Construction of mechanical and mathematical model of viscoelastic block element for solving geomechanics dynamic problems using discrete element method

Authors

  • Mikhail A. Nikolaitchik Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus
  • Zhang Shiqi Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

Keywords:

numerical simulation, mechanic-mathematical modelling, mechanics of deformable solids, discrete method elements, boundary conditions, underground geomechanics, deformable block element
Supporting Agencies
This research was carried out as part of the joint project «High-performance discrete element method for granular materials of arbitrary shape and its application in geotechnics of cold regions and mining areas» of the Belarusian Republican Foundation for Fundamental Research and the National Natural Science Foundation of China.

Abstract

Numerical simulation methods have become one of the effective tools to solve geomechanical engineering problems. The paper presents a procedure for constructing a mechanical and mathematical model of one type of viscoelastic block element. Based on this type of block element, it seems possible to apply the discrete element method for modelling the state of a rock massif in areas where the continuity assumption is violated. The resulting equations describing the behaviour of the proposed block element are obtained using classical laws of mechanics. A number of numerical experiments were carried out, different variants of initial conditions were considered, as well as parameters of connections between the elements of the block. An algorithm is developed to describe the block consisting of n elements dynamics. The performance of the developed algorithm using sequential and parallel computations has been evaluated. The obtained results can be used to solve dynamic problems of geomechanics by the discrete element method in the areas of rock massif where the continuity hypothesis is violated.

Author Biographies

  • Mikhail A. Nikolaitchik, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics); head of the laboratory of applied mechanics, faculty of mechanics and mathematics

  • Zhang Shiqi, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

    masterʼs degree student at the department of theoretical and applied mechanics, faculty of mechanics and mathematics

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Published

2024-12-05

Issue

No. 3 (2024): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical and Applied Mechanics

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How to Cite

[1]
Nikolaitchik, M.A. and Shiqi, Z. 2024. Construction of mechanical and mathematical model of viscoelastic block element for solving geomechanics dynamic problems using discrete element method. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2024), 40–61.