3D dynamic Green’s functions in a multilayered poroelastic half-space

Zheng, Pei; Ding, B.Z.; Zhao, Shengfeng; Ding, Ding

doi:10.1016/j.apm.2013.05.041

Cited by 36 publications

(11 citation statements)

References 32 publications

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“…Figure show the depth profiles of vertical displacements for (1,0,0 → 10) subjected to a horizontal point force and a fluid injection point source. As expected, an excellent match between the results computed with the Pei Zheng's method …”

Section: Numerical Resultssupporting

confidence: 80%

“…To provide a means to check the validity of the solutions presented in this article, sotropic problems of a poroelastic half‐space are selected, which are presented analytical solution by Zheng . Figure show the variation of vertical displacements along the x 1 ‐axis at the surface of a uniform poroelastic half‐space subjected to a horizontal point force and a fluid injection point source.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Dynamic Green's functions for an anisotropic poroelastic half‐space

Wang

Ding

Han

et al. 2020

Num Anal Meth Geomechanics

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Summary The dynamic responses of an anisotropic poroelastic half‐space under an internal point load and fluid source are investigated in the frequency domain in this paper. By virtue of Fourier transform and Stroh formalism, the three‐dimensional (3D) general solutions of the anisotropic Biot's coupling dynamics equations are derived in the frequency domain. Considering the two surface conditions, permeable and impermeable, the analytical solutions for displacement fields and pore pressure in half‐space under a point source (point load or a fluid source) are obtained. When the material properties are isotropic, the numerical results of the poroelastic half‐space are in excellent agreement with the existing analytical solutions. For anisotropic half‐space cases, numerical results show the strong dependence of the dynamic Green's functions on the material properties.

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Section: Numerical Resultssupporting

confidence: 80%

Section: Numerical Resultsmentioning

confidence: 99%

Dynamic Green's functions for an anisotropic poroelastic half‐space

Wang

Ding

Han

et al. 2020

Num Anal Meth Geomechanics

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“…Using the Fourier transform and omitting the e i w t terms from all quantities, Equations and can be transformed into the frequency domain as follows:

((), λ + G) \nabla \nabla \cdot bold-italicū + G \nabla^{2} \overset{u}{true} + ω^{2} ρ \overset{u}{true} - α \nabla \overset{p}{true} = bold0

\nabla^{2} \overset{p}{true} + \frac{ω^{2} ρ_{m}}{Q_{b}} \overset{p}{true} + ω^{2} α ρ_{m} \nabla \cdot ū = 0

where

\overset{u}{true}

and

\overset{p}{true}

are the displacement and pore pressure vectors in frequency domain; ω is the circular frequency; the frequency‐dependent imaginary parameter

ρ_{m 1} = - \frac{1}{\overset{k}{true}} \frac{i}{ω}

is introduced in Equation resulting a similar form of Equation to the wave propagation equation. The displacements of solid and fluid phases can be written in terms of the potential functions as follows using the Helmholtz decomposition:

({, \begin{matrix} array \\ array \bar{bold-italicu} = \nabla φ_{s} + \nabla \times ψ_{s} e & array a) \\ array \bar{bold-italicw} = \nabla φ_{f} + \nabla \times ψ_{f} e & array b) \end{matrix})

where

\overset{w}{true}

is the displacement of the fluid phase with respect to the solid phase; φ s and φ f represent the translational potential functions of the displacement of the solid and fluid phase, respectively; ψ s and ψ f represent the rotational potential function of the displacement of the solid and fluid phase, respectively; e is the unit vector.…”

Section: Artificial‐boundary Conditionmentioning

confidence: 99%

“…Using the Fourier transform and omitting the e iwt terms from all quantities, Equations (4) and (5) can be transformed into the frequency domain [76,77] as follows:…”

Section: The Assumption Of Outgoing Wavesmentioning

confidence: 99%

A local artificial‐boundary condition for simulating transient wave radiation in fluid‐saturated porous media of infinite domains

Jia

et al. 2017

Numerical Meth Engineering

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Summary The dynamic problem of wave propagation in infinite fluid‐saturated porous media is usually solved using the finite element method. Therefore, proper artificial‐boundary conditions are required to be imposed on the truncated boundaries of the dynamic finite‐element model to consider the radiation damping effect of the truncated media. A local artificial‐boundary condition is proposed for the dynamic problems in fluid‐saturated porous media in the u−p formulation. It avoids making the unrealistic assumption of zero permeability that is widely used in the existing artificial‐boundary conditions. Moreover, the proposed method can be implemented easily into finite element or finite difference codes as stress and flow velocity boundary conditions. Numerical results obtained from the finite element model using the proposed artificial boundary indicate that the proposed method is stable for long time and is more accurate than several existing methods. Copyright © 2017 John Wiley & Sons, Ltd.

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“…Moreover, Rajapakse and Senjuntichai and Jianwen and Hongbin evaluated dynamic response of multilayered poroelastic isotropic half‐space with the aid of dynamic stiffness matrix method . Lu and Hanyga, with the use of the reflection and transmission matrix method, presented fundamental dynamic solution for an axissymmetric multilayered poroelastic isotropic medium, and Zheng et al, with the same method, reported the 3D dynamic Green's functions for a multilayered poroelastic isotropic half‐space. Ai and Wang have utilized analytical layer element method for each layer and assembled the global stiffness matrix to obtain dynamic response of multilayered poroelastic isotropic half‐space in frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Surface load dynamic solution of saturated transversely isotropic multilayer half‐space

Jafarzadeh

Eskandari‐Ghadi

2019

Num Anal Meth Geomechanics

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Summary This paper treats the dynamic response of a multilayered transversely isotropic fluid saturated poroelastic half‐space under surface time‐harmonic traction. The governing system of partial differential equations is uncoupled with the use of a set of physically meaningful and complete potential functions that decompose different body waves in a saturated poroelastic transversely isotropic medium. After expressing the equations in the Hankel‐Fourier domain, a proper algebraic factorization is applied to generate reflection and transmission matrices for decomposed waves. All responses including displacements, stresses, and pore fluid pressure for both general patch load and point load are presented in the form of semi‐infinite line integrals. The verification of the method is confirmed with the degeneration of the solutions presented here to the existing solutions for dried both homogeneous and multilayered elastic half‐spaces as well as poroelastic half‐space. Selected numerical results are depicted to investigate the effects of layering and pore pressure on responses of a transversely isotropic poroelastic medium. The load distribution effects are studied by comparison of the patch and point load responses. Also, resonance notion and effective parameters on this phenomenon such as layering system and anisotropy contrast are discussed. Significant influence of materials and layering configuration on number and amplitude of resonances depicted through the numerical evaluation.

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3D dynamic Green’s functions in a multilayered poroelastic half-space

Cited by 36 publications

References 32 publications

Dynamic Green's functions for an anisotropic poroelastic half‐space

Dynamic Green's functions for an anisotropic poroelastic half‐space

A local artificial‐boundary condition for simulating transient wave radiation in fluid‐saturated porous media of infinite domains

Surface load dynamic solution of saturated transversely isotropic multilayer half‐space

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