A variational method of slope stability assessment

DOI: https://doi.org/10.30686/1609-9192-2024-3S-06-13

Читать на русскоя языкеA.V. Zhabko1, 2
1 Ural Branch, VNIMI JSC, Ekaterinburg, Russian Federation
2 Ural State Mining University, Ekaterinburg, Russian Federation
Russian Mining Industry №3S / 2024 стр. 06-13

Abstract: The article discusses the variational method of assessing slope stability, which is based on the limit equilibrium method, but in contrast to the engineering techniques of stability assessment allows a mathematical justification (the variational calculus) of a single most dangerous slip surface in the rock mass, including the torsion angles and distribution of the interslice forces in its various sections. The main ideas and provisions of the proposed theory or concept, i.e. the variational method of slope stability calculation, are: 1) definition of the shape and position of the slip surface in the rock mass should be justified by strict mathematical (variational) methods, rather than by selection of the slip surface of a specified shape, for example, a circular slip surface; 2) calculation or assessment of stability, and more specifically, calculation of the shear and cohesion forces at various sections of the slip surface, depending on the geometry of the slip surface and the slope, as well as mechanical characteristics of the rocks and contact surfaces, is carried out using different composite functions (summarized force). The author demonstrates in the article that when applying engineering methods for calculating the stability of slopes for various types of their stability loss, in contrast to the variational method, their limiting (design) parameters are sharply overestimated. The author believes this to be the root cause of many accidents associated with the failure of slope structures. Application of the variational method of slope stability assessment allowed to establish new forms of slope stability loss and explain the abnormally steep slope angles of shear sites observed in practice.

Keywords: slope, stability calculation, limiting parameters of slopes, slip surface, weakening surface, angle of friction, toe landslide, sub-toe landslide

For citation: Zhabko A.V. A variational method of slope stability assessment. Russian Mining Industry. 2024;(3S):06–13. (In Russ.) https://doi.org/10.30686/1609-9192-2024-3S-06-13

Article info

Received: 10.05.2024

Revised: 18.06.2024

Accepted: 25.06.2024

Information about the author

Andrey V. Zhabko – Dr. Sci. (Eng.), Associate Professor, Head of the Laboratory of Open Pit Wall Stability, Ural Branch, VNIMI JSC; Head of the Mine Surveying Department, Ural State Mining University, Ekaterinburg, Russian Federation; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

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