Multi-Level Loess Slope Displacement Calculation Based on Lumped Mass Method

Earthquakes are highly unpredictable and often lead to secondary disasters such as slope collapses, landslides, and debris flows, posing serious threats to human life and property. To explore how multi-stage loess slopes respond to seismic loading, improve both the efficiency and precision of seismic analysis, and better capture the random characteristics of earthquakes in reliability assessment, this research proposes a new analytical framework. The approach adopts the pseudo-dynamic method, divides the slope soil into layers through the lumped mass scheme, and applies the Newmark-β integration method to construct a displacement response model that incorporates seismic variability. By comparing and analyzing results from Geo-Studio finite element simulations, the study reveals the dynamic response behavior of multi-level loess slopes subjected to seismic loads. The key findings are as follows: (1) The formation of unloading platforms introduces a graded energy dissipation effect that significantly reduces stress concentration along potential sliding surfaces; (2) The combined influence of the additional vertical load from the overlying soil and the presence of double free faces has a notable effect on the stability of secondary slopes; (3) The peak displacement response exhibits a nonlinear relationship with slope height, initially increasing and then decreasing. The proposed improved analysis method demonstrates clear advantages over traditional approaches in terms of computational efficiency and accuracy, and provides a valuable theoretical basis for the seismic design of high loess slopes.