Analytical Solution to Estimate the Effect of Underlying Tunnel Excavations on the Existing Tunnel

The tunneling underlying inevitably leads to the displacement of adjacent soil, greatly influencing the deformation of the tunnel above. Most theoretical studies primarily concentrate on analyzing the mechanical equilibrium of individual tunnel sections, ignoring the energy generated by the system during tunnel deformation. Based on this, in view of the energy relationship, the overlying tunnel's deformation is simulated by using the Rayleigh–Ritz method. Further, its potential energy equation can be established based on the Vlasov foundation. The corresponding energy variational solution is solved according to the minimum potential energy principle, leading to an analytical solution for the shield tunneling‐induced overlying tunnel's response. The efficacy of the suggested method is verified by contrasting it with centrifuge experiments and field case studies derived from prior studies. Relative to the Winkler foundation model, which deviated from the suggested approach, the results derived from the suggested method show a closer correlation with the collected measurement data. Further parameter studies show that the vertical clearance and skew angle between two tunnels, the volume loss rate, and elastic modulus are significant factors affecting the tunnel behaviors due to tunneling underneath. The suggested theoretical model can be applied to forecast potential risks that an existing tunnel may encounter during the excavation of a new tunnel underlying in similar engineering projects.