Direct Calculation Method for the Analysis of Non-linear Behavior of Ground-Support Interaction of a Circular Tunnel Using Convergence Confinement Approach

The convergence-confinement method is widely used in conventional tunneling at a preliminary stage of the support design. A circular tunnel through the ground in an initially isotropic stress state and the behavior of ground-support interaction simplified utilizing a two-dimensional plane-strain are postulated. From a point of view of practical application, the direct algorithm process so-called the direct calculation method (DCM) is proposed in this paper to deal with solving the solution of stresses/displacements between the ground reaction curve (GRC) and the support confining curve (SCC) in the final equilibrium state by applying the simultaneous equations in the elastic region and using the numerical analysis known as the Newton recursion method for finding roots of the non-linear equations in the plastic region. This explicit procedure also can realize the analytical solution to an executable computation that can be stepwise estimated by using a simple calculation spreadsheet. The validity of the developed method for the analytical solution was examined by the finite element analysis (FEM) to investigate the influence of mechanical properties of the ground and the time-dependent effects of the shotcrete lining-support on the GRC, SCC and stress path at the intrados of the tunnel. The agreement of results between DCM and FEM was found to be excellent in the elastic and elastic-perfectly plastic media.