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The vibration impact force from the long-term operation of a subway affects the comfort of the residents living above the superstructure and the long-term settlement deformation of the tunnel foundation. A method for evaluating the dynamic responses of superstructure–tunnel systems is important, especially because of the randomness of vibration impact force. The coupling effect of the randomness of train-vibration excitation and the nonlinearity of the geotechnical properties that are subjected to dynamic action leads to challenges in the evaluation of the performance of superstructure–underground tunnel–soil systems under train vibration. In this study, a stochastic dynamic model of subway vibration-load excitation was established; then, the time histories of samples with rich probability characteristics in the same set system were generated. According to the nonlinear dynamic finite element analysis, several nonlinear dynamic responses of the deterministic superstructure–tunnel soil-foundation system were obtained. Finally, the probabilistic performance evolution of the superstructure–tunnel soil-foundation system was obtained by integrating the first-passage and probability density evolution theories, and the long-term deformation performance of the tunnel foundation was evaluated using time-varying reliability. This study presents a novel probabilistic method and a more objective performance index for the dynamic performance assessment of superstructure–underground tunnel–soil systems that are subjected to subway-traffic excitation.

A reliable assessment and design of engineering structures requires appropriate estimation and consideration of different sources of uncertainty. The randomness of seismic ground motion is one major uncertainty that needs to be considered from the perspective of performance-based earthquake engineering. To properly account for this uncertainty and its corresponding effect on pile foundations, a stochastic seismic response analytical framework based on a probability density evolution method and a stochastic ground motion model is proposed for the nonlinear stochastic seismic response analysis of pile foundations. A three-dimensional finite element model of a reinforced concrete pile with a large diameter embedded in the soil foundation is firstly established and calibrated using the full-scale lateral load test results from the literature, in which the nonlinear behavior of soil, the soil–pile interaction, the concrete damaged plasticity, and the steel yielding of the pile are properly modeled. Then, the calibrated three-dimensional numerical model is employed as an illustrative example for the stochastic seismic response analysis using the proposed framework. The mean, standard deviation, and probability density function of pile settlement and the dynamic reliabilities of the pile concerning various performance requirements are obtained in the present study. The settlements of the pile show great variability under the excitation of various stochastic ground motions, and the maximum mean value of the pile settlements is about 8 mm. The changing shape of the settlement probability density functions in every moment demonstrates that it is unreasonable to use assumed probabilistic distribution models to characterize the seismic responses of pile foundations during a seismic reliability analysis. Based on the proposed method, it is found that the dynamic reliabilities of the selected reinforced concrete pile concerning four different performance levels are 0, 0.1293, 0.8247, and 1, respectively. The proposed stochastic seismic response analytical method in the present study can provide a proper and comprehensive way to quantify various uncertainties and their corresponding effects on the seismic performance of pile foundations. It can also be used to estimate the actual reliability level of pile foundations that are designed by the current codes when they are subjected to seismic loads.