Transfer matrix solutions to axisymmetric and non-axisymmetric consolidation of multilayered soils

Ai, Zhi Yong; Wang, Quan Sheng; Han, Jie

doi:10.1007/s00707-009-0224-x

Cited by 13 publications

(3 citation statements)

References 22 publications

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“…Analytical solutions for the consolidation of a semi-infinite poroelastic body and a single or multi-layered saturated poroelastic material system have been acquired Gibson, 1960a, 1960b;Schiffman and Fungaroli, 1965;Booker and Small, 1982a, 1982bVardoulakis and Harnpattanapanich, 1986;Yue et al, 1994;Yue and Selvadurai, 1995;Senjuntichai and Rajapakse, 1995;Pan, 1999). An efficient analytical algorithm to solve Biot's consolidation of a multi-layered saturated poroelastic material system is the transfer matrix method (Bahar, 1972;Fang, 2001, 2003;Ai et al, 2008aAi et al, , 2008bAi et al, , 2010bAi et al, , 2010cAi and Cheng, 2009a). However, it is difficult to eliminate the positive exponential functions involved in the elements of the transfer matrix, which may lead to unstable numerical results or overflow in the calculation, due to the influence of numerically illconditioned matrices.…”

Section: Introductionmentioning

confidence: 98%

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

Ai¹,

Cang²

2013

Soils and Foundations

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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.

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Section: Introductionmentioning

confidence: 98%

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

Ai¹,

Cang²

2013

Soils and Foundations

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“…Ai and Cheng presented numerical analysis for 3D consolidation with the anisotropic permeability of a layered soil system, and the effect of anisotropic permeability on the consolidation behavior has been discussed [12]. Ai et al [13] and Ai and Cheng [14] presented alternative approaches to solving Biot's consolidation problem and obtained an organized solution to the consolidation problems. Ai and Wang [15] and Ai et al [16] also developed an analytical procedure to solve Biot's consolidation equations by directly using the Laplace transform method.…”

Section: Introductionmentioning

confidence: 99%

Effect of Vertical Pressure on Horizontal and Vertical Permeability of Soil and Effect of Surcharge Pressure on 3D Consolidation of Soil

Laskar

Pal

2018

Advances in Civil Engineering

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Permeability and consolidation of soil are known as the most variable soil properties. The values of permeability and consolidation of soil may vary with depth even in case of homogeneous soil layers, and because of that, the determination of appropriate values of permeability and consolidation is a complex and complicated engineering task. In this study, horizontal and vertical permeability apparatus and a 3D (three-dimensional) consolidation apparatus are developed to determine the effects of vertical pressure on horizontal and vertical permeability and the effects of vertical surcharge pressures on three-dimensional consolidation of soil. A series of horizontal and vertical permeability tests of soil under different vertical pressures and a series of 3D consolidation tests under different surcharge pressures are performed. From the study, it is observed that the horizontal and vertical permeability of soil changes with the changes in vertical pressures, and 3D consolidation of soil also changes with the changes in surcharge pressures. The horizontal and vertical permeability values obtained from the newly developed horizontal and vertical permeability apparatus are used in Terzaghi’s one-dimensional consolidation theory to find out the consolidation characteristics of the soil, and it is compared with the results obtained from the newly developed 3D consolidation apparatus.

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“…The corresponding problem of circular loading has been discussed by Ai et al (2010a). Subsequently, Ai et al (2010b) presented transfer matrix solutions to study the axisymmetric and non-axisymmetric consolidation of a multilayered soil under arbitrary loading. However, in all the above three studies, the medium is assumed to be incompressible and permeability isotropic.…”

Section: Introductionmentioning

confidence: 99%

Consolidation of a Poroelastic Half-Space

Singh

Rani

Kumar³

2013

MJIS

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A porous medium is an elastic solid permeated by an interconnected network of pores filled with a fluid. Both solid and pore network are assumed to be continuous so as to form two interpenetrating continua. The theory of poroelasticity investigates the time-dependent coupling between the deformation of the elastic solid skeleton and fluid flow within the skeleton. The solid-to-fluid and fluid-to-solid couplings are assumed to occur instantaneously in the quasi-static approximation in which elastic wave propagation is ignored. Consolidation of a poroelastic body takes place when it is acted upon by surface loads. The study of consolidation of a poroelastic half-space or stratum has received much attention due to its geophysical and engineering applications. The aim of the present paper is to review recent work on the subject, indicating the assumptions made, methods used and conclusions drawn.

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Transfer matrix solutions to axisymmetric and non-axisymmetric consolidation of multilayered soils

Cited by 13 publications

References 22 publications

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

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

Effect of Vertical Pressure on Horizontal and Vertical Permeability of Soil and Effect of Surcharge Pressure on 3D Consolidation of Soil

Consolidation of a Poroelastic Half-Space

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