The Dynamic Theory of the Deformation of a Granular Solid Fully Saturated with a Liquid

Abstract

The author, at first, derives the 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 the skeleton constituted by solid particles is a linear visco-elastic solid. The theory consists of three fundamental equations, that is, the equations of motion for pore liquid and solid skeleton, and the equation of continuity between the particles and the liquid. In the second place, a formal method is considered for solving the fundamental equations in a case where the liquid and the particles are incompressible in the gravitational field, and we have the respective equations of the dilatation, rotation in the solid skeleton and of the piezometric head of the liquid. Finally, it will be found that these respective equations obtained by a quasi-static treatment 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. An example is shown for the motion of ground water in a simple model as seen in the figure.