Probabilistic density evolution analysis of seismic tunnel response considering soil spatial variability

Soil parameters typically exhibit significant spatial variability. For tunnel structures, seismic responses are strongly influenced by the properties of the surrounding soil. To quantify the impact of such uncertainty on structural safety, this paper proposes a probabilistic method for seismic damage analysis of tunnel structures that accounts for soil spatial variability, using an improved dimension‑reduction spectral representation method. The enhanced method requires only two random variables to generate a non‑stationary random field that reasonably captures the statistical depth-dependent characteristics of soil parameters. Subsequently, by incorporating the probability density evolution method, the probabilistic evolution law of tunnel seismic responses under spatially variable soil conditions is revealed, enabling efficient computation of the exceedance probabilities for different damage states. The results indicate that accounting for soil spatial variability significantly expands the uncertainty range of structural responses, whereas conventional deterministic designs that assume a homogeneous soil stratum may underestimate local damage risks in tunnel sections. This study provides an effective approach that balances computational efficiency and result reliability for incorporating soil spatial variability into tunnel seismic response analysis, thereby offering a scientific basis for rationally setting safety margins in seismic design.