Analytical solutions of noncircular tunnels in viscoelastic semi-infinite ground subjected to surcharge loadings

Abstract The construction of noncircular tunnels at shallow depths has become increasingly common in urban areas to efficiently utilize underground space. In general, noncircular tunnels may cause high stress concentrations and large settlements. In addition, the stability of shallow tunnels affected by the structural loads/surcharge loads on the surface is too significant to ignore. This study presents new analytical solutions to efficiently predict the stresses and displacements around shallow noncircular tunnels in rheological rock. The key factors, i.e., any viscoelastic characteristics of the surrounding rock, arbitrarily distributed loads exerted on the ground surface, arbitrary tunnel shapes and pressures exerted at the internal tunnel boundaries due to liners or water pressures, are fully taken into account. A noncircular tunnel in the half-plane was mapped into an anulus by employing the conformal mapping function. Then, the elastic solutions of the problem are obtained by complex variable theory combined with the mapping function. Based on the elastic solutions and the extended corresponding principle for the viscoelastic problem, time-dependent analytical solutions are obtained for the ground assuming any viscoelastic models. The analytical solutions are verified by the good agreement between the analytical and FEM results under the same assumptions. Then, a parametric study is finally performed to investigate the influence of the location or range of the surcharge, tunnel burial depth and lateral pressure coefficient on the ground stresses and displacements. The proposed analytical solution can provide insight into the mechanical behavior of shallow noncircular tunnels under surcharge loads, as well as an alternative method in the preliminary designs of future shallow tunnels.