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Advances in Civil Engineering
Volume 2018 (2018), Article ID 8401482, 14 pages
https://doi.org/10.1155/2018/8401482
Research Article

Using the Schwarz Alternating Method to Identify Critical Water-Resistant Thickness between Tunnel and Concealed Cavity

1International Joint Research Laboratory of Henan Province for Underground Space Development and Disaster Prevention, Jiaozuo, Henan 454003, China
2School of Civil Engineering, Henan Polytechnic University, Jiaozuo, Henan 454003, China
3School of Highway, Chang’an University, Xi’an 710064, China
4College of Chemistry and Chemical Engineering, Henan Polytechnic University, Jiaozuo, Henan 454003, China

Correspondence should be addressed to Jianxun Chen

Received 25 August 2016; Revised 11 July 2017; Accepted 27 July 2017; Published 29 January 2018

Academic Editor: Cumaraswamy Vipulanandan

Copyright © 2018 Jiaqi Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Q.-L. Cui, S.-L. Shen, Y.-S. Xu, H.-N. Wu, and Z.-Y. Yin, “Mitigation of geohazards during deep excavations in karst regions with cavers: a case study,” Engineering Geology, vol. 195, no. 9, pp. 16–27, 2015. View at Publisher · View at Google Scholar · View at Scopus
  2. K.-I. Song, G.-C. Cho, and S.-B. Chang, “Identification, remediation, and analysis of karst sinkholes in the longest railroad tunnel in South Korea,” Engineering Geology, vol. 135-136, no. 5, pp. 92–105, 2012. View at Publisher · View at Google Scholar · View at Scopus
  3. S.-c. Li, Z.-q. Zhou, L.-p. Li, Z.-h. Xu, Q.-q. Zhang, and S.-s. Shi, “Risk assessment of water inrush in karst tunnels based on attribute synthetic evaluation system,” Tunnelling and Underground Space Technology, vol. 38, no. 6, pp. 50–58, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. B. Luo, J. X. Chen, S. T. Gao, X. G. Deng, and P. S. Diao, “Stability analysis of super-large-section tunnel in loess ground considering water infiltration caused by irrigation,” Environmental Earth Sciences, vol. 76, p. 763, 2017. View at Publisher · View at Google Scholar · View at Scopus
  5. H. R. Zarei, A. Uromeihy, and M. Sharifzadeh, “Identifying geological hazards related to tunneling in carbonate karstic rocks-Zagros, Iran,” Arabian Journal of Geosciences, vol. 5, no. 3, pp. 457–464, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. Zhao, P. Li, and S. Tian, “Prevention and treatment technology of railway tunnel water inrush and mud gushing in China,” Journal of Rock Mechanics and Geotechnical Engineering, vol. 5, no. 6, pp. 468–477, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. Z. Ming-jie, L. Xu-hua, A. O. Jian-hua, and W. Biao, “Numerical analysis of influence of karst caves in top of tunnel on stability of surrounding rock masses,” Rock and Soil Mechanics, vol. 24, no. 3, pp. 445–449, 2003, (in Chinese). View at Google Scholar
  8. S. Zhanping, Research on the influence of concealed karst caverns upon the stability of tunnels and its application structure [Ph.D. Thesis], Xi’an University of Technology, Xi’an, China, 2006, (in Chinese).
  9. T. Junhua, B. Haibo, Y. Banghua, and W. Yu, “Theoretical analysis on water-inrush mechanism of concealed collapse pillars in floor,” Mining Science and Technology, vol. 21, no. 1, pp. 57–60, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. X. Wang and M. Wang, “Analysis of the mechanism of water inrush in karst tunnels,” in Proceedings of GeoShanghai International Conference, Shanghai, China, May 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Q. Guo, L. W. Ren, and G. Y. Wang, “Stability analysis of rock pillar between tunnel and large-scale concealed cave on top of tunnel,” Applied Mechanics and Material, vol. 256–259, pp. 1325–1328, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Zhe, Z. Yi, and H. Chao, “Mechanical mechanism of water inrush in the side of karst tunnel under the effect of fault,” Electronic Journal of Geotechnical Engineering, vol. 19, pp. 4611–4622, 2014. View at Google Scholar
  13. J. Peng and X. G. Li, “Water-inrush mechanism during construction and determination of safety distance form the water source in a karst tunnel,” Electronic Journal of Geotechnical Engineering, vol. 20, no. 8, pp. 2345–2354, 2015. View at Google Scholar
  14. L. Liping, Study on catastrophe evolution mechanism of karst water inrush and its engineering application of high risk karst tunnel, Shandong University, Jinan, China, 2009, Ph.D. thesisThesis.
  15. D.-x. Liang, Z.-q. Jiang, S.-y. Zhu, Q. Sun, and Z.-w. Qian, “Experimental research on water inrush in tunnel construction,” Natural Hazards, vol. 81, no. 1, pp. 467–480, 2016. View at Publisher · View at Google Scholar · View at Scopus
  16. L. Q. Zhang and A. Z. Lu, “An analytic algorithm of stresses for any double hole problem in plane elastostatics,” Journal of Applied Mechanics, vol. 68, no. 2, pp. 350–353, 2001. View at Publisher · View at Google Scholar
  17. L. Zhi-kui, L. Jin-cheng, and Z. Shou-zeng, “Stability analysis of rock foundation with cave in karst area,” Chinese Journal of Geotechnical Engineering, vol. 25, in Chinese, no. 3, pp. 629–633, 2003. View at Google Scholar
  18. E. M. Criss, R. E. Criss, and G. R. Osburn, “Effect of stress on cave passage shape in karst terranes,” Rock Mechanics and Rock Engineering, vol. 41, no. 3, pp. 499–505, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. Z. Luqing, Y. Zhifa, and L. Aizhong, “Analytic study on the problem of two holes having arbitrary shapes and arrangements in plane elastostatics,” Science in China Series D: Earth Sciences, vol. 44, no. 2, pp. 146–158, 2001. View at Publisher · View at Google Scholar
  20. L. Aizhong and Z. Luqing, “Alternating method study on stress analysis of surrounding rock for two random geometry tunnels,” Journal of Coal Science and Engineering, vol. 3, no. 2, pp. 24–29, 1997. View at Google Scholar
  21. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, Tsinghua University Press, Beijing, China, 3rd edition, 2015.
  22. A. A. Griffth, “The phenomena of rupture and flow in solid,” Philosophical Transactions of the Royal Society London, (Series A): Containing Papers of a Mathematical or Physical Character, vol. 221, pp. 163–198, 1921. View at Publisher · View at Google Scholar
  23. P. Yan, W. Lu, M. Chen, and C. Zhou, “Effect of initial geo-stress dynamic unloading during tunnel excavation,” Chinese Journal of Geotechnical Engineering, vol. 31, in Chinese, no. 12, pp. 1888–1894, 2009. View at Google Scholar
  24. J. Guo, J. Chen, and Q. Liu, “Study on against-inrush thickness and waterburst mechanism of karst tunnel,” Electronic Journal of Geotechnical Engineering, vol. 21, no. 4, pp. 1689–1700, 2016. View at Google Scholar
  25. W. Xiuying, T. Zhongsheng, W. Mengshu, Z. Mi, and H. Ming, “Theoretical and experiment study of external water pressure on tunnel lining in controlled drainage under high water level,” Tunnelling and Underground Space Technology, vol. 23, no. 5, pp. 552–560, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. X. Li and Y. Li, “Research on risk assessment system for water inrush in the karst tunnel construction based on GIS: case study on the diversion tunnel groups of the Jingping II Hydropower Station,” Tunnelling and Underground Space Technology, vol. 40, no. 2, pp. 182–191, 2014. View at Publisher · View at Google Scholar · View at Scopus
  27. C. Xi, Study on Safe Thickness for Rock between Tunnel and Karst Cave in Karst Region, Beijing Jiaotong University, Beijing, China, 2010, M.S. thesisThesis.
  28. P. Volko and M. J. Economides, “Propagation of hydraulically induced fractures-a continuum damage mechanics approach,” International Journal of Rock Mechanics and Min Science & Geomechanics Abstracts, vol. 31, no. 3, pp. 221–229, 1994. View at Google Scholar
  29. X. X. Miao, S. C. Li, and Z. Q. Chen, “Bifurcation and catastrophe of seepage flow system in broken rock,” Mining Science and Technology, vol. 19, no. 1, pp. 1–7, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. J. Guo, X. Liu, and C. Qiao, “Experimental study of mechanical properties and energy mechanism of karst limestone under natural and saturated states,” Chinese Journal of Rock Mechanics and Engineering, vol. 33, in Chinese, no. 2, pp. 296–308, 2014. View at Google Scholar
  31. P. Papanastasiou and D. Durban, “Elastoplastic analysis of cylindrical cavity problems in geomaterials,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 21, no. 2, pp. 133–149, 1997. View at Publisher · View at Google Scholar
  32. C. B. Ling, “On the stresses in a plate containing two circular holes,” Journal of Applied Physics, vol. 19, no. 1, pp. 77–82, 1948. View at Publisher · View at Google Scholar · View at Scopus
  33. R. A. W. Haddon, “Stress in an infinite plate with two unequal circular holes,” Quarterly Journal of Mechanics and Applied Mathematics, vol. 20, no. 3, pp. 277–291, 1967. View at Publisher · View at Google Scholar · View at Scopus
  34. I. S. Sokolnikoff, Mathematical Theory of Elasticity, McGraw-Hill, New York, USA, 2nd edition, 1956.
  35. H. Schwarz, “Über einen Grenzübergang durch alternierends Verfahren,” Vieteljahrsschriftder Naturforschenden Gesellschaft in Zurich, vol. 15, pp. 272–286, 1870. View at Google Scholar
  36. S. G. Mikhlin, Method of Successive Approximation in Solutions to Biharmonic Equations, vol. 39, Trudy, Seisomological, USSR, 1934.
  37. S. Soboleff, Schwarz Algorithm in the Theory of Elasticity, vol. IV, Reports from Academy of Science, USSR, 1936.
  38. V. L. Salerno and J. B. Mahoney, “Stress solution for and infinite plate containing two arbitrary circular holes under equal biaxial stress,” Journal of Engineering for Industry, vol. 90, no. 4, pp. 656–665, 1968. View at Publisher · View at Google Scholar
  39. V. G. Ukadgaonker, “Stress analysis of a plate containing two circular holes having tangential stresses,” AIAA Journal, vol. 18, no. 1, pp. 125–128, 1980. View at Publisher · View at Google Scholar · View at Scopus
  40. R. W. Zimmerman, “Second-order approximation for the compression of an elastic plate containing a pair of circular holes,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 68, no. 11, pp. 575–577, 1988. View at Publisher · View at Google Scholar · View at Scopus
  41. V. G. Ukadgaonker and D. B. Patil, “Stress analysis of a plate containing two elliptical holes subjected to uniform pressure and tangential stresses at the boundaries,” Journal of Engineering for Gas Turbines and Power, vol. 115, pp. 93–101, 1993. View at Google Scholar
  42. C. B. Kooi and A. Verruijt, “Interaction of circular holes in an infinite elastic medium,” Tunnelling & Underground and Space Technology, vol. 16, no. 1, pp. 59–62, 2001. View at Publisher · View at Google Scholar · View at Scopus
  43. L. Q. Zhang and A. Z. Lu, “Study of alternating method for stress analysis on surrounding rock of two circular holes,” Chinese Journal of Rock Mechanics and Engineering, vol. 17, in Chinese, no. 5, pp. 534–543, 1998. View at Google Scholar
  44. L. Q. Zhang, Z. Q. Yue, C. F. Lee, L. G. Tham, and Z. F. Yang, “Stress solution of multiple elliptic hole problem in plane elasticity,” ASCE Journal of Engineering Mechanics, vol. 129, no. 12, pp. 1394–1407, 2003. View at Publisher · View at Google Scholar · View at Scopus
  45. L. Q. Zhang, A. Z. Lu, Z. Q. Yue, and Z. F. Yang, “An efficient and accurate iterative stress solution for an infinite elastic plate around two elliptic holes, subjected to uniform loads on the hole boundaries and at infinity,” European Journal of Mechanics A/Solids, vol. 28, no. 1, pp. 189–193, 2009. View at Publisher · View at Google Scholar · View at Scopus
  46. F. Q. Chen, F. Su, and Y. Z. Shi, “Analysis solution for tunnels due to the influence of adjacent ellipse karst cave,” Chinese Journal of Computational Mechanics, vol. 31, in Chinese, no. 1, pp. 54–60, 2014. View at Publisher · View at Google Scholar · View at Scopus
  47. J. Y. Fu, J. S. Yang, Y. Li, and S. Muntazir Abbas, “An analytical solution for deforming with twin-parallel tunnels in an elastic half plane,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 39, no. 5, pp. 524–538, 1997. View at Publisher · View at Google Scholar · View at Scopus
  48. J. Y. Rao, H. L. Fu, T. Xie, W. Xiao-min, Y. Quan, and L. Wen-bo, “Analytical solutions to the stress of surrounding rock containing tubular double-ellipse caves considering internal water pressure,” Rock and Soil Mechanics, vol. 37, in Chinese, no. 1, pp. 76–60, 2016. View at Google Scholar
  49. H. N. Wang, G. S. Zeng, S. Utili, M. J. Jiang, and L. Wua, “Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock,” International Journal of Rock Mechanics and Mining Sciences, vol. 93, pp. 13–29, 2017. View at Publisher · View at Google Scholar · View at Scopus
  50. W. C. Song, Y. T. Gao, S. C. Wu et al., “Reasonable spacing of parallel tunnels based on the complex function theory and D-P yield criterion,” Chinese Journal of Engineering, vol. 38, no. 2, pp. 291–298, 2016. View at Google Scholar
  51. E. T. Brown, J. W. Bray, B. Ladanyi, and E. Hoek, “Ground response curves for rock tunnels,” ASCE Journal of Geotechnical Engineering, vol. 109, no. 1, pp. 15–39, 1983. View at Publisher · View at Google Scholar · View at Scopus
  52. T. Ogawa and K. Y. Lo, “Effects of dilatancy and yield criteria on displacements around tunnels,” Canadian Geotechnical Journal, vol. 24, no. 1, pp. 100–113, 1987. View at Publisher · View at Google Scholar
  53. C. Carranza-Torres and C. Fairhurst, “The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion,” International Journal of Rock Mechanics and Mining Sciences, vol. 36, no. 6, pp. 777–809, 1999. View at Publisher · View at Google Scholar · View at Scopus
  54. S. K. Sharan, “Elastic-brittle-plastic analysis of circular openings in Hoek-Brown media,” International Journal of Rock Mechanics and Mining Sciences, vol. 40, no. 6, pp. 817–824, 2003. View at Publisher · View at Google Scholar · View at Scopus
  55. S. K. Sharan, “Exact and approximate solutions of displacements around circular openings in elastic-brittle-plastic Hoek-Brown rock,” International Journal of Rock Mechanics and Mining Sciences, vol. 42, no. 4, pp. 524–532, 2005. View at Publisher · View at Google Scholar · View at Scopus
  56. S. K. Sharan, “Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock,” International Journal of Rock Mechanics and Mining Sciences, vol. 45, no. 1, pp. 78–85, 2008. View at Publisher · View at Google Scholar · View at Scopus
  57. K. Mogi, “Effect of intermediate principal stress on rock failure,” Journal of Geophysical Research, vol. 72, no. 20, pp. 5117–5131, 1967. View at Publisher · View at Google Scholar
  58. B. Singh, R. K. Goel, V. K. Meharotra, S. K. Garg, and M. R. Allu, “Effect of intermediate principal stress on strength of anisotropic rock mass,” Tunnelling & Underground Space Technology, vol. 13, no. 1, pp. 71–79, 1998. View at Publisher · View at Google Scholar · View at Scopus
  59. S. Q. Xu and M. H. Yu, “The effect of the intermediate principal stress on the ground response of circular openings in rock mass,” Rock Mechanics and Rock Engineering, vol. 39, no. 2, pp. 169–181, 2006. View at Publisher · View at Google Scholar · View at Scopus
  60. C. Z. Zhang, J. H. Zhao, Q. H. Zhang, and X. Hu, “A new closed-form solution for circular openings modeled by the Unified Strength Theory and radius-dependent Young’s modulus,” Computers and Geotechnics, vol. 42, no. 22, pp. 118–128, 2012. View at Publisher · View at Google Scholar · View at Scopus
  61. D. Durban and P. Papanastasiou, “Cylindrical cavity expansion and contraction in pressure sensitive geomaterials,” Acta Mechanica, vol. 122, no. 1–4, pp. 99–122, 1997. View at Publisher · View at Google Scholar
  62. L. Chen, X. B. Mao, M. Li et al., “Elastoplastic analysis of cracked surrounding rock in deep roadway based on Drucker-Prager criterion,” Journal of China Coal Society, vol. 42, no. 2, pp. 484–491, 2017. View at Google Scholar
  63. L. Obert and W. I. Duvall, Rock Mechanics and the Design of Structures in Rock, John Wiley & Sons, New York, NY, USA, 1967.
  64. O. Yarali and E. Soyer, “The effect of mechanical rock properties and brittleness on drillability,” Scientific Research and Essays, vol. 6, no. 5, pp. 1077–1088, 2011. View at Publisher · View at Google Scholar
  65. B. H. G. Brady and E. T. Brown, Rock Mechanics for Underground Mining. Rock Strength, Springer, Netherlands, 2006.
  66. H. Y. Wang, Study on the Stability of Water-resistant Strata of Karst Tunnel based on Releasable Strain Energy, Chang’an, Xi’an, China, 2016, M.S. thesis.