Mathematical modeling of the displacements dynamics of landslide slopes under the conditions of technogenic impacts

The article discusses the features of mathematical modeling of the stress-strain state of landslide slopes to predict their movements. Regular control and monitoring of exogenous geological processes are important elements of a qualitative assessment of landslide events, including both the timely identification of areas with the greatest danger and the elimination of their consequences. The natural and technogenic features of the study area are considered. The previous results of the processing of geodetic observation data are presented, which are the basis for mathematical modeling of the stress-strain state of landslide slopes and for predicting their movements. Based on the Fourier transform, a spectral study of the vertical displacements of landslide signs was carried out and an analysis of the obtained spectrograms was made. Modeling of movements of landslide slopes subject to technogenic impacts (blasting and removal of a large amount of soil) is implemented on the basis of a forecast dynamic model. The model is presented in a recurrent form in the form of the first two conditional moment functions, which made it possible to predict the movements of controlled landslide slopes with a sufficiently high accuracy.