On the Relationship between Stress and Elastic Strain for Porous and Fractured Rock Page: 2 of 31
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Abstract
Modeling the mechanical deformations of porous and fractured rocks requires a
stress-strain relationship. Experience with inherently heterogeneous earth materials
suggests that different varieties of Hook's law should be applied within regions of the
rock having significantly different stress-strain behavior, e.g., such as solid phase and
various void geometries. We apply this idea by dividing a rock body conceptually into
two distinct parts. The natural strain (volume change divided by rock volume at the
current stress state), rather than the engineering strain (volume change divided by the
unstressed rock volume), should be used in Hooke's law for accurate modeling of the
elastic deformation of that part of the pore volume subject to a relatively large degree of
relative deformation (i.e., cracks or fractures). This approach permits the derivation of
constitutive relations between stress and a variety of mechanical and/or hydraulic rock
properties. We show that the theoretical predictions of this method are generally
consistent with empirical expressions (from field data) and also laboratory rock
experimental data.
Keywords: Stress-strain relationship; Hooke's law; Constitutive relationships2
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Liu, Hui-Hai; Rutqvist, Jonny & Berryman, James G. On the Relationship between Stress and Elastic Strain for Porous and Fractured Rock, article, February 25, 2008; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc897926/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.