Seepage consolidation during elastic body deformation under normal load

F.M. Kadyrov ^∗, A.V. Kosterin ^∗∗, E.V. Skvortsov ^∗∗∗

Kazan Federal University, Kazan, 420008 Russia

E-mail:  ^∗Farhad1987@mail.ru,  ^∗∗Alexander.Kosterin@kpfu.ru,  ^∗∗∗Eduard.Scvortsov@mail.ru

Received October 13, 2018

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DOI: 10.26907/2541-7746.2019.1.66-74

For citation: Kadyrov F.M., Kosterin A.V., Skvortsov E.V. Seepage consolidation during elastic body deformation under normal load. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 1, pp. 66–74. doi: 10.26907/2541-7746.2019.1.66-74. (In Russian)

Abstract

The process of seepage consolidation of an elastic saturated body under the normal load that is instantly applied to its surface has been considered. An equality obtained using the conditions of compatibility of deformations has been added to the well-known spatial consolidation scheme. It has been shown that the sum of effective normal stresses satisfies the heat equation and can be found as a solution to the corresponding boundary value problem. A pressure-related auxiliary function that satisfies the Laplace equation has been 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 has been illustrated by the example of uniform normal loading on the surface of an elastic porous sphere. 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 have been found. It has been demonstrated that the pressure of the fluid at each fixed point inside the sphere decreases with increasing time.

Keywords: consolidation, elastic body, load, pressure

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