Rock Mech Rock Engng (2009) 42: 131–146 DOI 10.1007/s00603-009-0176-4 Printed in The Netherlands Improved Longitudinal Displacement Profiles for Convergence Confinement Analysis of Deep Tunnels By N. Vlachopoulos 1 , M. S. Diederichs 2 1 Royal Military College, Ontario, Canada 2 Queen’s University, Ontario, Canada Received December 2 2008; Accepted February 23 2009; Published online April 17 2009 # Springer-Verlag 2009 Summary Convergence-confinement analysis for tunneling is a standard approach for preliminary anal- ysis of anticipated wall deformation and support design in squeezing ground. Whether this analysis is performed using analytical (closed form) solutions or with plane strain numerical models, a longitudinal displacement profile (LDP) is required to relate tunnel wall deforma- tions at successive stages in the analysis to the actual physical location along the tunnel axis. This paper presents a new and robust formulation for the LDP calculation that takes into account the significant influence of ultimate (maximum) plastic radius. Even after all param- eters are appropriately normalized, the LDP function varies with the size of the ultimate plastic zone. Larger yield zones take a relatively longer normalized distance to develop, requiring an appropriately calculated LDP. Failure to use the appropriate LDP can result in significant errors in the specification of appropriate installation distance (from the face) for tunnel support systems. Such errors are likely to result in failure of the temporary support. The equations presented here are readily incorporated into analytical solutions and a graphical template is provided for use with numerical modeling. Keywords: Tunnelling, convergence-confinement, displacement, squeezing, ground reaction 1. Introduction Convergence-confinement analysis (Duncan-Fama, 1993; Panet, 1993, 1995; Carranza- Torres and Fairhurst, 2000 and others) is a widely used tool for preliminary assess- ment of squeezing potential and support requirements for circular tunnels in a variety Correspondence: M. S. Diederichs, Associate Professor, Queen’s University, Ontario, Canada e-mail: mdiederi@geol.queensu.ca