Visco-Elastic Theory of the Deformation of a Confined Aquifer

Abstract

The author derived a dynamic theory for the deformation of a granular solid saturated with a liquid, assuming that the liquid filling up the pore space is a Newtonian viscous fluid and that the skeleton constituted by solid particles is a linear visco-elastic solid. The theory consists of the three fundamental equations, that is, the equations of motion of the liquid and the skeleton and the equation of continuity between the particles and the liquid. In a case where the particle and liquid are taken to be incompressible and the deformation of soil takes place on a quasi-static process, these equations are accepted as the theory of three-dimensional consolidation, including Terzaghi's well-known equation as a special case, and are also recognized as the basic equations of motion of confined ground water in a visco-elastic aquifer. A theoretical example will be shown for the rheological deformation of an infinite confined aquifer with uniform thickness caused by pumping up water at a constant rate.