Abstract
This chapter offers a comprehensive derivation of the constitutive equations of linear poroelasticity. A main purpose of this survey is to assist with the formulation of experimental strategies for the measurement of poroelastic constants. The complete set of linearized constitutive relations is phrased alternatively in terms of undrained bulk parameters or drained skeleton parameters. Displayed in the form of a mnemonic diagram, this can provide a rapid overview of the theory. The principal relationships between alternative sets of material parameters are tabulated, among them the well-known Gassmann or Brown-Korringa fluid substitution relations that are rederived here without any pore-scale considerations. The possibility of an isotropic unjacketed response is pointed out, which — if verified experimentally — will make for an interesting and practically useful special case of anisotropic poroelasticity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Berge, P.A., and J.G. Berryman (1995). Realizability of negative pore compressibility in poroelastic composites. J. Appl. Mech. 62, 1053–1062.
Berryman, J.G. (1995). Mixture theories for rock properties. In: Rock Physics and Phase Relations. A Handbook of Physical Constants, edited by T.J. Ahrens, Am. Geophys. Union, Washington D.C., pp. 205–228.
Biot, M.A. (1941). General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155–164.
Biot, M.A. (1955). Theory of elasticity and consolidation for a porous anisotropic solid. J. Appl. Phys. 26, 182–185.
Biot, M.A. (1956a). Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 240–253.
Biot, M.A. (1972). Theory of finite deformation of porous solids. Indiana Univ. Math. J. 21(7), 597–620.
Biot, M.A. (1973). Nonlinear and semilinear rheology of porous solids. J. Geophys. Res. 78, 4924–4937.
Biot, M.A., and D.G. Willis (1957). The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24, 594–601.
Brown, R.J.S., and J. Korringa (1975). On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid. Geophysics 40, 608–616.
Callen, H.B. (1960). Thermodynamics, John Wiley, New York.
Carcione, J.M., and U. Tinivella (2001). The seismic response to overpressure: a modelling study based on laboratory, well and seismic data. Geophysical Prospecting 49, 523–539.
Carroll, M.M. (1979). An effective stress law for anisotropic elastic deformation. J. Geophys. Res. 84, 7510–7512.
Cheng, A.H.D. (1997). Material coefficients of anisotropic poroelasticity. Int. J. Rock Mech. Min. Sci. 34, 199–205.
Coussy, O. (2004). Poromechanics, John Wiley & Sons Ltd., Chichester UK.
Detournay, E., and A.H.D. Cheng (1993). Fundamentals of poroelasticity. In: Comprehensive Rock Engineering Vol. 2, edited by J. A. Hudson, Pergamon Press, Oxford, Chap. 5, pp. 113–171.
Gassmann, F. (1951). Über die Elastizität poröser Medien. Vierteljahrsschr. Naturforsch. Ges. Zürich 96, 1–23.
Geertsma, J. (1957a). A remark on the analogy between thermoelasticity and the elasticity of saturated porous media. J. Mech. Phys. Solids 6, 13–16.
Geertsma, J. (1957b). The effect of fluid pressure decline on volumetric changes in porous rocks. Trans. AIME 210, 331–340.
Geertsma, J. (1966). Problems of rock mechanics in petroleum production engineering. Proc. 1st Congr. Int. Society of Rock Mechanics, 585–594.
Green, D.H., and H.F. Wang (1986). Fluid pressure response to undrained compression in saturated sedimentary rocks. Geophysics 51, 948–956.
Green, D.H., and H.F. Wang (1990). Specific storage as a poroelastic coefficient. Water Resources Res. 26, 1631–37.
Guéguen, Y., L. Dormieux, and M. Boutéca (2004). Fundamentals of Poromechanics. In: Mechanics of Fluid-Saturated Rocks, edited by Y. Guéguen and M. Boutéca, Elsevier Academic Press, Burlington MA, pp. 1–54.
Jaeger, J.C., N.G.W. Cook, and R.W. Zimmerman (2007). Fundamentals of Rock Mechanics (4th edition), Blackwell Publishing Ltd, Oxford, etc.
Kümpel, H-J. (1991). Poroelasticity: parameters reviewed. Geophys. J. Int. 105, 783–799.
Mavko, G., T. Mukerji, and J. Dvorkin (1998). The Rock Physics Handbook. Tools for Seismic Analysis in Porous Media. Cambridge U. Press, Cambridge UK.
McTigue, D.F. (1986). Thermoelastic response of fluid-saturated porous rock. J. Geophys. Res. 91, 9533–9542.
Nur, A., and J.D. Byerlee (1971). An exact effective stress law for elastic deformation of rock with fluids. J. Geophys. Res. 76, 6414–6419.
Nye, J.F. (1957). Physical Properties of Crystals. Oxford University Press, Oxford etc., (reprinted in 1979).
Rice, J.R., and M.P. Cleary (1976). Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev. Geophys. Space Phys. 14, 227–241.
Rudnicki, J.W. (1985). Effect of pore fluid diffusion on deformation and failure of rock. In: Mechanics of Geomaterials, edited by E. Bažant, John Wiley & Sons Ltd., New York, Chap. 15, pp. 315–347.
Rudnicki, J.W. (2001). Coupled deformation-diffusion effects in the mechanics of faulting and failure of geomaterials. Appl. Mech. Rev. 54, 1–20.
Terzaghi, K., and O.K. Fröhlich (1936). Theorie der Setzung von Tonschichten, F. Deutike, Wien.
Thompson, M., and J.R. Willis (1991). A reformulation of the equations of anisotropic poroelasticity. J. Appl. Mech. 58, 612–616.
Wang, H.F. (2000). Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press, Princeton and Oxford.
Weiner, J.H. (1983). Statistical Mechanics of Elasticity, John Wiley & Sons, New York.
Zimmerman, R.W., W.H. Somerton, and M.S. King (1986). Compressibility of porous rocks. J. Geophys. Res. 91,12,765–12,777.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 CISM, Udine
About this chapter
Cite this chapter
Lehner, F.K. (2011). The Linear Theory of Anisotropic Poroelastic Solids. In: Leroy, Y.M., Lehner, F.K. (eds) Mechanics of Crustal Rocks. CISM Courses and Lectures, vol 533. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0939-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-7091-0939-7_1
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-0938-0
Online ISBN: 978-3-7091-0939-7
eBook Packages: EngineeringEngineering (R0)