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Analytical Solution for Interaction between Tunnel Surrounding Rock and Supports in Red Sandstone Stratum

  • Tunnel Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

Improving the flexibility of the support system is an effective measure to prevent structural failure caused by large deformation of the surrounding rock in tunnels passing through red sandstone stratum. By utilizing the staged support installation method, the initial install location of the supports can be adjusted to control the flexibility of the support system. However, there is currently no corresponding analytical solution available to accurately predict the mechanical behavior of the surrounding rock and supports. This paper proposes an analytical solution for the whole process of interaction between the surrounding rock and supports. Firstly, based on the improved unified strength criterion and non-associated flow rule, an elastoplastic analysis of the surrounding rock of a circular tunnel in red sandstone stratum is conducted, which takes into account intermediate principal stress, dilatancy, and nonlinear strain-softening properties. Next, six types of interaction between the surrounding rock and supports are proposed, along with corresponding judge theorems. Furthermore, an analytical solution for the mechanical response of the surrounding rock and supports during the whole construction process are presented. After verifying its effectiveness, a parametric analysis is performed to investigate the influence of design parameters on the supporting effect. Finally, the application effect of the staged support installation method is compared with that of the traditional method, and the cost savings advantage of the former is demonstrated.

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References

  • Bernaud D, Quevedo FPM (2020) Analytical solution of deep tunnels in a strain-hardening elasto-plastic rock mass. Latin American Journal of Solids and Structures 17(6), DOI: https://doi.org/10.1590/1679-78256023

  • Chu ZF, Wu ZJ, Liu BG, Liu QS (2019) Coupled analytical solutions for deep-buried circular lined tunnels considering tunnel face advancement and soft rock rheology effects. Tunnelling and Underground Space Technology 94:103111, DOI: https://doi.org/10.1016/j.tust.2019.103111

    Article  Google Scholar 

  • Chu Z, Wu Z, Liu Q, Liu B, Sun J (2021) Analytical solution for lined circular tunnels in deep viscoelastic burgers rock considering the longitudinal discontinuous excavation and sequential installation of liners. Journal of Engineering Mechanics 147(4), DOI: https://doi.org/10.1061/(ASCE)EM.1943-7889.0001912

  • Deng CJ, Zheng YR, Wang K, Gao F (2009) Some discussion on the dilatancy of geotechnical materials. Chinese Journal of Geotechnical Engineering 27(3):283–287 (in Chinese)

    Google Scholar 

  • Drescher A, Detournay E (1993) Limit load in translational failure mechanisms for associative and non-associative materials. Geotechnique 43(3):443–456, DOI: https://doi.org/10.1680/geot.1993.43.3.443

    Article  Google Scholar 

  • Duan SQ, Jiang XQ, Jiang Q, Xiong JC, Li CY (2023) Theoretical solution and failure analysis of water pressure on lining of deep-buried non-circular hydraulic tunnel based on the equivalent hydraulic radius method. Engineering Failure Analysis 148:107163, DOI: https://doi.org/10.1016/j.engfailanal.2023.107163

    Article  Google Scholar 

  • Guo W, Gao Y, Wu XZ, Liu SY, Fan PX (2022) Elastoplastic analysis of the enhancing mechanism of tensile performance of ductile thin-walled circular tubes with internal support. Thin-Walled Structures 171:108694, DOI: https://doi.org/10.1016/j.tws.2021.108694

    Article  Google Scholar 

  • Hu XR, Yu MH (2005) Amendment of the twin-shear criterion and its application to calculation of earth pressure. Chinese Journal of Geotechnical Engineering 27(3):283–287 (in Chinese)

    Google Scholar 

  • Huang SB, He YB, Liu GF, Lu ZX, Xin ZK (2020) Effect of water content on the mechanical properties and deformation characteristics of the clay-bearing red sandstone. Bulletin of Engineering Geology and the Environment 80(2):1767–1790, DOI: https://doi.org/10.1007/s10064-020-01994-6

    Article  Google Scholar 

  • Jiang YF, Yu JY, Zhou P, Zhou FC, Lin JY, Li JY, Lin M, Lei FY, Wang ZJ (2023) Influence of traffic on the temperature field of tunnel in cold region: A case study on the world’s longest highway spiral tunnel. Underground Space 8:196–209, DOI: https://doi.org/10.1016/j.undsp.2022.03.002

    Article  Google Scholar 

  • Li KS, Chen LX, Zhao Z, Liu CX (2023) Experimental investigation on mechanical, acoustic, and fracture behaviors and the energy evolution of sandstone containing non-penetrating horizontal fissures. Theoretical and Applied Fracture Mechanics 123, DOI: https://doi.org/10.1016/j.tafmec.2022.103703

  • Li WT, Li SC, Feng XD, Li SC, Yuan C (2011) Study of post-peak strain softening mechanical properties of rock based on Mohr-Coulomb criterion. Chinese Journal of Rock Mechanics and Engineering 30(7):1460–1466 (in Chinese)

    Google Scholar 

  • Lin LB, Chen FQ, Lu YP, Li DY (2020) Complex variable solutions for tunnel excavation at great depth in visco-elastic geomaterial considering the three-dimensional effects of tunnel advance. Applied Mathematical Modelling 82:700–730, DOI: https://doi.org/10.1016/j.apm.2020.01.070

    Article  MathSciNet  MATH  Google Scholar 

  • Liu C, Zhang DL, Zhang SL, Sun ZY (2023) Interaction analysis between composite supports and rheological rock considering progressive hardening characteristic of shotcrete. Construction and Building Materials 374:130876, DOI: https://doi.org/10.1016/j.conbuildmat.2023.130876

    Article  Google Scholar 

  • Luo Y (2018) Elastoplastic analysis on strain softening and fracture expansion of roadway surrounding rock based on D-P criterion. Journal of Safety Science and Technology 14(11):108–113, DOI: https://doi.org/10.11731/j.issn1673-193x.2018.11.017

    MathSciNet  Google Scholar 

  • Qiu JT, Shen YS, Zhang X, Zhang YF, Gan YH, Zhou XJ (2022) Simplified method for predicting time-dependent behavior of deep-buried tunnel considering tunnel excavation rate and stress release effects. International Journal of Applied Mechanics 14(5), DOI: https://doi.org/10.1142/S1758825122500430

  • Riabokon E, Poplygin V, Turbakov M, Kozhevnikov E, Kobiakov D, Guzev M, Wiercigroch M (2021) Nonlinear Young’s modulus of new red sandstone: Experimental studies. Acta Mechanica Solida Sinica 34(6):989–999, DOI: https://doi.org/10.1007/s10338-021-00298-w

    Article  Google Scholar 

  • Sun ZY, Zhang DL, Fang Q, Dui GS, Tai QM, Sun FW (2021) Analysis of the interaction between tunnel support and surrounding rock considering pre-reinforcement. Tunnelling and Underground Space Technology 115:104074, DOI: https://doi.org/10.1016/j.tust.2021.104074

    Article  Google Scholar 

  • Vlachopoulos N, Diederichs MS (2009) Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels. Rock Mechanics and Rock Engineering 42(2):131–146, DOI: https://doi.org/10.1007/s00603-009-0176-4

    Article  Google Scholar 

  • Wang Q, Hu XL, Zheng WB, Li LX, Zhou C, Ying CY, Xu C (2021) Mechanical properties and permeability evolution of red sandstone subjected to hydro-mechanical coupling: Experiment and discrete element modelling. Rock Mechanics and Rock Engineering 54(5): 2405–2423, DOI: https://doi.org/10.1007/s00603-021-02396-0

    Article  Google Scholar 

  • Wang ZJ, Xu JX, Xu JX, Zhou P, Xia Y, Li RY, Tang L (2018) Research on the deformation characteristics of tunnel surrounding rock in water-rich quaternary red sandstone stratum. Journal of Railway Engineering Society 35(9):54–60+109 (in Chinese)

    Google Scholar 

  • Wen SY, Han LJ, Zong YJ, Meng QB, Zhang J (2013) Study on emission characteristics of sandstone uniaxial compression test with different moisture content. Coal Science and Technology 41(8):46–48+52, DOI: https://doi.org/10.13199/j.cnki.cst.2013.08.016 (in Chinese)

    Google Scholar 

  • Wu K, Shao ZS, Qin S, Zhao NN, Chu ZF (2022b) An improved nonlinear creep model for rock applied to tunnel displacement prediction. International Journal of Applied Mechanics 13(8):2150094, DOI: https://doi.org/10.1142/S1758825121500940

    Article  Google Scholar 

  • Wu K, Shao ZS, Sharifzadeh M, Hong SY, Qin S (2022a) Analytical computation of support characteristic curve for circumferential yielding lining in tunnel design. Journal of Rock Mechanics and Geotechnical Engineering 14(1):144–152, DOI: https://doi.org/10.1016/j.jrmge.2021.06.016

    Article  Google Scholar 

  • Xu HY, Shao ZM, Wang ZJ, Cai LB, Li Z, Jiang XZ (2021) Sub-level classification and prediction system of fully weathered red sandstone rock mass based on physical property indices. KSCE Journal of Civil Engineering 25(3):1066–1085, DOI: https://doi.org/10.1007/s12205-021-0014-0

    Article  Google Scholar 

  • Yu MH (1994) Unified strength theory for geomaterials and its application. Chinese Journal of Geotechnical Engineering 16(2):1–10 (in Chinese)

    Google Scholar 

  • Yu DM, Fan YF, Duan JX, Luo XW (2013) Elastoplastic unified solutions to deep-buried circular tunnels considering intermediate principal stress. Journal of Shanghai Jiao Tong University 47(9):1447–1453, DOI: https://doi.org/10.16183/j.cnki.jsjtu.2013.09.022 (in Chinese)

    Google Scholar 

  • Zhang CG, Zhao JH, Zhang QH (2012) Convergence - confinement analysis of deep circular rock tunnels based on unified strength theory. Chinese Journal of Geotechnical Engineering 34(1):110–114 (in Chinese)

    Google Scholar 

  • Zhao NN, Shao ZS, Chen XY, Yuan B, Wu K (2022) Prediction of mechanical response of “a flexible support system” supported tunnel in viscoelastic geomaterials. Archives of Civil and Mechanical Engineering 22(4), DOI: https://doi.org/10.1007/s43452-022-00485-7

  • Zhou H, Chen J, Lu JJ, Jiang Y, Meng FZ (2018) A new rock brittleness evaluation index based on the internal friction angle and class I stress-strain curve. Rock Mechanics and Rock Engineering 51(7): 2309–2316, DOI: https://doi.org/10.1007/s00603-018-1487-0

    Article  Google Scholar 

  • Zhou SY, Guo XF, Zhang Q, Dias D, Pan QJ (2020) Influence of a weak layer on the tunnel face stability - Reliability and sensitivity analysis. Computers and Geotechnics 122, DOI: https://doi.org/10.1016/j.compgeo.2020.103507

  • Zhou P, Zhou FC, Lin JY, Li JY, Jiang YF, Yang B, Wang ZJ (2021) Decoupling analysis of interaction between tunnel surrounding rock and support in xigeda formation strata. KSCE Journal of Civil Engineering 25(12):4897–4912, DOI: https://doi.org/10.1007/s12205-021-0618-4

    Article  Google Scholar 

Download references

Acknowledgments

This research was financially supported by the National Natural Science Foundation of China (No.51678498) and the High Speed Railway and Natural Science United Foundation of China (U1934213).

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Authors and Affiliations

  1. Dept. of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai, 200092, China

    Zhen Li

  2. School of Civil Engineering, Sichuan Agricultural University, Chengdu, 611830, China

    Haiyan Xu

  3. Key Laboratory of Transportation Tunnel Engineering of Ministry of Education, Southwest Jiaotong University, Chengdu, 610031, China

    Zhijie Wang

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  1. Zhen Li
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  2. Haiyan Xu
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  3. Zhijie Wang
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Correspondence to Haiyan Xu.

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Li, Z., Xu, H. & Wang, Z. Analytical Solution for Interaction between Tunnel Surrounding Rock and Supports in Red Sandstone Stratum. KSCE J Civ Eng 27, 4993–5007 (2023). https://doi.org/10.1007/s12205-023-0889-z

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  • DOI: https://doi.org/10.1007/s12205-023-0889-z

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