Experimental investigation of influence of alternating cyclic loadings on creep behaviors of sandstone

  • Chongfeng Chen
  • Tao XuEmail author
  • Guanglei Zhou
  • Tao Qin


Cyclic stress variation induced by mining activities has a significant effect on the stability of surrounding rock and mining pillar in deep underground engineering. The influence of alternating cyclic loading and unloading tests on creep behavior of sandstone was investigated to explore the mechanism of the effect of the cyclic stress variation on the stability of rock. Firstly, a series of uniaxial constant strain rate and multi-step monotonic creep tests of sandstone were carried out to determine the maximum high loading stress and the minimum low loading stress in the alternating cyclic creep tests. Then the alternating cyclic loading and unloading creep tests were conducted to investigate the effects of loading paths and loading histories of cyclic high stress creep and low stress creep on the creep behavior of sandstone. Acoustic emission events, axial strain rate and lateral strain rate were also analyzed. The experimental results show that loading paths and loading histories of high stress creep and low stress creep have a significant influence on the alternating cyclic creep behavior of sandstone. The loading paths could accelerate the damage in the rock sample, which can be demonstrated by much larger plastic strain occurring in the damaged sample and larger viscous strain in the creep behavior of less damaged sample. The loading histories could increase viscous strain and plastic strain in the damaged sample. The maximum and the minimum loading stresses determined by the unstable crack threshold provide the basis of the unstable cracks growth in rock sample. The work presented in the present paper is helpful to understand the mechanical behaviors of rock mass under cyclic underground mining activities.


Creep behavior Damage cracks Volumetric compaction Volumetric dilatancy Alternating cyclic creep tests 



  1. Armand, G., Noiret, A., Zghondi, J., Seyedi, D.M.: Short-and long-term behaviors of drifts in the Callovo-Oxfordian claystone at the Meuse/Haute-Marne Underground Research Laboratory. J. Rock Mech. Geotech. Eng. 5, 221–230 (2013). CrossRefGoogle Scholar
  2. Atsushi, S., Mitri, H.S.: Numerical investigation into pillar failure induced by time-dependent skin degradation. J. China Univ. Min. Technol. 27, 591–597 (2017). CrossRefGoogle Scholar
  3. Bell, A.F., Naylor, M., Heap, M.J., Main, I.G.: Forecasting volcanic eruptions and other material failure phenomena: an evaluation of the failure forecast method. Geophys. Res. Lett. 38, 165–176 (2011). CrossRefGoogle Scholar
  4. Brady, B.H.G., Brown, E.T.: Rock Mechanics for Underground Mining. Springer, Berlin (2013) Google Scholar
  5. Brantut, N., Heap, M.J., Meredith, P.G., Baud, P.: Time-dependent cracking and brittle creep in crustal rocks: a review. J. Struct. Geol. 52, 17–43 (2013). CrossRefGoogle Scholar
  6. Brouard, B., Berest, P., de Greef, V., Beraud, J.F., Lheur, C., Hertz, E.: Creep closure rate of a shallow salt cavern at Gellenoncourt, France. Int. J. Rock Mech. Min. Sci. 62, 42–50 (2013). CrossRefGoogle Scholar
  7. Cerfontaine, B., Collin, F.: Cyclic and fatigue behaviour of rock materials: review, interpretation and research perspectives. Rock Mech. Rock Eng. 51, 391–414 (2018). CrossRefGoogle Scholar
  8. Challamel, N., Lanos, C., Casandjian, C.: Stability analysis of quasi-brittle materials-creep under multiaxial loading. Mech. Time-Depend. Mater. 10, 35–50 (2006). CrossRefGoogle Scholar
  9. Chen, H., Qi, H., Long, R., Zhang, M.: Research on 10-year tendency of China coal mine accidents and the characteristics of human factors. Saf. Sci. 50, 745–750 (2012). CrossRefGoogle Scholar
  10. Chen, C., Xu, T., Heap, M.J., Baud, P.: Influence of unloading and loading stress cycles on the creep behavior of Darley Dale Sandstone. Int. J. Rock Mech. Min. Sci. 112, 55–63 (2018a). CrossRefGoogle Scholar
  11. Chen, C.F., Xu, T., Li, S.H.: Microcrack evolution and associated deformation and strength properties of sandstone samples subjected to various strain rates. Minerals 8, 231 (2018b). CrossRefGoogle Scholar
  12. Diederichs, M.S., Kaiser, P.K., Eberhardt, E.: Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation. Int. J. Rock Mech. Min. Sci. 41, 785–812 (2004). CrossRefGoogle Scholar
  13. Eberhardt, E., Stead, D., Stimpson, B., Read, R.S.: Identifying crack initiation and propagation thresholds in brittle rock. Can. Geotech. J. 35, 222–233 (1998). CrossRefGoogle Scholar
  14. Eberhardt, E., Stead, D., Stimpson, B.: Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression. Int. J. Rock Mech. Min. Sci. 36, 361–380 (1999). CrossRefGoogle Scholar
  15. Eslami, J., Hoxha, D., Grgic, D.: Estimation of the damage of a porous limestone using continuous wave velocity measurements during uniaxial creep tests. Mech. Mater. 49, 51–65 (2012). CrossRefGoogle Scholar
  16. Fabre, G., Pellet, F.: Creep and time-dependent damage in argillaceous rocks. Int. J. Rock Mech. Min. Sci. 43, 950–960 (2006). CrossRefGoogle Scholar
  17. Fairhurst, C.: Stress estimation in rock: a brief history and review. Int. J. Rock Mech. Min. Sci. 40, 957–973 (2003). CrossRefGoogle Scholar
  18. Hamrin, H., Hustrulid, W.: Underground mining methods and applications. In: Hustrulid, W.A., Hustrulid, W.A., Bullock, R.L., Bullock, R.C. (eds.) Underground Mining Methods: Engineering Fundamentals and International Case Studies, Society for Mining, Metallurgy, and Exploration, Colorado, United States, pp. 3–14. (2001) Google Scholar
  19. Heap, M.J., Baud, P., Meredith, P.G.: Influence of temperature on brittle creep in sandstones. Geophys. Res. Lett. 36, L19305 (2009a). CrossRefGoogle Scholar
  20. Heap, M.J., Baud, P., Meredith, P.G., Bell, A.F., Main, I.G.: Time-dependent brittle creep in Darley Dale sandstone. J. Geophys. Res., Solid Earth 114, 2150–2202 (2009b). CrossRefGoogle Scholar
  21. Heap, M.J., Baud, P., Meredith, P.G., Vinciguerra, S., Bell, A.F., Main, I.G.: Brittle creep in basalt and its application to time-dependent volcano deformation. Earth Planet. Sci. Lett. 307, 71–82 (2011). CrossRefGoogle Scholar
  22. Hu, B., Yang, S-q., Xu, P.: A nonlinear rheological damage model of hard rock. J. Cent. South Univ. Technol. 25, 1665–1677 (2018). CrossRefGoogle Scholar
  23. Islam, M.R., Hayashi, D., Kamruzzaman, A.B.M.: Finite element modeling of stress distributions and problems for multi-slice longwall mining in Bangladesh, with special reference to the Barapukuria coal mine. Int. J. Coal Geol. 78, 91–109 (2009). CrossRefGoogle Scholar
  24. Jeng, F.S., Weng, M.C., Huang, T.H., Lin, M.L.: Deformational characteristics of weak sandstone and impact to tunnel deformation. Tunn. Undergr. Space Technol. 17, 263–274 (2002). CrossRefGoogle Scholar
  25. Jeong, S.J., Kim, W.S., Sung, S.J.: Numerical investigation on the flow characteristics and aerodynamic force of the upper airway of patient with obstructive sleep apnea using computational fluid dynamics. Med. Eng. Phys. 29, 637–651 (2007). CrossRefGoogle Scholar
  26. Kaiser, P.K., Cai, M.: Design of rock support system under rockburst condition. J. Rock Mech. Geotech. Eng. 4, 215–227 (2012). CrossRefGoogle Scholar
  27. Kobayashi, M.: Verification of crack opening criterion deduced by newly derived micro-crack evolution equation. Int. J. Solids Struct. 106, 139–151 (2017). CrossRefGoogle Scholar
  28. Konicek, P.: Rockburst prevention via destress blasting of competent roof rocks in hard coal longwall mining. J. S. Afr. Inst. Min. Metall. 118, 235–242 (2018). CrossRefGoogle Scholar
  29. Konicek, P., Soucek, K., Stas, L., Singh, R.: Long-hole destress blasting for rockburst control during deep underground coal mining. Int. J. Rock Mech. Min. Sci. 61, 141–153 (2013). CrossRefGoogle Scholar
  30. Kranz, R.L., Harris, W.J., Carter, N.L.: Static fatigue of granite at 200 C. Geophys. Res. Lett. 9, 1–4 (1982). CrossRefGoogle Scholar
  31. Li, S., Feng, X.-T., Li, Z., Chen, B., Zhang, C., Zhou, H.: In situ monitoring of rockburst nucleation and evolution in the deeply buried tunnels of Jinping II hydropower station. Eng. Geol. 137–138, 85–96 (2012). CrossRefGoogle Scholar
  32. Li, X.B., Gong, F.Q., Tao, M., Dong, L.J., Du, K., Ma, C.D., Zhou, Z.L., Yin, T.B.: Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: a review. J. Rock Mech. Geotech. Eng. 9, 767–782 (2017). CrossRefGoogle Scholar
  33. Li, S.H., Zhu, W.C., Niu, L.L., Yu, M., Chen, C.F.: Dynamic characteristics of green sandstone subjected to repetitive impact loading: phenomena and mechanisms. Rock Mech. Rock Eng. 51, 1921–1936 (2018). CrossRefGoogle Scholar
  34. Liu, H.Z., Xie, H.Q., He, J.D., Xiao, M.L., Zhuo, L.: Nonlinear creep damage constitutive model for soft rocks. Mech. Time-Depend. Mater. 21, 73–96 (2017). CrossRefGoogle Scholar
  35. Lyakhovsky, V., Ben-Zion, Y.: Scaling relations of earthquakes and aseismic deformation in a damage rheology model. Geophys. J. Int. 172, 651–662 (2008). CrossRefGoogle Scholar
  36. Mazaira, A., Konicek, P.: Intense rockburst impacts in deep underground construction and their prevention. Can. Geotech. J. 52, 1426–1439 (2015). CrossRefGoogle Scholar
  37. Nicksiar, M., Martin, C.D.: Evaluation of methods for determining crack initiation in compression tests on low-porosity rocks. Rock Mech. Rock Eng. 45, 607–617 (2012). CrossRefGoogle Scholar
  38. Niemeijer, A., Spiers, C.J., Bos, B.: Compaction creep of quartz sand at 400–600 degrees C: experimental evidence for dissolution-controlled pressure solution. Earth Planet. Sci. Lett. 195, 261–275 (2002). CrossRefGoogle Scholar
  39. Petr, K., Mani Ram, S., Hani, M.: Destress blasting in coal mining—state-of-the-art review. Proc. Eng. 26, 179–194 (2011). CrossRefGoogle Scholar
  40. Shah, K.R., Labuz, J.F.: Damage mechanisms in stressed rock from acoustic emission. J. Geophys. Res., Solid Earth 100, 15527–15539 (1995). CrossRefGoogle Scholar
  41. Sone, H., Zoback, M.D.: Mechanical properties of shale-gas reservoir rocks—part 1: static and dynamic elastic properties and anisotropy. Geophysics 78, D381–D392 (2013a). CrossRefGoogle Scholar
  42. Sone, H., Zoback, M.D.: Mechanical properties of shale-gas reservoir rocks — part 2: ductile creep, brittle strength, and their relation to the elastic modulus. Geophysics 78, D393–D402 (2013b). CrossRefGoogle Scholar
  43. Sone, H., Zoback, M.D.: Time-dependent deformation of shale gas reservoir rocks and its long-term effect on the in situ state of stress. Int. J. Rock Mech. Min. Sci. 69, 120–132 (2014). CrossRefGoogle Scholar
  44. Szwedzicki, T.: Rock mass behaviour prior to failure. Int. J. Rock Mech. Min. Sci. 40, 573–584 (2003). CrossRefGoogle Scholar
  45. Wang, J.B., Liu, X.R., Liu, X.J., Huang, M.: Creep properties and damage model for salt rock under low-frequency cyclic loading. Geomech. Eng. 7, 569–587 (2014). CrossRefGoogle Scholar
  46. Wang, J.B., Liu, X.R., Song, Z.P., Shao, Z.S.: An improved Maxwell creep model for salt rock. Geomech. Eng. 9, 499–511 (2015). CrossRefGoogle Scholar
  47. Wang, Q.Y., Zhu, W.C., Xu, T., Niu, L.L., Wei, J.: Numerical simulation of rock creep behavior with a damage-based constitutive law. Int. J. Geomech. 17, 04016044 (2016). CrossRefGoogle Scholar
  48. Xu, T., Tang, C.A., Zhao, J., Li, L.C., Heap, M.J.: Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks. Geophys. J. Int. 189, 1781–1796 (2012). CrossRefGoogle Scholar
  49. Xu, T., Zhou, G.L., Heap, M.J., Zhu, W.C., Chen, C.F., Baud, P.: The influence of temperature on time-dependent deformation and failure in granite: a mesoscale modeling approach. Rock Mech. Rock Eng. 50, 2345–2364 (2017). CrossRefGoogle Scholar
  50. Xu, T., Zhou, G.L., Heap, M.J., Yang, S.Q., Konietzky, H., Baud, P.: The modeling of time-dependent deformation and fracturing of brittle rocks under varying confining and pore pressures. Rock Mech. Rock Eng. 51, 3241–3263 (2018). CrossRefGoogle Scholar
  51. Xue, L., Qin, S.Q., Sun, Q., Wang, Y.Y., Lee, L.M., Li, W.C.: A study on crack damage stress thresholds of different rock types based on uniaxial compression tests. Rock Mech. Rock Eng. 47, 1183–1195 (2014). CrossRefGoogle Scholar
  52. Yang, J.W., Edwards, R.N.: Predicted groundwater circulation in fractured and unfractured anisotropic porous media driven by nuclear fuel waste heatgeneration. Can. J. Earth Sci. 37, 1301–1308 (2000). CrossRefGoogle Scholar
  53. Yang, S.Q., Hu, B.: Creep and long-term permeability of a red sandstone subjected to cyclic loading after thermal treatments. Rock Mech. Rock Eng. 51, 2981–3004 (2018). CrossRefGoogle Scholar
  54. Yang, S.Q., Xu, P., Ranjith, P.G., Chen, G.F., Jing, H.W.: Evaluation of creep mechanical behavior of deep-buried marble under triaxial cyclic loading. Arab. J. Geosci. 8, 6567–6582 (2015). CrossRefGoogle Scholar
  55. Zhang, Y., Shao, J., Xu, W., Jia, Y.: Time-dependent behavior of cataclastic rocks in a multi-loading triaxial creep test. Rock Mech. Rock Eng. 49, 3793–3803 (2016a). CrossRefGoogle Scholar
  56. Zhang, Q.Z., Shen, M.R., Ding, W.Q., Jang, H.S., Jang, B.A.: Experimental investigation of long-term characteristics of greenschist. Geomech. Eng. 11, 531–552 (2016b). CrossRefGoogle Scholar
  57. Zhao, Y.L., Cao, P., Wang, W.J., Wan, W., Liu, Y.K.: Viscoelasto-plastic rheological experiment under circular increment step load and unload and nonlinear creep model of soft rocks. J. Cent. South Univ. Technol. 16, 488–494 (2009). CrossRefGoogle Scholar
  58. Zhao, Y.L., Wang, Y.X., Wang, W.J., Wan, W., Tang, J.Z.: Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment. Int. J. Rock Mech. Min. Sci. 93, 66–75 (2017a). CrossRefGoogle Scholar
  59. Zhao, Y.L., Zhang, L.Y., Wang, W.J., Wan, W., Li, S.Q., Ma, W.H., Wang, Y.X.: Creep behavior of intact and cracked limestone under multi-level loading and unloading cycles. Rock Mech. Rock Eng. 50, 1409–1424 (2017b). CrossRefGoogle Scholar
  60. Zhou, H.W., Wang, C.P., Mishnaevsky, L., Duan, Z.Q., Ding, J.Y.: A fractional derivative approach to full creep regions in salt rock. Mech. Time-Depend. Mater. 17, 413–425 (2013). CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Center for Rock Instability & Seismicity ResearchNortheastern UniversityShenyangChina
  2. 2.Xi’an Research InstituteChina Coal Technology and Engineering GroupXi’anChina
  3. 3.Heilongjiang Ground Pressure and Gas Control in Deep Mining Key LabHeilongjiang University of Science and TechnologyHarbinChina

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