Benchmark solutions of large-strain cavity contraction for deep tunnel convergence in geomaterials

Abstract

To provide precise prediction of tunnelling-induced deformation of the surrounding geomaterials, a framework for derivation of rigorous large-strain solutions of unified spherical and cylindrical cavity contraction is presented for description of confinement-convergence responses for deep tunnels in geomaterials. Considering the tunnelling-induced large deformation, logarithmic strains are adopted for cavity contraction analyses in linearly elastic, non-associated Mohr–Coulomb, and brittle Hoek–Brown media. Compared with approximate solutions, the approximation error indicates the importance of release of small-strain restrictions for estimating tunnel convergence profiles, especially in terms of the scenarios with high stress condition and stiffness degradation under large deformation. The ground reaction curve is therefore predicted to describe the volume loss and stress relaxation around the tunnel walls. The stiffness of circular lining is calculated from the geometry and equivalent modulus of the supporting structure, and a lining installation factor is thus introduced to indicate the time of lining installation based on the prediction of spherical cavity contraction around the tunnel opening face. This study also provides a general approach for solutions using other sophisticated geomaterial models, and serves as benchmarks for analytical developments in consideration of nonlinear large-deformation behaviour and for numerical analyses of underground excavation.