Critical safe distance of shield tunnels crossing pile foundation of existing bridges at orthogonal side

In order to investigate the safe construction distance of shield tunnel crossing the pile foundation of the existing bridges, taking the crossing construction at the orthogonal side as an example and considering the influences of the pile shear effects, we use the Pasternak two-parameter foundation model to establish the equilibrium differential equations for the horizontal displacements of the soil in the middle of the pile foundation of the existing bridges and the tunnels under construction, and the analytical solutions for the horizontal displacements of the pile-tunnel intermediate soil are derived. Based on the cusp catastrophe theory, the standard expression for the potential function of the pile-tunnel intermediate soil and the sufficient and necessary conditions for its system to be suddenly destabilized are determined. Accordingly, the method for calculating the critical safe distance of the pile foundation of the existing bridges is established, and its engineering applicability is verified through the numerical simulations and field measurements. The method is used to analyze the main influencing factors for the critical safe distance of the pile foundation of an existing bridge. The results show that the critical safe distance is approximately an exponential function with the diameter ratio of the pile foundation of the bridge, and the two parameters are positively correlated, while it follows a quadratic function of the shield tunnel depth ratio, and first increasing and then decreasing as the depth ratio increases, and reaches the maximum value when the depth ratio of the shield tunnel is 8.1. The theoretical values obtained by the proposed method and the estimated ones by the numerical simulation are well fitted, and the measured results and the relevant specifications also further verify the engineering applicability of this method. The proposed method provides theoretical guidance for the rational development of the design and construction program of similar tunnel crossing projects.