Micromechanical Approach to Nonlinear Poroelasticity: Application to Cracked Rocks
Publication: Journal of Engineering Mechanics
Volume 128, Issue 8
Abstract
This paper considers a saturated porous medium in which the matrix is a cracked solid. Progressive crack closure is responsible for an overall nonlinear poroelastic behavior. The state equations of nonlinear poroelasticity are derived in a differential form within a micromechanical framework. When a hydraulic connection exists between the cracks and the pores of the porous space, the tangent drained stiffness tensor as well as the tangent Biot tensor and modulus are shown to depend on Terzaghi effective stress. Estimates for these coefficients as functions of Terzaghi effective stress are then derived with the tools of homogenization for disordered media. They are based on a crack closure criterion giving the condition for a crack to be closed under a given macroscopic stress state, depending on its aspect ratio. In the case of an isotropic orientation of cracks, it is shown that the influence of cracks on the overall poroelastic properties is governed by the crack density parameter which characterizes the distribution of aspect ratios. Conversely, an experimental methodology for the determination of the distribution of aspect ratios from the measurement of the macroscopic compliance is proposed.
Get full access to this article
View all available purchase options and get full access to this article.
References
Auriault, J.-L., and Sanchez-Palencia, E.(1977). “Etude du comportment macroscopique d’un milieu poreux saturé déformable.” J. Mec., 16(4), 575–603.
Berryman, (1998). “Rocks as poroelastic composites.” Poromechanics, Thimus et al., eds., Balkema, Rotterdam, The Netherlands, 11–16.
Biot, M. A.(1941). “General theory of three-dimensional consolidation.” J. Appl. Phys., 12, 155–164.
Biot, M. A.(1973). “Nonlinear and semilinear rheology of porous solids.” J. Geophys. Res., 78(23), 4924–4937.
Boutéca, M., Bary, D., Piau, J.-M., Kessler, N., Boisson, M., and Fourmaintraux, D. (1994). “Contribution of poroelasticity to reservoir engineering: Lab experiments, application to core decompression and implication in HP-HT reservoirs depletion.” Proc., Eurock’94, Delft, Balkema, Rotterdam, The Netherlands.
Budiansky, B., and O’Connell, R. J.(1976). “Elastic moduli of cracked solid.” Int. J. Solids Struct., 12, 81–97.
de Buhan, P., Chateau, X., and Dormieux, L.(1998). “The constitutive equations of finite strain poroelasticity in the light of a micro-macro approach.” Eur. J. Mech. A/Solids, 17, 909–921.
Dormieux, L., Molinari, A., and Kondo, D. (2002). “Micromechanical approach of the behavior of poroelastic materials.” J. Mech. Phys. Solids, in press.
Horii, H., and Nemat-Nasser, S.(1983). “Overall moduli of solids with microcracks: Load-induced anisotropy.” Int. J. Mech. Phys. Solids, 31(2), 155–171.
Poutet, J.et al. (1996). “The effective mechanical properties of reconstructed porous media.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33 (4), 409–415.
Vincké, O. (1994). “An estimation of bulk moduli of sandstones as a function of confining pressure using their petrographic and petrophysic description.” Proc., Eurock’94, Delft, Balkema, Rotterdam, The Netherlands.
Zimmermann, R. W. (1991). Compressibility of sandstones, Elsevier, Amsterdam, The Netherlands.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 128 • Issue 8 • August 2002
Pages: 848 - 855
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Mar 25, 2002
Accepted: Apr 1, 2002
Published online: Jul 15, 2002
Published in print: Aug 2002
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.