Authors: D.I. Nazarov

Title of the article: Catastrophe theory in geomechanics problems and mine engineering structures: practice of restoring (reinforcing) load-bearing structures that have collapsed due to bifurcation

Year: 2025, Issue: 4, Pages: 68-87

Branch of knowledge: 2.8.8 Mining machines, geotechnology (engineering)

Index UDK: 622.8:624.046

DOI: 10.26730/2618-7434-2025-4-68-87

Abstract: Over the past decades, finite element analysis programs such as Plaxis, Fidesys, Midas, Rocscience (for geomechanics tasks), Lira, SCAD-office, SAP2000, ETABS (for calculating supports and structures of mining buildings and structures), ANSYS, Nastran, Abaqus for complex research tasks, have effectively, and not only in terms of regulations and legislation, become virtually the only means of analyzing stress-strain states, completely replacing analytical calculations. However, research into the physical and mathematical theory of finite element analysis and software implementations, including those legally approved for solving geomechanical problems and calculating supports and structures of mining buildings and structures, shows that structural bifurcations are being ignored. Both analytically and practically (experimentally), it has been proven that the bifurcation of deformable structures causes irreversible abrupt changes in the structural scheme and can lead to brittle failure and plastic deformation. A study of the capabilities of the physical and mathematical theory of finite element analysis for determining stability and geometrically nonlinear (deformed) states shows that it is impossible to correctly determine the ultimate bearing capacity based on the bifurcation criterion using modern methods. The impossibility of reliably determining the ultimate bearing capacity in a geometrically nonlinear (deformed) model is demonstrated by examples and justified by the absence of a strict physical definition and corresponding mathematical formulations for such fundamental concepts as: static force, static loading, stability, and load-bearing capacity, without which it is impossible to create a correct physical and mathematical model of finite element analysis. The reliability of finite element analysis is not only a pressing scientific issue, but also a requirement of federal legislation in the field of designing particularly dangerous, technically complex, and unique facilities. It is necessary to take bifurcation into account as a criterion for ultimate load-bearing capacity. Until a correct physical and mathematical model of finite element analysis is created and implemented in practice, analytical verification of structures based on the bifurcation criterion is mandatory.

Key words: collapse reinforcement catastrophe theory bifurcation load-bearing capacity stability finite element method mechanics of deformable solids geomechanics structural mechanics

Receiving date: 06.10.2025

Approval date: 17.11.2025

Publication date: 23.12.2025

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