Non-Classical Solutions of Critical Rock Behavior

Article Preview

Abstract:

Strain-gradient and non-Euclidean continuum theories are used for the construction of non-classical solutions of continuum models. Both models result in identical structures in terms of their kinematic and force characteristics. The obtained solutions exhibit a critical behavior with respect to the external loading parameter. The proposed analysis allows us to use different theoretical approaches for descriptions of rock critical behavior under different loading conditions.

You might also be interested in these eBooks

Info:

Periodical:

Advanced Materials Research (Volumes 891-892)

Pages:

1663-1668

Citation:

Online since:

March 2014

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] D.R. Cloete, A.J. Jager, The nature of the fracture zone in gold mines as revealed by diamond core drilling, Association of Mine Managers. (1972-1973).

Google Scholar

[2] G.R. Adams and A.J. Jager, Petroscopic observations of rock fracturing ahead of stope faces in deep-level gold mine, Journal of the South African Institute of Mining and Metallurgy. 80 (1980) 204-209.

DOI: 10.1016/0148-9062(80)90623-3

Google Scholar

[3] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, V.N. Oparin, Zone disintegration of rocks around underground workings—Part I: Data of in-site observations, Journal of Mining Science. 22 (1986) 157-168.

DOI: 10.1007/bf02500863

Google Scholar

[4] E.I. Shemyakin, M.V. Kyrlenya, V.N. Reva, et al. Effect of zonal disintegration of rocks around underground workings, Dokl. Acad. Nauk USSR. 289 (1986) 1088-1094.

Google Scholar

[5] R.A. Toupin, Elastic materials with couple stresses, Arch. Ration. Mech. Anal. 11 (1962) 385–414.

DOI: 10.1007/bf00253945

Google Scholar

[6] R.D. Mindlin, 1964. Micro-structure in linear elasticity. Arch. Ration. Mech. Anal., 16, 1, 51–78.

DOI: 10.1007/bf00248490

Google Scholar

[7] R. Chambon, D. Caillerie, C. Tamagnini, A strain space gradient plasticity theory for finite strain, Comput. Methods Appl. Mech. Eng. 193 (2004) 2797–2826.

DOI: 10.1016/j.cma.2003.10.016

Google Scholar

[8] K. Kondo, On the geometrical and physical foundations of the theory of yielding, Proc. Japan. Nat. Congr. Apll. Mech. 2 (1952) 41-47.

Google Scholar

[9] B.A. Bilby, R. Bullough, E. Smith, Continuous distributions of dislocations: a new application of the methods of non-Reimannian geometry, Proc. Roy. Soc. A 231 (1955) 263-273.

Google Scholar

[10] V. P. Myasnikov, M.A. Guzev, Thermo-mechanical model of elastic-plastic materials with defect structures, Theoretical and Applied Fracture Mechanics. 33 (2000) 165-171.

DOI: 10.1016/s0167-8442(00)00011-2

Google Scholar

[11] M.A. Guzev, The Non-Euclidean model of zonal disintegration of rocks around an underground working, Abstracts Book of XXII International Congress of Theoretical and Applied Mechanics. (2008) 257.

Google Scholar

[12] A. Kadi´c , D.G.B. Edelen, A gauge theory of dislocations and disclinations, Lecture Notes in Physics 174, (1983).

Google Scholar

[13] K.C. Valanis, The concept of physical metric in thermodynamics, Acta Mechanica. 113 (1995) 169-184.

DOI: 10.1007/bf01212641

Google Scholar

[14] V. Ciancio, M. Francaviglia, Non-Euclidean Structures as Internal Variables in Non-Equilibrium Thermomechanics, Balkan Journal of Geometry and Its Applications. 8 (2003) 33-43.

Google Scholar

[15] M.A. Guzev, Non-Euclidean models of elastoplastic materials with structure defects, Lambert Academic Publishing, (2010).

Google Scholar

[16] J.D. Eshelby, Continuum theory of lattice defects, Solid State Physics. 3 (1956) 79–144.

DOI: 10.1016/s0081-1947(08)60132-0

Google Scholar

[17] M. A. Guzev , Structure of kinematic and force fields in the Riemannian continuum model, Journal of Applied Mechanics and Technical Physics. 52 (2011) 709–716.

DOI: 10.1134/s002189441105004x

Google Scholar

[18] M. Galanin, M. Guzev, T. Nizkaya, Threshold behavior of the Riemann curvature in non-euclidean continious medium, Abstracts Book of XXII International Congress of Theoretical and Applied Mechanics. (2008) 270.

Google Scholar