Study of Internal Stresses of Mining Massif within the Framework of Elastic Layered Block Models with Inclusions of the Hierarchical Structure of L-th Rank

International Journal of Geoinformatics and Geological Science

© 2021 by SSRG - IJGGS Journal

Volume 8 Issue 1

Year of Publication : 2021

Authors : Olga Hachay, Andrey Khachay

10.14445/23939206/IJGGS-V8I1P102

How to Cite?

Olga Hachay, Andrey Khachay, "Study of Internal Stresses of Mining Massif within the Framework of Elastic Layered Block Models with Inclusions of the Hierarchical Structure of L-th Rank," SSRG International Journal of Geoinformatics and Geological Science, vol. 8,  no. 1, pp. 9-14, 2021. Crossref, https://doi.org/10.14445/23939206/IJGGS-V8I1P102

Abstract:

In recent years, new models of continuum mechanics, generalizing the classical theory of elasticity, have been intensively developed. These models are used to describe composite and statistically heterogeneous media, new structural materials, as well as for complex arrays in mine conditions. The paper presents an algorithm for the propagation of acoustic waves in the framework of active monitoring of elastic layered block media with inclusions of the hierarchical type of L-th rank. Relations for internal stresses and deformations for each hierarchical rank are obtained, which constitute the nonlocal theory of elasticity. The essential differences between the nonlocal theory of elasticity and the classical one and the connection between them are investigated. A characteristic feature of the theory of media with a hierarchical structure is the presence of scale parameters in explicit or implicit form, i.e. explicit or implicit non locality of the theory. This work focuses on the study of the effects of non locality and internal degrees of freedom, reflected in internal stresses, which are not described by the classical theory of elasticity and which can be potential precursors of the development of a catastrophic process in a mountain range.

Keywords:

internal stresses, hierarchical inclusions, acoustic field, iterative modeling algorithm, non local theory of elasticity, stress tensor monitoring.

References:

[1] V.E.Panin, V.A.Likhachev, Yu.V.Grinyaev Structural levels of deformation of solids. Novosibirsk,Russia:Nauka.(1985),254.
[2] I.Prigogine Introduction to the thermodynamics of irreversible processes. Time, structure and fluctuations. Nobel Lecture in Chemistry 1977. Mjscow, Russia: Scientific Publishing Center ,Regular and Chaotic Dynamics. (2001),123-155.
[3] I.A.Kunin Theory of elastic media with a microstructure, nonlocal theory of elasticity, M. The main editorial office of physical and mathematical literature of the publishing house Moscow,Russia:Nauka.(1975),416.
[4] E.I.Shemyakin, G.L.Fisenko, M.V.Kurlenya, V.N.Oparin et al. Effect of zonal disintegration of rocks around underground holes. DAN USSR.(1986),289,5.830-832.
[5] V.E. Panin, V.E. Egorushkin, A.V. Panin Nonlinear wave processes in a deformable solid as a multilevel hierarchically organized system. UFN.(2012).182,12.13511357.DOI:10.336//UFNr.0182/201212i.1351
[6] K.T.Tazhibaev, A.S.Tashmamatov Residual stresses in rocks and a method for their determination. I.Ts “Technik” Bishkek,Kyrgizstan. (2014).126.
[7] O.A.Hachay, A.Yu. Khachay On the integration of seismic and electromagnetic active methods for mapping and monitoring the state of two-dimensional inhomogeneities in an N-layer medium. Bulletin of SURGU, series ,Computer technologies, control, radio electronics.,2(219), (2011), 49-56.
[8] O.A.Hachay, A.Yu. Khachay Modeling of electromagnetic and seismic fields in hierarchically inhomogeneous media.Bulletin SUSU. Series ,Computational Mathematics and Informatics.,2(2),(2013),48−55.
[9] L.D. Landau, E. M. Lifshits Theoretical physics: Textbook. manual: Foruniversities.In10(7),Theory of elasticity, 5th ed., Stereot.Moscow,Russia.: FIZMAT LIT (2003) 264p.