Probabilistic Seismic Response and Time-Dependent Reliability Evaluation of Pile-Group Foundations Using PDEM

Pile-group foundations exhibit highly nonlinear seismic behavior due to coupled pile-cap inertia, kinematic soil–pile interaction (SPI), and nonlinear soil response under strong earthquakes. Existing studies have not yet systematically captured the coupled stochastic response and time-dependent reliability evolution of pile groups, particularly the interaction between earthquake ground motion (EGM) uncertainty and group effects. To address this issue, this study develops a probability density evolution method (PDEM)–based framework for stochastic seismic analysis and time-dependent reliability assessment of pile-group foundations. The framework incorporates physics-based nonstationary stochastic EGM modeling, nonlinear pile-cap-soil-water coupling, and a dual-scale performance criterion that links local strain demand with global displacement demand. Results show that stochastic EGMs induce pronounced dispersion and non-Gaussian evolution of pile responses. Boundary piles, subjected to stronger inertial-kinematic coupling, exhibit response amplitudes 30%–40% larger than those of the center pile. The time-dependent reliability displays a nonsmooth, stepwise degradation pattern, with a particularly pronounced reduction as peak ground acceleration (PGA) increases from 0.4 g to 0.6 g . Moreover, reliability evaluated using strain-based criteria is systematically 10%–30% lower than that based on displacement criteria, indicating that local strain demand is more sensitive to early nonlinear damage accumulation.