Non-axisymmetric Biot consolidation analysis of multi-layered saturated poroelastic materials with anisotropic permeability

Abstract

To start with, an analytical layer-element (i.e., a symmetric stiffness matrix), which describes the relationship between the generalized displacements and the stress levels of a layer subjected to non-axisymmetric loading, is exactly derived in the transformed domain by the application of a Laplace-Hankel transform with respect to variables t and r, a Fourier expansion with respect to variable θ, and a Laplace transform and its inversion with respect to variable z, based on the governing equations of Biot's consolidation of multi-layered saturated poroelastic materials with anisotropic permeability. The analytical layer-element experiences considerable improvement in computation efficiency and stability, since it only contains negative exponential functions in its elements. In addition, a global stiffness matrix for multi-layered saturated poroelastic media is obtained by assembling the interrelated layer-elements based on the continuity conditions between adjacent layers. By introducing the boundary conditions and solving the global stiffness matrix, the solutions in the Laplace-Hankel transformed domain are obtained, and the final solutions can be recovered by a numerical inversion of the Laplace-Hankel transform. Finally, numerical examples are presented to verify the theory and to study the effect of the property of anisotropic permeability on vertical displacements and excess pore pressure. The calculation results show that the property of anisotropic permeability has a great influence on the process of consolidation.

Study on One-Dimensional Large Deformation Consolidation of Soil considering Liquid Phase Inertia

“…In accordance with Terzaghi's theory of effective stress (11a) and by calculating partial derivatives with respect to time variable at both sides of (11b), the equivalent relationship between the rate of void ratio with total stress in soil and excess pore pressure is obtained in (12).…”

“…Combining equation (7), equation (12), and consolidation equation (10), equation ( 13) is obtained. Further simplification can obtain the large deformation consolidation control equation with the excess pore pressure as the control variable in (14).…”

“…Based on this model, Li and Xie [11] made relevant calculations for solution. Ai and Cang [12] consider the nonaxisymmetric nature of soil penetration, and the calculation of multilayered saturated soil shows that permeability has a significant effect on consolidation. It can be concluded that researchers have been exploring how to elaborate the physical process of soil consolidation under the condition of large deformation.…”

Analysis of axisymmetric thermo-elastic problem in multilayered material with anisotropic thermal diffusivity

“…The objective of this paper is to introduce the analytical layerelement method [15][16][17][18] to study the behavior of multilayered material with anisotropic thermal diffusivity containing a heat source at an arbitrary depth. Three types of heat sources, a point heat source, a circular area source and a ring heat source, are considered to satisfy different practices.…”

BEM analysis of elastic foundation beams on multilayered isotropic soils

“…Over the past several decades, various methods for the boundary value problems in multilayered elastic materials have been developed, including the transfer matrix method (Bufler, 1971;Bahar, 1972;Ai et al, 2002), the stiffness matrix method (Kausel and Seak, 1987), the finite layer method Booker, 1984, 1986), and the analytical layerelement method (Ai et al, 2010;Ai and Cang, 2013). These methods have created conditions for the interaction analysis of foundations and multilayered soils.…”