Porous Half-space Research Articles

Dynamics of Love-type wave propagation in composite transversely isotropic porous structures

The present study aims to analyze the propagation behavior of Love-type wave in a composite transversely isotropic porous structure. The structure comprises an inhomogeneous sandy porous layer lying between a non-homogeneous magneto-poroelastic layer and a heterogeneous fractured porous half-space. Analytic solutions of the field equations of the respective media involve the application of the variable separable method and Wentzel-Kramers-Brillouin (WKB) asymptotic approach for the conversion of partial differential equations into ordinary differential equations. Through careful imposition of boundary conditions and subsequent elimination of arbitrary constants, we derive a complex dispersion relation governing the propagation of Love-type waves. This dispersion equation yields both the phase velocity curve, corresponding to the real expression, and the damping velocity curve, derived from the imaginary expression. To represent our findings, we conduct extensive calculations and graphical simulations illustrating the influence of various material parameters such as heterogeneity, porosity, volume fraction of fractures, sandiness, magnet-oelastic coupling, angle at which wave crosses the magnetic field, and layer thickness on the dispersive nature of Love-type waves using MATHEMATICA software. Furthermore, we conduct case-specific analyses, revealing instances where the dispersion equation simplifies to the standard Love wave equation, thereby validating our mathematical framework. Our findings underscore the significant influence of the aforementioned material parameters on the phase and damping velocities of Love-type wave. This interdisciplinary investigation into different porous media opens new avenues for future research and has significant implications in various disciplines, ranging from engineering and geophysics to environmental science and beyond.

Comparative analysis of double and single porosity effects on SH-wave induced vibrations in periodic porous lattices

The manuscript presents a novel study comparing the impact of single and double porosity on horizontally polarized shear wave (SH-wave) propagation in corrugated elastic void materials. The considered mathematical model comprises two cases; the first one depicts SH-wave propagation through a void porous layer having creased boundaries and resting over a heterogeneous anisotropic fluid-saturated fractured porous half-space, whereas according to the second case, heterogeneous anisotropic fluid-saturated porous semi-infinite medium without fractures has been considered. In both cases, rigidity and density of the half-space vary quadratically with depth. The separable variable method is used to attain the complex frequency equation for each case that leads to two different dispersion relations associated with two distinct wave fronts. The first wave front depends on the void parameters, whereas the second wave front defines the propagation of SH-waves in an elastic layer without void pores. In each case, the complex dispersion relation has been separated into two equations that illustrate the dispersion and attenuation properties of SH-waves. Using the variations in the inhomogeneity, position, fluctuation, flatness, total porosity, and anisotropy parameters, case I and case II have been compared in each graphical execution. In addition, the surface response of shear stress and displacement have been implemented graphically.

The modified physics-informed neural network (PINN) method for the thermoelastic wave propagation analysis based on the Moore-Gibson-Thompson theory in porous materials

This paper presents novel contributions to both theory and solution methodology in AI-based analysis of solid mechanics. The physics-informed neural network (PINN) method is developed for thermoelastic wave propagation and Moore-Gibson-Thompson (MGT) coupled thermoelasticity analysis of porous media, a first in the field. The coupled thermoelasticity governing equations, based on the MGT heat conduction model, are derived for a porous half-space, with the thermal relaxation coefficient and strain relaxation factor being considered. Mechanical and thermal shock loading boundary conditions are imposed. The behavior of a magnesium-made porous body is analyzed using the PINN method, with highly accurate results being achieved for the system of coupled PDEs. An adaptive hyperparameter tuning approach, integrating a generalized subset design (GSD) and Bayesian optimization algorithm, is used to automatically select the optimal structure based on the L2 relative error. This hybrid methodology eliminates manual adjustment concerns. The proposed method is verified through a thorough comparison with the Lord-Shulman theory of coupled thermoelasticity. The strength of the methodology lies in its ability to operate without domain data, with only boundary and initial points being required. Four example sets are examined to demonstrate the capabilities of the modified PINN, and high-quality predictions of dimensionless fields’ variables over an extended time interval are obtained, confirming its extrapolation abilities.

Analysis of Love-type wave in a piezoelectric layer bonded between fiber-reinforced viscoelastic and dual porous media

Love-type wave propagation in a piezoelectric layer bonded by a layer of fiber-reinforced viscoelastic and a heterogeneous fluid-saturated cracked dual porous half-space is investigated in this paper. The heterogeneity of fracture double porous medium is assumed to be exponential distribution functions. With the help of the variable separation technique, the governing equations of each layer and half-space are solved to get the solutions of mechanical displacement and electric potential function. The results are confirmed by comparison with the classical case of Love wave, and special cases of the problem are also discussed. The phase velocity is calculated numerically and plotted graphically for various material characteristics of the layers and half-space. The analysis reveals that the phase velocity rises with an increase in viscoelastic parameters and the dielectric constant, as well as the reinforcement parameters, while it decreases with an increase in the inhomogeneity parameter, piezoelectric constant, and thickness ratio parameter. A comparative study has also been conducted to analyze the effect of these parameters on the phase velocity using two piezoelectric materials, PZT-4 and PZT-7. The importance of parameter effects increases for Love-type waves with shorter wavelengths and small guiding layer thicknesses.

Memory effect on the thermoelastic responses of a porous half-space with a novel fractional heat conduction model

Studies have shown that the existence of the anomalous diffusion of porous media leads to the abnormal heat conduction, which can be well described by fractional derivatives. In the present work, memory dependent derivative is introduced into the existing linear thermoelastic theory to analyze the transient thermoelastic responses of a porous half-space subjected to a thermal loading at the boundary. By using the method of Laplace transform and its numerical inversion, the closed form solutions of temperature, volume fraction, displacement, and stress are obtained. The effects of time delay, kernel function and a memory-dependent parameter on the physical fields are discussed. The results show that the memory dependent derivative plays an essential role in controlling the heat transfer process of porous materials.

1-D Finite Element Artificial Boundary Method for Saturated Layered Half-Space Site Response under Obliquely Incident P-SV Waves

A novel finite element scheme is derived to evaluate the transient dynamic response of a multi-layered saturated porous half-space due to obliquely incident P or SV wave. The system consists of N − 1 layers with different thickness and properties that overlay on a saturated half-space from which the wave is input. Biot theory is utilized to describe the mechanism of saturated poroelastic media. In this method finite computational area is truncated from the infinite domain by a horizontal artifitial boundary introduced in the underlying half-space. Wave inputting effects and absorbing boundary condition at the bounday are derived. The spatial problem is then transformed approximatedly into a one-dimensional problem based on the Snell's law. The transient 1-D problem is descritized spacially by means of FEM and solved by the standard time intergration algorithm. Numerical examples show that the proposed 1-D finite element artificial boundary method can provide accurate results for seismic performance of saturated layerd half-space under obliquely incident waves with low values of permeability or frequency content. The method is applied in site response analysis of Hong Kong-Zhuhai-Macao immersed tunnel project. By comparison with the analytical solutions, it is demonstrated for geotechnic earthquake engineering problems, site response solutions with satisfactory accuracy can be achieved by the proposed method.

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.

Love wave propagation in a piezoelectric layer imperfectly bonded over a cracked porous half-space

This article explores the characteristics of Love wave in a piezoelectric layer imperfectly bonded over a heterogeneous fluid-saturated cracked dual porous half-space. The governing equations of the piezoelectric layer are solved analytically to determine mechanical displacement and electrical potential. Dispersion equations have been established using suitable boundary conditions for electrically open and electrically short conditions. In a particular case, the dispersion equation is reduced to the classical Love wave equation, which validates the present mathematical model. The effect of different parameters (like imperfection, dielectric constant, piezoelectric, and inhomogeneity) on phase velocity has been discussed theoretically and graphically, along with a comparative study by considering two piezoelectric materials, namely, PZT-4 and BaTiO3.

Acoustic signature of impermeable barriers in porous media

SUMMARY Impermeable barriers are abundant in rock formations and their delineation via seismic reflections are of prime importance. However, such barriers have received little attention in the poroelasticity literature. For this reason, we revisit the reflection–transmission problem for two porous half-spaces which are in welded contact and across which no fluid exchange is possible. We carry out this analysis in the poroelastic theory initiated by de la Cruz and Spanos (1985), which describes four waves: the fast P, fast S-, slow P and slow S waves. The fast P and S waves account for the in-phase motion in compression and shear nature, whereas the slow P and S waves are the out-of-phase motion. We find that the often times suggested notion of effective elastic scattering is not quite correct because of the generation of slow waves at the impermeable contact. The energy flux the slow waves carry is negligibly small at low frequencies when the fluid is viscously coupled to the solid frame. In contrast, slow waves carry substantial energy flux at high frequencies when the fluid is viscously decoupled. Moreover, the reflection–transmission behaviour at an impermeable contact is distinctively different when compared to that of a permeable contact, which means that, in principle, amplitudes of scattered waves can be used to identify the kind of contact. A seemingly unnoted but important result is the strong conversion scattering from a fast S wave into the slow P wave at high frequencies, which may be an alternative way to observe slow P waves in the laboratory as well as a means to characterize impermeable contacts.

Behavior of Love-Wave Fields Due to the Reinforcement, Porosity Distributions, Non-Local Elasticity and Irregular Boundary Surfaces

Investigations are carried out to predict the characteristic behavior of Love-wave fields propagating in a non-local elastic model under the effects of irregular boundary surfaces, reinforcement, and porosity distributions. The model includes an anisotropic fiber-reinforced medium lying over an anisotropic porous half-space. Two different porosity distributions are investigated within the porous half-space, namely uniform porosity and asymmetrical porosity. Analytical solutions to the displacement fields for both the upper layer and the lower porous half-space are calculated. Solutions to the latter porosity distribution are obtained by using the asymptotic expansions of the Kummer hypergeometric functions of the second kind. Both the interface and the upper surface of the two-layered media are subjected to irregular boundary conditions, which leads to a complex form of the dispersion relation. We analyze the phase velocity and damped velocity behavior of the traveling Love-wave fields separately by using the real and imaginary components of the velocity dispersion relation. The calculated phase velocity curves obtained at the same parameters have been compared to demonstrate the accuracy of the established model. The effects of corrugation parameters, porosity distributions, non-local elasticity, and reinforcement on the phase velocity and the damped velocity curves are analyzed in detail using MATLAB software.

Dynamic response of a multi-scale layered saturated porous half-space due to seismic dislocation source by using a revised dynamic stiffness matrix method

The study investigating the dynamic response of seismic dislocation source in a layered saturated porous half-space, particularly the multi-scale characteristic of half-space, from crustal to geotechnical scale, is still lacking in the literature. particularly in will lead to the computation bottlenecks for multi-scale seismic wave propagation. Based on Biot's theory of wave propagation in a fluid-saturated porous solid, a dynamic stiffness matrix method is proposed to investigate the dynamic response of a multi-scale layered saturated porous half-space due to the seismic dislocation source. Assembling each layer stiffness matrix in the frequency-wavenumber domain, the global dynamic stiffness matrix is constructed to avoid errors accumulative compared to the reflection and transmission matrix method. The divergent index terms of the stiffness matrix with respect to thickness and wavenumber are extracted to revise the dynamic stiffness matrix adapted for multi-scale half-space. The seismic dislocation source action is equal to the external forces imposed on the total saturated porous half-space, which can obtain the dynamic response by using revised dynamic stiffness matrix method. The accuracy of the proposed method is verified via the comparison between the calculated results and of three published literatures. The multi-scale model with realistic near-surface fine structure is selected to investigate the effects of superficial fine structures on the dynamic responses. The numerical simulations results show that the presence of low-velocity saturated porous layers has a prominent impact on ground motion. The dynamic response seems to be sensitive to the porosity conditions, especially for high frequency, which cause the difference in variation of peak displacement value.

An analytical study of coupled heat and mass transfer freeze-drying with convection in a porous half body: A moving boundary problem

The freeze-drying of a porous body is the most commonly used process in food technology to capture the coupled heat and mass transfer phenomena which appears in a class of moving boundary problem. The modern technology demand encourages investigators to provide techniques for accelerated food drying (AFD) and preservation of material to be denatured. Experimental study of freeze-drying of a porous body may be difficult and exploration of robust theoretical models with convection is critical. Further, the problem concerning in coupled heat and mass transfer, there is lack of mathematical analysis in the previous literatures which does not accounts the convective heat and mass transfer, convective term due to water vapour and condition for the limitation of sublimation and desorption. It is therefore, essential to develop mathematical formulation to discuss these type of freeze-drying phase change processes. In the current paper, the mathematical work is devoted to study a coupled heat and mass transfer problem describing freeze-drying of a material in a porous half-space. The problem accounts convection in porous frozen, sublimated and desorbed regions and a convective term due to moisture flow of the water vapour in the sublimated region. The exact solution of the proposed problem is obtained via similarity transformation. Condition for the limitation of sublimation and desorption is obtained and illustrated graphically. The effect of various parameters on thermal properties is discussed in detailed. The range values of governing problem parameters are taken as: 0 to 2 for Pe, 0.01 to 1.0 for β, 0.1 to 0.9 for α21, 0.1 to 2.1 for γ1, 0.5 to 2.0 for γ3, 0.2 to 0.8 for ω, 0.01 to 0.85 for (ϵ ‐ ω), 0 to 50 for v and 0.21 to 1.65 for ϵ. In current work, it is shown that the freeze-drying process becomes faster in the presence of convection rather than in the absence of convection. Furthermore, the rate of water vaporization from the surface of the porous body enhanced, as a result freeze-drying process deterred. The current work may be expected aid in accelerated freeze drying (AFD) technology.

Influence of a Nonstationary Surface Load on an Elastic Porous Half-Space

In this paper, we develop a method for solving planar nonstationary problems on the influence of surface pressure on an elastic-porous half-space. Using surface influence functions, we obtain an integral relation, which expresses the desired displacements with the surface pressure. A numericalanalytical algorithm is constructed. For calculating singular integrals, we derive special quadrature formulas based on the canonical regularization of integrands.

The reflection and transmission of waves at an imperfect interface between two nonlocal transversely isotropic liquid-saturated porous half-spaces

The present study is concerned with the reflection and transmission of plane waves at an imperfect interface between two nonlocal transversely isotropic liquid-saturated porous half-spaces. The model is considered for two different cases with one is for excluding fluid nonlocal effect, and the other is for including fluid nonlocal effect. The expression for the reflection and transmission coefficients (RTC) which are the ratios of the amplitude of reflected and transmitted waves to the amplitude of incident waves are obtained for an imperfect interface, perfect interface and loose interface. The numerical examples are provided to show the effect of the imperfect interface, nonlocal parameter and incident angle on the reflection and transmission coefficients.

An Analytical Solution of Wave Motion in a Transversely Isotropic Poroelastic Half-Space Underlying a Liquid Layer

In this paper, an analytical method is developed for the axisymmetric dynamic response of a finite thickness liquid layer overlying a transversely isotropic porous solid half-space due to body waves. Potential functions and integral transforms are used together to handle the equations of wave motion in two media. The time-harmonic excitation with axisymmetric shape is assumed to be distributed in the interface of liquid and porous media. Green’s functions of stress and displacement are derived as closed-form integral expressions. Demonstration of the effect of the liquid thickness, degree of material anisotropy, and frequency of excitation on the dynamic response is considered here. Numerical results for a uniform distributed disk load are comprised with the existing elastic and poroelastic solutions to illustrate the quality of the method. The results of the current paper can be used in analysis and modelling the rigid or flexible foundations in marine structures.

Waves Propagation at an Interface of Two Liquid Saturated Porous Solid Half Spaces

This manuscript is concerned with reflected and refracted elastic waves when transverse waves are incident at the interface between two fluid-saturated porous solid half-spaces. Perfect and imperfect both types of contact of the interfaces are discussed. It has observed that for a specific model the behaviour of different reflected, refracted waves and the ratio of their amplitudes depend on the physical properties of the medium, angle of emergence, the porosity of the fluid, the porosity of fluid drenched incompressible porous medium and stiffness of imperfect boundary. The computer numerically results for this model have been presented graphically by taking a particular case of empty porous solid.

Investigation on the transient response of a porous half-space with strain and thermal relaxations due to laser pulse heating

Porous materials have been extensively used in electronic communications, aerospace, bio-medicine and petrochemical, etc. due to their attractive attributes such as low relative density, thermal and acoustical insulation and good permeability. Ultrashort laser pulses have a series of unique advantages including high energy density, ultrashort interaction time and high accuracy, which are widely used in the fields of precision machining and microelectronic manufacture. For porous materials heated by an ultrashort laser pulse, revealing the interplay between deformation field and temperature field is crucial to guide their engineering application and optimization design. The present work devotes to investigating the transient response of a porous half-space heated by a non-Gaussian laser beam on its boundary surface based on the newly established linear thermoelastic theory with strain and thermal relaxations. The coupled governing equations are formulated and solved through the Laplace transform and its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress as well as volume fraction field are obtained and illustrated graphically. In calculation, the effects of the thermal relaxation factor, the strain relaxation factor on the temperature field, volume fraction field, displacement field as well as stress field are examined and discussed in detail.

Finite difference modeling of shear wave propagation in multilayered fractured porous structures

This study aimed to investigate shear wave (SH-wave) propagation through a multilayered cracked porous model with exponential heterogeneity. Moreover, the stability criterion of SH-wave propagation was analyzed by determining phase and group velocities of SH-wave. Haskell’s matrix method was used to determine complex dispersion relation for n − 1 media overlying an inhomogeneous porous half-space with fractures. Stability analysis was performed through the finite difference method. Moreover, the phase and group velocities were determined using the Courant number. Dispersion and damping equations were derived for n = 2 and 3. Classical Love wave equation was attained in each case using certain conditions. This equation validated the developed mathematical model. Stability analysis was conducted for reducing the errors and determining the conditions of convergence. The effects of the heterogeneity parameter, porosity, attenuation coefficient, Courant number, and discretization ratio on phase and group velocities were graphically observed. A two-dimensional plot was used to perform comparative analysis between the fractured porosity and isotropy. Cracked porous material, which has various applications in real world, was analyzed in this study. To the best of the authors’ knowledge, wave propagation in a multilayered system consisting of heterogeneous cracked porous material has not been examined previously. Thus, this study explores a new research area. The developed model can be successfully used to interpret seismic behavior during earthquakes. More complex structures can be developed on the basis of the considered model.

Rayleigh waves in porous nonlocal orthotropic thermoelastic layer lying over porous nonlocal orthotropic thermoelastic half space

ABSTRACT The present paper deals with the propagation of Rayleigh surface waves in a nonlocal thermoelastic orthotropic layer which is lying over a nonlocal thermoelastic orthotropic half space. The problem is considered in the context of Green-Naghdi type III model of hyperbolic thermoelasticity and Eringen’s nonlocal elasticity theory in the presence of voids. The problem is solved using eigenfunction expansion method. Frequency equation of Rayleigh waves is derived and different particular cases are also deduced. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically.

Propagation and attenuation characteristics of Rayleigh waves in the irregular bottom of the ocean in porous half-spaces

The Rayleigh wave propagation in the irregular bottom of the ocean, which is the interface of a homogeneous non-viscous liquid layer overlaying a porous half-space, under the influence of different factors has been discussed. The mathematical model is established by formula derivation. The propagation and attenuation characteristics of Rayleigh waves in a liquid layer over a transverse isotropy liquid-saturated porous half-space with irregular interface were studied. In addition, the dispersion and attenuation equations of the phase velocity and the attenuation coefficient with respect to the wave number were derived by which the effects of different parameters were analyzed. It was found that the magnitude of phase velocity varies with respect to the corrugation degree of the interface. In addition, irrespective of the type of interface, initially the attenuation coefficient rapidly increases and after the maximum value, it becomes constant. Furthermore, it has been observed that the change of the permeability coefficient affects the Rayleigh wave attenuation for the low wave number. For the low wave number, smaller permeability coefficient results in larger phase velocity and smaller attenuation. Moreover, both the phase velocity and the attenuation coefficient will eventually approach constant value in the high wave number region, for all parameters.