Possibilities and limits of applying the method of assessing the stability of soil massifs using FEM and graph theory

Abstract

The selection of a method for solving complex engineering problems is an integral part of any calculation process, on which the accuracy and reliability of the obtained results largely depend. At the same time, all methods and approaches, even the most universal, have certain limits of their rational application. In this case, it is important to determine the limits and possibilities of using certain methods. This paper briefly considers the limits of using a combined approach based on the finite element method and graph theory, as well as options for its use as a separate toolkit or in combination with other methods to eliminate their shortcomings or to perform alternative calculations. In addition, the possibility of combining the approach based on graph theory with other numerical methods is considered.

The paper also presents the results of practical use of this combined approach in assessing the stability of a non-uniform landslide-prone slope, the calculation and analysis of the stress-strain state of which were carried out using the semi-analytical finite element method in the spatial formulation of the problem, and the stability assessment was carried out using graph theory approaches for the specified calculation sections. In the course of solving this problem, five different settings were considered in stages, from the slope in its natural state to the built-up slope, taking into account a possible option for engineering protection of this area. Accordingly, for one of the calculation sections, the obtained values of the stability coefficients and the shapes of potential sliding surfaces are given in accordance with some of them, shear pressure diagrams were determined and constructed, which can be used as initial data for the placement and calculations of engineering protection structures.