Seepage consolidation under elastic body's deformation under normal load

Abstract

© 2019 IOP Publishing Ltd. The process of seepage consolidation of an elastic saturated body under the action of a normal load that is instantly applied to its surface is considered. The fluid and the skeleton grains are assumed to be incompressible and the volume skeleton strains are related to grain repacking. To the well-known spatial consolidation scheme is added the equality obtained using the conditions of compatibility of deformations. It is shown that the sum of effective normal stresses satisfies the heat equation and with a known boundary condition can be found as a solution to the corresponding boundary value problem. On the surface of the body for pressure is adopted the condition high-permeability piston. A pressure-related auxiliary function that satisfies the Laplace equation is introduced. The boundary condition for it is determined by the boundary condition for the above sum. The proposed scheme for studying the consolidation of an elastic body is illustrated by the example of uniform normal loading of the surface of an elastic porous sphere. The formulations of the corresponding boundary value problems are given. In the analytical form the pressure of the fluid, the total and effective normal stresses of the skeleton, the displacement of points of the sphere and its surface in the process of consolidation were found. It is shown that the pressure of the fluid at each fixed point inside the sphere decreases with increasing time.