The unconfined compression of a poroelastic annular cylindrical disk

Abstract

The analytical solution to the problem of a saturated annular poroelastic disk subjected to unconfined compression in the case when the fluid and solid constituents of the poroelastic medium are both compressible is recorded. Infinitesimal deformations and transverse isotropy are assumed. The algebraic complexity of the problem stems from the need to have the solution to the problem for three different sets of boundary drainage conditions on fluid flow or no flow through the inner and outer boundaries of the annular disk. The analytical solution demonstrates the effects of the assumptions of isotropy versus transverse isotropy and compressibility versus incompressibility of the poroelastic constituents. The advantages of this solution are that they provide insight into the nature of the elastic response and fluid flow of soft tissues versus hard tissues and saturated swampy soils versus saturated rocks and as an analytical tool to analyze unconfined compression experiments performed on these materials.