Analytical solutions for elliptical tunnels in rheological rock considering excavation

Sequential excavation is often adopted in construction of large tunnels. The analytical solutions for deeply buried elliptical tunnels in rheological rock considering the time-dependent excavation are derived. In order to simulate the design process of excavation, the values of the major and the minor axes are assumed to be arbitrarily time-dependent functions. First, the general expressions for the stresses and the additional displacements due to excavation are derived by using the complex variable method and the corresponding principle of time-dependent boundary problem. In the derivation, the inverse mapping function is introduced to detach the time variable which should participate in the Laplace transformation. Then, the explicit analytical expressions in integral form are obtained by simulating the rock mass in the Boltzmann viscoelastic model. Finally, the parametric analysis of the stresses and displacements is then performed to investigate the influence of the excavation process and the rate for different types of rock. The results show that the stresses and displacements are greatly affected by the excavation process. The proposed solutions can be used in the mechanical analysis of excavation of elliptical tunnels, and are valuable in the preliminary design of underground tunnels.