Geotechnical and Geological Engineering

, Volume 36, Issue 5, pp 3281–3309 | Cite as

Explicit Procedure and Analytical Solution for the Ground Reaction Due to Advance Excavation of a Circular Tunnel in an Anisotropic Stress Field

  • Yu-Lin Lee
Original Paper


The convergence–confinement method applied in boring a circular tunnel through a rock-mass assumed to be subject to a non-hydrostatic stress is investigated. The closed-form analytical solutions of the stresses/displacements in the elastic region and plastic region for the ground reaction due to excavation of the tunnel in an anisotropic stress state field are presented in a theoretically consistent way. The explicit procedure realized the analytical solution to an executable computation that can be estimated using a simple spreadsheet. The validity of the procedure for the analytical solution was examined by numerical analysis to investigate the influence of in situ stress ratio on the ground reaction curve, the stress path at the intrados of the tunnel, and the distribution of stresses/displacements on the cross-sections of a circular tunnel. The agreement between the finite element results and the proposed closed-form solutions with the explicit procedure was found to be excellent.


Tunneling Convergence–confinement method (CCM) Confinement loss Anisotropic stress field Analytical solution Explicit procedure 



The author appreciates the financial support of the National Science Council of Taiwan (Project Nos.: NSC 96-2221-E-216-020-MY2 and NSC 97-2221-E-216-020-MY2).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringChung-Hua UniversityHsinchuTaiwan, ROC

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