Since the permanent displacement induced by earthquake can be regarded as an effective criterion for stability estimation and anti-seismic design of slopes, a new method for evaluating the displacement and improve its estimating accuracy was proposed. The forward and reverse critical acceleration of potential landslide were derived based on the limit analysis upper bound theorem, and the influence of sliding surface angle and vertical acceleration on critical acceleration was then discussed. According to the principle of energy conservation, the energy response equations of landslide system were established, the process of energy transferring, transforming and dissipating during earthquake were analyzed. A permanent displacement calculation formula of the slope with energy method was presented. In addition, the contribution of gravitational potential energy to permanent displacement was analyzed. Result showed that the reverse displacement can not be neglected when the slope has a small angle of sliding surface and weak stability, while the earthquake is strong. The critical acceleration will become an acceleration time history varying with time when take the vertical acceleration into account. Farther precision in displacement calculation can be reached via considering the effect of reverse critical acceleration and vertical acceleration wholly. Earthquake plays an important role on triggering landslides, and the permanent displacement is mainly determined by gravitational potential energy.
