Geotechnical and Geological Engineering

, Volume 37, Issue 1, pp 491–499 | Cite as

Upper Bound Solution for Required Supporting Pressure Applied on a Deep Shield Tunnel Face Under Different Groundwater Levels

  • Jia-hua ZhangEmail author
  • Wei-jun Wang
  • Biao Zhang
  • Dao-bing Zhang
  • Jia-cheng Song
Technical Note


The construction of shield tunnels is greatly influenced by the presence of groundwater. Based on the upper bound theorem of limit analysis, this paper presents an analytical investigation on the stability of shield tunnel face subjected to the impact of pore water pressure. Considering the nonlinear strength feature of soil mass, the nonlinear failure criterion of power-law type is employed, and the tangential technique is utilized to determine its equivalent Mohr–Coulomb strength parameters. The log-spiral failure mechanism for shield tunnel face is constructed, and three different cases of the relation between groundwater level and this mechanism are summarized. After that, rates of work of external forces and rate of internal energy dissipation are computed and analytical expression for the supporting pressure is deduced. Numerical solution with respect to specified parameters is calculated through optimization. Parametric analysis is performed and the variation of required supporting pressure with increasing height of groundwater level is presented.


Upper bound analysis Shield tunnel Pore water pressure Supporting pressure 



The preparation of the paper has received financial supports from National Natural Science Foundation of China (51434006, 51374105 and 51674115). The financial supports are greatly appreciated.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jia-hua Zhang
    • 1
    Email author
  • Wei-jun Wang
    • 1
  • Biao Zhang
    • 2
  • Dao-bing Zhang
    • 1
  • Jia-cheng Song
    • 3
  1. 1.Work Safety Key Lab on Prevention and Control of Gas and Roof Disasters for Southern Coal Mines, Hunan Provincial Key Laboratory of Safe Mining Techniques of Coal MinesHunan University of Science and TechnologyXiangtanChina
  2. 2.School of Civil EngineeringCentral South UniversityChangshaChina
  3. 3.School of Resource Environment and Safety EngineeringHunan University of Science and TechnologyXiangtanChina

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