Application graph theory to evaluate the stability of landslide slopes

Abstract

Evaluation of the stability of slopes is a complex and important engineering task, the solution of which requires the analysis of a significant number of factors. Many different methods of slope stability calculation have been developed to solve this type of problem. However, two groups of methods - limit equilibrium methods and the finite element method (FEM) - have become the most widely used. However, these methods have certain disadvantages. Limit equilibrium methods are limited by the assumptions used during the calculation, including the hypothesis of a solid compartment, which does not allow analyzing the stress-strain state. The FEM of the elements does not make it possible to unambiguously localize the sliding surface of the slope, and the determination of the stability coefficient using the method of reducing the strength of the soil requires a large number of complex iterative calculations. The methods and approaches of graph theory can be used precisely to combat the shortcomings of FEM. The paper examines the basics of graph theory. The main methods of specifying graphs, as well as certain types of graphs with an indication of their key features, are presented. The concept of isomorphism of graphs and some features of their graphical representation are revealed. The article presents the basic idea of using graph theory to calculate the stability of slopes. The main questions that must be solved when applying graph theory to the given type of problem are outlined. Two methods of converting a mesh of finite elements into a graph are considered in detail. The advantages and disadvantages of the proposed methods are analyzed. The transformation of the calculation scheme of an imaginary slope with a given geometry, which was simulated in the LIRA-SAPR software complex, into graphs using the above methods is demonstrated. An overview of the approaches that can be used to create a graph weight function is given.