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

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

doi:10.1007/s10665-009-9299-6

Cited by 7 publications

(4 citation statements)

References 35 publications

(25 reference statements)

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“…Wang and Fang 30,31 applied the state vector and the transfer matrix method to solve the consolidation problem of axisymmetric and asymmetric multi-layered saturated poroelastic media. Considering the fluid compressibility and the permeability anisotropy of the soil, Chen 32 and Ai et al [33][34][35] obtained the transfer matrix solution of the layered poroelastic soil. Booker and Small 36,37 applied the theory of the finite layer method 38 to the consolidation analysis of horizontal layered soil, which reduces the partial differential equation to ordinary differential equation and improves the calculation efficiency greatly.…”

Section: Introductionmentioning

confidence: 99%

“…Wang and Fang 30,31 applied the state vector and the transfer matrix method to solve the consolidation problem of axisymmetric and asymmetric multi‐layered saturated poroelastic media. Considering the fluid compressibility and the permeability anisotropy of the soil, Chen 32 and Ai et al 33–35 . obtained the transfer matrix solution of the layered poroelastic soil.…”

Section: Introductionmentioning

confidence: 99%

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The consolidation behavior of layered fractional viscoelastic soils considering groundwater

Ai,

Ye,

Jiang

et al. 2024

Num Anal Meth Geomechanics

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This paper investigates the consolidation behavior of multi‐layered viscoelastic soils considering groundwater. First, the fractional Merchant viscoelastic model is introduced to describe the behavior of multi‐layered viscoelastic soils considering groundwater. Later, the governing equations are extended to a viscoelastic medium by virtue of the elastic‐viscoelastic corresponding principle in the Laplace–Hankel domain. According to the extended precise integration method, the soil layer is divided into a series of layer units. Then the relationship between general stress vector and general displacement vector on the top and bottom planes is established. Every two adjacent layer units are combined into one layer in each computational iteration. The solutions in the Laplace–Hankel domain are obtained by considering the boundary conditions, and numerical inversion is performed to obtain the solutions in the physical domain. The practicability of the present method is assessed by comparing the numerical results with those in the existing literature and done by ABAQUS. Finally, the effects of groundwater table, properties of the soils above groundwater table, load depth, viscoelastic parameters, and soil stratification are investigated.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The consolidation behavior of layered fractional viscoelastic soils considering groundwater

Ai,

Ye,

Jiang

et al. 2024

Num Anal Meth Geomechanics

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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: 99%

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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“…solved Biot's three-dimensional consolidation problem for a saturated poroelastic multi-layered soil due to loading at an arbitrary interface in the Cartesian coordinate system using transfer matrix method. 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.…”

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

Cited by 7 publications

References 35 publications

The consolidation behavior of layered fractional viscoelastic soils considering groundwater

The consolidation behavior of layered fractional viscoelastic soils considering groundwater

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

Consolidation of a Poroelastic Half-Space

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