Deformation parameters of permeable media

Abstract

Summary Using the static form of a system of equations for seismic waves (de la Cruz & Spanos 1989), we show how various compressibilities can be calculated in a straightforward manner. The results obtained have many points of contact with those found in the literature. In particular, we verify all identities among drained compressibilities given in, e.g., Zimmerman (1991), thus providing an alternative route towards them. The undrained compressibility is described within the context of this work and its relation to the various drained compressibilities (Gassmann 1951) is verified. For greater experimental flexibility, we introduce a one-parameter family of compressibilities which includes the drained and the undrained compressibilities as members. The family of compressibilities is also used to obtain an expression for the pore-pressure build-up coefficient. In this work we also address the problem of macroscopic shearing. Experiments are proposed for the determination of the macroscopic shear modulus, leading to natural expressions for ‘Young's modulus’ and ‘Poisson's ratio’ for the porous medium under drained conditions. We also establish connections with Biot's (1956a) parameters.