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

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 dis-tribution 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 ob-tained within safety domain to provide new perspective for the performance-based seismic design of slope en-gineering under different seismic fortification levels and needs.

Automated summary

This paper proposes a probabilistic simulation method of slope stochastic dynamic reliability considering the randomness of seismic ground motions and the failure time. The method combines the finite element method and the limit equilibrium method, along with Monte Carlo Simulation and first-passage theory, to obtain probability density functions and fluctuation characteristics of factor of safety and displacement indicators. The results indicate the importance of considering the first passage event in the evaluation of slope nonlinear dynamic time-history stability and suggest caution in using normal distribution hypothesis for slope systems under strong seismic loading.