Tunnels are a vital component of urban infrastructure that must be robust against seismic hazards. Given the randomness of earthquake occurrence, the seismic response of tunnel structures mut be studied by stochastic analysis methods. To this end, this study proposes a probability density evolution method (PDEM)-based framework to investigate the seismic performance of a circular tunnel under stochastic earthquake excitation. First, a suite of nonstationary earthquake motions compatible with the seismic design code was derived using a stochastic earthquake model. Then, a series of nonlinear dynamic numerical simulations were conducted for a typical circular tunnel that considers the soil-structure interaction. Finally, using the tunnel inclination angle as the performance index, the probability density function of the structural response of the tunnel was solved using the PDEM to obtain the corresponding exceedance probabilities of the tunnel under various damage states. The results show that the PDEM-based framework can be applied to evaluate the seismic performance of circular tunnels and could serve as a reference on the seismic fragility of tunnels and underground structures.

Ground motion, geotechnical materials, and structural materials are three primary uncertainty sources in the seismic design and assessment of metro station structures. However, the effects of the latter two have often been ignored, which brings doubts about the rationality of the design and evaluation results. In this paper, based on the probability density evolution theory, the non-linear stochastic seismic analyses and reliability analyses under multi-source uncertainty conditions were carried out for a metro station structure in soft soils, and the effects of three primary uncertainty sources, i.e., ground motion, geotechnical materials, and structural materials, were explored. Random variable models were established to quantify the involved uncertainties of non-linear materials. The results showed that for underground structures, the uncertainty of geotechnical materials is nonnegligible, because it not only changes the soil-structure relative stiffness, but also changes the deformation mode of strata, resulting in both an increase in the elastic reliability and a decrease in the elastic-plastic reliability. The uncertainty source of structural materials changes the soil-structure relative stiffness, but has little effect on the lateral deformation response and elastic-plastic reliability of the station structure.