Dynamics of Saturated Rocks. I: Equations of Motion

Abstract

The field and constitutive equations expressing the dynamic behavior of fully saturated elastic rocks with two degrees of porosity—one due to the pores and the other due to the fissures—are developed. The corresponding linearized governing equations of motion are then constructed to form a system of 11 partial differential equations with 11 unknowns. The various phenomenological coefficients of the theory are identified and expressed in terms of measurable quantities. The quasi‐static case with two degrees of porosity and the dynamic case with one degree of porosity are easily obtained as special cases of the present formulation and compared with those due to Aifantis and Biot, respectively. A comparison of the present equations of motion against those due to Wilson and Aifantis is also made.