A Reformation of the Equations of Anisotropic Poroelasticity

[+] Author and Article Information
M. Thompson

Schlumberger Cambridge Research, Cambridge CB3 OHG, U.K.

J. R. Willis

School of Mathematical Sciences, University of Bath, Bath BA2 7AY, U.K.

J. Appl. Mech 58(3), 612-616 (Sep 01, 1991) (5 pages) doi:10.1115/1.2897239 History: Received September 26, 1989; Revised March 10, 1990; Online March 31, 2008


The constitutive equations of linear poroelasticity presented by Biot (1955) and Biot and Willis (1957) extended the description of rock behavior into the realm of saturated porous rocks. For isotropic material behavior, Rice and Cleary (1976) gave a formulation which involved material constants whose physical interpretation was particularly simple and direct; this is an aid both to their measurement and to the interpretation of predictions from the theory. This paper treats anisotropic poroelasticity in terms of material tensors with interpretations similar to those of the constants employed by Rice and Cleary. An effective stress principle is derived for such anisotropic material. The material tensors are defined, rigorously, from the stress field and pore fluid content changes produced by boundary displacements compatible with a uniform mean strain and uniform pore pressure increments. Such displacements and pore pressure increments lead to homogeneous deformation on all scales significantly larger than the length scale of microstructural inhomogeneities. This macroscopic behavior is related to the microscopic behavior of the solid skeleton. The tensors which describe the microscopic behavior of the solid skeleton would be difficult, even impossible, to measure, but their introduction allows relationships between measurable quantities to be identified. The end product of the analysis is a set of constitutive equations in which the parameters are all measurable directly from well-accepted testing procedures. Relationships exist between measurable quantities that can be used to verify that the constitutive equations described here are valid for the rock under consideration. The case of transverse isotropy is discussed explicitly for illustration.

Copyright © 1991 by The American Society of Mechanical Engineers
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