Fluid-saturated Porous Material Research Articles

On propagation characteristics of ultrasonic guided waves in layered fluid-saturated porous media using spectral method.

Fluid-saturated porous media plays an increasingly important role in emerging fields such as lithium batteries and artificial bones. Accurately solving the governing equations of guided wave is the key to the successful application of ultrasonic guided wave nondestructive testing technology in fluid-saturated porous media. This paper derives the Lamb wave equation in layered fluid-saturated porous materials based on Biot theory and proposes the spectral method suitable for solving complex wave equations. The spectral method reconstructs the fundamental wave equations in the form of a matrix eigenvalue problem using spectral differentiation matrices. It introduces boundary conditions by replacing corresponding rows in the wave equation matrix with stress or displacement in matrix form. For complex differential equations, such as the governing equations of guided waves in porous media, the spectral method has the significant advantages of faster computation speed, less root loss, and easier encoding process. The spectral method is used to calculate the acoustic field characteristics under different boundary conditions and environments of the layer fluid-saturated porous media. Results show that the surface treatment details and environment of fluid-saturated porous materials play an important role in the propagation of guided waves.

Effective mechanical behaviors of transverse isotropic materials containing compressible liquid inclusions with surface effects

Porous media with fluid-saturated microchannels, prevalent in biomaterials, tissue engineering materials and flexible electronic devices, can be modelled as transverse isotropic materials. Surface effects can influence significantly the macro-mechanical responses of such materials, particularly for soft materials with micro- or nano-scale channels. In this study, we first develop constitutive laws for fluid saturated porous materials with microchannels by integrating the top-down (homogenization) approach with the bottom-up (micromechanics) approach. We then explicitly establish a connection between surface effects and macro-mechanical responses. Employing the generalized self-consistent model (GSCM), we estimate the effective parameters (i.e., coefficients in constitutive equations governing macro-mechanical responses), with fluid compressibility and surface effects accounted for. Our findings reveal that, as surface energy increases, the effective transverse shear modulus is enlarged, the effective plane strain bulk modulus, the unit uniaxial straining modulus and the cross modulus are all reduced, but the axial shear modulus remains nearly unchanged. As an application, we characterize the mechanical behaviors of the transverse isotropic fluid-saturated porous material with surface effects by connecting the classic Mandel solution with the estimated effective parameters. The pore pressure exhibits the Mandel-Cryer effect. The insights gained from this study are valuable for comprehending and exploring the intricate ways in which surface effects influence the mechanical responses of transversely isotropic fluid-saturated porous materials featuring sufficiently small channels.

FINITE DIFFERENCE METHOD BASED-NUMERICAL SIMULATIONS AND CAVITY TILTING ANALYSIS ON MAGNETOCONVECTION IN AN INCLINED PARALLELOGRAMMIC POROUS ENCLOSURE

This article numerically investigates the buoyancy-assisted convective flow and associated thermal characteristics in an inclined parallelogram-shaped porous geometry containing heat source and sink of different lengths placed at various locations. The left tilted wall has a hot source, and right tilted wall contains a cold sink, while the remaining regions of the inclined sidewalls are thermally insulated. The geometry is filled with fluid-saturated porous material and, in addition, an externally applied magnetic field (MF) has been supplied in lateral direction. The model equations governing the physical processes involve Darcy's law for the momentum equations and energy equations to account thermal variations. Using a stable and implicit finite difference methodology, these set of coupled and nonlinear partial differential equations are solved by reducing them to a system of linear algebraic equations. A wide range of numerical experiments are performed to determine the influence of various physical and geometrical parameters on the flow and thermal structure as well as thermal dissipation rate inside the geometry. Further, a suitable pair of inclination angles is found, at which maximum heat transport could be produced as compared to other combination of angles. Furthermore, an optimum size and location for the source-sink combination has been predicted which induces higher heat transport rates.

The Porothermoelastic Stress Evolution of Inhomogeneous Solid due to Near-Surface Reservoir

Anisotropic and heterogeneous solids, comprising a minimum of two or more elements with different properties, appear pervasively in rock materials including the pore structure and mineral composition of quartz and granite and usually have extensive applications in construction aggregates, dimension stone, geotechnical engineering, and petrology/geology. The elastic stress fields of inhomogeneous materials or composites inevitably change due to the presence of heterogeneous microstructure under applied external conditions, and hence the total mechanical and physical properties are affected by the temperature and pore pressure fluctuations beneath the surface. In this paper, the thermoporoelastic (TPE) approach on the basis of eigenstrain concept is introduced to predict the stress fields in fluid-saturated porous geologic materials like hydrocarbon reservoirs or aquifers by accounting for the coupling between thermal, poroelastic, and mechanical effects. It is an extension of the micromechanical theory that also incorporates thermal effects like pore pressure changes and temperature alternations. In addition, the TPE approach provides an important multiphysical modeling tool for understanding subsurface fluid-rock interactions and stress states in applications like unconventional oil/gas and geothermal energy.

Elastic waves in fluid-saturated porous materials with a couple-stress solid phase

Fluid-saturated porous materials have attracted extensive attention in micro/nanoscale applications owing to their excellent mechanical properties. Couple-stress theory can be used to depict the size effect of micro/nanoelastic materials, which cannot be ignored when the internal characteristic length of materials is comparable with the material size or wavelength. However, it has not been extended to porous materials. In this paper, we investigate the size effect of elastic-wave propagation in micro/nano fluid-saturated porous materials by combining couple-stress theory with Biot theory and introducing the higher order micro-inertia effect, establish the motion equations for elastic waves in fluid-saturated porous materials containing a couple-stress solid phase. The reflection and transmission properties of elastic waves at the interface between an elastic solid and a couple-stress fluid-saturated porous material are numerically analyzed. The results suggest that an increase in characteristic length can lead to an increase in the phase velocity of shear wave and further influence the reflection and transmission of elastic waves. A comparison among the proposed theory, Biot theory and experimental data indicates that the introduction of couple-stress and higher order micro-inertia effects allows for a more accurate calculation of the propagation properties of elastic waves in fluid-saturated porous materials, and it can provide a theoretical basis for applications of elastic waves in micro/nano porous materials, such as nondestructive testing.

A cuboidal open cell model for constitutive modeling of surface effects in fluid-saturated porous materials

Fluid-saturated porous elastic materials, made up of connected networks of solid ligaments and characteristically having open pores, are commonly found in geological, biological and engineering materials. Surface effects can affect significantly the mechanical performance of such porous materials at macro scale, especially when the solid ligaments and the pores have micro or nano scale sizes. In the present study, in order to explicitly link pore-level geometrical parameters and surface effects with effective poroelastic properties as well as constitutive equations governing poroelastic deformation, we combine the top-down homogenization approach presented a previous study (Chen et al., 2021) with the bottom-up micromechanics approach. Inspired by the Gibson-Ashby cubic cell model for open-cell foams and the cellular networks typically found in fluid-saturated porous materials, we propose a cuboidal open cell model, with surface effects and fluid compressibility accounted for. For two limiting cases, i.e., the undrained state and the drained state, we demonstrate that both the surface moduli and residual surface stress (i.e., surface tension) prevent the deformation of solid ligaments, thus stiffening the porous material with enlarged effective Young's moduli. Further, we reveal that the two surface effect parameters (i.e., residual surface stress versus surface moduli) exhibit a coupling effect on effective moduli: when one parameter is large enough, the variation of the other affects significantly the effective moduli. As applications of the proposed model, we characterize mechanical behaviors of the porous material under typical loadings (e.g., uniaxial and non-proportional multiaxial tension) in both undrained and drained states; we also describe, for the first time, the stress concentration of a compressible liquid inclusion (e.g., a cell) with surface tension embedded in a fluid-saturated porous material with surface effects. Results of this study are beneficial for understanding and investigating how surface effects influence the poroelastic parameters of fluid-saturated porous materials having sufficiently small open pores.

The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces

The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface.

Convergence analysis and validation of a discrete element model of the human lumbar spine

Degenerative diseases of the spine can lead to or hasten the onset of additional spinal problems that significantly reduce human mobility. The spine consists of vertebral bodies and intervertebral discs. The most degraded are intervertebral discs. The vertebral body consists of a shell (cortical bone tissue) and an internal content (cancellous bone tissue). The intervertebral disc is a complex structural element of the spine, consisting of the nucleus pulposus, annulus fibrosus, and cartilaginous plates. To develop numerical models for the vertebral body and intervertebral disc, first, it is necessary to verify and validate the models for the constituent elements of the lumbar spine. This paper, for the first time, presents discrete elements-based numerical models for the constituent parts of the lumbar spine, and their verification and validation. The models are validated using uniaxial compression experiments available in the literature. The model predictions are in good qualitative and quantitative agreement with the data of those experiments. The loading rate sensitivity analysis revealed that fluid-saturated porous materials are highly sensitive to loading rate: a 1000-fold increase in rate leads to the increase in effective stiffness of 130 % for the intervertebral disc, and a 250-fold increase in rate leads to the increase in effective stiffness of 50 % for the vertebral body. The developed model components can be used to create an L4-L5 segment model, which, in the future, will allow investigating the mechanical behavior of the spine under different types of loading.

Equations and fundamental characteristics of compressional waves propagating in fluid-saturated porous materials

The main purpose of the paper is to present an extended analysis of the coupled system of linear equations describing compressional wave propagation in fluid-saturated porous materials, and to determine their fundamental characteristics. The present paper is a continuation of the analysis of equations for transverse waves that is presented in the manuscript (Cieszko and Kubik, 2020). The starting point of considerations in both works are nonlinear equations describing the dynamic behavior of the two-phase medium formulated in the spirit of the theory of interacting continua in which the parameters of an isotropic pore space structure are explicitly present in the model, and constitutive equations are formulated for each physical component (porous solid and fluid) separately. This system of equations contains all of the fundamental mechanical couplings between the components of such a medium in the general nonlinear form and of clear physical meaning. The linear coupled equations of this theory for a viscous barotropic fluid and a hyperelastic skeleton are equivalent to Biot's model, widely used in the description and analysis of wave propagation in saturated porous materials and wave interactions with the boundary of such media, and they are the subject of the ongoing analysis. A new method of analysis of the system of differential equations written in matrix form is proposed, based on the spectral decomposition of this system in the vector space of dilatations of the solid and fluid particles, and on the method of differential operator decomposition. Such an approach enabled to obtain two separated differential equations describing the propagation of two attenuated compressional waves called the fast and slow wave. This also allowed expressions for parameters characterizing both elastic compressional waves to be derived: velocities, effective mass densities and elastic modules, and also wave impedances which have been determined for the first time for saturated porous materials. In turn, the separated equations for attenuated waves enabled direct derivation of the dispersion equations for the plane harmonic waves of both types and determination of their frequency characteristics, i.e. phase velocities and attenuation coefficients. The obtained frequency characteristics of the fast and slow waves are fully defined by their velocities in the elastic and in the compact medium, and the coefficient characterizing the viscous interaction of the fluid with the skeleton. The results show that the phase velocity of the long slow wave can be greater than the phase velocity of the long fast wave, and the attenuation of the fast wave can be greater than attenuation of the slow wave. It was also proven that both waves can be anomalously dispersed which means that some porous materials saturated with fluid are metamaterials.

Model order reduction for deformable porous materials in thin domains via asymptotic analysis

We study fluid-saturated porous materials that undergo poro-elastic deformations in thin domains. The mechanics in such materials are described using a biphasic model based on the theory of porous media (TPM) and consisting of a system of differential equations for material’s displacement and fluid’s pressure. These equations are in general strongly coupled and nonlinear, such that exact solutions are hard to obtain and numerical solutions are computationally expensive. This paper reduces the complexity of the biphasic model in thin domains with a scale separation between domain’s width and length. Based on standard asymptotic analysis, we derive a reduced model that combines two sub-models. Firstly, a limit model consists of averaged equations that describe the fluid pore pressure and displacement in the longitudinal direction of the domain. Secondly, a corrector model re-captures the mechanics in the transverse direction. The validity of the reduced model is finally tested using a set of numerical examples. These demonstrate the computational efficiency of the reduced model, while maintaining reliable solutions in comparison with original biphasic TPM model in thin domain.

Role of fluid phase in compression of nonlinear elastic fluid-saturated porous medium

This paper is about the role of the fluid in supporting the overall compressive stress applied to nonlinear elastic fluid-saturated porous material. The case of large deformation and compressible hyperelastic matrix material is considered. Due to complexity of the problem, a simple model of the porous medium consisting of an assemblage of fluid-filled cylinders is studied in more detail. The procedure for computing the stress partitioning between the solid phase of the cylinder and the fluid in withstanding the overall stress consists of two steps. In the first step, the radial stress σ of given magnitude is applied to outer radius of the fluid-filled cylinder and the radial displacement is determined. In the second step, the displacement of the outer surface of the cylinder is equal to that of the first step but the cavity of the cylinder is empty. The radial stress acting on the outer boundary of the cylinder in the second step is defined as an effective stress in the solid skeleton of the porous medium, σsk. For the given overall stress σ and the computed value of the effective stress σsk, the effective stress supported by the fluid Peff is computed as the difference σ−σsk. Each of the two steps requires a solution to a boundary value problem which is solved numerically with the help of Python bvp solver.

Dynamics landscape for acoustic superradiance.

We analyse the behaviour of acoustic vortex beams interacting with rotating, fluid-saturated porous materials. Regions of the parameter space that exhibit distinct dynamical features are identified, with a focus on features that are relevant to the characterization of rotational superradiance. We discuss the similarities and differences between two recent proposals to observe acoustic superradiance with rotating, air-saturated sound absorbers. Finally, theoretical predictions for macroscopic acoustic scattering, obtained by averaging over interactions between the fluid and the porous material at the microscopic level, are compared with predictions of the first-Born approximation. This article is part of a discussion meeting issue 'The next generation of analogue gravity experiments'.

Equations and fundamental characteristics of transverse waves propagating in fluid-saturated porous materials

The main purpose of the paper is to present an extended analysis of the coupled system of linear equations describing wave propagation in fluid-saturated porous materials used for the determination of their fundamental characteristics. The present paper is the first part, mainly devoted to the analysis of the system of equations describing transverse wave propagation. The analysis of equations for compressional waves will be presented in a separate paper. The starting point of considerations are nonlinear equations describing the dynamic behavior of the medium formulated in the spirit of the theory of interacting continua in which parameters of isotropic pore space structure are explicitly present in the model, and constitutive equations are formulated for each physical component separately. They contain all fundamental mechanical couplings between components of this medium in the general nonlinear form and of clear physical meaning. Linear equations of this theory for barotropic fluid and hyperelastic skeleton are the subject of the analysis performed in the paper. They are equivalent to Biot's model, widely used in the description and analysis of wave propagation in saturated porous materials and wave interaction with the boundary of such media. A new method of analysis is proposed in the paper, based on spectral decomposition of the system of equations in the two-dimensional vector space of rotations of solid and fluid particles. It is shown that each choice of the base in this vector space defines the division of the medium into two new components and transforms the system of equation to the form describing the dynamic behavior of these components, and the requirement of the basic dynamic properties of the medium to be invariant in each chosen base uniquely determines the mass densities and bulk modules of the new components. Such an approach enabled decomposition of the system of equations for particle rotations to two uncoupled scalar equations, the only one of which describes propagation of the transverse wave. This also allowed obtaining expressions characterizing transverse wave propagation in fluid-saturated porous materials: velocity, effective mass densities and wave impedance of the medium associated with this wave and its frequency characteristics: phase velocity and attenuation coefficient. It is shown that both frequency characteristics are fully defined by the effective mass densities of both components associated with the transverse wave, the tortuosity of the pore space, and the coefficient characterizing the viscous interaction of the fluid with the skeleton.

Evanescent waves in two-dimensional fluid-saturated porous metamaterials with a transversely isotropic matrix

Wave propagation in a two-dimensional periodic fluid-saturated porous metamaterial (FSPM) is investigated. The constitutive relation considered for fluid-saturated porous materials is based on Biot’s homogeneization theory. Such media generally support two shear and two longitudinal elastic waves. Anisotropic wave propagation results both from anisotropy of the solid matrix and from the periodic structure of the metamaterial. Special attention is devoted to the dispersion and attenuation of evanescent Bloch waves in a FSPM whose matrix is transversely isotropic in which case in-plane elastic waves are a superposition of one shear wave and of two longitudinal waves. Bloch waves, complex band structures, and transmission properties are obtained numerically using finite element analysis. The case of homogeneous fluid-saturated porous media is considered since numerical simulations can be compared directly with analytic results in this case. The effects of material anisotropy and of fluid viscosity on wave propagation in two-dimensional FSPM are then discussed. It is found that wave-number band gaps appear in the complex band structure of the lossless FSPM due to the interference of waves with different but nonorthogonal polarizations. Wave-number band gaps are connected continuously by complex-frequency bands, hence, defining stop bands in the time domain. No complete frequency band gaps are found in two-dimensional lossless FSPM, in contrast to the one-dimensional case [Y.-F. Wang et al. Phys. Rev. B 99, 134304 (2019)] due to the presence of the additional quasishear wave accompanying the two quasi-longitudinal waves. Both the complex band structure and the transmission properties are affected by the anisotropy of the solid matrix. Wide transmission dips come up when viscosity is introduced as a result of the strong attenuation and the coupling of all wave polarizations. Concurrently, wave-number band gaps are washed out by viscosity. This theoretical paper has relevance to practical applications of fluid-saturated porous metamaterials, e.g., in concrete structures and geological soils.

Feasibility of in-situ evaluation of soil void ratio in clean sands using high resolution measurements of Vp and Vs from DPCH testing

For engineering purposes, the density of soil is often expressed in terms of void ratio. Void ratio is a key parameter in critical state soil mechanics and governs our understanding of soil compressibility, permeability, and shear strength. Typically, in-situ void ratio is evaluated based on laboratory measurements on high-quality, samples of soil. While undisturbed sampling of clayey soils is commonplace in geotechnical practice, high-quality samples of granular soils are difficult and expensive to obtain. Hence, void ratio of granular soils is typically estimated using empirical relationships to in-situ measurements from penetration testing. Even for clean sands there is significant variability in these estimates, and for mixed-grain soils the applicability and performance of the empirical relationships is quite uncertain. Therefore, a more reliable way of measuring in-situ void ratio is needed. This paper examines the feasibility of evaluating in-situ soil void ratio based on the theory of linear poroelasticity and the propagation velocity of compression and shear waves (i.e., vp and vs, respectively) through fluid-saturated porous materials. Specifically, soil void ratio is evaluated via a porosity relationship that is a function of vp, vs, and four additional parameters describing the physical properties of the soil (i.e., the Poisson's ratio of the soil skeleton, the bulk modulus and mass density of water, and the mass density of the solid soil particles). In this study, the effectiveness of using high-resolution vp and vs measurements from direct-push crosshole testing to estimate in-situ void ratios is investigated at ten, predominantly clean-sand case history sites in Christchurch, New Zealand, via a comparison with void ratio estimates developed from penetration testing measurements. The seismic-based void ratio estimates are shown to be particularly sensitive to vp, requiring a measurement error of less than 2%. Given the need to make such precise in-situ measurements of vp, the DPCH method is believed to show particular promise for enabling accurate, seismic-based estimates of void ratio in the future.

Nonlocal scale effect on Rayleigh wave propagation in porous fluid-saturated materials

In this paper, a Rayleigh wave model in fluid saturated porous materials based on a nonlocal Biot theory is proposed. The general characteristic equations expressed in terms of the Rayleigh wavenumbers are obtained. A specific fluid saturated porous material is used for numerical analysis. The present study shows that the nonlocal parameter does not have significant influence on the characteristics of Rayleigh waves within a low frequency range when comparing with the prediction of using the classical Biot theory. However, the influence of the nonlocal scale effect on the Rayleigh wave velocity and the displacement field becomes stronger as the response frequency increases. When the frequency exceeds a critical value, the Rayleigh wave velocity exhibits a negative dispersion. The displacement fields induced by the Rayleigh wave propagating in porous materials are also presented. An interesting phenomenon of the displacement fields is observed that the major axis of the displacement field ellipse will have a contra-rotation with respect to the vertical direction with increasing depth. This is different from the classical prediction in homogeneous materials. The presence of the nonlocal scale effect can also change the geometry property of displacement fields. In addition, the amplitude of the vertical displacement is attenuated along the depth, while the increment of the nonlocal parameters can strengthen the attenuation.

Optimal bounds for attenuation of elastic waves in porous fluid-saturated media.

Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions.

Mesoscale Validation of Simplifying Assumptions for Modeling the Plastic Deformation of Fluid-Saturated Porous Material

Mesoscale simulation of fluid-saturated porous materials is used to investigate unvalidated assumptions in continuum modeling of geomaterials at high rates. The importance of pressure-dependence of the matrix material on the applicability of the effective-stress approach during plastic deformation is explored. The hydrostatic load-unload response of saturated porous structures having both pressure-dependent and pressure-independent matrix materials is modeled using the material point method. Results are used to validate a semi-empirical strain-to-yield effective-stress model in which the pore pressure evolves with local material deformation, an approach that is applicable to materials with closed porosity or those loaded at sufficiently high rates that fluid transport can be neglected. Mesoscale simulations are used to estimate the strain rates beyond which fluid flow through the matrix can be neglected.

Deriving Biot-Gassmann relationship by inclusion-based method

The quasi-static theory of poroelasticity presented by Biot and Gassmann provides a relationship between the drained and undrained elastic constants of an isotropic fluid-saturated porous material in terms of the porosity of the material, bulk modulus of the solid grains, and bulk modulus of the pore fluid. We have developed an alternative approach to derive the Biot-Gassmann (BG) relationship while including the effects of the pore microstructure. First, the Eshelby transformation is used to express the local inclusion/pore strain tensor in terms of the applied strain tensor and reference material elastic properties by the superposition of a void strain and a perturbation term due to induced inclusion stress. Second, the inclusion strain expression and Hill’s average principles are combined with the Mori-Tanaka/Kuster-Toksöz scheme to obtain inclusion-stress-dependent effective elastic moduli of porous materials. For an isolated pore system, the effective modulus tensor corresponds to the original Mori-Tanaka/Kuster-Toksöz’s expression. Although for communicating pore system, it is proven to satisfy the BG relation. In the second case, the deformation is assumed to occur so slowly that the infiltrating fluid mass has sufficient time to diffuse between material elements and, consequently, the pore fluid pressure is equilibrated within the whole pore system. It is noteworthy that we arrive at a BG relationship without applying reciprocity theorem and that the porous material effective strain is defined from Hill’s principles instead of solid phase average strain. A potential application of the stress-independent effective modulus is to help develop a dynamical modulus model of rock physics for a specific pore microstructure.

On wave propagation characteristics in fluid saturated porous materials by a nonlocal Biot theory

A nonlocal Biot theory is developed by combing Biot theory and nonlocal elasticity theory for fluid saturated porous material. The nonlocal parameter is introduced as an independent variable for describing wave propagation characteristics in poroelastic material. A physical insight on nonlocal term demonstrates that the nonlocal term is a superposition of two effects, one is inertia force effect generated by fluctuation of porosity and the other is pore size effect inherited from nonlocal constitutive relation. Models for situations of excluding fluid nonlocal effect and including fluid nonlocal effect are proposed. Comparison with experiment confirms that model without fluid nonlocal effect is more reasonable for predicting wave characteristics in saturated porous materials. The negative dispersion is observed theoretically which agrees well with the published experimental data. Both wave velocities and quality factors as functions of frequency and nonlocal parameter are examined in practical cases. A few new physical phenomena such as backward propagation and disappearance of slow wave when exceeding critical frequency and disappearing shear wave in high frequency range, which were not predicted by Biot theory, are demonstrated.