Fluctuation characteristics of probability density function and first-passage dynamic reliability of slope systems under seismic excitations

Abstract

Dynamic reliability based on the full time-history domain analysis is an important result of slope dynamic analysis when random factors are considered and also a useful tool to consider the strong coupling effect of seismic ground motions and nonlinear characteristics of rock and soil parameters. However, the effect of failure time associated with the first passage event in the time history process is seldom considered. To effectively evaluate earthquake-induced geological disasters, a probabilistic simulation method of slope stochastic dynamic reliability considering the randomness of seismic ground motions and the failure time is proposed. Clough and Penzien power spectrum model is used to simulate the non-stationary and random physical properties of seismic ground motions. Stochastic dynamic reliability analysis based on a coupling method of finite element method and limit equilibrium method (FEM-LEM) is performed considering the triggering mechanism of slope failure, integrated with Monte Carlo Simulation (MCS) and first-passage theory to obtain probability density functions (PDFs) of factor of safety (FOS) and displacement indicators, and their fluctuation characteristics with time and different peak ground acceleration (PGA) levels. The results showed that dynamic reliability of slope in the whole seismic history may be overestimated when first passage event is not considered in the evaluation of slope nonlinear dynamic time-history stability. PDFs of FOS had a significantly non-Gaussian, and even skewed distribution during slope nonlinear failure process. Normal distribution hypothesis may be unreasonable when calculating dynamic reliability of FOS index and should be used carefully for slope system under strong seismic loading. Finally, slope stochastic dynamic reliability time-history curves based on first-passage event was obtained within safety domain to provide new perspective for the performance-based seismic design of slope engineering under different seismic fortification levels and needs.