Determination of elastic constants of rocks

M. A. Kulagina ; B. A. Rychkov ; Yu. Yu. Stepanova

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 2, pp. 284-303.

Résumé

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 $0.05{\div}0.15$ 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.

Détail

Keywords: sandstone, compaction and strain hardening of porous material, generalized Hooke's law, nonlinear nature of the stress-strain diagram, strain tensor.
Mots-clés : triaxial compression

Bibliographie

[1] Stavrogin A. N., Protosenya A. G., Plastichnost' gornykh porod [Plasticity of rocks], Nedra, Moscow, 1979, 305 pp. (In Russian)

[2] Kartashev Yu. M., Matveev B. V., Mikheev G. V., Fadeev A. B., Prochnost' i deformiruyemost' gornykh porod [Strength and deformability of rock], Nedra, Moscow, 1979, 262 pp. (In Russian)

[3] 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.

[4] Stavrogin A. N., Protosenya A. G., Prochnost' gornykh porod i ustoichivost' vyrabotok na bol'shikh glubinakh [The strength of rocks and the stability of workings at great depths], Nedra, Moscow, 1985, 271 pp. (In Russian)

[5] Stefanov Yu. P., “Numerical modeling of deformation and failure of sandstone specimens”, J. Min. Sci., 44:1 (2008), 64–72 | DOI

[6] Paterson M. S., Wong T., Experimental Rock Deformation-The Brittle Field, Springer, Berlin, 2005, x+348 pp. | DOI

[7] Kachanov M., “On the Effective Elastic Properties of Cracked Solids – Editor's Comments”, Int. J. Fract., 146:4 (2007), 295–299 | DOI

[8] Kitaeva D. A., Pazylov Sh. T., Rudaev Ya. I, “On applications of nonlinear dynamics methods for mechanics of materials”, Vestn. Perm. Gos. Tekhn. Univ., Ser. Matem. Model. Sistem Protsessov, 2007, no. 15, 46–70 (In Russian)

[9] Schwab A. A., “Experimental analytical method for quasi-homogeneous material characteristics determination based on elasto-plastic analysis of experimental data”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, no. 2(27), 65–71 (In Russian) | DOI | MR

[10] 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 | DOI

[11] Suknev S. V., Fedorov S. P., “Methods of determination of rock elastic properties”, Nauka i obrazovanie, 2014, no. 1(73), 18–24 (In Russian)

[12] 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)

[13] Suknev S. V., “Determination of the modulus of elasticity of rocks upon compression”, Industrial Laboratory. Diagnostics of Materials, 83:12 (2017), 52–57 (In Russian) | DOI

[14] Małkowski P., Ostrowski Ł., “The Methodology for the Young Modulus Derivation for Rocks and Its Value”, Procedia Engineering, 191 (2017), 134–141 | DOI

[15] 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 | DOI | MR

[16] Mogi K., Experimental rock mechanics, CRC Press, London, 2007, 375 pp. | DOI

[17] Komartsov N. M., Kulagina M. A., Rychkov B. A., “On the interpretation of rocks elasticity modulus”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:3 (2018), 487–503 (In Russian) | DOI | Zbl

[18] Annin B. D., Ostrosablin N. I., “Anisotropy of elastic properties of materials”, J. Appl. Mech. Tech. Phys., 49:6 (2008), 998–1014 | DOI | MR

[19] Rychkov B. A., “The concept of slipping and mechanics of orthotropic material”, Izvestiia Rossiiskoi akademii nauk. Mechanics of Solids, 1996, no. 1, 70–79 (In Russian)

[20] Rychkov B. A., “On strain hardening of rock materials”, Mechanics of Solids, 34:2 (1999), 97–104

[21] Stavrogin A. N., Georgievskii V. S., Katalog mekhanicheskikh svoistv gornykh porod [Catalog of mechanical properties of rocks], VNIMI, Leningrad, 1972, 267 pp. (In Russian)