Permanent Displacement Analysis of Multistage Loess Slopes with Multiple Slip Surfaces Based on Energy Methods

As an important basis for slope stability evaluation, the permanent displacement of the slope has been widely used in the seismic design of slope engineering. This paper aims at the situation of multiple slip surfaces and multiple sliding masses in multistage loess slopes under earthquake action. After fully discussing the occurrence of two and three slip surfaces and the successive sliding of each sliding mass of the multistage loess slope under the action of an earthquake, combined with the principle of energy conservation of slope soil and Newmark slider analysis method, the calculation model of multistage loess slope sliding with multiple slip surfaces is established and the calculation method of multistage loess slope sliding with multiple sliders based on energy method is proposed. The positive and negative critical acceleration of each sliding mass is calculated according to the interaction of forces between each sliding mass, and then the influence of slope slip surface inclination and soil parameters on the positive and negative critical acceleration is discussed. Finally, the permanent displacement expression of each sliding mass is obtained by solving the energy equation. The research conclusion is drawn through the verification of an example: the results obtained by the quasi-static method of GEO-Studio (version 2012) numerical simulation software are close to each other, with a difference of 6%. If the peak value of seismic acceleration is small and the inclination of the slip surface is large, the negative critical acceleration may not be considered when calculating the permanent displacement of sliding mass of multistage loess slope under seismic action.