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At present, there are still some gaps in the theoretical calculation of the permanent displacement of the multi-stage loess slope under the action of earthquake. Therefore, this paper firstly uses the GEO-Studio finite element software to explore the influence of the comprehensive slope rate on the permanent displacement when the slope rate of each grade of multi-stage loess slope changes and the stage of multi-stage slope changes. The results show that it is feasible to use the comprehensive slope rate to calculate the permanent displacement of the sliding body of the multi-stage loess slope under the action of earthquake. On the basis of this conclusion, in order to simplify the calculation of permanent displacement of potential sliding soil, the other geometric parameters of the multi-stage loess slope are replaced by the comprehensive slope rate, combined with the Newmark slider displacement analysis method and energy conservation principle, and then the calculation method of permanent displacement of potential sliding soil of multi-stage loess slope under the action of earthquake is deduced. Through an example, the permanent displacement calculated by the proposed algorithm are compared with those calculated by the PLAXIS 3D software and GEO-Studio software. The results show that the permanent displacement calculated by this method is close to that calculated by the GEO-Studio software, and the difference is only 2%, and thus, the rationality of the proposed method for calculating the permanent displacement of the multi-stage loess slope under the action of earthquake is verified. The algorithm proposed in this paper provides a theoretical reference for the calculation of the permanent displacement of multi-stage loess slope under the action of earthquake.

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