A novel method for time-dependent small failure probability estimation of slope instability subjected to stochastic seismic excitations

The computational demand limits the estimation of small failure probabilities in geotechnical engineering under seismic excitation. This study proposes a novel method to estimate the time-dependent small failure probability of slope instability under non-stationary random seismic excitation. Initially, the kernel density estimation (KDE) with appropriate bandwidth is employed for preliminary estimation with the permanent displacement time history is utilized as the evaluation metric for the extreme value distribution (EVD). Subsequently, the EVD is refined using a two-step approach: a shifted generalized lognormal distribution (SGLD) models the main components, while a quadratic function models the tail, enabling the derivation of probability of exceedance (POE) curves on a logarithmic scale. The proposed method's effectiveness is verified through examples of soil and rock slopes subjected to non-stationary random seismic excitation, comparing direct KDE and Monte Carlo simulation (MCS). Results show that the method accurately estimates small failure probabilities of slope instability, has strong numerical stability and flexibility for various slope conditions.