Abstract
AbstractTime 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.
Highlights
Analytical solutions are invaluable to gather understanding of the physical generation of deformations and stresses taking place during the excavation of tunnels
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
Analytical expressions of the stresses and displacements in the rock for deeply buried elliptical tunnels excavated in viscoelastic rocks were derived accounting for sequential excavation processes
Summary
Analytical solutions are invaluable to gather understanding of the physical generation of deformations and stresses taking place during the excavation of tunnels. It is very difficult to obtain analytical solutions for most of the viscoelastic problems, especially in case of time-dependent boundaries, some closed-form solutions have been developed (Brady and Brown 1985; Gnirk and Johnson 1964; Ladanyi and Gill 1984) In all these works, only tunnels with circular cross-section are considered, with the excavation being assumed to take place instantaneously. The analytical solutions here introduced can be employed to predict tunnel convergence to assess whether the presence of a lining would be necessary in the preliminary design phase They allow obtaining a first estimate of the magnitude of the excavation-induced displacement field before installation of linings. Several dimensionless charts of results are plotted for the ease of use of practitioners
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