3-D consolidation of multilayered porous medium with anisotropic permeability and compressible pore fluid

Excerpt

Porous medium can be reckoned as one of the most common existences in natural or artificial environment, and many engineering problems such as the wave propagation problem [1] and the flow and heat transfer problem [2, 3] in porous medium have been modeled and solved. Saturated soils and rocks can also be regarded as porous medium, and their consolidation problems under external loads are usually difficult problems encountered in geotechnical engineering. The general theory of three-dimensional consolidation, which considers the coupling between the solid and the fluid in a porous medium, was first introduced by Biot [4]. In the past few decades, analytical solutions based on the Biot’s consolidation theory have been developed by many investigators [5‐14]. To provide alternative approaches to solve the Biot’s consolidation problem of multilayered soils, the first author and his cooperators [15, 16] took full use of the displacement functions proposed in Refs. [5‐7, 17] and obtained a systemic solution to the discussed problems including axisymmetric, non-axisymmetric, plane-strain and three-dimensional Biot’s consolidation of multilayered soils; furthermore, a novel analytical technique [18, 19] was developed to solve the Biot’s consolidation equations directly by using the Laplace transform with respect to z, which facilitated the deduction of the corresponding solutions. …