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KSCE Journal of Civil Engineering

, Volume 23, Issue 9, pp 4141–4153 | Cite as

Complex Analysis of Ground Deformation and Stress for a Shallow Circular Tunnel with a Cavern in the Strata considering the Gravity Condition

  • Gongbiao Yang
  • Chengping ZhangEmail author
  • Yi Cai
  • Bo Min
Tunnel Engineering
  • 13 Downloads

Abstract

In the urban strata, the caverns appear inevitably due to the leakage of pipelines, the constructions of underground structures and other factors. For shallow tunnels, the influences of caverns on the ground deformation and stress during the tunneling construction cannot be ignored, which may endangers the surrounding understructures and nearby superstructures. Therefore, the interaction between the tunnel and the cavern should be considered seriously. In order to achieve ground deformation and stress for a shallow circular tunnel with a cavern in the strata, an analytical model that can take into account the gravity and the interaction between the tunnel and the cavern is proposed in this paper. In the model, the initial gravity condition is considered on the tunnel boundary, and the stress free condition is taken into account on the cavern boundary. During the solving process, the complex variable method and the Schwarz alternating method are applied. Then the analytical solution is verified by a corresponding numerical model. The results show that the analytical solution for the deformation and stress on the tunnel boundary agrees very well with the numerical solution. Finally, the influences of the cavern on the hoop stresses, radial deformations along the tunnel boundary and the surface settlements are discussed based on the solution proposed. The research shows important theoretical significances and application potentials for the prediction of the ground stress and deformation caused by the shallow tunnel with a cavity in the stratum.

Keywords

complex variables Schwarz alternating method shallow tunnel cavern stress and displacement 

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Notes

Acknowledgements

The research is supported by the Beijing Municipal Natural Science Foundation of China (Grant no.8172037) and the National Natural Science Foundation of Chia (Grant no: 51378002).

References

  1. Addenbrooke, T. I. and Potts, D. M. (2001). “Twin tunnel interaction: Surface and subsurface effects.” International Journal of Geomechanics, Vol. 1, No. 2, pp. 249–271, DOI:  https://doi.org/10.1061/(ASCE)1532.-3641(2001)1:2(249).CrossRefGoogle Scholar
  2. Augarde, C. E., Lyamin, A. V., and Sloan, S. W. (2003). “Prediction of undrained sinkhole collapse.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 129, No. 3, pp. 197–205, DOI:  https://doi.org/10.1061/(ASCE)1090-0241(2003)129:3(197).CrossRefGoogle Scholar
  3. Bobet, A. (2001). “Analytical solutions for shallow tunnels in saturated ground.” Journal of Engineering Mechanics, Vol. 127, No. 12, pp. 1258–1266, DOI:  https://doi.org/10.1061/(asce)0733-9399(2001)127:12(1258).CrossRefGoogle Scholar
  4. Do, N. A., Dias, D., and Oreste, P. (2016). “3D numerical investigation of mechanized twin tunnels in soft ground-influence of lagging distance between two tunnel face.” Engineering Structures, Vol. 109, pp. 117–125, DOI:  https://doi.org/10.1016/j.engstruct.2015.11.053.CrossRefGoogle Scholar
  5. Fang, Q., Zhang, D. L., and Wong, L. N. Y. (2011). “Environmental risk management for a cross interchange subway station construction in China.” Tunnelling and Underground Space Technology, Vol. 26, No. 6, pp. 750–763, DOI:  https://doi.org/10.1016/j.tust.2011.05.003.CrossRefGoogle Scholar
  6. Fu, J. Y., Yang, J. S., Yan, L., and Abbas, S. M. (2015). “An analytical solution for deforming twin-parallel tunnels in an elastic half plane.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 39, No. 5, pp. 524–538, DOI:  https://doi.org/10.1002/nag.2322.CrossRefGoogle Scholar
  7. Goodings, D. J. and Abdulla, W. A. (2002). “Stability charts for predicting sinkholes in weakly cemented sand over karst limestone.” Engineering Geology, Vol. 65, Nos. 2–3, pp. 179–184, DOI:  https://doi.org/10.1016/S0013-7952(01)00127-2.CrossRefGoogle Scholar
  8. Lee, K. M. and Rowe, R. K. (1990). “Finite element modelling of the three-dimensional ground deformations due to tunnelling in soft cohesive soils. Part I. Methods of analysis.” Computers and Geotechnics, Vol. 10, No. 2, pp. 87–109, DOI:  https://doi.org/10.1016/0266-352X(90)90001-C.CrossRefGoogle Scholar
  9. Lee, K. M., Rowe, R. K., and Lo, K. Y. (1992). “Subsidence owing to tunneling. I. Estimating the gap parameter.” Canadian Geotechnical Journal, Vol. 29, No. 6, pp. 929–940, DOI:  https://doi.org/10.1139/t92-104.CrossRefGoogle Scholar
  10. Li, Q. Q., Zhang, D. L., and Fang, Q. (2014). “Analytic solution to initial damage of cavern strata by complex function method.” Chinese Journal of Geotechnical Engineering, Vol. 36, No. 11, pp. 2110–2117. DOI:  https://doi.org/10.11779/CJGE201411018 (In Chinese).Google Scholar
  11. Liu, X. R., Liu, Y. Q., Yang, Z. P., and He, C. M. (2017). “Numerical analysis on the mechanical performance of supporting structures and ground settlement characteristics in construction process of subway station built by pile-beam-arch method.” KSCE Journal of Civil Engineering, Vol. 21, No. 5, pp. 1690–1705, DOI:  https://doi.org/10.1007/s12205-016-0004-9.CrossRefGoogle Scholar
  12. Loganathan, N. and Poulos, H. G. (1998). “Analytical prediction for tunneling-induced ground movements in clays.” Journal of Geotechnical & Geoenvironmental engineering. Vol. 124, No. 9, pp. 846–856, DOI:  https://doi.org/10.1061/(ASCE)1090-0241(1998)124:9(846).CrossRefGoogle Scholar
  13. Lu, A. Z., Zeng, X. T., and Xu, Z. (2016). “Solution for a circular cavity in an elastic half plane under gravity and arbitrary lateral stress.” International Journal of Rock Mechanics & Mining Sciences, Vol. 89, No. 8, pp. 34–42, DOI:  https://doi.org/10.1016/j.ijrmms.2016.08.004.CrossRefGoogle Scholar
  14. Migliazza, M., Chiorboli, M., and Giani, G. P. (2009). “Comparison of analytical method, 3D finite element model with experimental subsidence measurements resulting from the extension of the Milan underground.” Computers and Geotechnics, Vol. 36, Nos. 1–2, pp. 113–124, DOI:  https://doi.org/10.1016/j.compgeo.2008.03.005.CrossRefGoogle Scholar
  15. Park, K. H. (2004). “Elastic solution for tunneling-induced ground movement in clay.” International Journal of Geomechanics, Vol. 4, No. 1, pp. 310–318, DOI:  https://doi.org/10.1061/(ASCE)1532-3641(2004)4:4(310).CrossRefGoogle Scholar
  16. Peck, R. B. (1969). “Deep excavations and tunneling in soft ground.” Proc. of the 7th Int. Conf. on Soil Mechanics and Foundation Engineering, State of Art, Mexico City, Mexico, pp. 225–290.Google Scholar
  17. Sagaseta, C. (1987). “Analysis of undrained soil deformation due to ground loss.” Géotechnique, Vol. 37, No. 3, pp. 301–320, DOI:  https://doi.org/10.1680/geot.1987.37.3.301.CrossRefGoogle Scholar
  18. Strack, O. E. and Verruijt, A. (2002). “A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 26, No. 12, pp. 1235–1252, DOI:  https://doi.org/10.1002/nag.246.CrossRefzbMATHGoogle Scholar
  19. Verruijt, A. (1997). “A complex variable solution for a deforming circular tunnel in an elastic half-plane.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 21, No. 2, pp. 77–89, DOI:  https://doi.org/10.1002/(sici)1096-9853(199702)21:2<77::aid-nag857>3.0.co;2-m.CrossRefzbMATHGoogle Scholar
  20. Verruijt, A. (1998). “Deformations of an elastic half-plane with a circular cavity.” International Journal for Solids and Structures, Vol. 35, No. 21, pp. 2795–2804, DOI:  https://doi.org/10.1016/S0020-7683(97)00194-7.CrossRefzbMATHGoogle Scholar
  21. Zhang, Z. G., Huang, M. S., Xi, X. G., and Yang, X. (2018). “Complex variable solutions for soil and liner deformation due to tunneling in clays.” International Journal of Geomechanics, Vol. 18, No. 7, pp. 1–19, DOI:  https://doi.org/10.1016/(asce)gm.1943-5622.0001197.Google Scholar
  22. Zhang, L. Q., Yang, Z. F., and Lu, A. Z. (2000). “Analytical study on plane elastic problem of two random geometry tunnels.” Science in China (Series D), Vol. 30, No. 5, pp. 509–518, DOI:  https://doi.org/10.3321/j.issn:1006-9267.2000.05.009 (In Chinese).Google Scholar
  23. Zhang, Z. G., Zhang, M. X., Jiang, Y. J., Bai, Q. M., and Zhao, Q. H. (2017). “Analytical prediction for ground movements and liner internal forces induced by shallow tunnels considering non-uniform convergence pattern and ground-liner interaction mechanism.” Soils and Foundations, Vol. 57, No. 2, pp. 211–226, DOI:  https://doi.org/10.1016/j.sandf.2017.03.004.CrossRefGoogle Scholar
  24. Zhang, Z. G., Zhang, C. P., Jiang, K. M., Wang, Z. W., Jiang, Y. J., Zhao, Q. H., and Lu, M. H. (2019). “Analytical prediction for tunnel-soilpile interaction mechanics based on Kerr foundation model.” KSCE Journal of Civil Engineering, Vol. 23, No. 6, pp. 2756–2771, DOI:  https://doi.org/10.1007/s12205-019-0791-x.CrossRefGoogle Scholar
  25. Zhang, C. P., Zhang, X., Li, H., and Zhang, D. L. (2016). “Model tests on failure laws of ground with voids induced by shallow tunneling.” Chinese Journal of Geotechnical Engineering, Vol. 38, No. 2, pp. 263–270, DOI:  https://doi.org/10.11779/CJGE201602009 (In Chinese).Google Scholar
  26. Zhou, S. W., Rabczuk, T., and Zhuang, X. Y. (2018). “Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies.” Advances in Engineering Software, Vol. 122, pp. 31–49, DOI:  https://doi.org/10.1016/j.advengsoft:2018.03.012.CrossRefGoogle Scholar
  27. Zhou, S. W., Zhuang, X. Y., and Rabczuk, T. (2019). “Phase-field modeling of fluid-driven dynamic cracking in porous media.” Computer Methods in Applied Mechanics and Engineering, Vol. 350, pp. 169–198, DOI:  https://doi.org/10.1016/j.cma:2019.03.001.MathSciNetCrossRefGoogle Scholar

Copyright information

© Korean Society of Civil Engineers 2019

Authors and Affiliations

  1. 1.Key Laboratory of Urban Underground Engineering of Ministry of EducationBeijing Jiaotong UniversityBeijingChina

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