Dynamic Response of a Multilayered Poroelastic Half-Space to Harmonic Surface Tractions

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

doi:10.1007/s11242-013-0182-6

Cited by 16 publications

(9 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this study, when d = 0, it is the Lamb's problem. As shown in Figure , the results calculated by the present method is in excellent agreement with the analytical solution obtained by Philippacopoulous …”

Section: Numerical Resultssupporting

confidence: 87%

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

Wang

Ding

Han

et al. 2020

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

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.

show abstract

Section: Numerical Resultssupporting

confidence: 87%

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

Wang

Ding

Han

et al. 2020

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

show abstract

“…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%

“…l P 1 , l P 2 and l S are the numbers of the P1, P2 and S wave, respectively. Moreover, other parameters are defined as follows:

({, \begin{matrix} array \\ array ρ_{1, 2} = ρ (d_{2} \mp \sqrt{d_{2}^{2} - d_{1} d_{3}}) \\ array d_{1} = \frac{λ + 2 G}{Q_{b}} \\ array d_{2} = \frac{1}{2 ρ} [ρ_{m} \frac{λ + 2 G + α^{2} Q_{b}}{Q_{b}} + ρ] \\ array d_{3} = \frac{ρ_{m}}{ρ} \end{matrix}), η_{1, 2} = \frac{α Q_{b}}{ρ_{m} {\overset{C}{true}}_{P 1, 2}^{2} - Q_{b}}

The potential functions of the displacements of the solid and fluid phase respectively are expressed in Equation by introducing the potential functions of the P1 and P2 waves

({, \begin{matrix} array \\ array φ_{s} = φ_{P 1} + φ_{P 2} \\ array φ_{f} = η_{1} φ_{P 1} + η_{2} φ_{P 2} \end{matrix})

where φ P 1 and φ P 2 represent the potential functions of P1 and P2 waves, respectively.…”

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%

“…The potential functions of the displacements of the solid and fluid phase respectively are expressed in Equation (16) by introducing the potential functions of the P1 and P2 waves [76]…”

Section: The Assumption Of Outgoing Wavesmentioning

confidence: 99%

See 2 more Smart Citations

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

View full text Add to dashboard Cite

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.

show abstract

Dynamic behaviour of layered transversely isotropic poroelastic media subjected to rectangular harmonic loads

2022

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

This paper aims to investigate the dynamic behaviour of layered transversely isotropic (TI) poroelastic media subjected to rectangular harmonic loads. First, governing equations of a medium layer derived from Biot's dynamic theory of porous media and constitutive equations of TI materials are converted into the ordinary differential domain by means of integral transform techniques. Next, by introducing boundary and load conditions, the extended precise integration method (PIM) is applied to obtain the solution for a multi-layered system. Then, after an inverse integral treatment, the numerical results in the physical domain are verified with published work, and some examples are designed to unravel the effect of transverse isotropy, load frequencies and stratification on the dynamic behaviour of media.

show abstract

Dynamic Response of a Multilayered Poroelastic Half-Space to Harmonic Surface Tractions

Cited by 16 publications

References 29 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

Dynamic behaviour of layered transversely isotropic poroelastic media subjected to rectangular harmonic loads

Contact Info

Product

Resources

About