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A rheological constitutive model for damaged zone evolution of a tunnel considering strain hardening and softening

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Abstract

A rheological constitutive model for damaged zone evolution of a tunnel is proposed in this paper to describe the strain hardening and softening properties of the excavation-disturbed rock mass. Firstly, the one-dimension rheological model is introduced by connecting the improved St. Venant body with the Nishihara model, and this model can be used to describe the whole process including transient viscoplastic creep under a low-stress state, steady-state and accelerative creep under a high-stress state. Secondly, the constitutive equations of the rheological model under three-dimensional condition of the improved St. Venant body based on generalized plasticity potential theory are deduced, and the generic three-dimensional rheological model is developed. Thirdly, the creep and stress relaxation properties of the rheological model are studied and discussed. Furthermore, numerical analysis of triaxial compression tests and triaxial compression creep tests are conducted and the rheological model are validated. The results show that the rheological model can be used to study the evolution of excavation damaged zone in underground tunnel engineering.

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References

  • Alejano LR, Alonso E (2005) Considerations of the dilatancy angle in rocks and rock masses. Int J Rock Mech Min Sci 42(4):481–507

    Article  Google Scholar 

  • Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10(1–2):1–54

    Article  Google Scholar 

  • Chen Z, Wang ML, Lu T (1997) Study of tertiary creep of rock salt. J Eng Mech 123(1):77–82

    Article  Google Scholar 

  • Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Q Appl Math 10(2):157–165

    Article  MathSciNet  Google Scholar 

  • He GH, Wang EZ, Liu XL (2016) Modified governing equation and numerical simulation of seepage flow in a single fracture with three-dimensional roughness. Arab J Geosci 9:81

    Article  Google Scholar 

  • Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186

    Article  Google Scholar 

  • Hunsche U, Hampel A (1999) Rock salt—the mechanical properties of the host rock material for a radioactive waste repository. Eng Geol 52(3):271–291

    Article  Google Scholar 

  • Kang JQ, Zhu JB, Zhao J (2019) A review of mechanisms of induced earthquakes: from a view of rock mechanics. Geomech Geophys Geo-Energy Geo-Resour 5:171–196

    Article  Google Scholar 

  • Li S, Liu XL, Li R, Su YW (2017) Shear deformation dominates in the soft adhesive layers of the laminated structure of flexible electronics. Int J Solids Struct 110:305–314

    Article  Google Scholar 

  • Liu XL, Wang SJ, Wang EZ, Xue Q (2006a) Study on time-dependent swelling constitute relation of swelling rock. J Hydraul Eng 37(2):195–199 (In Chinese)

    Google Scholar 

  • Liu XL, Wang SJ, Wang EZ, Xue Q (2006b) Double-medium constitutive model of geological material in uniaxial tension and compression. Appl Math Mech 27:1361–1372

    Article  Google Scholar 

  • Liu XL, Wang SJ, Wang SY, Wang EZ (2015) Fluid-driven fractures in granular materials. Bull Eng Geol Environ 74(2):621–636

    Article  Google Scholar 

  • Liu XL, Han GF, Wang EX, Wang SJ, Kumar N (2018) Multiscale hierarchical analysis of rock mass and prediction of its mechanical and hydraulic properties. J Rock Mech Geotech Eng 10:694–702

    Article  Google Scholar 

  • Liu XL, Wang F, Huang J, Wang SJ, Zhang ZZ, Kumar N (2019) Grout diffusion in silty fine sand stratum with high groundwater level for tunnel construction. Tunn Undergr Space Technol 93:103051

    Article  Google Scholar 

  • Maranini E, Yamaguchi T (2001) A non-associated viscoplastic model for the behaviour of granite in triaxial compression. Mech Mater 33(5):283–293

    Article  Google Scholar 

  • Nicolae M (1999) Non-associated elasto–viscoplastic models for rock salt. Int J Eng Sci 37(3):269–297

    Article  Google Scholar 

  • Sun J (2007) Rock rheological mechanics and its advance in engineering applications. Chin J Rock Mechan Eng 26(6):1081–1106

    Google Scholar 

  • Sun H, Liu XL, Zhu JB (2019) Correlational fractal characterisation of stress and acoustic emission during coal and rock failure under multilevel dynamic loading. Int J Rock Mech Min Sci 117:1–10

    Article  Google Scholar 

  • Tang H, Wang D, Huang R, Pei X, Chen W (2018) A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics. Bull Eng Geol Environ 77(1):375–383

    Article  Google Scholar 

  • Wu F, Chen J, Zou Q (2019) A nonlinear creep damage model for salt rock. Int J Damage Mech 28(5):758–771

    Article  Google Scholar 

  • Xia CC, Wang XD, Xu CB, Zhang CS (2008) Method to identify rheological models by unified rheological model theory and case study. Chin J Rock Mech Eng 27(8):1594–1600

    Google Scholar 

  • Xie HP, Zhu JB, Zhou T, Zhang K, Zhou CT (2020) Conceptualization and preliminary study of engineering disturbed rock dynamics. Geomech Geophys Geo-Energy Geo-Resour 6:34. https://doi.org/10.1007/s40948-020-00157-x

    Article  Google Scholar 

  • Yang SQ, Xu P, Xu T (2015) Nonlinear visco-elastic and accelerating creep model for coal under conventional triaxial compression. Geomech Geophys Geo-Energy Geo-Resour 1(3–4):109–120

    Article  Google Scholar 

  • Yin GZ, Wang H, Zhang DM (2011) Creep experimental and theory model on coal containing gas under the condition of unloading confining pressure. J China Coal Soc 36(12):1963–1967 (in Chinese)

    Google Scholar 

  • Yu MH, Yang SY, Fan SC (1999) Unified elasto-plastic associated and non-associated constitutive model and its engineering applications. Comput Struct 71(6):627–636

    Article  Google Scholar 

  • Yuan SC, Harrison JP (2004) An empirical dilatancy index for the dilatant deformation of rock. Int J Rock Mech Min Sci 41(4):679–686

    Article  Google Scholar 

  • Zhao XG, Cai M (2010) A mobilized dilation angle model for rocks. Int J Rock Mech Min Sci 47(3):368–384

    Article  Google Scholar 

  • Zhao Y, Zhang L, Wang W, Wan W, Ma W (2018) Separation of elastoviscoplastic strains of rock and a nonlinear creep model. Int J Geomech 18(1):1–18

    Article  Google Scholar 

  • Zhou HW, Wang CP, Han BB, Duan ZQ (2011) A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min Sci 48(1):116–121

    Article  Google Scholar 

  • Zienkiewicz OC, Panda GN (1977) Some useful forms of isotropic yield surfaces for soil and rock mechanics. In: Gudehus G (ed) Finite element in geomechanics. Wiley, London, pp 179–190

    Google Scholar 

Download references

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 51934003, 51774020 and U1204509), Program for Yunnan Thousand Talents Plan High-level Innovation and Entrepreneurship Team, and Program for Innovative Research Team (in Science and Technology) in University of Yunnan Province.

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Correspondence to Xiaoli Liu.

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Zhang, Z., Liu, X., Cheng, L. et al. A rheological constitutive model for damaged zone evolution of a tunnel considering strain hardening and softening. Geomech. Geophys. Geo-energ. Geo-resour. 6, 56 (2020). https://doi.org/10.1007/s40948-020-00181-x

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