Improved Longitudinal Displacement Profiles for Convergence Confinement Analysis of Deep Tunnels

Convergence-confinement analysis for tunneling is a standard approach for preliminary analysis 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 deformations 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 parameters 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.