Email this article Determination of elastic constants of rocks
- Authors: Kulagina M.A.1, Rychkov B.A.1, Stepanova Y.Y.1
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Affiliations:
- Kyrgyz-Russian Slavic University named after B. N. Eltsin
- Issue: Vol 23, No 2 (2019)
- Pages: 284-303
- Section: Articles
- URL: https://journal-vniispk.ru/1991-8615/article/view/20626
- DOI: https://doi.org/10.14498/vsgtu1595
- ID: 20626
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Abstract
The A. N. Stavrogin's experimental data are observed during triaxial compression of sandstone samples under proportional loading according to T. Karman's scheme. Sandstones have a sufficiently high porosity in the initial state, so their deformation within elasticity has the following peculiar properties. When the cylindrical sample is uniaxially compressed at small initial stresses (of the order of 0.05÷0.15 of the elastic limit), a nonlinear part is observed on the longitudinal strain diagram, which is associated with the material densification occurring on this section. This circumstance causes a certain difficulty in determining the modulus of elasticity. An elaboration of the method for determination the elastic constants (Young's modulus and Poisson's ratio) are proposed taking into account the initial deformation diagram's special feature, which was mentioned. Earlier A. N. Stavrogin proposed to consider on the longitudinal strain diagram a linear part from the indicated initial stress to the conditional elastic limit. The elastic modulus is determined by this part of the diagram. Linear extrapolation of this segment to zero stress level provides a virtually new point of origin for the longitudinal strain under consideration. In this paper, it is shown that under triaxial compression of a cylindrical specimen, the longitudinal strain (satisfying Hooke's law) can be measured from the same new point of origin, which is established under uniaxial compression. In this case, the lateral strain of the sample is considered in the such range of stress variation, at which the increment of the axial stress causes a negative increment in the lateral strain. Based on the initial experimental values of longitudinal and lateral strain, which were adjusted by this method, the conditional elastic limit was determined.
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##article.viewOnOriginalSite##About the authors
Margarita Alekseevna Kulagina
Kyrgyz-Russian Slavic University named after B. N. Eltsin
Email: kulagina_m.a@mail.ru
without scientific degree, no status 44, Kievskaya st., Bishkek, 720000 Kyrgyz Republic
Boris Aleksandrovich Rychkov
Kyrgyz-Russian Slavic University named after B. N. Eltsin
Email: rychkovba@mail.ru
Doctor of physico-mathematical sciences, Professor 44, Kievskaya st., Bishkek, 720000 Kyrgyz Republic
Yulya Yurevna Stepanova
Kyrgyz-Russian Slavic University named after B. N. Eltsin
Email: stepanova_yulya_1995@mail.ru
without scientific degree, no status 44, Kievskaya st., Bishkek, 720000 Kyrgyz Republic
References
- Ставрогин А. Н., Протосеня А. Г., Пластичность горных пород, Недра, М., 1979, 305 с.
- Карташев Ю. М., Матвеев Б. В., Михеев Г. В., Фадеев А. Б., Прочность и деформируемость горных пород, Недра, М., 1979, 262 с.
- An introduction to rock mechanics, ed. H. Bock, Dept. of Civil and Systems Engineering, James Cook University of North Queensland, Townsville, Q., 1978, 342 pp.
- Ставрогин А. Н., Протосеня А. Г., Прочность горных пород и устойчивость выработок на больших глубинах, Недра, М., 1985, 271 с.
- Стефанов Ю. П., "Численное моделирование деформирования разрушения горных пород на примере расчета поведения образцов песчаника", Физико-технические проблемы разработки полезных ископаемых, 2008, № 1, 73-83
- Paterson M. S., Wong T., Experimental Rock Deformation-The Brittle Field, Springer, Berlin, 2005, x+348 pp.
- Kachanov M., "On the Effective Elastic Properties of Cracked Solids - Editor's Comments", Int. J. Fract., 146:4 (2007), 295-299
- Китаева Д. А., Пазылов Ш. Т., Рудаев Я. И., "О приложении методов нелинейной динамики в механике материалов", Вестник Пермского государственного технического университета. Математическое моделирование систем и процессов, 2007, № 15, 46-70 с.
- Шваб А. А., "Экспериментально-аналитический метод определения характеристик квазиоднородного материала по упругопластическому анализу экспериментальных данных", Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2012, № 2(27), 65-71
- Zhang J. C., Zhou S. H., Xu S. H., Fang L. G., "Evolution of the elastic properties of a bedded argillite damaged in cyclic triaxial tests", International Journal of Rock Mechanics and Mining Sciences, 58 (2013), 103-110
- Сукнëв С. В., Фëдоров С. П., "Методы определения упругих свойств горных пород", Наука и образование, 2014, № 1(73), 18-24
- DIN EN 14580:2005-07. Prüfverfahren für Naturstein - Bestimmung des statischen Elastizitätsmoduls [Natural stone test methods - Determination of static elastic modulus], Deutsches Institut für Normung, Berlin, 2005, 15 pp. (In German)
- Сукнëв С. В., "Определение модуля упругости горных пород при сжатии", Заводская лаборатория. Диагностика материалов, 83:12 (2017), 52-57
- Malkowski P., Ostrowski Ł., "The Methodology for the Young Modulus Derivation for Rocks and Its Value", Procedia Engineering, 191 (2017), 134-141
- Peng J., Cai M, Liu D., He M., Zhou Ch., "A Phenomenological Model of Brittle Rocks under Uniaxial Compression", International Journal of Georesources and Environment, 1:2 (2015), 53-62
- Mogi K., Experimental rock mechanics, CRC Press, London, 2007, 375 pp.
- Комарцов Н. М., Кулагина М. А., Рычков Б. А., "О трактовке модуля упругости горных пород", Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 22:3 (2018), 487-503
- Аннин Б. Д., Остросаблин Н. И., "Анизотропия упругих свойств материалов", Прикладная механика и техническая физика, 49:6 (2008), 131-151
- Рычков Б. А., "Концепция скольжения и механика ортотропного материала", Изв. РАН. МТТ, 1996, № 1, 70-79
- Рычков Б. А., "О деформационном упрочнении горных пород", Изв. РАН. МТТ, 1999, № 2, 115-124
- Ставрогин А. Н., Георгиевский В. С., Каталог механических свойств горных пород, ВНИМИ, Л., 1972, 267 с.
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