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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:

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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, Volume 23, Number 2, Pages 284–303 (Mi vsgtu1595)  

Mechanics of Solids

Determination of elastic constants of rocks

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

Kyrgyz-Russian Slavic University named after B. N. Eltsin, Bishkek, 720000, Kyrgyz Republic

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 $0.05{\div}0.15$ 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.

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


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Bibliographic databases:

UDC: 539.32:624.13
MSC: 74L10
Received: December 22, 2017
Revised: March 25, 2019
Accepted: June 10, 2019
First online: June 24, 2019

Citation: M. A. Kulagina, B. A. Rychkov, Yu. Yu. Stepanova, “Determination of elastic constants of rocks”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:2 (2019), 284–303

Citation in format AMSBIB
\by M.~A.~Kulagina, B.~A.~Rychkov, Yu.~Yu.~Stepanova
\paper Determination of elastic constants of rocks
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2019
\vol 23
\issue 2
\pages 284--303

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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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