Analytical Solutions for Tunnels of Elliptical Cross-Section in Rheological Rock Accounting for Sequential Excavation

Time dependency in tunnel excavation is mainly due to the rheological properties of rock and sequential excavation. In this paper, analytical solutions for deeply buried tunnels with elliptical cross-section excavated in linear viscoelastic media are derived accounting for the process of sequential excavation. For this purpose, an extension of the principle of correspondence to solid media with time varying boundaries is formulated for the first time. An initial anisotropic stress field is assumed. To simulate realistically the process of tunnel excavation, solutions are developed for a time-dependent excavation process with the major and minor axes of the elliptical tunnel changing from zero until a final value according to time-dependent functions specified by the designers. In the paper, analytical expressions in integral form are obtained assuming the incompressible generalized Kelvin viscoelastic model for the rheology of the rock mass, with Maxwell and Kelvin models solved as particular cases. An extensive parametric analysis is then performed to investigate the effects of various excavation methods and excavation rates. Also the distribution of displacements and stresses in space at different times is illustrated. Several dimensionless charts for ease of use of practitioners are provided.