TJ (1999) Triaxial compression tests on a granite at different strain rates and confining pressures. Int J Rock Mech Min Sci 36:1057–1063CrossRefGoogle Scholar
  30. Lin QX, Liu YM, Tham LG, Tang CA, Lee PKK, Wang J (2009) Time-dependent strength degradation of granite. Int J Rock Mech Min Sci 46:1103–1114CrossRefGoogle Scholar
  31. Lockner D (1993) Room temperature creep in saturated granite. J Geophys Res 98:475–487CrossRefGoogle Scholar
  32. Lockner D, Byerlee J (1977) Acoustic emission and creep in rock at high confining pressure and differential stress. Bull Seismol Soc Am 67:247–258Google Scholar
  33. Lockner DA, Byerlee JD (1986) Changes in complex resistivity during creep in granite. Pure Appl Geophys 124:659–676CrossRefGoogle Scholar
  34. Maranini E, Yamaguchi T (2001) A non-associated viscoplastic model for the behaviour of granite in triaxial compression. Mech Mater 33:283–293CrossRefGoogle Scholar
  35. Masuda K (2001) Effects of water on rock strength in a brittle regime. J Struct Geol 23:1653–1657CrossRefGoogle Scholar
  36. Masuda K, Mizutani H, Yamada I (1987) Experimental study of strain-rate dependence and pressure dependence of failure properties of granite. J Phys Earth 35:37–66CrossRefGoogle Scholar
  37. Masuda K, Mizutani H, Yamada I, Imanishi Y (1988) Effects of water on time-dependent behavior of granite. J Phys Earth 36:291–313CrossRefGoogle Scholar
  38. Mellor M, Hawkes I (1971) Measurement of tensile strength by diametral compression of discs and annuli. Eng Geol 5:173–225CrossRefGoogle Scholar
  39. Mogi K (1962) Study of elastic shocks caused by the fracture of heterogeneous materials and its relations to earthquake phenomena. Bull Earthq Res Inst 40:125–173Google Scholar
  40. Ohnaka M (1983) Acoustic emission during creep of brittle rock. Int J Rock Mech Min Sci Geomech Abstr 20:121–134CrossRefGoogle Scholar
  41. Okubo S, Fukui K (2006) An analytical investigation of a variable-compliance-type constitutive equation. Rock Mech Rock Eng 39:233–253CrossRefGoogle Scholar
  42. Okubo S, Nishimatsu Y (1985) Uniaxial compression testing using a linear combination of stress and strain as the control variable. Int J Rock Mech Min Sci Geomech Abstr 22:323–330CrossRefGoogle Scholar
  43. Okubo S, Nishimatsu Y, He C (1990) Loading rate dependence of class II rock behaviour in uniaxial and triaxial compression tests—an application of a proposed new control method. Int J Rock Mech Min Sci Geomech Abstr 27:559–562CrossRefGoogle Scholar
  44. Okubo S, Nishimatsu Y, Fukui K (1991) Complete creep curves under uniaxial compression. Int J Rock Mech Min Sci Geomech Abstr 28:77–82CrossRefGoogle Scholar
  45. Okubo S, Hashiba K, Fukui K (2013) Loading rate dependency of the strengths of some Japanese rocks. Int J Rock Mech Min Sci 58:180–185Google Scholar
  46. Parsons RC, Hedley DGF (1966) The analysis of the viscous property of rocks for classification. Int J Rock Mech Min Sci 3:325–335CrossRefGoogle Scholar
  47. Peng SS (1973) Time-dependent aspects of rock behavior as measured by a servocontrolled hydraulic testing machine. Int J Rock Mech Min Sci Geomech Abstr 10:235–246CrossRefGoogle Scholar
  48. Read RS (2004) 20 years of excavation response studies at AECL’s Underground Research Laboratory. Int J Rock Mech Min Sci 41:1251–1275CrossRefGoogle Scholar
  49. Sanada H, Hikima R, Tanno T, Matsui H, Sato T (2013) Application of differential strain curve analysis to the Toki granite for in situ stress determination at the Mizunami underground research laboratory, Japan. Int J Rock Mech Min Sci 59:50–56Google Scholar
  50. Sano O, Ito I, Terada M (1981) Influence of strain rate on dilatancy and strength of Oshima granite under uniaxial compression. J Geophys Res 86:9299–9311CrossRefGoogle Scholar
  51. Sano O, Terada M, Ehara S (1982) A study on the time-dependent microfracturing and strength of Oshima granite. Tectonophysics 84:343–362CrossRefGoogle Scholar
  52. Schmidtke RH, Lajtai EZ (1985) The long-term strength of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 22:461–465CrossRefGoogle Scholar
  53. Scholz CH (1968) Mechanism of creep in brittle rock. J Geophys Res 73:3295–3302CrossRefGoogle Scholar
  54. Takemura T, Oda M, Kirai H, Golshani A (2012) Microstructural based time-dependent failure mechanism and its relation to geological background. Int J Rock Mech Min Sci 53:76–85CrossRefGoogle Scholar
  55. Wawersik WR, Brace WF (1971) Post-failure behavior of a granite and diabase. Rock Mech 3:61–85CrossRefGoogle Scholar
  56. Wilkins BJS (1980) Slow crack growth and delayed failure of granite. Int J Rock Mech Min Sci Geomech Abstr 17:365–369CrossRefGoogle Scholar
  57. Wu FT, Thomsen L (1975) Microfracturing and deformation of Westerly granite under creep condition. Int J Rock Mech Min Sci Geomech Abstr 12:167–173CrossRefGoogle Scholar
  58. Yanagidani T, Ehara S, Nishizawa O, Kusunose K, Terada M (1985) Localization of dilatancy in Oshima granite under constant uniaxial stress. J Geophys Res 90:6840–6858CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Department of Systems InnovationThe University of TokyoTokyoJapan

Personalised recommendations