KSCE Journal of Civil Engineering

, Volume 23, Issue 2, pp 866–878 | Cite as

Dimensionless Parameter Diagrams for the Active and Passive Stability of a Shallow 3D Tunnel Face

  • LianHeng Zhao
  • DeJian Li
  • Feng YangEmail author
  • Liang Li
  • Xiao Cheng
Tunnel Engineering


The methods for calculating the elliptical cone’s geometric parameters of multiple elliptical cone sliders were improved by introducing expression of elliptical path in 3D space. This elliptical path is the intersecting line of a cone and inclined cutting plane. Based on upper-bound limit analysis method and an improved method, Sequential Quadratic Programming (SQP) method was employed to obtain optimal upper bound solutions of failure pressure. The effectiveness of this method was verified by a comparative analysis, and a detailed parametric study on the failure pressure and failure modes was presented. In this study, the stability and failure modes of tunnel face are significantly affected by internal friction angle φ and dimensionless parameter C/D for both active and passive failure; by contrast, dimensionless parameters γD/c and σs/c have small effects. It is also found that dimensionless parameters C/D and σs/c have no effect on the results if the failure region does not reach the ground surface.


tunnel face active and passive failure expression of elliptical path 


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Copyright information

© Korean Society of Civil Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • LianHeng Zhao
    • 1
  • DeJian Li
    • 1
  • Feng Yang
    • 1
    Email author
  • Liang Li
    • 1
  • Xiao Cheng
    • 1
  1. 1.School of Civil EngineeringCentral South UniversityChangsha, HunanChina

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