The convergence-confinement method

The convergence-confinement method provided an important breakthrough in the development of roadway and tunnelling engineering. One of the main disadvantages of this methodology is that ground reaction curves (GRC) for tunnels can only be analytically calculated for very restrictive initial conditions. So although the method permits understanding different issues on the excavation and support procedure, it cannot be directly applied to many real cases. In this work, the authors have tried to overcome some of these limitations for circular excavations under non-hydrostatic loading by means of numerical modeling. In order to show that numerical calculation of GRC by means of numerical techniques is accurate enough, curves are obtained numerically in some cases in which the semi-analytical solution is available. Finally, some examples are presented for cases in which it is not possible to obtain GRC according to semi-closed-form solutions. These include excavations in perfect elastoplastic continua under highly non-hydrostatic stress fields – where butterfly shape plastic zone is developed– and excavations under non-hydrostatic loading in strain-softening materials –where different shaped softening and residual plastic zones are observed–. Some interesting conclusions are obtained mainly regarding the use of numerical modeling to solve these problems and also future work trends are provided.