Analytical solutions for stresses and displacements of tunnels under static and seismic loading

Abstract

Analytical solutions can quickly and simply evaluate stresses and displacements in tunnels and are widely adopted in the preliminary design phase of tunnels. Tunnels must be able to withstand static loading and seismic loading. This paper proposes new analytical solutions for the stresses and displacements of tunnels under static and seismic loading. The tunnel lining is treated as a thick-walled cylinder. Moreover, the contact stiffness coefficient k0 and the stress release coefficient η0 are introduced to consider the arbitrary contact conditions at the ground–lining interface and the amount of excavation unloading. The new analytical solutions are verified by comparison with finite element analysis results. The results demonstrate the accuracy and applicability of the proposed analytical solutions. In addition, parametric analyses are conducted to explore the effects of the stress release coefficient η0 and stiffness coefficient k0 at the ground–lining interface, as well as the incident angle α of shear waves. The analysis results indicate that the proposed analytical solutions offer satisfactory performance and can be applied as an effective tool for preliminary tunnel design.