Abstract
Water inrush is a serious geological hazard in the deep buried tunnel construction in karst areas. Lining and grouting ring are often built to prevent tunnel from water inrush. The estimation of external water pressure and water inflow is of great significance to the structure design of lining and grouting ring. In this paper, the axisymmetric analytic solutions of external water pressure and water inflow were derived for deep karst tunnels under saturated steady-state flow conditions. A simplified formula for the reduction coefficient of external water pressure was established. This paper analyzed the changing rule of water inflow coefficient and the reduction coefficient of external hydraulic pressure on linings, which varies with the parameters of lining and grouting circle. The rational and available coefficients of grouting circle in karst deep buried tunnel construction are drawn: the grouting ring thickness is 6 m and the hydraulic conductivity ratio of surrounding rock and lining is 100. In addition, the accuracy of the simplified formula was verified by the comparison of analytical solution and numerical analysis. This study provides a reliable calculation method for water inflow and lining water pressure of the deep buried tunnel and have certain reference value for the structural design of deep buried tunnel to reduce water inflow and ensure construction safety.
Similar content being viewed by others
References
Barani, O. R. and Khoei, A. R. (2014). “3D modeling of cohesive crack growth in partially saturated porous media: A parametric study.” Engineering Fracture Mechanics, Vol. 124–125, pp. 272–286, DOI: https://doi.org/10.1016/j.engfracmech.2014.04.016.
Barani, O. R., Khoei, A. R., and Mofid, M. (2011). “Modeling of cohesive crack growth in partially saturated porous media; A study on the permeability of cohesive fracture.” International Journal of Fracture, Vol. 167, No. 1, pp. 15–31, DOI: https://doi.org/10.1007/s10704-010-9513-6.
Butscher, C. (2012). “Steady-state groundwater inflow into a circular tunnel.” Tunnelling and Underground Space Technology Incorporating Trenchless Technology Research, Vol. 32, No. 6, pp. 158–167, DOI: https://doi.org/10.1016/j.tust.2012.06.007.
Fahimifar, A. and Zareifard, M. R. (2009). “A theoretical solution for analysis of tunnels below groundwater considering the hydraulic-mechanical coupling.” Tunnelling and Underground Space Technology, Vol. 24, No. 6, pp. 634–646, DOI: https://doi.org/10.1016/j.tust.2009.06.002.
Fahimifar, A. and Zareifard, M. R. (2013). “A new closed-form solution for analysis of unlined pressure tunnels under seepage forces.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 37, No. 11, pp. 1591–1613, DOI: https://doi.org/10.1002/nag.2101.
Fang, Y., Guo, J., Grasmick, J., and Mooney, M. (2016). “The effect of external water pressure on the liner behavior of large cross-section tunnels.” Tunnelling and Underground Space Technology Incorporating Trenchless Technology Research, Vol. 60, pp. 80–95, DOI: https://doi.org/10.1016/j.tust.2016.07.009.
Font-Capó, J., Vázquez-Suñé, E., Carrera, J., Martí, D., Carbonell, R., and Pérez-Estaun, A. (2011). “Groundwater inflow prediction in urban tunneling with a tunnel boring machine (TBM).” Tunnelling and erground Space Technology, Vol. 121, No. 1, pp. 46–54, DOI: https://doi.org/10.1016/j.enggeo.2011.04.012.
Hassani, A. N., Farhadian, H., Katibeh, H. (2018). “A comparative study on evaluation of steady-state groundwater inflow into a circular shallow tunnel.” Tunnelling and Underground Space Technology, Vol. 73, pp. 15–25, DOI: https://doi.org/10.1016/j.tust.2017.11.019.
Hassani, A. N., Katibeh, H., and Farhadian, H. (2015). “Numerical analysis of steady-state groundwater inflow into tabriz line 2 metro tunnel, northwestern iran, with special consideration of model dimensions.” Bulletin of Engineering Geology and the Environment, Vol. 75, No. 4, pp. 1–11, DOI: https://doi.org/10.1007/s10064-015-0802-1.
Huang, Y., Fu, Z., Chen, J., Zhou, Z., Wang, J. (2015). “The external water pressure on a deep buried tunnel in fractured rock.” Tunnelling and Underground Space Technology, Vol. 48, pp. 58–66, DOI: https://doi.org/10.1016/j.tust.2015.02.003.
Kolymbas, D. and Wagner, P. (2007). “Groundwater ingress to tunnels — The exact analytical solution.” Tunnelling and erground Space Technology, Vol. 22, No. 1, pp. 23–27, DOI: https://doi.org/10.1016/j.tust.2006.02.001.
Li, P. F., Fang, Q., and Zhang, D. L. (2014). “Analytical solutions of stresses and displacements for deep circular tunnels with liners in saturated ground.” Journal of Zhejiang University-SCIENCE A (Applied Physics and Engineering), Vol. 15, No. 6, pp. 395–404, DOI: https://doi.org/10.1631/jzus.A1400023.
Li, S. C., Wu, J., Xu, Z. H., and Li, L. P. (2017). “Unascertained measure model of water and mud inrush risk evaluation in karst tunnels and its engineering application.” KSCE Journal of Civil Engineering, Vol. 21, No. 4, pp. 1170–1182, DOI: https://doi.org/10.1007/s12205-016-1569-z.
Liu, M. and Chen, C. (2015). “A micromechanical analysis of the fracture properties of saturated porous media.” International Journal of Solids and Structures, Vol. 63, pp. 32–38, DOI: https://doi.org/10.1016/j.ijsolstr.2015.02.031.
Ma, D. and Bai, H. (2015). “Groundwater inflow prediction model of karst collapse pillar: A case study for mining-induced groundwater inrush risk.” Natural Hazards, Vol. 76, No. 2, 1319–1334, DOI: https://doi.org/10.1007/s11069-014-1551-3.
Ming, H. F., Wang, M. S., Tan, Z. S., and Wang, X. Y. (2010). “Analytical solutions for steady seepage into an underwater circular tunnel.” Tunnelling and erground Space Technology, Vol. 25, No. 4, pp. 391–396, DOI: https://doi.org/10.1016/j.tust.2010.02.002.
Roshan, H. and Rahman, S. (2011a). “Analysis of pore pressure and stress distribution around a wellbore drilled in chemically active elastoplastic formations.” Rock Mechanics and Rock Engineering, Vol. 44, No. 5, pp. 541–552, DOI: https://doi.org/10.1007/s00603-011-0141-x.
Roshan, H. and Rahman, S. (2011b). “A fully coupled chemo-poroelastic analysis of pore pressure and stress distribution around a wellbore in water active rocks.” Rock Mechanics and Rock Engineering, Vol. 44, No. 2, pp. 199–210, DOI: https://doi.org/10.1007/s00603-010-0104-7.
Singh, K. K., Singh, D. N., and Ranjith, P. G. (2015). “Laboratory simulation of flow through single fractured granite.” Rock Mechanics and Rock Engineering, Vol. 48, No. 3, pp. 987–1000, DOI: https://doi.org/10.1007/s00603-014-0630-9.
Su, K., Zhou, Y., Wu, H., Shi, C., and Zhou, L. (2017). “An analytical method for groundwater inflow into a drained circular tunnel.” Ground Water, Vol. 55, No. 5, pp. 712–721, DOI: https://doi.org/10.1111/gwat.12513.
Tani, M. E. (2010). “Helmholtz evolution of a semi-infinite aquifer drained by a circular tunnel.” Tunnelling and Underground Space Technology Incorporating Trenchless Technology Research, Vol. 25, No. 1, pp. 54–62, DOI: https://doi.org/10.1016/j.tust.2009.08.005.
Wang, Z. J., He, S. Y., Yuan, Y., Wang, N., and He, M. L. (2015). “Study on water pressure load and internal force of tunnel lining based on the method of equivalent perimeter alternative.” Journal of Railway Science and Engineering, Vol. 12, No. 3, pp. 577–583.
Wang, X. T., Li, S. C., Xu, Z. H., Hu, J., Pan, D. D., and Xue, Y. G. (2018). “Risk assessment of water inrush in karst tunnels excavation based on normal cloud model.” Bulletin of Engineering Geology and the Environment, Vol. 77, No. 138, pp. 1–16, DOI: https://doi.org/10.1007/s10064-018-1294-6.
Wang, X. T., Li, S. C., Xu, Z. H., Lin, P., Hu, J., and Wang, W. Y. (2019). “Analysis of factors influencing floor water inrush in coal mines: A nonlinear fuzzy interval assessment method.” Mine Water and the Environment, Vol. 34, No. 115, pp. 1–12, DOI: https://doi.org/10.1007/s10230-018-00578-x.
Wang, X., Tan, Z., Wang, M., Zhang, M., and Ming, H. (2008). “Theoretical and experimental 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, DOI: https://doi.org/10.1016/j.tust.2007.10.004.
Yang, F., Zhang, J., Yang, J., Zhao, L., and Zheng, X. (2015). “Stability analysis of unlined elliptical tunnel using finite element upper-bound method with rigid translatory moving elements.” Tunnelling and Underground Space Technology, Vol. 50, pp. 13–22, DOI: https://doi.org/10.1016/j.tust.2015.06.005.
Zhou, S., Rabczuk T., and Zhuang, X. (2018a). “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.
Zhou, S. and Xia, C. (2018). “Propagation and coalescence of quasistatic cracks in brazilian disks: An insight from a phase field model.” Acta Geotechnica, Vol. 14, No. 66, pp. 1–20, DOI: https://doi.org/10.1007/s11440-018-0701-2.
Zhou, S. and Zhuang, X. (2018). “Adaptive phase field simulation of quasi-static crack propagation in rocks.” Underground Space, Vol. 3, No. 3, pp. 190–205, DOI: https://doi.org/10.1016/j.undsp.2018.04.006.
Zhou, S., Zhuang, X., and Rabczuk, T. (2018b). “A phase-field modeling approach of fracture propagation in poroelastic media.” Engineering Geology, Vol. 240, pp. 189–203, DOI: https://doi.org/10.1016/j.enggeo.2018.04.008.
Zhou, S., Zhuang, X., Zhu, H., and Rabczuk, T. (2018c). “Phase field modelling of crack propagation, branching and coalescence in rocks.” Theoretical and Applied Fracture Mechanics, Vol. 96, pp. 174–192, DOI: https://doi.org/10.1016/j.tafmec.2018.04.011.
Zhu, Z. Q., Qian, S., Mei, S. H., and Zhang, Z. R. (2009). “Improved ubiquitous-joint model and its application to underground engineering in layered rock masses.” Rock and Soil Mechanics, Vol. 30, No. 10, pp. 3115–3121.
Acknowledgements
Much of the work presented in this paper was supported by the National Natural Science Foundation of China (Grant No.s: 51509147) and the promotive research fund for excellent young and middle-aged scientists of Shandong Province (Grant No.: BS2014NJ004).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, Z., Wang, X., Li, S. et al. Parameter Optimization for the Thickness and Hydraulic Conductivity of Tunnel Lining and Grouting Rings. KSCE J Civ Eng 23, 2772–2783 (2019). https://doi.org/10.1007/s12205-019-1509-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-019-1509-9