Babii K., Larionov H., Ryabko A., Hovorukha O., Zhelyazov T. Developing a multiplicative mathematical model for geomechanical stability of tailings dams by successive approximation method
- Details
- Parent Category: Geo-Technical Mechanics, 2025
- Category: Geo-Technical Mechanics, 2025, Issue 175
Geotech. meh. 2025, 175, 38-53
https://doi.org/10.15407/geotm2025.175.038
DEVELOPING A MULTIPLICATIVE MATHEMATICAL MODEL FOR GEOMECHANICAL STABILITY OF TAILINGS DAMS
BY SUCCESSIVE APPROXIMATION METHOD
1M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine
2National Institute of Geophysics, Geodesy and Geography - Bulgarian Academy of Sciences
UDC 622.83
Language: English
Abstract. The issue of developing the model-based tools for monitoring, assessing, and forecasting safe natural and technological states of hydraulic structures, including slope structures of tailings dams, is one of the topical problems. The models represented in regulatory documents that establish requirements for the design, construction, and operation of hydraulic structures are primarily based on semi-empirical limit state models for calculating permissible stability parameters of dams. At the same time, modern international practice shows that in the design and operation of hydraulic structures, models based on the theory of deformable solid bodies combined with the finite element method are most commonly used.
The purpose of this work is to develop a multiplicative mathematical model for determining the sensitivity of the dam’s stability function to variations in its structural parameters and the physical-mechanical properties of its components using the method of successive iterative approximation.
In the course of the study, during model development, the approximation of the stability coefficient was carried out in a multiplicative form, where the components of the product are power functions, each depending only on a single parameter. The sensitivity to parameter variation was determined by the exponent indicators of these functions. The approximation coefficient, or multiplier, served as a free parameter that regulated the adequacy of the model parameters at the forecast point during the extrapolation procedure. The input data for obtaining the approximation model of the stability factor of slope structures were generated through a series of numerical experiments based on the geomechanical characteristics of a real object – the internal dam of a tailings storage facility.
The scientific results of the study are as follows: the construction of a model for the stability safety factor based on the method of successive approximation (SAM), which made it possible not only to obtain an analytical form of the criterion in the neighbourhood of a point but also to extend the solution to the entire domain of the function, with errors not exceeding values acceptable for applied geomechanics problems; and the formulation of a hypothesis regarding the availability of a representation of functions in the form of a product of functions, each depending on a single parameter. It has been established that through the synthesis of the SAM and computer-based experimental studies, it is possible to obtain families of deterministic multiplicative mathematical models of various types of objects.
The practical results of the study include a derived formula for determining a stability safety factor of slope systems in tailings dam structures, which allows for an approximate assessment of the risks of stability loss due to variations in parameter values.
Keywords: numerical experiment, sensitivity theory, variation of the parameters, approximation of a function, approximate evaluation, low error, tailings storage facility, geomechanical stability of the dam.
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About the authors
Babii Kateryna, Corresponding Member of the National Academy of Sciences of Ukraine, (D.Sc.), Head of Department of Geomechanical Basis of Open-Pit Technology, Deputy Director for Research of M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine (IGTM of the NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. , ORCID 0000-0002-0733-2732
Larionov Hryhoryi, Doctor of Technical Sciences (D. Sc.), Senior Researcher, Senior Researcher in Rock Mechanics Department, M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine (IGTM of the NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. , ORCID 0000-0002-4774-0992
Ryabko Andriy, Junior Researcher in Department of ecology of natural resources development, M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine (IGTM of the NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. (Corresponding author), ORCID0000-0001-6305-3853
Hovorukha Oleh, Postgraduate Student, M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine (IGTM of the NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. , ORCID 0009-0001-8574-8717
Zhelyazov Todor, National Institute of Geophysics, Geodesy and Geography - Bulgarian Academy of Sciences, Sofia, Bulgaria, This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it. , ORCID 0009-0001-1889-3789