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Limit variation analysis of shallow rectangular tunnels collapsing with double-layer rock mass based on a three-dimensional failure mechanism

基于三维破坏机制的浅埋矩形硐室顶部双层围岩塌落上限变分分析

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Abstract

In the framework of upper bound theorem of limit analysis, the progressive collapse of shallow rectangular tunnels with double-layer rock mass has been theoretically analyzed based on the three-dimensional (3D) velocity discontinuity surfaces. According to the virtual work principle, the difference theorem and the variation method, the collapse surface of double-layer rock mass is determined based on the Hoek-Brown failure criterion. The formula can be degenerated to a single-layer rock collapsing problem when the rock mass is homogeneous. To estimate the validity of the result, the numerical simulation software PLAXIS 3D is used to simulate the collapse of shallow tunnels with double-layer rock mass, and the comparative analysis shows that numerical results are in good agreement with upper-bound solutions. According to the results of parametric analysis, the potential range of collapse of a double-layer rock mass above a shallow cavity decreases with a decrease in A1/A2, σci1/σci2 and σtm1/σtm2 and an increase in B1/B2, γ1/γ2. The range will decrease with a decrease in support pressure q and increase with a decrease in surface overload σ;s. Therefore, reinforced supporting is beneficial to improve the stability of the cavity during actual construction.

摘要

根据极限分析上限定理, 基于三维速度间断面破坏机制理论分析了浅埋矩形硐室顶部双层围岩 的渐进式塌落。根据虚功原理、差分定理和变分法, 确定了Hoek-Brown 破坏准则条件下双层岩体的 塌落面。该公式可退化为岩体性质均匀时的单层岩体塌落问题。为验证计算结果的有效性, 采用数值 模拟软件PLAXIS 3D 分析了浅埋硐室顶部双层围岩的塌落, 对比分析表明, 数值模拟结果与上限解 吻合较好。参数分析表明, 浅埋隧道顶部双层岩体的潜在塌落范围随A1/A2、σci1/σci2、σtm1/σtm2 的减小 而减小, 随B1/B2、γ1/γ2 的增大而减小。塌落范围随着支护压力q 的减小而减小, 随着表面超载σs 的 减小而增大。因此, 加强支护有利于提高实际施工中隧道的稳定性

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References

  1. FRALDI M, GUARRACINO F. Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(4): 665–673. DOI: https://doi.org/10.1016/j.ijrmms.2008.09.014.

    Article  Google Scholar 

  2. FRALDI M, GUARRACINO F. Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections [J]. International Journal of Solids and Structures, 2010, 47(2): 216–223. DOI: https://doi.org/10.1016/j.ijsolstr.2009.09.028.

    Article  MATH  Google Scholar 

  3. FRALDI M, GUARRACINO F. Evaluation of impending collapse in circular tunnels by analytical and numerical approaches [J]. Tunnelling and Underground Space Technology, 2011, 26(4): 507–516. DOI: https://doi.org/10.1016/j.tust.2011.03.003.

    Article  Google Scholar 

  4. FRALDI M, GUARRACINO F. Limit analysis of progressive tunnel failure of tunnels in Hoek-Brown rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 2012, 50: 170–173. DOI: https://doi.org/10.1016/j.ijrmms.2011.12.009.

    Article  Google Scholar 

  5. HUANG F, YANG X L. Upper bound limit analysis of collapse shape for circular tunnel subjected to pore pressure based on the Hoek-Brown failure criterion [J]. Tunnelling and Underground Space Technology, 2011, 26: 614–618. DOI: https://doi.org/10.1016/j.tust.2011.04.002.

    Article  Google Scholar 

  6. YANG X L, HUANG F. Collapse mechanism of shallow tunnel based on nonlinear Hoek-Brown failure criterion [J]. Tunnelling and Underground Space Technology, 2011, 26(6): 686–691. DOI: https://doi.org/10.1016/j.tust.2011.05.008.

    Article  Google Scholar 

  7. YANG X L, YAN R M. Collapse mechanism for deep tunnel subjected to seepage force in layered soils [J]. Geomechanics and Engineering, 2015, 8(5): 741–756. DOI: https://doi.org/10.12989/gae.2015.8.5.741.

    Article  Google Scholar 

  8. YANG X L, XU J S, LI Y X. Collapse mechanism of tunnel roof considering joined influences of nonlinearity and non-associated flow rule [J]. Geomechanics and Engineering, 2016, 10(1): 21–35. DOI: https://doi.org/10.12989/gae.2016.10.1.021.

    Article  Google Scholar 

  9. QIN C B, YANG X L, PAN Q J, SUN Z B, WANG L L, MIAO T. Upper bound analysis of progressive failure mechanism of tunnel roofs in partly weathered stratified Hoek-Brown rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 2015, 74: 157–162. DOI: https://doi.org/10.1016/j.ijrmms.2014.10.002.

    Article  Google Scholar 

  10. YANG X L, HUANG F. Three-dimensional failure mechanism of a rectangular cavity in a Hoek-Brown rock medium [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 61: 189–195. DOI: https://doi.org/10.1016/j.ijrmms.2013.02.014.

    Article  Google Scholar 

  11. LUO W H, LI W T. Reliability analysis of supporting pressure in tunnels based on three-dimensional failure mechanism [J]. Journal of Central South University, 2016, 23(5): 1243–1252. DOI: https://doi.org/10.1007/s11771-016-0374-7.

    Article  Google Scholar 

  12. QIN C B, SUN Z B, LIANG Q. Limit analysis of roof collapse in tunnels under seepage forces condition with three-dimensional failure mechanism [J]. Journal of Central South University, 2013, 20(8): 2314–2322. DOI: https://doi.org/10.1007/s11771-013-1739-9.

    Article  Google Scholar 

  13. XIA C C, ZHAO X, ZHANG G Z, WANG C B. Stability analysis by strength reduction method in shallow buried tunnels [J]. Tunneling and Underground Construction, 2014, 242: 321–331. DOI: https://doi.org/10.1061/9780784413449.032.

    Article  Google Scholar 

  14. LIU J, LIU X R, LAI Y, HE C M, WANG Z J. Failure mode of shallow-buried weak tunnel under different thickness-span ratios [J]. Journal of Central South University: Science and Technology, 2016, 47(5): 1744–1751. DOI: https://doi.org/10.11817/j.issn.1672-7207.2016.05.038. (in Chinese)

    Google Scholar 

  15. QIN C B, CHIAN S C, YANG X L. 3D limit analysis of progressive collapse in partly weathered hoek-brown rock banks [J]. International Journal of Geomechanics, 2017, 17(7), 04017011(1-10). DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0000885.

    Article  Google Scholar 

  16. QIN C B, CHIAN S C, YANG X L, DU D C. 2D and 3D limit analysis of progressive collapse mechanism for deep-buried tunnels under the condition of varying water table [J]. International Journal of Rock Mechanics and Mining Sciences, 2015, 80: 255–264. DOI: https://doi.org/10.1016/j.ijrmms.2015.09.024.

    Article  Google Scholar 

  17. QIN C B, CHIAN S C. Revisiting crown stability of tunnels deeply buried in non-uniform rock surrounds [J]. Tunnelling and Underground Space Technology, 2018, 73: 154–161. DOI: https://doi.org/10.1016/j.tust.2017.12.006.

    Article  Google Scholar 

  18. HOEK E, BROWN E T. Practical estimate the rock mass strength [J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(8): 1165–1186. DOI: https://doi.org/10.1016/S0148-9062(97)00305-7.

    Article  Google Scholar 

  19. ZHAO L H, TAN Y G, NIE Z H, YANG X P, HU S H. Variation analysis of ultimate pullout capacity of shallow horizontal strip anchor plate with 2-layer overlying soil based on nonlinear M-C failure criterion [J]. Journal of Central South University, 2018, 25: 2802–2818. DOI: https://doi.org/10.1007/s11771-018-3954-x.

    Article  Google Scholar 

  20. ZHANG R, LU S P. Kinematic analysis of shallow tunnel in layered strata considering joined effects of settlement and seepage [J]. Journal of Central South University, 2018, 25(2): 368–378. DOI: https://doi.org/10.1007/s11771-018-3743-6.

    Article  Google Scholar 

  21. ZHAO L H, YANG X P, HUANG F, TAN Y G, HU S H. Variational analysis of the ultimate pullout capacity of shallow circular anchor plates in rock foundations based on the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2018, 106: 190–197. DOI: https://doi.org/10.1016/j.ijrmms.2018.04.027.

    Article  Google Scholar 

  22. ZHAO L H, TAN Y G, HU S H, DENG D P, YANG X P. Upper bound analysis of the ultimate pullout capacity of shallow 3-D circular plate anchors based on the nonlinear mohr-coulomb failure criterion [J]. Journal of Central South University, 2018, 25: 2272–2288. DOI: https://doi.org/10.1007/s11771-018-3912-7.

    Article  Google Scholar 

  23. BRINKGREVE R B J, VERMEER P A. Finite element code for soil and rock analyses [M]. Rotterdam: A.A. Balkema, 1998.

    Google Scholar 

  24. HUANG F, ZHAO L H, LING T H, YANG X L. Rock mass collapse mechanism of concealed Karst cave beneath deep tunnel [J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 91: 133–138. DOI: https://doi.org/10.1016/j.ijrmms.2016.11.017.

    Article  Google Scholar 

  25. HUANG F, OU R C, LI Z L, YANG X L, LING T H. Limit analysis for the face stability of a shallow-shield tunnel based on a variational approach to the blow-out failure mode [J]. International Journal of Geomechanics, 2018, 18(6): 04018038. DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0001150.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410075, China

    Lian-heng Zhao  (赵炼恒), Shi-hong Hu  (胡世红), Xin-ping Yang  (杨新平) & Shi Zuo  (左仕)

  2. Key Laboratory of Heavy-Haul Railway Engineering Structure (Ministry of Education), Central South University, Changsha, 410075, China

    Lian-heng Zhao  (赵炼恒)

  3. School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha, 410004, China

    Fu Huang  (黄阜)

Authors
  1. Lian-heng Zhao  (赵炼恒)
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  2. Shi-hong Hu  (胡世红)
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  3. Xin-ping Yang  (杨新平)
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  4. Fu Huang  (黄阜)
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  5. Shi Zuo  (左仕)
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Corresponding authors

Correspondence to Fu Huang  (黄阜) or Shi Zuo  (左仕).

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Foundation item

Projects(51478477, 51878074) supported by the National Natural Science Foundation of China; Project(2017-123-033) supported by the Guizhou Provincial Department of Transportation Foundation, China; Projects(2018zzts663, 2018zzts656) supported by the Fundamental Research Funds for the Central Universities, China

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Zhao, Lh., Hu, Sh., Yang, Xp. et al. Limit variation analysis of shallow rectangular tunnels collapsing with double-layer rock mass based on a three-dimensional failure mechanism. J. Cent. South Univ. 26, 1794–1806 (2019). https://doi.org/10.1007/s11771-019-4134-3

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