Hydro‐Mechanical Viscoelastic Analytical Solutions for Deeply Noncircular Tunnels Constructed in Saturated Time‐Dependent Ground

ABSTRACT When noncircular tunnels are constructed in the time‐dependent rock mass, stress and displacement around the tunnels are time‐dependent. Furthermore, when considering the influence of seepage flow, the ground responses are more complex. In this study, hydro‐mechanical viscoelastic analytical solutions are developed for deeply noncircular tunnels constructed in saturated time‐dependent ground. In the determining procedures, analytical solutions are developed to describe the temporal and spatial distributions of stress and displacement around arbitrarily shaped tunnels, by employing the complex variable theory. These solutions are derived from both fractional‐order viscoelastic models and classical viscoelastic models through the correspondence principle, considering factors such as time‐varying pore pressure, longitudinal advancement, and non‐uniform initial stresses in the model. Finally, the detailed explicit formulations of viscoelastic analytical solutions are developed by the separation of variables in the potential function. As a verification step, a good agreement is observed between the proposed analytical solutions and numerical predictions. In the parametric investigation, the mechanism of ground responses versus time and locations is analysed. Meanwhile, sensitivity analyses are performed to investigate the effect of viscoelastic model selections on ground behaviours. It is found that the stability of the opening progressively decreases with the increase in rheological time. In summary, the proposed solutions offer an alternative and efficient approach to predict the time‐dependent ground behaviour around tunnels, taking into account the influence of seepage flow.