Journal of the Belarusian State University. Mathematics and Informatics, 2024 Volume 3,Pages 40–61(Mi bgumi695)
Theoretical and practical mechanics
Construction of mechanical and mathematical model of viscoelastic block element for solving geomechanics dynamic problems
using discrete element method
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.
Keywords:numerical simulation; mechanic-mathematical modelling; mechanics of deformable solids; discrete method elements; boundary conditions; underground geomechanics; deformable block element
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