Rock Mechanics and Rock Engineering

, Volume 51, Issue 2, pp 391–414 | Cite as

Cyclic and Fatigue Behaviour of Rock Materials: Review, Interpretation and Research Perspectives

  • B. Cerfontaine
  • F. Collin
Original Paper


The purpose of this paper is to provide a comprehensive state of the art of fatigue and cyclic loading of natural rock materials. Papers published in the literature are classified and listed in order to ease bibliographical review, to gather data (sometimes contradictory) on classical experimental results and to analyse the main interpretation concepts. Their advantages and limitations are discussed, and perspectives for further work are highlighted. The first section summarises and defines the different experimental set-ups (type of loading, type of experiment) already applied to cyclic/fatigue investigation of rock materials. The papers are then listed based on these different definitions. Typical results are highlighted in next section. Fatigue/cyclic loading mainly results in accumulation of plastic deformation and/or damage cycle after cycle. A sample cyclically loaded at constant amplitude finally leads to failure even if the peak load is lower than its monotonic strength. This subcritical crack is due to a diffuse microfracturing and decohesion of the rock structure. The third section reviews and comments the concepts used to interpret the results. The fatigue limit and SN curves are the most common concepts used to describe fatigue experiments. Results published from all papers are gathered into a single figure to highlight the tendency. Predicting the monotonic peak strength of a sample is found to be critical in order to compute accurate SN curves. Finally, open questions are listed to provide a state of the art of grey areas in the understanding of fatigue mechanisms and challenges for the future.


Fatigue Cyclic loading Review Natural Rock Fatigue strength 



This work is supported by the Walloon Region (Belgium) through SMARTWATER project. The authors would like to gratefully acknowledge Pr. Imai for providing useful papers and references as well as Pr. Michael Heap for providing original figures and data.


  1. Åkesson U, Hansson J, Stigh J (2004) Characterisation of microcracks in the Bohus granite, western Sweden, caused by uniaxial cyclic loading. Eng Geol 72(1–2):131–142. doi: 10.1016/j.enggeo.2003.07.001 CrossRefGoogle Scholar
  2. Alarcon-Guzman A, Leonards G, Chameau J (1989) Undrained monotonic and cyclic strength of sand. J Geotech Eng ASCE 114(10):1089–1109CrossRefGoogle Scholar
  3. Anderson O, Grew P (1977) Stress corrosion theory of crack propagation with applications to geophysics. Rev Geophys 15(1):77–104CrossRefGoogle Scholar
  4. Antonaci P, Bocca P, Masera D (2012) Fatigue crack propagation monitoring by acoustic emission signal analysis. Eng Fract Mech 81:26–32. doi: 10.1016/j.engfracmech.2011.09.017 CrossRefGoogle Scholar
  5. Atkinson B (1984) Subcritical crack growth in geological materials. J Geophys Res 89(B6):4077. doi: 10.1029/JB089iB06p04077 CrossRefGoogle Scholar
  6. Attewell P, Farmer W (1973) Fatigue behaviour of rock. Int J Rock Mech Min Sci 10:1–9CrossRefGoogle Scholar
  7. Attewell P, Sandford M (1974) Intrinsic shear strength of a brittle, anisotropic rock: experimental and mechanical interpretation. Int J Rock Mech Min Sci Geomech Abstr 11(11):423–430CrossRefGoogle Scholar
  8. Bagde M, Petroš V (2005) Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. Int J Rock Mech Min Sci 42(2):237–250. doi: 10.1016/j.ijrmms.2004.08.008 CrossRefGoogle Scholar
  9. Bagde MN, Petroš V (2005) Waveform effect on fatigue properties of intact sandstone in uniaxial cyclical loading. Rock Mech Rock Eng 38(3):169–196. doi: 10.1007/s00603-005-0045-8 CrossRefGoogle Scholar
  10. Bastian T, Connelly B, Lazo Olivares C, Yfantidis N, Taheri A (2014) Progressive damage of hawkesbury sandstone subjected to systematic cyclic loading. Min Educ Aust J Res Proj Rev 3:7–14Google Scholar
  11. Baud P, Zhu W, Wong T-F (2000) In the brittle faulting regime, damage mechanics models predict that the uniaxial compressive strength scales with presence of water the confined brittle strength the pore will be denoted by Pt. J Geophys Res 105:371–389Google Scholar
  12. Bertuzzi R, Douglas K, Mostyn G (2016) Comparison of intact rock strength criteria for pragmatic design. Int J Geotech Geoenviron Eng. doi: 10.1061/(ASCE)GT.1943-5606.0001644 Google Scholar
  13. Bieniawski Z (1967) Mechanism of brittle fracture of rock: part II experimental studies. Int J Rock Mech Min Sci 4:407–423CrossRefGoogle Scholar
  14. Brantut N, Heap M, Baud P, Meredith P (2014) Rate- and strain-dependent brittle deformation of rocks. J Geophys Res Solid Earth. doi: 10.1002/2013JB010448.Received Google Scholar
  15. Brantut N, Heap M, Meredith P, Baud P (2013) Time-dependent cracking and brittle creep in crustal rocks: a review. J Struct Geol 52:17–43. doi: 10.1016/j.jsg.2013.03.007 CrossRefGoogle Scholar
  16. Brown E, Hudson J (1974) Fatigue failure characteristics of some models of jointed rocks. Earthq Eng Struct Dyn 2:379–386CrossRefGoogle Scholar
  17. Bubeck A, Walker R, Healy D, Dobbs M, Holwell D (2017) Pore geometry as a control on rock strength. Earth Planet Sci Lett 457:38–48. doi: 10.1016/j.epsl.2016.09.050 CrossRefGoogle Scholar
  18. Burdine N (1963) Rock failure under dynamic loading conditions. Soc Petrol Eng J 3(01):1–8CrossRefGoogle Scholar
  19. Cardani G, Meda A (2004) Marble behaviour under monotonic and cyclic loading in tension. Constr Build Mater 18(6):419–424. doi: 10.1016/j.conbuildmat.2004.03.012 CrossRefGoogle Scholar
  20. Cattaneo S, Labuz J (2001) Damage of marble from cyclic loading. J Mater Civ Eng 13(December):459–465CrossRefGoogle Scholar
  21. Celestino T, Bortolucci A, Nobrega C (1995) Determination of rock fracture toughness under creep and fatigue. In: Proceedings of the 35th US symposium on rock mechanics. Reno, New York, pp 147–152Google Scholar
  22. Cho S, Ogata Y, Kaneko K (2003) Strain-rate dependency of the dynamic tensile strength of rock. Int J Rock Mech Min Sci 40(5):763–777CrossRefGoogle Scholar
  23. Chow TM, Meglis IL, Young RP (1995) Progressive microcrack development in tests on Lac du Bonnet granite—II. Ultrasonic tomographic imaging. Int J Rock Mech Min Sci 32(8):751–761. doi: 10.1016/0148-9062(95)00015-9 CrossRefGoogle Scholar
  24. Ciantia M, Castellanza R, di Prisco C (2014) Experimental study on the water-induced weakening of calcarenites. Rock Mech Rock Eng 48(2):441–461. doi: 10.1007/s00603-014-0603-z CrossRefGoogle Scholar
  25. Cosenza P, Ghoreychi M, Bazargan-Sabet B, de Marsily G (1999) In situ rock salt permeability measurement for long term safety assessment of storage. Int J Rock Mech Min Sci 36:509–526. doi: 10.1016/S0148-9062(99)00017-0 Google Scholar
  26. Costin LS, Holcomb DJ (1981) Time-dependent failure of rock under cyclic loading. Tectonophysics 79(3–4):279–296. doi: 10.1016/0040-1951(81)90117-7 CrossRefGoogle Scholar
  27. Cruden D (1974) The static fatigue of brittle rock under uniaxial compression. Int J Rock Mech Min Sci Geomech Abstr 11(2):67–73CrossRefGoogle Scholar
  28. David E, Brantut N, Schubnel A, Zimmerman R (2012) Sliding crack model for nonlinearity and hysteresis in the uniaxial stress strain curve of rock. Int J Rock Mech Min Sci 52:9–17. doi: 10.1016/j.ijrmms.2012.02.001 CrossRefGoogle Scholar
  29. Eberhardt E, Stead D, Stimpson B (1999) Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression. Int J Rock Mech Min Sci 36(3):361–380CrossRefGoogle Scholar
  30. Erarslan N (2016) Microstructural investigation of subcritical crack propagation and fracture process zone (FPZ) by the reduction of rock fracture toughness under cyclic loading. Eng Geol 208:181–190. doi: 10.1016/j.enggeo.2016.04.035 CrossRefGoogle Scholar
  31. Erarslan N, Alehossein H, Williams DJ (2014) Tensile fracture strength of Brisbane tuff by static and cyclic loading tests. Rock Mech Rock Eng 47(4):1135–1151. doi: 10.1007/s00603-013-0469-5 CrossRefGoogle Scholar
  32. Erarslan N, Williams D (2012a) Investigating the effect of cyclic loading on the indirect tensile strength of rocks. Rock Mech Rock Eng 45(3):327–340. doi: 10.1007/s00603-011-0209-7 CrossRefGoogle Scholar
  33. Erarslan N, Williams D (2012) Mechanism of rock fatigue damage in terms of fracturing modes. Int J Fatigue 43:76–89. doi: 10.1016/j.ijfatigue.2012.02.008 CrossRefGoogle Scholar
  34. Evans A, Fuller R (1974) Crack propagation in ceramic materials under cyclic loading conditions. Metall Trans 5:27–33Google Scholar
  35. Fan J, Chen J, Jiang D, Chemenda A, Chen J, Ambre J (2017) Discontinuous cyclic loading tests of salt with acoustic emission monitoring. Int J Fatigue 94:140–144. doi: 10.1016/j.ijfatigue.2016.09.016 CrossRefGoogle Scholar
  36. Fan J, Chen J, Jiang D, Ren S, Wu J (2016) Fatigue properties of rock salt subjected to interval cyclic pressure. Int J Fatigue 90:109–115. doi: 10.1016/j.ijfatigue.2016.04.021 CrossRefGoogle Scholar
  37. Faoro I, Vinciguerra S, Marone C, Elsworth D, Schubnel A (2013) Linking permeability to crack density evolution in thermally stressed rocks under cyclic loading. Geophys Res Lett 40(February):2590–2595. doi: 10.1002/grl.50436 CrossRefGoogle Scholar
  38. Fredrich J, Evans B, Wong T (1989) Micromechanics of the brittle to plastic transition in Carrara marble. J Geophys Res 94:4129–4145. doi: 10.1029/JB094iB04p04129 CrossRefGoogle Scholar
  39. Fuenkajorn K, Phueakphum D (2010) Effects of cyclic loading on mechanical properties of Maha Sarakham salt. Eng Geol 112(1–4):43–52. doi: 10.1016/j.enggeo.2010.01.002 CrossRefGoogle Scholar
  40. Gatelier N, Pellet F, Loret B (2002) Mechanical damage of an anisotropic porous rock in cyclic triaxial tests. Int J Rock Mech Min Sci 39(3):335–354. doi: 10.1016/S1365-1609(02)00029-1 CrossRefGoogle Scholar
  41. Ghamgosar M, Erarslan N (2016) Experimental and numerical studies on development of fracture process zone (FPZ) in rocks under cyclic and static loadings. Rock Mech Rock Eng 49(3):893–908. doi: 10.1007/s00603-015-0793-z CrossRefGoogle Scholar
  42. Ghamgosar M, Erarslan N, Williams D (2017) Experimental Investigation of fracture process zone in rocks damaged under cyclic loadings. Exp Mech 57:97–113. doi: 10.1007/s11340-016-0216-4 CrossRefGoogle Scholar
  43. Gong M, Smith I (2003) Effect of waveform and loading sequence on low-cycle compressive fatigue life of spruce. J Mater Civ Eng 15(February):93–99CrossRefGoogle Scholar
  44. Griffiths L, Heap M, Xu T, Chen C-F, Baud P (2017) The influence of pore geometry and orientation on the strength and stiffness of porous rock. J Struct Geol 96:149–160. doi: 10.1016/j.jsg.2017.02.006 CrossRefGoogle Scholar
  45. Grover H, Dehlinger P, McClure G (1950) Investigation of fatigue characteristics of rocks. Technical report, Drilling Research IncGoogle Scholar
  46. Guo Y, Yang C, Mao H (2012) Mechanical properties of Jintan mine rock salt under complex stress paths. Int J Rock Mech Min Sci 56:54–61. doi: 10.1016/j.ijrmms.2012.07.025 Google Scholar
  47. Haimson BC, Kim CM (1971) Mechanical behaviour of rock under cyclic fatigue. In: Cording EJ (ed) Stability of rock slopes. Proceedings of the 13th symposium on rock mechanics. ASCE, New York, pp 845–863Google Scholar
  48. Hale P, Shakoor A (2003) A laboratory investigation of the effects of cyclic heating and cooling, wetting and drying, and freezing and thawing on the compressive strength of selected sandstones. Environ Eng Geosci 9(2):117–130. doi: 10.2113/9.2.117 CrossRefGoogle Scholar
  49. Hashash Y, Hook J, Schmidt B, I-Chiang Yao J (2001) Seismic design and analysis of underground structures. Tunn Undergr Space Technol 16(4):247–293. doi: 10.1016/S0886-7798(01)00051-7 CrossRefGoogle Scholar
  50. Hawkins A, Mcconnell B (1992) Sensitivity of sandstone strength and deformability to changes in moisture content: sandstones studied. Q J Eng Geol 25:115–130. doi: 10.1144/GSL.QJEG.1992.025.02.05 CrossRefGoogle Scholar
  51. Heap M, Faulkner D (2008) Quantifying the evolution of static elastic properties as crystalline rock approaches failure. Int J Rock Mech Min Sci 45:564–573. doi: 10.1016/j.ijrmms.2007.07.018 CrossRefGoogle Scholar
  52. Heap M, Faulkner D, Meredith P, Vinciguerra S (2010) Elastic moduli evolution and accompanying stress changes with increasing crack damage: implications for stress changes around fault zones and volcanoes during deformation. Geophys J Int 183(1):225–236. doi: 10.1111/j.1365-246X.2010.04726.x CrossRefGoogle Scholar
  53. Heap MJ, Vinciguerra S, Meredith PG (2009) The evolution of elastic moduli with increasing crack damage during cyclic stressing of a basalt from Mt. Etna volcano. Tectonophysics 471(1–2):153–160. doi: 10.1016/j.tecto.2008.10.004 CrossRefGoogle Scholar
  54. Heimisson E, Einarsson P, Sigmundsson F, Brandsdóttir B (2015) Kilometer-scale Kaiser effect identified in Krafla volcano, Iceland. Geophys Res Lett 42:7958–7965. doi: 10.1002/2015GL065680.Received CrossRefGoogle Scholar
  55. Hoek E, Brown E (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186. doi: 10.1016/S1365-1609(97)80069-X CrossRefGoogle Scholar
  56. Holcomb D (1993) General theory of the Kaiser effect. Int J Rock Mech Min Sci Geomech Abstr 30(7):929–935CrossRefGoogle Scholar
  57. Hudson J, Harrison J (1997) Engineering rock mechanics—an introduction to the principles, 1st edn. Elsevier, AmsterdamGoogle Scholar
  58. Jamali Zavareh S, Baghbanan A, Hashemolhosseini H, Haghgouei H (2017) Effect of micro-structure on fatigue behaviour of intact rocks under completely reversed load. Anal Numer Methods Min Eng 6:55–62Google Scholar
  59. Jamshidi A, Nikudel M, Khamehchiyan M (2013) Predicting the long-term durability of building stones against freeze-thaw using a decay function model. Cold Reg Sci Technol 92:29–36. doi: 10.1016/j.coldregions.2013.03.007 CrossRefGoogle Scholar
  60. Jiang D, Fan J, Chen J, Li L, Cui Y (2016) A mechanism of fatigue in salt under discontinuous cycle loading. Int J Rock Mech Min Sci 86:255–260. doi: 10.1016/j.ijrmms.2016.05.004 Google Scholar
  61. Jiang X, Shu-chun L, Yun-qi T, Xiao-jun T, Xin W (2009) Acoustic emission characteristic during rock fatigue damage and failure. Proc Earth Planet Sci 1(1):556–559. doi: 10.1016/j.proeps.2009.09.088 CrossRefGoogle Scholar
  62. Jobli A, Noor M, Tawie R, Hampden A, Julai N (2017) Uniaxial compressive strength of Malaysian weathered granite due to cyclic loading. J Eng Appl Sci 12(14):4298–4301Google Scholar
  63. Kaiser J (1950) An investigation into the occurrence of noises in tensile tests, or a study of acoustic phenomena in tensile tests. Ph.D. thesis, Technische Hochschule MunichGoogle Scholar
  64. Karakus M, Akdag S, Bruning T (2016) Rock fatigue damage assessment by acoustic emission. In: International conference on geomechanics, geo-energy and geo-resources, September, Melbourne, AustraliaGoogle Scholar
  65. Kendrick J, Smith R, Sammonds P, Meredith P, Dainty M, Pallister J (2013) The influence of thermal and cyclic stressing on the strength of rocks from Mount St. Helens, Washington. Bull Volcanol. doi: 10.1007/s00445-013-0728-z
  66. Ko T (2005) Crack coalescence in rock-like material under cyclic loading. Ph.D. thesis, Massachusetts Institute of TechnologyGoogle Scholar
  67. Kranz R, Harris W, Carter N (1982) Static fatigue of granite at 200. Geophys Res Lett 9(1):1–4. doi: 10.1029/GL009i001p00001 CrossRefGoogle Scholar
  68. Kranz RL (1983) Microcracks in rocks: a review. Tectonophysics 100(1–3):449–480. doi: 10.1016/0040-1951(83)90198-1 CrossRefGoogle Scholar
  69. Kumar A (1968) The effect of stress rate and temperature on the strength of basalt and granite. Geophysics 33(3):501–510CrossRefGoogle Scholar
  70. Lavrov A (2001) Kaiser effect observation in brittle rock cyclically loaded with different loading rates. Mech Mater 33(11):669–677. doi: 10.1016/S0167-6636(01)00081-3 CrossRefGoogle Scholar
  71. Lavrov A (2003) The Kaiser effect in rocks: principles and stress estimation techniques. Int J Rock Mech Min Sci 40:151–171. doi: 10.1016/S1365-1609(02)00138-7 CrossRefGoogle Scholar
  72. Lavrov A, Vervoort A, Wevers M, Napier JAL (2002) Experimental and numerical study of the Kaiser effect in cyclic Brazilian tests with disk rotation. Int J Rock Mech Min Sci 39(3):287–302. doi: 10.1016/S1365-1609(02)00038-2 CrossRefGoogle Scholar
  73. Le J, Manning J, Labuz J (2014) Scaling of fatigue crack growth in rock. Int J Rock Mech Min Sci 72:71–79. doi: 10.1016/j.ijrmms.2014.08.015 Google Scholar
  74. Lee MK, Barr BG (2004) An overview of the fatigue behaviour of plain and fibre reinforced concrete. Cement Concr Compos 26(4):299–305. doi: 10.1016/S0958-9465(02)00139-7 CrossRefGoogle Scholar
  75. Li C, Nordlund E (1993) Experimental verification of the Kaiser effect in rocks. Rock Mech Rock Eng 26(4):333–351. doi: 10.1007/BF01027116 CrossRefGoogle Scholar
  76. Li G, Moelle K, Lewis J (1992) Fatigue crack growth in brittle sandstones. Int J Rock Mech Min Sci 29(5):469–477CrossRefGoogle Scholar
  77. Li N, Zhang P, Chen Y, Swoboda G (2003) Fatigue properties of cracked, saturated and frozen sandstone samples under cyclic loading. Int J Rock Mech Min Sci 40(1):145–150. doi: 10.1016/S1365-1609(02)00111-9 CrossRefGoogle Scholar
  78. Liu E, He S (2012) Effects of cyclic dynamic loading on the mechanical properties of intact rock samples under confining pressure conditions. Eng Geol 125:81–91. doi: 10.1016/j.enggeo.2011.11.007 CrossRefGoogle Scholar
  79. Liu J, Xie H, Hou Z, Yang C, Chen L (2014) Damage evolution of rock salt under cyclic loading in unixial tests. Acta Geotech 9(1):153–160. doi: 10.1007/s11440-013-0236-5 CrossRefGoogle Scholar
  80. Liu Q, Huang S, Kang Y, Liu X (2015) Cold regions science and technology a prediction model for uniaxial compressive strength of deteriorated rocks due to freeze thaw. Cold Reg Sci Technol 120:96–107. doi: 10.1016/j.coldregions.2015.09.013 CrossRefGoogle Scholar
  81. Liu Y, Dai F, Fan P, Xu N, Dong L (2017a) Experimental investigation of the influence of joint geometric configurations on the mechanical properties of intermittent jointed rock models under cyclic uniaxial compression. Rock Mech Rock Eng 50(6):1453–1471. doi: 10.1007/s00603-017-1190-6 CrossRefGoogle Scholar
  82. Liu Y, Dai F, Xu N, Zhao T (2017b) Cyclic flattened Brazilian disc tests for measuring the tensile fatigue properties of brittle rocks cyclic flattened Brazilian disc tests for measuring the tensile fatigue properties of brittle rocks. Rev Sci Instrum. doi: 10.1063/1.4995656 Google Scholar
  83. Lockner D (1993) The role of acoustic emission in the study of rock fracture. Int J Rock Mech Min Sci Geomech Abstr 30(7):883–899CrossRefGoogle Scholar
  84. Lockner DA, Byerlee JD, Kuksenko V, Ponomarev A, Sidorin A (1992) Chapter 1 observations of quasistatic fault growth from acoustic emissions. Int Geophys 51:3–31. doi: 10.1016/S0074-6142(08)62813-2
  85. Ma L, Liu X, Wang M, Xu H, Hua R, Fan P, Jiang S, Wang G, Yi Q (2013) Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading. Int J Rock Mech Min Sci 62:34–41. doi: 10.1016/j.ijrmms.2013.04.003 Google Scholar
  86. Martin C, Chandler N (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci 31(6):643–659CrossRefGoogle Scholar
  87. Martin C, Maybee W (2000) The strength of hard-rock pillars. Int J Rock Mech Min Sci 37(8):1239–1246CrossRefGoogle Scholar
  88. Martinez-Martinez J, Benavente D, Gomez-Heras M, Marco-Castano L, Garcia-Del-Cura M (2013) Non-linear decay of building stones during freeze-thaw weathering processes. Constr Build Mater 38:443–454. doi: 10.1016/j.conbuildmat.2012.07.059 CrossRefGoogle Scholar
  89. Meglis IL, Chow TM, Young RP (1995) Progressive microcrack development in tests on Lac du Bonnet granite—I. Acoustic emission source location and velocity measurement. Int J Rock Mech Min Sci 32(8):741–750. doi: 10.1016/0148-9062(95)00015-9 CrossRefGoogle Scholar
  90. Meng Q, Zhang M, Han L, Pu H, Nie T (2016) Effects of acoustic emission and energy evolution of rock specimens under the uniaxial cyclic loading and unloading compression. Rock Mech Rock Eng 49(10):3873–3886. doi: 10.1007/s00603-016-1077-y CrossRefGoogle Scholar
  91. Michalske T, Freiman S (1982) A molecular interpretation of stress corrosion in silica. Nature 295:511–512CrossRefGoogle Scholar
  92. Michalske T, Freiman S (1983) A molecular mechanism for stress corrosion in vitreous silica. J Am Ceram Soc 66(4):284–288CrossRefGoogle Scholar
  93. Miner M (1945) Cumulative damage in fatigue. J Appl Mech 12(3):159–164Google Scholar
  94. Mitchell T, Faulkner D (2008) Experimental measurements of permeability evolution during triaxial compression of initially intact crystalline rocks and implications for fluid flow in fault zones. J Geophys Res Solid Earth 113(11):1–16. doi: 10.1029/2008JB005588 Google Scholar
  95. Momeni A, Karakus M, Khanlari GR, Heidari M (2015) Effects of cyclic loading on the mechanical properties of a granite. Int J Rock Mech Min Sci 77:89–96. doi: 10.1016/j.ijrmms.2015.03.029 Google Scholar
  96. Morales Demarco M, Jahns E, Rüdrich J, Oyhantcabal P, Siegesmund S (2007) The impact of partial water saturation on rock strength: an experimental study on sandstone. Zeitschrift der Deutschen Gesellschaft für Geowissenschaften 158(4):869–882. doi: 10.1127/1860-1804/2007/0158-0869 CrossRefGoogle Scholar
  97. Munoz H, Taheri A (2017) Local damage and progressive localisation in porous sandstone during cyclic loading. Rock Mech Rock Eng. doi: 10.1007/s00603-017-1298-8 Google Scholar
  98. Nara Y, Kaneko K (2006) Sub-critical crack growth in anisotropic rock. Int J Rock Mech Min Sci 43(3):437–453. doi: 10.1016/j.ijrmms.2005.07.008 CrossRefGoogle Scholar
  99. Nara Y, Morimoto K, Hiroyoshi N, Yoneda T, Kaneko K, Benson P (2012) Influence of relative humidity on fracture toughness of rock: implications for subcritical crack growth. Int J Solids Struct 49(18):2471–2481. doi: 10.1016/j.ijsolstr.2012.05.009 CrossRefGoogle Scholar
  100. Nejati H, Ghazvinian A (2014) Brittleness effect on rock fatigue damage evolution. Rock Mech Rock Eng 47(5):1839–1848. doi: 10.1007/s00603-013-0486-4 CrossRefGoogle Scholar
  101. Ni XH (2014) Failure characteristic of granite under cyclic loading with different frequencies. Appl Mech Mater 638:1967–1970CrossRefGoogle Scholar
  102. Pola A, Crosta G, Fusi N, Castellanza R (2014) General characterization of the mechanical behaviour of different volcanic rocks with respect to alteration. Eng Geol 169:1–13. doi: 10.1016/j.enggeo.2013.11.011 CrossRefGoogle Scholar
  103. Pouya A, Zhu C, Arson C (2016) Micro-macro approach of salt viscous fatigue under cyclic loading. Mech Mater 93:13–31. doi: 10.1016/j.mechmat.2015.10.009 CrossRefGoogle Scholar
  104. Prikryl R, Lokajicek T, Li C, Rudajev V (2003) Acoustic emission characteristics and failure of uniaxially stressed granitic rocks: the effect of rock fabric. Rock Mech Rock Eng 36:255–270. doi: 10.1007/s00603-003-0051-7 CrossRefGoogle Scholar
  105. Pujades E, Willems T, Bodeux S, Orban P, Dassargues A (2016) Underground pumped storage hydroelectricity using abandoned works (deep mines or open pits) and the impact on groundwater flow. Hydrogeol J. doi: 10.1007/s10040-016-1413-z Google Scholar
  106. Rajaram V (1981) Mechanical behavior of granite under cyclic compression. In: First international conference on recent advances in geotechnical earthquake engineeringGoogle Scholar
  107. Rao M, Ramana YV (1992) A study of progressive failure of rock under cyclic loading by ultrasonic and AE monitoring techniques. Rock Mech Rock Eng 25(4):237–251. doi: 10.1007/BF01041806 CrossRefGoogle Scholar
  108. Ritchie R (1999) Mechanisms of fatigue-crack propagation in ductile and brittle solids. Int J Fract 100:55–83. doi: 10.1023/A:1018655917051 CrossRefGoogle Scholar
  109. Royer-Carfagni G, Salvatore W (2000) The characterization of marble by cyclic compression loading: experimental results. Mech Cohes Frict Mater 5(7):535–563. doi: 10.1002/1099-1484(200010)5:7<535::AID-CFM102>3.0.CO;2-D CrossRefGoogle Scholar
  110. Schaefer L, Kendrick J, Oommen T, Lavallée Y, Chigna G, Costa A (2015) Geomechanical rock properties of a basaltic volcano. Front Earth Sci 3(June):1–15Google Scholar
  111. Schijve J (2003) Fatigue of structures and materials. Fatigue Struct Mater 25:679–702. doi: 10.1007/978-1-4020-6808-9 Google Scholar
  112. Scholz C, Kranz R (1974) Notes on dilatancy recovery. J Geophys Res 79(14):2132–2135CrossRefGoogle Scholar
  113. Scholz CH, Koczynski TA (1979) Dilatancy anisotropy and the response of rock to large cyclic loads. J Geophys Res 84(B10):5525. doi: 10.1029/JB084iB10p05525 CrossRefGoogle Scholar
  114. Shao J, Zhou H, Chau KT (2005) Coupling between anisotropic damage and permeability variation in brittle rocks. Int J Numer Anal Methods Geomech 29(12):1231–1247. doi: 10.1002/nag.457 CrossRefGoogle Scholar
  115. Shreiner LA, Pavlova NN (1958) Experimental data on the fatigue breakdown of rocks. Trudy Instituta Nefti Akademii Nauk SSSR, vol 2, Neftepromyslovoe Delo. Associated Technical Services, East Orange, NJ, pp 46–52Google Scholar
  116. Singh S (1989) Fatigue and strain hardening behaviour of graywacke from the flagstaff formation, New South Wales. Eng Geol 26(2):171–179CrossRefGoogle Scholar
  117. Sondergeld C, Estey L (1981) Acoustic emission study of microfracturing during the cyclic loading of Westerly granite. J Geophys Res 86(B4):2915–2924. doi: 10.1029/JB086iB04p02915 CrossRefGoogle Scholar
  118. Song H, Zhang H, Fu D, Zhang Q (2016) Experimental analysis and characterization of damage evolution in rock under cyclic loading. Int J Rock Mech Min Sci 88:157–164. doi: 10.1016/j.ijrmms.2016.07.015 Google Scholar
  119. Song R, Yue-ming B, Jing-Peng Z, De-yi J, Chun-he Y (2013) Experimental investigation of the fatigue properties of salt rock. Int J Rock Mech Min Sci 64:68–72. doi: 10.1016/j.ijrmms.2013.08.023 Google Scholar
  120. Sorgi C, De Gennaro V (2011) Water-rock interaction mechanisms and ageing processes in chalk. In: Chen D (ed) Advances in data, methods, models and their applications in geoscience. In Tech. doi: 10.5772/1133
  121. Steffen B (2012) Prospects for pumped-hydro storage in Germany. Energy Policy 45:420–429CrossRefGoogle Scholar
  122. Taheri A, Royle A, Yang Z, Zhao Y (2016) Study on variations of peak strength of a sandstone during cyclic loading. Geomech Geophys Geo-Energy Geo-Resour 2(1):1–10. doi: 10.1007/s40948-015-0017-8 CrossRefGoogle Scholar
  123. Tien Y, Lee D, Juang C (1990) Strain, pore pressure and fatigue characteristics of sandstone under various load conditions. Int J Rock Mech Min Sci Geomech Abstr 27(4):283–289CrossRefGoogle Scholar
  124. Tomkins B (1981) Subcritical crack growth: fatigue, creep and stress corrosion cracking. Philos Trans R Soc A Math Phys Eng Sci 299:31–44CrossRefGoogle Scholar
  125. Trippetta F, Collettini C, Meredith P, Vinciguerra S (2013) Tectonophysics evolution of the elastic moduli of seismogenic triassic evaporites subjected to cyclic stressing. Tectonophysics 592:67–79. doi: 10.1016/j.tecto.2013.02.011 CrossRefGoogle Scholar
  126. Voznesenskii A, Krasilov M, Kutkin Y, Tavostin M, Osipov Y (2017) Features of interrelations between acoustic quality factor and strength of rock salt during fatigue cyclic loadings. Int J Fatigue 97:70–78. doi: 10.1016/j.ijfatigue.2016.12.027 CrossRefGoogle Scholar
  127. Voznesenskii A, Kutkin Y, Krasilov M, Komissarov A (2015) Predicting fatigue strength of rocks by its interrelation with the acoustic quality factor. Int J Fatigue 77(March):194–198. doi: 10.1016/j.ijfatigue.2015.02.012 CrossRefGoogle Scholar
  128. Voznesenskii A, Kutkin Y, Krasilov M, Komissarov A (2016) The influence of the stress state type and scale factor on the relationship between the acoustic quality factor and the residual strength of gypsum rocks in fatigue tests. Int J Fatigue 84:53–58. doi: 10.1016/j.ijfatigue.2015.11.016 CrossRefGoogle Scholar
  129. Wang H, Xu W, Cai M, Xiang Z, Kong Q (2017) Gas permeability and porosity evolution of a porous sandstone under repeated loading and unloading conditions. Rock Mech Rock Eng 50:2071–2083. doi: 10.1007/s00603-017-1215-1 CrossRefGoogle Scholar
  130. Wang W, Wang M, Liu X (2016) Study on mechanical features of Brazilian splitting fatigue tests of salt rock. Adv Civ Eng 2016:5436240. doi: 10.1155/2016/5436240 Google Scholar
  131. Wang Z, Li S, Qiao L, Zhang Q (2015) Finite element analysis of the hydro-mechanical behavior of an underground crude oil storage facility in granite subject to cyclic loading during operation. Int J Rock Mech Min Sci 73:70–81. doi: 10.1016/j.ijrmms.2014.09.018 CrossRefGoogle Scholar
  132. Wang Z, Li S, Qiao L, Zhao J (2013) Fatigue behavior of granite subjected to cyclic loading under triaxial compression condition. Rock Mech Rock Eng 46(6):1603–1615. doi: 10.1007/s00603-013-0387-6 CrossRefGoogle Scholar
  133. Widhalm C, Tschegg E, Eppensteiner W (1996) Anisotropic thermal expansion causes deformation of marble claddings. J Perform Constr Facil 10(February):5–10CrossRefGoogle Scholar
  134. Wiederhorn S (1967) Influence of water vapor on crack propagation in soda-lime glass. J Am Ceram Soc 50(8):407–414CrossRefGoogle Scholar
  135. Xiao J, Ding D, Jiang F, Xu G (2010a) Fatigue damage variable and evolution of rock subjected to cyclic loading. Int J Rock Mech Min Sci 47(3):461–468. doi: 10.1016/j.ijrmms.2009.11.003 CrossRefGoogle Scholar
  136. Xiao J, Ding D, Xu G, Jiang F (2009) Inverted S-shaped model for nonlinear fatigue damage of rock. Int J Rock Mech Min Sci 46(3):643–648. doi: 10.1016/j.ijrmms.2008.11.002 CrossRefGoogle Scholar
  137. Xiao J, Feng X, Ding D, Jiang F (2010b) Investigation and modeling on fatigue damage evolution of rock as a function of logarithmic cycle. Int J Numer Anal Meth Geomech 35:1127–1140. doi: 10.1002/nag CrossRefGoogle Scholar
  138. Yamashita S, Sugimoto F, Imai T, Namsrai D, Yamauchi M, Kamoshida N (1999) The relationship between the failure process of the creep or fatigue test and of the conventional compression test on rock. In: 9th ISRM congress, international society for rock mechanicsGoogle Scholar
  139. Yang S, Tian W, Ranjith P (2017) Experimental investigation on deformation failure characteristics of crystalline marble under triaxial cyclic loading. Rock Mech Rock Eng. doi: 10.1007/s00603-017-1262-7 Google Scholar
  140. Yang S-Q, Ranjith P, Huang Y-H, Yin P-F, Jing H-W, Gui Y-L, Yu Q-L (2015) Sandstone under triaxial cyclic loading. Geophys J Int 201:662–682. doi: 10.1093/gji/ggv023 CrossRefGoogle Scholar
  141. Zang A, Yoon J, Stephansson O, Heidbach O (2013) Fatigue hydraulic fracturing by cyclic reservoir treatment enhances permeability and reduces induced seismicity. Geophys J Int 195(August):1282–1287. doi: 10.1093/gji/ggt301 CrossRefGoogle Scholar
  142. Zhang P, Xu J, Li N (2008) Fatigue properties analysis of cracked rock based on fracture evolution process. J Cent South Univ 15:95–99. doi: 10.1007/s1177100800196 CrossRefGoogle Scholar
  143. Zhang S, Lai Y, Zhang X, Pu Y, Yu W (2004) Study on the damage propagation of surrounding rock from a cold-region tunnel under freeze-thaw cycle condition. Tunn Undergr Space Technol 19(3):295–302. doi: 10.1016/j.tust.2003.11.011 CrossRefGoogle Scholar
  144. Zhang ZX, Kou SQ, Jiang LG, Lindqvist P-A (2000) Effects of loading rate on rock fracture characteristics and energy partitioning. Int J Rock Mech Min Sci 37:745–762CrossRefGoogle Scholar
  145. Zhao J (2000) Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock. Int J Rock Mech Min Sci 37(7):1115–1121. doi: 10.1016/S1365-1609(00)00049-6 CrossRefGoogle Scholar
  146. Zhenyu T, Haihong M (1990) An experimental study and analysis of the behaviour of rock under cyclic loading. Int J Rock Mech Min Sci Geomech Abstr 27(1):51–56CrossRefGoogle Scholar
  147. Zhu Q, Kondo D, Shao J, Pensee V (2008) Micromechanical modelling of anisotropic damage in brittle rocks and application. Int J Rock Mech Min Sci 45(4):467–477. doi: 10.1016/j.ijrmms.2007.07.014 CrossRefGoogle Scholar
  148. Zhu W, Tang C (2006) Numerical simulation of Brazilian disk rock failure under static and dynamic loading. Int J Rock Mech Min Sci 43(2):236–252. doi: 10.1016/j.ijrmms.2005.06.008 CrossRefGoogle Scholar
  149. Zoback M, Byerlee J (1975) The effect of cyclic differential stress on dilatancy in westerly reduced repeated plied the is sub- on dilatancy in westerly granite. J Geophys Res 80(11):1526–1530CrossRefGoogle Scholar

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© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  1. 1.LiègeBelgium

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