A three-dimensional finite element model considering the influence of groundwater on soil and bridges was established based on a deep foundation pit excavation project, in order to study the impact of additional displacements of high-speed railway bridge piers caused by adjacent foundation pit excavation on railway operation safety. The single factor sensitivity of additional displacements of high-speed railway bridge piers was analyzed. The Box-Behnken Design (BBD) experimental design method combined with the support vector machine algorithm (SVM) was used to establish a displacement prediction model for the top of high-speed railway bridge piers. By combining the Monte Carlo method, 10⁷ sampling calculations were performed on the parameters to obtain the reliable probability of additional displacements at the pier top. The research results showed that the change in the distance between the foundation pit and the high-speed railway bridge pier had the greatest impact on the horizontal and vertical displacements at the pier top. Among the eight different combinations of hyperparameters of the SVM model, the maximum error between the prediction values of the optimal model and the finite element calculation values was within 6%, indicating that the optimal model could replace the finite element for calculation. Under the limit of 2 mm lateral displacement at the pier top, the reliability probability of lateral additional displacement at pier top was 33.12% when the distance between the background engineering foundation pit and the bridge pier was 35 m; when the distance increased to 39 m, the reliability probability of lateral additional displacement at pier top reached 99.68%. The analysis method used can avoid uncertain evaluation results caused by large discretization of soil layer mechanical parameters, providing reference for safety evaluation of similar projects.