Viscoelastic analytical solution for shallow tunnel considering time-dependent displacement boundary

Abstract

A time-dependent unified displacement function is proposed to capture main deformation responses of the tunnel cross-section. When the expansion order n equals 2, this complete displacement mode is used as displacement boundary condition (DBC) of the tunnel cross-section. Complex variable method is adopted in order to obtain an elastic analytical solution. Considering the time effect of ground mechanical parameters and tunnel cross-section deformation, a viscoelastic analytical solution of ground displacement is obtained. By parametric analyses, time effects of settlement trough curve, ground displacement and the settlement at the center point of ground surface are analyzed.