Evaluation of the Tunnel Face Stability through a Ground Stress Analysis with a Hemispherical Geometry Approximation

The evaluation of the stability of the excavation face is an important aspect in the design of a tunnel. When it is not possible to ensure excavation face stability in natural conditions, it is in fact necessary to intervene with remarkably costly reinforcement operations. The analysis of the stability conditions of an excavation face can be conducted, with a certain degree of detail, through numerical modelling. Simplified analytical models exist for shallow tunnels, but fewer are available for deep tunnels. One of the analytical methods most commonly used in the study of the stress conditions at the excavation face in deep tunnels is described in this study: The convergence-confinement method adapted to a spherical geometry. This method has here been extended to rock masses, which present a more complex rupture criterion (curved and not simply linear) than that of soils. The presented solution is of a finite difference numerical type. An extensive parametric analysis conducted on soils and rock masses has led to the estimation of the maximum lithostatic stress that still foresees the absence of a plastic zone around the hemisphere, which has been used to represent the excavation face. Therefore, this study makes it possible to obtain a preliminary estimation of the maximum depth of a tunnel in a certain type of soil or in a rock mass in which it is still possible to advance without the necessity of excavation face reinforcement operations. However, a more detailed and reliable analysis still requires more sophisticated instruments, such as numerical modelling.