Three-dimensional slope dynamic stability reliability assessment based on the probability density evolution method

The dynamic stability of a slope is an important problem in geotechnical engineering, especially when subjected to a strong earthquake. In this paper, an efficient calculation method for the time-history analysis of the dynamic stability of a 3D slope is developed, which is combined with the probability density evolution method (PDEM) to establish a reliability evaluation method for the dynamic stability of a 3D slope. A newly developed dimensional-reduction spectrum-random function method combined with the stochastic process of ground motion provides an effective method for the stochastic seismic reliability analysis of complex nonlinear 3D slopes. Finally, the stochastic dynamic response and reliability analysis of 2D and 3D slopes are performed based on a safety factor, and then the extreme distribution probability is obtained. The results show that the seismic dynamic response of the 3D slope is larger than that of a 2D slope because of the three-dimensional effect. In addition, the probability density of the safety factor has a wider range of distribution in the three-dimensional situation. Therefore, the 3D slope has a higher risk when subjected to seismic excitation, and it is necessary to study the dynamic stability and reliability for some important slopes using 3D models in practical engineering. Moreover, the time-history analysis method of the dynamic stability of a 3D slope established in this paper can directly obtain the range and specific location of the slope instability failure and can provide a reliable basis for the prevention and reinforcement of landslides.