Complex Variable Solutions for Soil and Liner Deformation due to Tunneling in Clays

Abstract

Current research to predict the soil deformation due to tunneling pays little attention to the impact of soil–liner interaction. Moreover, the conventional solution for the stress function method has an inherent physical defect that leads to a nonzero ground displacement at infinity. To overcome these disadvantages, an analytical solution by the complex variable method is presented for problems in evaluating the liner and disturbed surrounding soil deformation due to tunneling in clays. The interaction mechanism between tunnel liners and surrounding soils is considered in this study, and the deterministic nonuniform convergence boundary model is composed as the displacement controlled condition on tunnel opening. The applicability of the proposed method is observed based on the existing analytical solutions and a series of field cases. It has been demonstrated that the proposed complex variable solution for the estimation of soil displacements considering the soil–liner interaction and nonuniform convergence model agrees well with the observation data. The impacts of key parameters on the tunneling-induced soil deformation are also assessed, including the tunneling gap, the soil and liner physical characteristics, and the buried depth liner thickness for the tunnel. In addition, the effects of the liner thickness and buried depth on the circular expression of liner deformation, including the radial and tangential displacements, are investigated by the parametric analyses considering the soil–liner interaction mechanism. To consider the liner stiffness influence and the nonuniform convergence boundary condition, the complex variable solution in this study can be regarded as an effective approach to conservatively predict the soil and liner deformation.