The Elastic Coefficients of the Theory of Consolidation

TLDR

Biot established the theory of deformation of a porous elastic solid containing a compressible fluid. This paper describes measurement methods to determine the elastic coefficients of that theory. The authors discuss physical interpretations of the coefficients and outline sufficient measurement combinations—including shear modulus, jacketed and unjacketed compressibility, fluid‑content coefficient, and porosity—for isotropic systems, noting that any adequate set of measurements can fix the system properties. They show that porosity is unnecessary when variables are properly expressed, that the fluid‑content coefficient measures fluid entering pores during unjacketed compressibility tests, provide four stress–strain expressions linking measured coefficients to the theory’s originals, and demonstrate that the method extends to anisotropic and nonlinear incremental cases.

Abstract

Abstract The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.