Application of Convergence – Confinement Method in Analysis for Longitudinal Displacements in Rock Tunnel

Abstract The application of convergence-confinement analysis in tunnel engineering serves as a conventional initial approach to evaluate wall movements and devise support frameworks in scenarios involving swelling rock. This analytical technique relies on either a closed-form solution or a finite element method (FEM) utilizing a plane strain numerical model. A crucial component of this analysis is the longitudinal displacement profile (LDP), which is essential for linking the displacements of tunnel walls during the excavation process. The evaluation is performed along the tunnel’s axis. In this research, the LDP formulation proposed by Vlachopoulos and Diederichs (2009) is employed to assess how factors such as the distance supported from the tunnel face (working surface), as well as the spacing of rock bolts—both diametrically and transversely—affect the safety factor and the maximum plastic radius produced during installation. The calculations are premised on the understanding that optimal conditions are influenced by variations in the plastic zone’s size, with larger zones requiring more extended normal excavation distances. Mistakes in applying the LDP can lead to substantial errors in determining the correct distances for installing tunnel support systems, potentially resulting in failures of temporary supports. This paper details the findings obtained from the analytical solutions utilized in this investigation.