Równania teorii konsolidacji w przypadku występowania źródeł cieczy i szkieletu

The object of the present considerations is to derive the equations of the theory of consolidation for a porous body in the case of a source of liquid and a skeleton. The equations derived are used to obtain the solutions for the particular cases of an instanteneous point source of liquid and a skeleton in the infinite space and a point source of constant intensity. The argument is based on the theory of liquid flow through deformable porous bodies established by Biot and on the generalized Darcy law. A set of coupled differential equations is obtained, composed of the three equations of displacement, the flow equation and an independent Poisson equation. In the limit case, in which the porosity f0 - 1, in the neighbourhood of the source, which corresponds to the action of a liquid source alone, the solution of this set of equations leads to the known equations of Derski. The set of equations of the theory of consolidation thus found and their solution may find application to hydro-geological problems and to those of the mining practice.