About one criteria of strength of rocks
Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 72-87.

Voir la notice de l'article provenant de la source Math-Net.Ru

Plastic deformation of rocks and generation of residual deformation field are related to shear and tensile cracks formation. For conditions of three-dimensional stress state a strength (yield) criterion is proposed that takes into consideration combined effect of two kinds of failure (shear and tensile failure) and is based on associated flow rule. The developed criteria relations were verified during description of results of rocks mechanical tests. Acceptable concordance between calculated and experimental values of breaking stresses and strains was obtained. Developed algorithm for critical stresses, elastic and plastic deformations determining is easy enough for numerical realization in three-dimensional problems of mathematical modelling of deformation and failure processes of large-scale mine technical objects.
Keywords: strength (yield) criterion, rocks, three-dimensional problems, plastic deformation, numerical simulation.
@article{CHEB_2017_18_3_a5,
     author = {A. A. Baryakh and N. A. Samodelkina},
     title = {About one criteria of strength of rocks},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {72--87},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a5/}
}
TY  - JOUR
AU  - A. A. Baryakh
AU  - N. A. Samodelkina
TI  - About one criteria of strength of rocks
JO  - Čebyševskij sbornik
PY  - 2017
SP  - 72
EP  - 87
VL  - 18
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a5/
LA  - ru
ID  - CHEB_2017_18_3_a5
ER  - 
%0 Journal Article
%A A. A. Baryakh
%A N. A. Samodelkina
%T About one criteria of strength of rocks
%J Čebyševskij sbornik
%D 2017
%P 72-87
%V 18
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a5/
%G ru
%F CHEB_2017_18_3_a5
A. A. Baryakh; N. A. Samodelkina. About one criteria of strength of rocks. Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 72-87. http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a5/

[1] Panasyuk V. V., Andreykiv A. E., Parton V. Z., Osnovyi mehaniki razrusheniya, v. 1, Mehanika razrusheniya i prochnost materialov, Naukova Dumka, Kiev, 1988, 488 pp.

[2] Kartashov Y. M., Matveev B. V., Mikheev G. V., Fadeev A. B., Strength and deformability of rocks, Nedra, M., 1979, 269 pp.

[3] Levin V. A., Models and methods. Formation and development of faults, Physmathlit, M., 2015, 456 pp.

[4] Olovyanny A. G., Rock mechanics. Failure modeling, Saint Petersburg University, Saint Petersburg, 2012, 278 pp.

[5] Baryakh A. A., Samodelkina N. A., “Mathematikal modelining of underworked rock strata failure process”, Solid State Phenomena, 243 (2016), 17–22 | DOI

[6] Baryakh A. A., Samodelkina N. A., “Water-tight stratum rupture under large-scale mining. Part II”, Journal of mining science, 48:6 (2012), 954–961 | DOI

[7] Botkin A. I., “On strength of bulk solids and brittle materials”, Izvestiya VNII gidrotehniki, 26 (1940), 205–236

[8] Mirolyubov I. N., “On the question of generalization of octahedral shear stress theory on brittle materials”, Tr. Leningr. tehnologich. in-ta, 1953, no. 2, 42–52

[9] Kuznetsov G. N., Mechanical properties of rock, Ugletechizdat, M., 1947, 247 pp.

[10] Kats Sh. N., “On plastic deformations under compound stress”, Theory of plasticity, Nauka, M., 1969, 400 pp.

[11] Baryakh A. A., Konstantinova S. A., Asanov V. A., Deformation of salt rocks, UrO RAN, Ekaterinburg, 1996, 203 pp.

[12] Zienkiewich O. C., The finite element method in engineering science, Mcgraw-Hill, London, 1971 521 | MR

[13] Fadeev A. B., The finite element method in geo mechanics, Nedra, M., 1987, 221 pp.

[14] Samodelkina N. A., “Forecast of earth surface deformations for different flooding scenarios of mine SKRU-2”, Sb. nauch. Tr., Strategiya i protsessyi osvoeniya georessursov, 14, Mine Institute of Ural Branch of Russian Academy of Science, Perm, 2016, 84–86

[15] Baryakh A. A., Samodelkina N. A., “Geomechanical estimation of deformation processes intensity over flooded potash mine”, Journal of mining science, 2017, no. 4, 33–46