Analytical solution for deformation of an existing tunnel induced by undercrossing twin tunnels considering rotational and shearing effects of joints

Excavating new twin tunnels can induce asymmetric deformation of the existing shield tunnel above them, potentially triggering issues such as segment cracking and water ingress. A streamlined analytical solution is proposed to assess the impact of twin-tunnel construction on the tunnel above. Within the mechanical model for tunnel deformation analysis, the existing tunnel is regarded as a series of short beams on a Kerr foundation, linked by compressive, tensile, and shear springs. The tunnel deformation contains the contributions from the joints’ rotational and shearing effects. Based on the superposition principle, the Loganathan-Polous solution is used to calculate the additional stress on the existing tunnel induced by the twin tunneling underneath. The energy variational governing equation is established based on the minimum potential energy principle to derive the analytical solution for the deformation of the existing tunnel. The effects of the horizontal distance between the new twin tunnels, the clearance distance between the new tunnels and the existing tunnel, and the bolt stiffness on the existing tunnel are quantified via parametric analysis. Two case studies showed that the tunnel settlements predicted by the proposed solution agreed well with field measurements, thus verifying the validity of the developed solution.