Fluid Saturated Porous Half Space Research Articles

Broadband surface wave attenuation in porous soil by elastic metasurfaces

To mitigate surface waves in ambient vibration, a novel broadband elastic metasurface is proposed by periodically burying the layered in-filled pipes below the ground surface. The present metasurface is a simple structure and can be easily implemented. In contrast to the existing studies of metasurfaces in single-phase elastic soil, the coupling of elastic metasurfaces with saturated porous soil is investigated within the framework of Biot's theory. Note that Biot's poroelasticity can capture the complexity of soils in the presence of fluids. Both dispersion and transmission analysis are comprehensively conducted. The present investigation shows that the elastic metasurfaces are suitable for a wide range of fluid-saturated porous soil, and a significant surface wave attenuation is observed within the attenuation zone of elastic metasurfaces. In addition, the burying depth is the key point of the design of elastic metasurfaces. Specifically, the surface wave attenuation zone (SWAZ) will vanish when the depth is larger than three times the periodic constant. Besides, the SWAZ will be widened by stacking the layers of elastic metasurfaces. Three layers is enough for the metasurface to attenuate more than 80 % surface wave energy. Due to the similar dynamic characteristics of elastic metasurface in the fluid-saturated porous half-space compared to dry half-space, single-phased soil can be used to simplify the analysis of saturated soil with ideal fluids. To widen the scope of application in elastic metasurfaces, the feasibility of ambient vibration mitigation by elastic metasurfaces is experimentally and numerically verified. The experimental results confirm an obvious wave attenuation within the SWAZ, and the average insertion loss (IL︸) is 9.8 dB. Last but not least, the performance of elastic metasurfaces to mitigate ground-borne vibration induced by trains is numerically studied in time domain. Elastic metasurfaces outperform traditional trenches within the main frequency range, and IL︸ is increased by 3.9–7 dB. Thanks to the excellent wave attenuation performance and subwavelength thickness, these novel elastic metasurfaces are expected to open new avenues in ambient vibration mitigation in the costal area of saturated soil.

Propagation characteristic of Love-type wave in different types of functionally graded piezoelectric layered structure

A mathematical model has been proposed for the analytical study of the propagation of Love-type wave in an initially stressed functionally graded piezoelectric material (FGPM) layer overlying an orthotropic fluid-saturated porous half-space. The expression of dispersion equation is derived in closed form for both electrically open and electrically short conditions. The impact of various affecting parameters viz. wave number, gradient parameter, tensile initial stress on the dispersion curve of Love-type wave has been revealed by means of graphical illustrations. Some remarkable observation has been made through numerical computation for different piezoelectric ceramics of BaTiO, PZT-4 and PZT-5A, respectively. The outcomes of the present study are momentous for both theoretical and practical implication for the surface acoustic wave (SAW) devices.

Impact of point source on fissured poroelastic medium: Green’s function approach

PurposeThe purpose of this paper is to investigate the mathematical model comprising a heterogeneous fluid-saturated fissured porous layer overlying a non-homogeneous anisotropic fluid-saturated porous half-space without fissures. The influence of point source on horizontally polarized shear-wave (SH-wave) propagation has been studied intensely.Design/methodology/approachTechniques of Green’s function and Fourier transform are applied to acquire displacement components, and with the help of boundary conditions, complex frequency equation has been constructed.FindingsComplex frequency relation leads to two distinct equations featuring dispersion and attenuation properties of SH-wave in a heterogeneous fissured porous medium. Using MATHEMATICA software, dispersion and damping curves are sketched to disclose the effects of heterogeneity parameters associated with both media, parameters related to rigidity and density of single porous half-space, attenuation coefficient, wave velocity, total porosity, volume fraction of fissures and anisotropy. The fact of obtaining classical Love wave equation by introducing several particular conditions establishes the validation of the considered model.Originality/valueTo the best of the authors’ knowledge, effect of point source on SH-wave propagating in porous layer containing macro as well as micro porosity is not analysed so far, although theory of fissured poroelasticity itself has vast applications in real life and impact of point source not only enhances the importance of fissured porous materials but also opens a new area for future research.

Reflection and transmission of elastic waves from an imperfect boundary between micropolar elastic solid half space and fluid saturated porous solid half space

ABSTRACTThis paper deals with the reflection and transmission of elastic waves from imperfect interface separating micropolar elastic solid half space and fluid saturated porous solid half space. Longitudinal and transverse waves impinge obliquely at the interface. Amplitude ratios of various reflected and transmitted waves are obtained and computed numerically and results obtained are depicted graphically. It is found that these amplitude ratios depend on angle of incidence of the incident wave, imperfect boundary and material properties of half spaces. A special case when fluid saturated porous half space reduces to empty porous solid is also deduced and discussed graphically.

Wave fields in the stratified fluid-saturated porous half-space induced by dislocation sources

In this study, the wave fields induced by both tensile and shear displacement dislocations in stratified fluid-saturated porous media are computed by using the reflection and transmission matrix method. The components of the source discontinuity vector across the source plane to describe those tensile and shear faults are explicitly displayed by using the surface vector harmonics. Numerical examples for a two layer model subjected to tensile and shear dislocations are provided. From the waveforms of surface displacements, the arrivals of transmitted and converted PS and SP waves at the interface of the two layer model can be clearly observed.

Poroelastodynamic potential method for transversely isotropic fluid-saturated poroelastic media

• A potential method is introduced for transversely isotropic fluid-saturated media. • A pair of scalar potentials is employed to uncouple the Biot's equations of motion. • Solutions are given for a half-space under an arbitrary surface time-harmonic loading. • The free surface is considered either completely permeable or impermeable boundary. • Half-space Green's functions for uniform circular surface patch loads are derived. By introduction of two scalar potentials, an analytical method is developed for the solution of poroelastodynamic boundary value problems in transversely isotropic fluid-saturated poroelastic media. The governing equations of motion are considered in the framework of Biot's complete model without any assumption or simplification. As a case of application, solutions in three dimensions for a transversely isotropic fluid saturated porous half space loaded by an arbitrary distribution of time harmonic tractions at the free surface is derived. The free surface of the half space may be considered either permeable or impermeable. As a particular solution, Green's functions for uniform vertical and horizontal circular patch loads are presented as semi-infinite integrals which may be evaluated by means of an appropriate numerical method proposed. The accuracy of the solutions is verified both analytically and numerically against the preceding solutions. Some numerical results are also presented to clarify the influence of different degrees of anisotropy and frequency of excitation on the response of the medium.

Torsional Surface Waves in an Inhomogeneous Layer over a Fluid Saturated Porous Half-Space

ABSTRACTIn the present paper the propagation of torsional surface waves is discussed in an inhomogeneous elastic layer lying over a fluid saturated porous half space. The inhomogeneity in rigidity and density in the inhomogeneous layer plays an important role in the propagation of torsional surface waves. The presence of fluid in the pores diminishes the velocity. Further, it is seen that if the layer becomes homogeneous and the porous half space is replaced by a homogeneous half space, the velocity of the torsional surface waves coincides with that of Love wave. The effect of inhomogeneity factors and porosity factor on the phase velocity of torsional surface wave is delimitated by means of graphs.

The vertical vibration of an elastic circular plate on a fluid-saturated porous half space

In this paper, the vertical vibration of an elastic circular plate on fluid-saturated porous half space is studied by a new analytical method. The contact between the elastic circular plate and the poroelastic half space is assumed to be smooth. The drainage conditions at the surface of the poroelastic half space are considered as either completely drained, or partially drained. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind. Numerical examples are given at the end of the paper.

Fluid point source and point forces in linear elastic diffusive half-spaces

Abstract This paper derives the fundamental solutions for the interior fluid point source and point forces embedded in a linear elastic fluid-saturated porous half-space. McNamee-Gibson and Schiffman-Fungaroli displacement functions are employed to uncouple the equilibrium equations of linear poroelasticity. Laplace-Hankel transform technique is used to solve the resulting partial differential equations for the displacement functions with appropriate boundary conditions. Analytic solutions in terms of inverse transforms are obtained. Numerical results show that the immediate radial displacement can be larger than the long terns movement under vertical point force; conversely, the immediate vertical displacement can be larger than the long term settlement under horizontal point force. As expected, Mindlin's solution is recovered as the steady state solution as the time factor ct/h2 approaches infinity (where c is the coefficient of consolidation, t the time variable and h the depth at which the point force or fluid point source is applied). The solutions for fluid point source compare well with the finite element predictions.