Current theoretical researches on shield tunneling induced existing metro tunnels deformation generally simplify the existing tunnels as Euler-Bernoulli beams without joints

neglecting the tunnel shear deformation and the local stiffness reduction caused by joints. Additionally

the existing foundation model theory rarely incorporates the coordination between lining cross-section and soil deformation. The study utilizes the Loganathan and Polous method to establish the shield tunneling-induced soil greenfield. To account for the local stiffness reduction

the paper then treats the existing tunnel as a Timoshenko beam

with the tunnel stiffness function varying along the axis. By combining the energy principle and the Mindlin solution

the paper stablishes the tunnel displacement equation considering the coordinated constraint between tunnel and soil. The soil greenfield is applied to the tunnel

resulting in longitudinal deformation

which is solved by Fourier series. Finally

the Fourier energy variational solution is verified by three sets of engineering data

achieving good consistency. To conduct parameter analysis

the relative effects among factors such as bending stiffness

shear stiffness

joint action

soil parameters and space relationship are also adopted. Analysis results indicate that the theoretical solution considering the coordinated constraints of cross-section aligns more closely with the field data. Tunnel displacement results obtained without considering the coordination constraints tend to be larger. The local stiffness weakening effect of joint will cause significant sudden variations in tunnel bending moments along the axis. The increase in both bending and shear stiffness coefficients leads to a decrease in the bending moment of the tunnel structure. Changes in shear stiffness coefficient from low to high would result in a three-stage process of the tunnel deformation mode

which is from bending controlled stage to bending-shear mixed stage and then to shear controlled stage. As the tunnel deformation mode enters the shear-controlled stage

the effect of bending stiffness coefficients gradually weakens. An increase in the joint coefficient generally causes a decrease in the bending moment of the tunnel

but the impact is slight as the bending coefficient increases.