Stochastic seismic responses and seismic reliability assessment of the immersed tunnel considering the coupling effect of water-soil

The seismic response of the immersed tunnel is very complex and involves the coupling effect of water-soil. However, the existing research predominantly employs one or a few typical ground motions as loading inputs, disregarding the non-stationary nature of earthquakes. Moreover, the influence of the water is commonly overlooked. To address these gaps, this study proposes a stochastic seismic response analysis framework by integrating the probability density evolution method (PDEM) with the coupled acoustic-structural method (CASM). Firstly, non-stationary ground motions are generated based on the evolutionary power spectrum and random function theory to reflect realistic site conditions. Then, the CASM is employed to simulate the seismic response of immersed tunnels considering the coupling effect of water-soil, validated by model tests. Subsequently, Python-based secondary development enables efficient data processing, and the PDEM is used to obtain the structural stochastic seismic response considering the coupling effect of water-soil. Finally, the seismic reliability of immersed tunnels is assessed using the equivalent extreme-value events theory. The findings indicate that under 0.2 g non-stationary ground motions, water exhibits certain damping effects, which help reduce the structural seismic response. Additionally, the plastic strain of the immersed tunnel experienced three stages: the elastic stage, the elastic–plastic stage, and the plastic stage. Moreover, the structure experiences brittle damage under ground motion. This framework provides a practical and robust tool for evaluating the probabilistic seismic behavior of immersed tunnels, offering more comprehensive and representative insights for seismic design and risk assessment.