Dynamic Green’s functions for a poroelastic half-space

Zheng, Pei; Zhao, Shengfeng; Ding, Ding

doi:10.1007/s00707-012-0720-2

Cited by 40 publications

(11 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, for the isotropic case, the matrixes m ij and b ij are reduced to two numbers, the tensor degenerates to a scalar α ij = δ ij α , and Equations a and 10b are the same as the isotropic equations derived in the literature …”

Section: Biot's Anisotropic Poroelastic Model and Its General Solutionsmentioning

confidence: 99%

“…Because most geophysical applications involve an infinite boundary with zero traction, so the half‐space fundamental solutions for fluid saturated porous solids seem more desirable in solving practical problems. The dynamic Green's functions for a poroelastic half‐space were widely investigated by Philippacopoulos, Jin and Liu, and Zheng et al The Green's functions for a horizontal point force buried in a poroelastic half‐space is given by Jin and Liu . The three‐dimensional time‐harmonic response of a poroelastic half space subjected to an arbitrary buried loading is investigated by Chen et al The dynamic responses of a poroelastic half‐space to an internal point load and fluid source are investigated in the frequency domain by Zheng et al By introducing the surface terms to fulfil the free‐surface boundary conditions, the complete 2.5‐D Green's function for a poroelastic half‐space is derived by Zhou et al The fully coupled model with the source functions (including the fluid dilation contribution) was presented by Pan for the layered poroelastic half‐space.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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: Biot's Anisotropic Poroelastic Model and Its General Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

“…It should be noted that the left hand side of Equation 43 represents the propagating waves from the interface of the ith and (i + 1)th layers into the layers ( Figure 3C), while the right-hand side represents the incident waves from the ith and (i + 1)th layers toward the interface ( Figure 3A). Also, in accordance with the physical context, the 3 × 3 matrices R u;i and R d;i are termed the PPS reflection matrices, respectively, for upward and downward waves encroaching the ith interface (z i ), while the 3 × 3 matrices T u;i and T d;i denote the complementary transmission matrices for the same surface of material discontinuity ( Figure 3B).…”

Section: Propagation Of Coupled Body Wavesmentioning

confidence: 99%

“…Senjuntichai and Rajapakse determined Green's functions for internal loads and fluid sources, which can be used in integral‐based numerical analysis of the same boundary value problems, however, with more complicated geometries. Also, Philippacopoulpos and Zheng et al have dealt with the response of poroelastic isotropic half‐space because of different loading configurations. 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 .…”

Section: Introductionmentioning

confidence: 99%

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

Jafarzadeh

Eskandari‐Ghadi

2019

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

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.

show abstract

“…[26] for the elastic substrate and from Ref. [38] for the poroelastic surface. The poroelastic surface layer thickness d was 0.4 (mm).…”

Section: Numericalmentioning

confidence: 99%

Influence of Poroelasticity of the Surface Layer on the Surface Love Wave Propagation

Baroudi

2018

Journal of Applied Mechanics

View full text Add to dashboard Cite

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This is an author-deposited version published in: https://sam.ensam.eu Handle IDThis work presents a theoretical method for surface love waves in poroelastic media loaded with a viscous fluid. A complex analytic form of the dispersion equation of surface love waves has been developed using an original resolution based on pressure-displacement formulation. The obtained complex dispersion equation was separated in real and imaginary parts. MATHEMATICA software was used to solve the resulting nonlinear system of equations. The effects of surface layer porosity and fluid viscosity on the phase velocity and the wave attenuation dispersion curves are inspected. The numerical solu-tions show that the wave attenuation and phase velocity variation strongly depend on the fluid viscosity, surface layer porosity, and wave frequency. To validate the original theo-retical resolution, the results in literature in the case of an homogeneous isotropic sur-face layer are used. The results of various investigations on love wave propagation can serve as benchmark solutions in design of fluid viscosity sensors, in nondestructive testing (NDT) and geophysics.

show abstract

Dynamic Green’s functions for a poroelastic half-space

Cited by 40 publications

References 24 publications

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

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

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

Influence of Poroelasticity of the Surface Layer on the Surface Love Wave Propagation

Contact Info

Product

Resources

About