The FEM of limiting equilibrium based on Dijkstra algorithm is introduced to the research the long-term stability of rock-slope

and to get the long-term safety factor of the slope. And this method is applied to research the stability of the abutment high-slope at Nuozhadu Hydropower Station. Comparisons between the result by limiting equilibrium method and the result by the FEM of limiting equilibrium method in the elastic-plastic condition

show that this method is credible. The latent sliding surfaces and the safety factor of several time steps are obtained by the FEM of limiting equilibrium method based on Dijkstra algorithm. All of these are based on the stress field of corresponding time steps from visco-elastoplastic FEM result of the abutment high-slope of Nuozhadu Hydropower Station. The stability of the slope is estimated from the above result. And the curve of safety factor vs. time

and long-term safety factor of the slope are also given.