Appropriate Uses and Practical Limitations of 2D Numerical Analysis of Tunnels and Tunnel Support Response

• Published in: Geotechnical and geological engineering 2014-04, Vol.32 (2), p.469-488
• Main Authors: Vlachopoulos, Nicholas, Diederichs, Mark S.
• Format: Article
• Language: English
• Subjects: Algorithms; Civil Engineering; Convergence; Dimensional analysis; Displacement; Dredging; Earth and Environmental Science; Earth Sciences; Excavation; Finite difference method; Finite element method; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Internal pressure; Mathematical analysis; Mathematical models; Numerical analysis; Original Paper; Staged; Strain analysis; Stresses; Terrestrial Pollution; Three dimensional analysis; Three dimensional models; Tunnel construction; Tunnel supports; Tunnels; Tunnels (transportation); Two dimensional; Two dimensional analysis; Two dimensional models; Waste Management/Waste Technology
• ISSN: 0960-3182; 1573-1529
• DOI: 10.1007/s10706-014-9727-x

In spite of the gradual development of three-dimensional analysis packages utilizing finite element models or finite difference algorithms for stress–strain calculations, two-dimensional (2D) analysis is still used as the primary engineering tool for practical analysis of tunnel behavior and tunnel support performance for design—particularly at the preliminary stage of a project. The applicability of 2D finite element analysis or analytical convergence confinement solutions to staged support installation depend on the application of an assumed or validated longitudinal displacement profile. Convergence in commonly applied 2D staged models is controlled by boundary displacement or internal pressure relaxation. While there have been developments to improve this methodology, this often assumes independence between the ground reaction curve and the support resistance, independence between the longitudinal displacement profile to support application, and the assumption that non-isotropic stresses and non-circular geometries can be handled in the same way as circular tunnels in isotropic conditions. This paper examines the validity of these assumptions and the error inherent in these extensions to 2D tunnel analysis. Anisotropic stresses and lagged (staged) excavation present a particular problem. Practical solutions are proposed for support longitudinal displacement LDPs in simplified conditions.