JUSTIFICATION OF THE CHOICE OF THE CALCULATION MODEL OF THE ESCALATOR TUNNEL IN FLAT AND SPATIAL SETTINGS

Abstract

Purpose. To perform an analysis of analytical and numerical methods of mathematical modeling of an escalator tunnel. To identify the main characteristics and differences of methods based on flat or spatial settings. To justify the choice of the calculation model of the escalator tunnel and its setting. To justify the choice of the calculation model of the escalator tunnel and its construction. Methodology. To achieve the goal, a number of analytical methods based on a flat (2D) setting (Gap method, Volume loss control method, Convergence-confinement method) were analyzed. Approaches in numerical methods, in particular in the method of finite elements, which have successfully applied flat setting, are considered. The spatial (3D) setting in the finite element method is also analyzed. Analysis of a numerical experiment based on 3D models shows that the three-dimensional structure forces interpretation decisions that are not taken into account in the cross-section, that is, in the two-dimensional model. Findings. Finite-element models of the escalator tunnel were developed in flat and spatial settings, and the 2D model with a thickness of 1 m repeated the conditions of the 3D model in its middle part. The obtained parameters of the stress-strain state were subjected to comparative analysis. It was found that the values of the norms of horizontal and vertical stresses in the fragment of the 3D model (middle) and in the 2D model differ by 3.2 and 7.2 %, respectively. Originality. Based on the results of the justification of the choice of the calculation model of the escalator tunnel, it was proved that the use of 2D models is adequate for the system of interaction of the escalator tunnel with the surrounding massif. This statement is evidenced by the almost identical distribution of stresses and strains in finite-element models in flat and spatial settings. Practical value. In the course of research, it has been proven that the flat finite-element model of the escalator tunnel is adequate for the given task, provided that it is used in several characteristic sections of the escalator tunnel, that is, the creation of a number of models in 2D, which allows considering its position along the length of the calculated tunnel.