State space solution to three-dimensional consolidation of multi-layered soils

Ai, Zhi Yong; Zehai, Cheng; Han, Jie

doi:10.1016/j.ijengsci.2007.12.003

Cited by 30 publications

(18 citation statements)

References 18 publications

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“…The state space equation of three-dimensional consolidation usually comprises eight coupled state vectors [11,12]. In order to simplify derivation and calculation, intermediate variables are introduced as follows:…”

Section: Uncoupled State Space Equations and Their Solutionsmentioning

confidence: 99%

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Uncoupled state space solution to layered poroelastic medium with anisotropic permeability and compressible pore fluid

Cheng

2011

Front. Archit. Civ. Eng. China

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This paper presents an uncoupled state space solution to three-dimensional consolidation of layered poroelastic medium with anisotropic permeability and compressible pore fluid. Starting from the basic equations of poroelastic medium, and introducing intermediate variables, the state space equation usually comprising eight coupled state vectors is uncoupled into two sets of equations of six and two state vectors in the LaplaceFourier transform domain. Combined with the continuity conditions between adjacent layers and boundary conditions, the uncoupled state space solution of a layered poroelastic medium is obtained by using the transfer matrix method. Numerical results show that the anisotropy of permeability and the compressibility of pore fluid have remarkable influence on the consolidation behavior of poroelastic medium.

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Section: Uncoupled State Space Equations and Their Solutionsmentioning

confidence: 99%

“…Many studies [2][3][4][5][6][7][8][9][10][11][12] have been conducted on Biot's consolidation problem, however, in almost all of these studies, permeability was assumed to be isotropic. In the actual engineering situations, the soils and rocks are formed through a sedimentation process which produces the horizontal stratification.…”

Section: Introductionmentioning

confidence: 99%

Uncoupled state space solution to layered poroelastic medium with anisotropic permeability and compressible pore fluid

Cheng

2011

Front. Archit. Civ. Eng. China

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“…Assume that the solid and the pore fluid in soils are incompressible [1][2][3][4][5][6][7][8][9][14][15][16][17][18]20] and the solid in soils is isotropic [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . The constitutive equations of plane strain Biot's consolidation are [3][4] …”

Section: Basic Governing Equationsmentioning

confidence: 99%

“…As above mentioned, the solid in soils usually can be modelled as an isotropic medium [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . However, the permeability of soils is often anisotropic because of their sedimentation process [19][20] .…”

Section: Basic Governing Equationsmentioning

confidence: 99%

Plane strain consolidation of soil layer with anisotropic permeability

2009

Appl. Math. Mech.-Engl. Ed.

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This paper presents an alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer is established between the ground surface (z = 0) and the depth z in the Laplace-Fourier transform domain. Combined with the boundary conditions, an exact solution is derived for plane strain Biot's consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform are adopted to obtain the actual solution in the physical domain. Numerical results of plane strain Biot's consolidation for a single soil layer show that the anisotropic of permeability has a great influence on the consolidation behavior of the soils.

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“…The solution to the ordinary-differential matrix equation (8) can be obtained using the theorem of the CayleyHamilton [32]; however, it will lead to a complex work load [22]. In this study, the solution of the ordinary-differential matrix equation (8) is obtained directly using the Laplace transform and its inversion [33] of the z-domain.…”

Section: Transfer Matrix For a Single Soil Layermentioning

confidence: 99%

Analytical solutions describing the consolidation of a multi-layered soil under circular loading

Wang

Han

2009

J Eng Math

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Analytical solutions describing the consolidation of a multi-layered soil under circular loading are presented. From the governing equations of saturated poroelastic soil in a cylindrical coordinate system, the eighthorder state-space equation of consolidation is obtained by eliminating the variation of time t using the Laplace transform together with the technique of Fourier expansions with respect to the coordinate θ and the Hankel transform with respect to coordinate r . The solution of the eighth-order state-space equation is derived directly by using the Laplace transform and its inversion of the z-domain. Based on the continuity between layers and the boundary conditions, the transfer-matrix method is utilized to derive the solutions for the consolidation of a multi-layered soil under circular loading in the transformed domain. By the inversion of the Laplace transform and the Hankel transform, the analytical solutions in the physical domain are obtained. A numerical analysis based on the solutions is carried out by a corresponding program.

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State space solution to three-dimensional consolidation of multi-layered soils

Cited by 30 publications

References 18 publications

Uncoupled state space solution to layered poroelastic medium with anisotropic permeability and compressible pore fluid

Uncoupled state space solution to layered poroelastic medium with anisotropic permeability and compressible pore fluid

Plane strain consolidation of soil layer with anisotropic permeability

Analytical solutions describing the consolidation of a multi-layered soil under circular loading

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