Seismic fragility denotes the probabilities of a system exceeding some prescribed damage levels under a range of seismic intensities. Classical seismic fragility studies in slope engineering usually construct fragility functions by making some assumptions for fragility curve shape, and always neglect spatial variability of soil materials. In this study, an assumption-free method on the basis of probability density evolution theory (PDET) is proposed for seismic fragility assessment of slopes. The random input earthquakes and spatially-variable soil parameters in slope are simultaneously quantified. By the proposed method, assumption-free fragility curves of a slope are established without limiting the fragility curve shape. The obtained fragility results are also compared with those from two classic parametric fragility methods (linear regression and maximum likelihood estimation) and Monte Carlo simulation. The results demonstrate that the proposed assumption-free method has potential to gives more rigorous and accurate fragility results than classical parametric fragility analysis methods. With the proposed method, more reliable fragility results can be obtained for slope seismic risk assessment.

Seismic fragility analysis can quantitatively evaluate the seismic performance of structures from a probabilistic viewpoint and accurately characterize the relationship between the degree of structural damage and ground motion intensity. This study investigates the seismic fragility of shield tunnels in three different liquefiable and non-liquefiable soils. A plane-strain finite element model of the saturated soil and shield tunnel is established via the OpenSees computational platform employing the multi-yield surface elastoplastic PressureDependMultiYield and PressureIndependMultiYield models to simulate the constitutive behaviour of liquefiable and non-liquefiable soils. The developed model is utilized to conduct nonlinear dynamic effective stress time history analyses to generate the seismic fragility curves and surfaces based on the incremental dynamic analysis method. Meanwhile, appropriate scalar- and vector-valued intensity measures are identified based on their correlation, efficiency, practicality and proficiency. Compared with the fragility curves based on scalar-valued intensity measures, the fragility surfaces based on the vector-valued intensity measures can better describe the effect of ground motion characteristics on the structural seismic demand, and thus can more accurately assess the structural seismic performance. The seismic damage probabilities derived from the fragility curves and surfaces reveal that the seismic damage risk of the shield tunnel in sandwiched liquefiable soil deposit is higher than that of the tunnel structure located in entirely liquefiable or non-liquefiable soil profiles. This finding underscores the importance of carefully evaluating the seismic safety of shield tunnels situated in sandwiched liquefiable soil deposits.