MATHEMATICAL AND COMPUTER MODELING OF CRITICAL AREAS OF LOSS OF STABILITY OF COMPLEX SYSTEMS

Akanova K. Myrkanova A. Zhumakhanova A.
31 July 2022 Little Lion Scientific

Journal of Theoretical and Applied Information Technology
2022 #100 Issue 14 5376 - 5386 pp.

In recent years, the pace and scale of the development of minerals and energy resources in mountainous areas has been increasing, so various ground and underground structures are being built and operated. Increasing anthropogenic load on the biosphere and technosphere leads to the intensification of natural and man-made disasters. In addition, the occurrence of a catastrophe of the first type can provoke the manifestation of a catastrophe of the second type, and vice versa. Using ideas about catastrophic phenomena and the dynamics of their development, rock mechanics and methods of mathematical and computer modeling, it became possible to apply theoretical knowledge in practice. The issues of forecasting, preventing and minimizing events leading to loss of life and economic damage are among the most relevant today [1]. The article shows a study of the stress-strain state of an underground tunnel, which is affected by the volumetric weight of a rock mass. Deformation and displacement of mountain ranges can lead to the loss of stability of the technical structure and to its collapse, and thus cause a man-made disaster. The analytical and numerical solution of the problem will allow engineers and specialists in the field of mining to improve the safety and reliability of underground structures and take preventive measures to prevent the risk of their destruction. In this article, formulas are obtained for determining the components of stresses, deformations and displacements in an untouched rock mass, as well as on the contour of a constructed underground structure at bifurcation points. With their help, zones of high concentration of stresses, deformations and displacements and changes in the nature of their distribution are identified, which signal a critical state of the system, in which it can lose stability. As an example, an underground working of an elliptical profile is considered.

Bifurcation , Catastrophe , Collapse , Deformation , Stress

Text of the article Перейти на текст статьи

Mathematical and computer modeling Department, L.N.Gumilyov Eurasian National University, Kazakhstan

Mathematical and computer modeling Department

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026