Analytical Method for the Deformation of an Existing Tunnel Undercrossed by New Twin Tunnels Considering Strengthening the Foundation

Abstract

The existing tunnel is protected and reinforced before excavation to control its deformation caused by new twin tunnel excavation in homogeneous foundations. In addition to soil, various other reinforced structures strengthen the foundation, which should be treated as nonhomogeneous. In this work, a simplified method is proposed to calculate the equivalent elastic parameters of inhomogeneous underground pile–beam–plate structures (PBPs). A calculation method for longitudinal deformation of soil induced by the excavation of a horseshoe-shaped tunnel considering the nonuniform deformation mode of soil is also developed. Based on the equivalent elastic parameters of PBPs and the displacement solutions of the uneven deformation model of soil, the additional stress induced by the new twin tunnels undercrossing the existing tunnel is calculated. Subsequently, a series of short beams with shear, tension, and compression springs are used as a simplified model to characterize the existing tunnel. The deformation of the existing tunnel can be solved using the principle of minimum potential energy. Finally, combined with the PBPs case, the influence of the deformation and internal forces of the existing tunnel is parametrically analyzed. The effectiveness of the analytical method proposed in the present work is validated by numerical simulation and on-site measurement.