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Theoretical Investigation to the Effect of Bolt Reinforcement on Tunnel Viscoelastic Behavior

  • Research Article - Civil Engineering
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Abstract

Rock bolts are widely applied in undergrounding excavation for strengthening rocks internally. For better understanding the effect of bolt reinforcement, the mechanical behavior of a circular bolt-liner combined supported tunnel is investigated using analytical method in this paper. Viscoelastic mechanical model of bolted rocks is established, and analytical solution for displacement and pressure in the rock/liner interface is provided, accounting for the installation delay of liner. Results show that the variations of displacement and pressure can be generally divided into three stages, rapid increasing stage, slow increasing stage and steady stage. Bolt parameter plays an important role on the evolution time of displacement and pressure. It will take shorter time for displacement and pressure to reach a steady state in the case with greater bolt parameter. In addition, installing rock bolts are able to effectively reduce displacement and pressure and there exists an exponential function relationship between displacement (pressure) and bolt parameter. The displacement and pressure decrease in a high rate with bolt parameter under the relatively low class. But, this decrease trend becomes flatter if bolt parameters reaching a certain value. There should be an appropriate bolt parameter for a certain tunnel project, taking into account mechanical parameters of rocks, load-bearing capacity of liner, or allowed deformation of design.

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Abbreviations

sij, eij :

Tensors of the stress and strain deviators

\( s_{ij}^{\text{M}} ,\;e_{ij}^{\text{M}} \) :

Tensors of the stress and strain deviators in Maxwell model

\( s_{ij}^{\text{K}} ,\;e_{ij}^{\text{K}} \) :

Tensors of the stress and strain deviators in Kelvin model

\( G^{\text{M}} ,\,\eta^{\text{M}} \) :

Spring constant and viscosity coefficient of dashpot in Maxwell model

\( G^{\text{K}} ,\,\eta^{\text{K}} \) :

Spring constant and viscosity coefficient of dashpot in Kelvin model

\( G^{\text{S}} \) :

Spring constant representing performance of rock bolts

\( \sigma_{ij} ,\,\varepsilon_{ij} \) :

Stress and strain tensors

\( \sigma_{kk} ,\,\varepsilon_{kk} \) :

Stress and strain subjected to Einstein summation convention

\( \delta_{ij} \) :

Kronecker delta

\( \sigma_{\text{r}} ,\,\sigma_{\theta } ,\sigma_{z} \) :

Radial, tangential and axial stress in cylindrical coordinate system

\( \varepsilon_{\text{r}} ,\,\varepsilon_{\theta } ,\varepsilon_{z} \) :

Radial, tangential and axial strain in cylindrical coordinate system

\( \sigma_{\text{mean}} ,\,\varepsilon_{\text{mean}} \) :

Mean stress and strain

\( \Delta \sigma_{\text{r}} ,\,\Delta \varepsilon_{\text{r}} \) :

Radial deviatoric stress and strain in polar coordinate system

\( \Delta \sigma_{\theta } ,\,\Delta \varepsilon_{\theta } \) :

Tangential deviatoric stress and strain in polar coordinate system

\( p_{0} ,\,p\left( t \right) \) :

Initial ground stress and pressure on liner/reaction force of liner

\( r,\,\theta \) :

Polar coordinates

R :

Radius of the tunnel

\( u\left( {r,t} \right),\,u_{\text{R}} \left( t \right) \) :

Radial displacement and radial displacement at tunnel wall

\( K_{\text{S}} \) :

Liner stiffness

h :

Liner thickness

E, ν :

Young’s modulus and Poisson’s ratio of the liner

t 0 :

Installation time of liner

References

  1. Wang, Y.; Liu, B.G.; Qi, Y.: A risk evaluation method with an improved scale for tunnel engineering. Arab. J. Sci. Eng. 43(4), 2053–2067 (2018)

    Article  Google Scholar 

  2. Wu, K.; Shao, Z.S.: Effects of pipe roof support and grouting pre-reinforcement on the track settlement. Adv. Civ. Eng. 2018, 6041305 (2018)

    Google Scholar 

  3. Cheng, W.C.; Wang, L.; Xue, Z.F.; Ni, J.C.; Rahman, M.M.; Arulrajah, A.: Lubrication performance of pipejacking in soft alluvial deposits. Tunn. Undergr. Space Technol. 91, 102991 (2019)

    Article  Google Scholar 

  4. Qiu, J.; Liu, H.; Lai, J.; Lai, H.; Chen, J.; Wang, K.: Investigating the long-term settlement of a tunnel built over improved loessial foundation soil using jet grouting technique. J. Perform. Constr. Fac. 32(5), 04018066 (2018)

    Article  Google Scholar 

  5. Qiao, R.J.; Shao, Z.S.; Wei, W.; Zhang, Y.Y.: Theoretical investigation into the thermal-mechanical behaviors of tunnel lining during RABT fire developmet. Arab. J. Sci. Eng. 44(5), 4807–4818 (2019)

    Article  Google Scholar 

  6. Wu, K.; Shao, Z.S.; Qin, S.; Li, B.X.: Determination of deformation mechanism and countermeasures in silty clay tunnel. J. Perform. Constr. Fac. (2019). https://doi.org/10.1061/(ASCE)CF.1943-5509.0001381

    Article  Google Scholar 

  7. Wu, X.; Jiang, Y.; Guan, Z.; Wang, G.: Estimating the support effect of energy-absorbing rock bolts based on the mechanical work transfer ability. Int. J. Rock Mech. Min. Sci. 103, 168–178 (2018)

    Article  Google Scholar 

  8. Zhang, B.; Li, S.C.; Xia, K.W.; et al.: Reinforcement of rock mass with cross-flaws using rock bolts. Tunn. Undergr. Space Technol. 51, 346–353 (2016)

    Article  Google Scholar 

  9. Li, Y.; Zhou, H.; Zhang, L.; et al.: Experimental and numerical investigations on mechanical property and reinforcement effect of bolted jointed rock mass. Constr. Build. Mater. 126, 843–856 (2016)

    Article  Google Scholar 

  10. Cui, L.; Zheng, J.J.; Sheng, Q.; Pan, Y.: A simplified procedure for the interaction between fully-grouted bolts and rock mass for circular tunnels. Comput. Geotech. 106, 177–192 (2019)

    Article  Google Scholar 

  11. Li, W.T.; Yang, N.; Yang, B.; et al.: An improved numerical simulation approach for bolt-arch supported tunnels with large deformation. Tun. Undergr. Space Technol. 77, 1–12 (2018)

    Article  Google Scholar 

  12. Cai, Y.; Esaki, T.; Jiang, Y.J.: An analytical model to predict axial load in grouted rock bolt for soft rock tunnelling. Tunn. Undergr. Space Technol. 19(6), 607–618 (2004)

    Article  Google Scholar 

  13. Tan, C.H.: Difference solution of passive bolts reinforcement around a circular opening in elasoplastic rock mass. Int. J. Rock Mech. Min. Sci. 81, 28–38 (2016)

    Article  Google Scholar 

  14. Wong, H.; Subrin, D.; Dias, D.: Convergence-confinement analysis of a bolt-supported tunnel using the homogenization method. Can. Geotech. J. 43(5), 462–483 (2006)

    Article  Google Scholar 

  15. Carranza-Torres, C.: Analytical and numerical study of the mechanics of rockbolt reinforcement around tunnels in rock masses. Rock Mech. Rock Eng. 42(2), 175–228 (2009)

    Article  Google Scholar 

  16. Wang, H.N.; Xiao, G.; Jiang, M.J.; Crosta, G.B.: Investigation of rock bolting for deeply buried tunnels via a new efficient hybrid DEM-analytical model. Tunn. Undergr. Space Technol. 82, 366–379 (2018)

    Article  Google Scholar 

  17. Bobet, A.; Einstein, H.H.: Tunnel reinforcement with rockbolts. Tunn. Undergr. Space Technol. 26, 100–123 (2011)

    Article  Google Scholar 

  18. Wu, K.; Shao, Z.S.: Visco-elastic analysis on the effect of flexible layer on mechanical behavior of tunnels. Int. J. Appl. Mech. 11(3), 1950027 (2019)

    Article  Google Scholar 

  19. Li, S.C.; Wang, M.B.: An elastic stress–displacement solution for a lined tunnel at great depth. Int. J. Rock Mech. Min. Sci. 45, 486–494 (2008)

    Article  Google Scholar 

  20. Kargar, A.R.; Rahmannejad, R.; Hajabasi, M.A.: A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method. Int. J. Solids Struct. 51(6), 1475–1482 (2014)

    Article  Google Scholar 

  21. Exadaktylos, G.E.; Stavropoulou, M.C.: A closed-form elastic solution for stresses and displacements around tunnels. Int. J. Rock Mech. Min. Sci. 39(7), 905–916 (2002)

    Article  Google Scholar 

  22. Vu, T.M.; Sulem, J.; Subrin, D.; Monin, N.: Semi-analytical solution for stresses and displacements in a tunnel excavated in transversely isotropic formation with non-linear behavior. Rock Mech. Rock Eng. 46(2), 213–229 (2013)

    Article  Google Scholar 

  23. Zhao, G.P.; Yang, S.L.: Analytical solutions for rock stress around square tunnels using complex variable theory. Int. J. Rock Mech. Min. Sci. 80, 302–307 (2015)

    Article  Google Scholar 

  24. Hu, B.; Yang, S.Q.; Xu, P.: A nonlinear rheological damage model of hard rock. J. Cent. South Univ. 25(7), 1665–1677 (2018)

    Article  Google Scholar 

  25. Hu, B.; Yang, S.Q.; Tian, W.L.: Creep-permeability behavior of sandstone considering thermal-damage. Geomech. Eng. 18(1), 71–83 (2019)

    Google Scholar 

  26. Sulem, J.; Panet, M.; Guenot, A.: An analytical solution for time-dependent displacements in a circular tunnel. In: International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol. 24, no. 3, pp. 155–164 (1987)

  27. Fahimifar, A.; Tehrani, F.M.; Hedayat, A.; Vakilzadeh, A.: Analytical solution for the excavation of circular tunnels in a visco-elastic Burger’s material under hydrostatic stress field. Tunn. Undergr. Space Technol. 25(4), 297–304 (2010)

    Article  Google Scholar 

  28. Song, F.; Wang, H.N.; Jiang, M.J.: Analytically-based simplified formulas for circular tunnels with two liner in viscoelastic rock under anisotropic initial stresses. Constr. Build. Mater. 175, 746–767 (2018)

    Article  Google Scholar 

  29. Nomikos, P.; Rahmannedjad, R.; Sofianos, A.: Supported axisymmetric tunnels within linear viscoelastic Burgers rocks. Rock Mech. Rock Eng. 44(5), 553–564 (2011)

    Article  Google Scholar 

  30. Lu, A.Z.; Zhang, N.; Wang, S.J.; Zhang, X.L.: Analytical solution for a lined tunnel with arbitrary cross sections excavated in orthogonal anisotropic rock mass. Int. J. Geomech. 17(9), 04017044 (2017)

    Article  Google Scholar 

  31. Wu, K.; Shao, Z.S.: Study on the effect of flexible layer on support structures of tunnel excavated in viscoelastic rocks. J. Eng. Mech. 145(10), 04019077 (2019)

    Article  Google Scholar 

  32. Wu, K.; Shao, Z.S.; Qin, S.; Zhao, N.N.: Mechanical analysis of tunnels supported by yieldable steel ribs in rheological rocks. Geomech. Eng. 19(1), 61–70 (2019)

    Google Scholar 

  33. Zhao, D.P.; Jia, L.L.; Wang, M.N.; Wang, F.: Displacement prediction of tunnels based on a generalised Kelvin constitutive model and its application in a subsea tunnel. Tunn. Undergr. Space Technol. 54, 29–36 (2016)

    Article  Google Scholar 

  34. Zhao, T.B.: Rock Creep Properties Test in Deep Mine and Deformation Mechanics of Anchored Surrounding Rock. Shandong University of Science and Technology, Qingdao (2009)

    Google Scholar 

  35. Goodman, R.E.: Introduction to Rock Mechanics, 2nd edn. Wiley, New York (1989)

    Google Scholar 

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Acknowledgements

This research work is supported by the National Natural Science Foundation of China (No. 11872287), the Found of Shaanxi Key Research and Development Program (No. 2019ZDLGY01-10).

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Authors and Affiliations

  1. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Kui Wu, Zhushan Shao, Chenglong Li & Su Qin

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  1. Kui Wu
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  2. Zhushan Shao
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Correspondence to Zhushan Shao.

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Wu, K., Shao, Z., Li, C. et al. Theoretical Investigation to the Effect of Bolt Reinforcement on Tunnel Viscoelastic Behavior. Arab J Sci Eng 45, 3707–3718 (2020). https://doi.org/10.1007/s13369-019-04215-9

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