MATHEMATICAL MODEL OF THE MOVEMENT OF A VISCOUS LAYER ALONG THE SLOPE OF A HILL

Changes in the viscous layers of sedimentary rocks lead to the occurrence of landslides under the influence of gravity or other external factors. The study of the occurrence of landslides of sedimentary rocks located on the surface of high ground is an urgent problem for mountainous regions. The article suggests using the method of mechanical and mathematical modeling for such studies, as a result of which a mathematical problem on a quasi-linear equation of a parabolic type is obtained. To solve the resulting mathematical problem, a finite-difference method was used; a nonlinear implicit calculation scheme was chosen, on the basis of which an algorithm for solving the problem was formulated and a computer program was developed. Mathematical modeling of the process under consideration was carried out, as a result, a numerical experiment was conducted for various possible variants; the mechanical characteristics of clay rocks were taken as the initial data of physical parameters. The results of the study are presented in the form of graphs and tables.