Study on the critical safety distance of shield tunnel orthogonal side passing through the pile foundation of the existing bridge

In order to investigate the safety construction distance of shield tunnel crossing the pile foundation of existing bridges, taking the construction of orthogonal side penetration as an example, considering the influence of pile shear effect, the Pasternak two-parameter foundation model was used to construct the equilibrium differential equations for the horizontal displacements of the soil in the middle of the pile foundation of existing bridges and tunnels in progress, and the analytical solutions for the horizontal displacements of the pile-tunnel intermediate soil was derived. Based on the cusp catastrophic theory, the standard expression of the potential function of the pile-tunnel intermediate soil and the sufficient necessary conditions for its system to be destabilized by mutation were determined. Accordingly, the calculation method for critical safety distance of the existing bridge pile foundation was established, and the engineering applicability of the calculation method was verified by numerical simulation and field measurements, and the method was also used to analyze the main influencing factors of the critical safety distance for the existing bridge pile foundation. The results show that the critical safety distance is approximately an exponential function with the diameter ratio of the bridge pile foundation, and the two are positively correlated, while it is approximately a quadratic function with the depth ratio of the shield tunnel, and increases and then decreases with the increase of the depth ratio of the shield tunnel, and reaches the maximum value when the depth ratio of the shield tunnel is 8.1. The theoretical values obtained by this study's method and the estimation values obtained by numerical simulation are well fitted, and the field measurement results and relevant specifications also further verify the engineering applicability of the calculation method in this study, which provides theoretical guidance for the rational development of similar tunnel crossing project design and construction program.