DOI QR코드

DOI QR Code

A generalized viscoelastic model and the corresponding parameter conversion method

  • Huang, Shuling (Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Changjiang River Scientific Research Institute) ;
  • Ding, Xiuli (Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Changjiang River Scientific Research Institute) ;
  • Huang, Xiaohua (College of Civil Engineering and Architecture, Guangxi University) ;
  • He, Jun (Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Changjiang River Scientific Research Institute) ;
  • Zhang, Yuting (Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources, Changjiang River Scientific Research Institute)
  • 투고 : 2020.05.04
  • 심사 : 2021.10.18
  • 발행 : 2021.11.25

초록

Obtaining applicable rheological model and corresponding rheological parameters are the key issues of the long-term stability analysis of engineering rock mass. In this study, a generalized viscoelastic combination model with considering the effects of stress level is proposed. The proposed model is composed of a brittle viscous body and several Kelvin bodies in series, which unites the generalized Kelvin attenuated creep model and the generalized Burgers non-attenuated creep model. In addition, the tension-compression parameters and the shear parameters are used to express the proposed model, respectively. As these two types of parameters are often converted in the creep tests and engineering applications or change occurs to parameter types when extend the creep model from one-dimensional to three-dimensional. Thus, based on the assumption of constant volumetric modulus, a new conversion equation between the tension-compression parameters and the shear parameters is created for the proposed generalized viscoelastic combination model. Based on the new conversion equation, the three-dimensional extension of the generalized viscoelastic combination model expressed by both the tension-compression parameters and the shear parameters are derived. The proposed creep model and parameter conversion equation are then verified by the laboratory uniaxial compression test and triaxial compression test. The above proposed creep model and parameter conversion equation are applied to the example of rock foundation age deformation. Based on the application, potential problems caused by parameter conversion during rheological numerical simulations are discussed. Based on the discussion, the superiority of the parameter conversion method proposed in this study is fully illustrated.

키워드

과제정보

The work was supported by the National Key Research and Development Project of China (Grant No. 2017YFC1501305), the National Science Foundation of China (Grant Nos. 51779018, 41807249 and 51979008) and the Basic Scientific Research Operating Expenses of Central Public Welfare Research Institutes of China (No. CKSF2021715/YT, CKSF2021458/YT). These supports are greatly acknowledged and appreciated.

참고문헌

  1. Amitrano, D. and Helmstetter, A. (2006), "Brittle creep, damage, and time to failure in rocks", J. Geophys. Res. Solid Earth, 111, B11201. https://doi.org/10.1029/2005jb004252.
  2. Bozzano, F., Martino, S., Montagna, A. and Prestininzi, A. (2012), "Back analysis of a rock landslide to infer rheological parameters", Eng. Geology, 131-132, 45-56. https://doi.org/10.1016/j.enggeo.2012.02.003.
  3. Brantut, N., Heap, M.J., Baud, P. and Meredith, P.G. (2014), "Rate- and strain-dependent brittle deformation of rocks", J. Geophys. Res. Solid Earth, 119, 1818-1836. https://doi.org/10.1002/2013jb010448.
  4. Callahan, G.D., Mellegard, K.D. and Hansen, F.D. (1998), "Constitutive behavior of reconsolidating crushed salt", Int. J. Rock Mech. Mining Sci., 35, 422-423. https://doi.org/10.1016/S0148-9062(98)00045-X.
  5. Chen, S.H. and Pande, G.N. (1994), "Rheological model and finite element analysis of jointed rock masses reinforced by passive, fully-grouted bolts", Int. J. Rock Mech. Mining Sci. Geomech. Abstracts, 31, 273-277. https://doi.org/10.1016/0148-9062(94)90472-3.
  6. Christensen, R.M. (1982), Theory of Viscoelasticity: An Introduction, Academic Press, New York, USA.
  7. Cornelius, R.R. and Scott, P.A. (1993), "A materials failure relation of accelerating creep as empirical description of damage accumulation", Rock Mech. Rock Eng., 26, 233-252. https://doi.org/10.1007/BF01040117.
  8. Costin, L.S. (1988), "Time-dependent deformation and failure", Int. J. Rock Mech. Mining Sci. Geomech. Abstracts, 25, A166. https://doi.org/10.1016/0148-9062(88)91561-6.
  9. Eberhart, R. and Kennedy, J. (1995), "A new optimizer using particle swarm theory", Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, Oct.
  10. Fahimifar, A., Karami, M. and Fahimifar, A. (2015), "Modifications to an elasto-visco-plastic constitutive model for prediction of creep deformation of rock samples", Soils Foundations, 55, 1364-1371. https://doi.org/10.1016/j.sandf.2015.10.003.
  11. Gavrus, A., Massoni, E. and Chenot, J.L. (1996), "An inverse analysis using a finite element model for identification of rheological parameters", J. Mater. Processing Technol., 60, 447-454. https://doi.org/10.1016/0924-0136(96)02369-2.
  12. Haupt, M. (1991), "A constitutive law for rock salt based on creep and relaxation tests", Rock Mech. Rock Eng., 24, 179-206. https://doi.org/10.1007/BF01045031.
  13. Huang, S., Ding, X., He, J. and Xiong, S. (2020), "Analytical solution for rock mass bearing plate rheological tests based on a novel viscoelastic combination model", European J. Environ. Civil Eng.. https://doi.org/10.1080/19648189.2020.1796819.
  14. Huang, P., Zhang, J., Zhang, Q., Damascene, N.J. and Guo, Y. (2020), "Nonlinear creep model of deep gangue backfilling material and time-dependent characteristics of roof deformation in backfilling mining", Geofluids, 2020(1), 1-10. https://doi.org/10.1155/2020/8816871.
  15. Huang, P., Zhang, J., Yan, X., Spearing, A.J.S., Li, M. and Liu, S. (2021), "Deformation response of roof in solid backfilling coal mining based on viscoelastic properties of waste gangue", Int. J. Mining Sci. Technol., 31(2), 279-289. https://doi.org/10.1016/j.ijmst.2021.01.004.
  16. Ito, H. and Sasajima, S. (1987), "A ten year creep experiment on small rock specimens", Int. J. Rock Mech. Mining Sci. Geomech. Abstracts, 24, 113-121. https://doi.org/10.1016/0148-9062(87)91930-9.
  17. Khaledi, K., Mahmoudi, E., Datcheva, M., Konig, D. and Schanz, T. (2016), "Sensitivity analysis and parameter identification of a time dependent constitutive model for rock salt", J. Comput. Appl. Math., 293, 128-138. https://doi.org/10.1016/j.cam.2015.03.049.
  18. Malan, D.F. (1999), "Time-dependent behaviour of deep level tabular excavations in hard rock", Rock Mech. Rock Eng., 32, 123-155. https://doi.org/10.1007/s006030050028.
  19. Maranini, E. and Brignoli, M. (1999), "Creep behaviour of a weak rock: Experimental characterization", Int. J. Rock Mech. Mining Sci., 36, 127-138. https://doi.org/10.1016/S0148-9062(98)00171-5.
  20. Miura, K., Okui, Y. and Horii, H. (2003), "Micromechanics-based prediction of creep failure of hard rock for long-term safety of high-level radioactive waste disposal system", Mech. Mater., 35, 587-601. https://doi.org/10.1016/S0167-6636(02)00286-7.
  21. Munson, D.E. (1997), "Constitutive model of creep in rock salt applied to underground room closure", Int. J. Rock Mech. Mining Sci., 34, 233-247. https://doi.org/10.1016/S0148-9062(96)00047-2.
  22. Okubo, S., Nishimatsu, Y. and Fukui, K. (1991), "Complete creep curves under uniaxial compression", Int. J. Rock Mech. Mining Sci. Geomech. Abstracts, 28, 77-82. https://doi.org/10.1016/0148-9062(91)93235-X.
  23. Park, S.W. and Schapery, R.A. (1999), "Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on prony series", Int. J. Solid. Struct., 36, 1653-1675. https://doi.org/10.1016/S0020-7683(98)00055-9.
  24. Sterpi, D. and Gioda, G. (2007), "Visco-plastic behaviour around advancing tunnels in squeezing rock", Rock Mech. Rock Eng., 42, 319-339. https://doi.org/10.1007/s00603-007-0137-8.
  25. Tsai, L.S., Hsieh, Y.M., Weng, M.C., Huang, T.H. and Jeng, F. S. (2008), "Time-dependent deformation behaviors of weak sandstones", Int. J. Rock Mech. Mining Sci., 45, 144-154. https://doi.org/10.1016/j.ijrmms.2007.04.008.
  26. Tschoegl, N.W. (1989), The Phenomenological Theory of Linear Viscoelastic Behavior, Springer, Berlin, Germany.
  27. Wang, J.B., Liu, X.R., Song, Z.P. and Shao, Z.S. (2015), "An improved maxwell creep model for salt rock", Geomech. Eng., 9, 499-511. https://doi.org/10.12989/gae.2015.9.4.499.
  28. Xie, S.Y., Shao, J.F. and Xu, W.Y. (2011), "Influences of chemical degradation on mechanical behaviour of a limestone", Int. J. Rock Mech. Mining Sci., 48, 741-747. https://doi.org/10.1016/j.ijrmms.2011.04.015.
  29. Xu, Ming, Jin, Dehai, Song, Erxiang, et al. (2018), "A rheological model to simulate the shear creep behavior of rockfills considering the influence of stress states", Acta Geotechnica, 13, 1313-1327. https://doi.org/10.1007/s11440-018-0716-8.
  30. Xu, T., Tang, C.A., Zhao, J., Li, L. and Heap, M.J. (2012), "Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks", Geophys. J. International, 189, 1781-1796. https://doi.org/10.1111/j.1365-246X.2012.05460.x.
  31. Yang, W., Luo, G., Duan, K., Jing, W., Zhang, L., Wang, S. and Zhao, Y. (2019), "Development of a damage rheological model and its application in the analysis of mechanical properties of jointed rock masses", Energy Sci. Eng., https://doi.org/10.1002/ese3.331.
  32. Zhang, C.Q., Zhou, H. and Feng, X.T. (2011), "An index for estimating the stability of brittle surrounding rock mass: FAI and its engineering application", Rock Mech. Rock Eng., 44, 401. https://doi.org/10.1007/s00603-011-0150-9.
  33. Zhang, C.Y., Ping, C.A.O., Pu, C.Z., Jie, L.I.U. and Wen, P.H. (2014), "Integrated identification method of rheological model of sandstone in sanmenxia bauxite", Transactions Nonferrous Metals Soc. China, 24, 1859-1865. https://doi.org/10.1016/s1003-6326(14)63264-7.
  34. Zhang, J.Z., Zhou, X.P. and Yin, P. (2019), "Visco-plastic deformation analysis of rock tunnels based on fractional derivatives", Tunnel. Underground Space Technol., 85, 209-219. https://doi.org/10.1016/j.tust.2018.12.019.
  35. Zhao, Y., Wang, Y., Wang, W., Wan, W. and Tang, J. (2017), "Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment", Int. J. Rock Mech. Mining Sci., 93, 66-75. https://doi.org/10.1016/j.ijrmms.2017.01.004.