Biot's Theory Research Articles

The U-net-based ice pore parameter extraction method for establishing the SAW icing sensing mechanism

The porous ice layer formed upon the SAW (surface acoustic wave) propagation path will produce transient acoustic attenuation, and a new icing sensing method can be constructed based on this feature. Obtaining the pore characteristics of an ice layer is a prerequisite and basis for deriving the sensing mechanism of SAW icing. Employing the U-net network, a segmentation model of frozen pores is developed by collecting frozen images and calibrating sample data sets for training in this work. The MIOU and the MPA of the model reach 92.16 % and 95.15 % respectively. Then, the watershed algorithm and post-processing were used to accurately obtain the pore characteristic parameters (porosity, pore number, and average pore area) of the ice layer. On this basis, applying the Biot's theory for two-phase porous media, a theoretical model of the SAW icing sensing mechanism was established, and the acoustic sensing response under different icing types was theoretically simulated. To prove the accuracy of the theoretical simulation, a SAW sensor using a waveguide structure of SU-8/ST-90 °X quartz operating at 80 MHz was constructed and evaluated experimentally. The results demonstrate that the acoustic sensing responses of different ice types are completely consistent with the theoretical results. This fully verifies the accuracy of the ice pore parameters extracted in this work and also confirms the feasibility of using pore microscopic information to achieve ice detection and ice type discrimination.

Simulation of dynamic pulsing fracking in poroelastic media by a hydro-damage-mechanical coupled cohesive phase field model

This study develops a hydro-damage-mechanical fully coupled numerical method capable of modelling complex fluid-driven transient dynamic crack propagation in quasi-brittle poroelastic media. In this method, the fluid flow in both fractures and porous media is described by a fluid continuity equation with the modified Darcy-Poiseuille law based on the Biot's poroelastic theory. The fluid pressure and the inertial force of solids are coupled by governing equations of the mesh-insensitive phase-field regularized cohesive zone model that can simulate quasi-brittle multi-crack initiation, propagation, branching and merging without remeshing or crack tracking. The resultant displacement-pressure-damage coupled multiphysics system of equations is solved using an alternative minimization Newton-Raphson iterative algorithm with an implicit Newmark integration scheme within the finite element framework. The new method was first validated by a few 2D problems, including crack branching and deflecting in solids, fracking in a concrete cube, and consolidation and stress wave propagation in poroelastic media, subjected to various impulsive loadings. It was then applied to pressure pulsing fracking of a 40 m granite rock reservoir with extensive parametric studies of fluid viscosity and pulsing injection rate, mode and period. It was found that pulsing injection with higher fluid rates and lower fluid viscosities resulted in more developed crack patterns, and in particular, there existed an optimal pulsing injection period that could promote fracking under relatively low injection pressures. 3D horizontal well problems with multiple non-planar crack propagation and bifurcation were also successfully simulated to demonstrate the capacity and potential of the new method for engineering design and optimization of pressure pulsing fracking.

Wave reflection and transmission in seawater-unconsolidated-consolidated sediment models based on VGS([formula omitted]) and Biot theories

It proves challenging to accurately describe wave propagation within layers of sediment with significant variations in physical properties and states, using a single sediment acoustic theory. In this paper, we construct a sedimentary wave field model applicable to sedimentary layers containing different physical properties, by combining Biot theory and viscous-grain-shearing theory, and give an analytical solution for the coefficients of the wavefield potential function. The acoustic reflection coefficients of the seafloor surface are obtained accordingly. The comparison against the in-situ test of the Seabed Characterization Experiment shows that our model is better capable to describing wave propagation in structures with multiple sediment types. We give the most suitable model for the New England Mud Patch sediment structure by establishing different assignments of sedimentary acoustic theories, and discuss the effect of porosity and thickness of different layers on the reflection coefficients of waves of different frequencies.

Theoretical and experimental study of attenuation in cancellous bone.

Photoacoustic (PA) technology shows great potential for bone assessment. However, the PA signals in cancellous bone are complex due to its complex composition and porous structure, making such signals challenging to apply directly in bone analysis. We introduce a photoacoustic differential attenuation spectrum (PA-DAS) method to separate the contribution of the acoustic propagation path to the PA signal from that of the source, and theoretically and experimentally investigate the propagation attenuation characteristics of cancellous bone. We modified Biot's theory by accounting for the high frequency and viscosity. In parallel with the rabbit osteoporosis model, we build an experimental PA-DAS system featuring an eccentric excitation differential detection mechanism. Moreover, we extract a PA-DAS quantization parameter-slope-to quantify the attenuation of high- and low-frequency components. The results show that the porosity of cancellous bone can be evaluated by fast longitude wave attenuation at different frequencies and the PA-DAS slope of the osteoporotic group is significantly lower compared with the normal group (**). Findings demonstrate that PA-DAS effectively differentiates osteoporotic bone from healthy bone, facilitating quantitative assessment of bone mineral density, and osteoporosis diagnosis.

Multi‐porous extension of anisotropic poroelasticity: Linkage with micromechanics

AbstractWe attempt to formalise the relationship between the poroelasticity theory and the effective medium theory of micromechanics. The assumptions of these two approaches vary, but both can be linked by considering the undrained response of a material; and that is the main focus of the paper. To analyse the linkage between poroelasticity and micromechanics, we do not limit ourselves to the original theory of Biot. Instead, we consider a multi‐porous extension of anisotropic poroelasticity, where pore fluid pressure may vary within the bulk medium of interest. As a consequence, any inhomogeneities in the material are not necessarily interconnected; instead, they may form isolated pore sets that are described by different poroelastic parameters and fluid pressures. We attempt to incorporate the effective methods inside Biot‐like theory and investigate the poroelastic response of various microstructures. We show the cases where such implementation is valid and the others that appear to be questionable. During micromechanical analysis, we derive a particular case of cylindrical transverse isotropy—commonly assumed in conventional laboratory triaxial tests—where the symmetry is induced by sets of aligned cracks.

Parallel finite layer method for land subsidence and its homotopy parameter inversion

Land subsidence is caused by the interaction between groundwater flow and soil deformation. At present, in the field of land subsidence calculation, there is an increasing tendency to use Biot's consolidation theory to precisely simulate the coupling processes of flow and deformation. However, there are some practical problems with large-scale numerical computation, such as large computational loads, low efficiency, and difficulty in obtaining parameters. The Finite Layer Method employs orthogonality of analytical functions to achieve decoupling among various series terms. And the method can be enhanced through parallel computing to optimize the efficiency of solving complex and extensive problems due to its decoupling property. Based on this, combined with the nonlinear homotopy method, a new approach for the reversal of land subsidence is proposed. The validity of the parallel program is confirmed through comparison with established solutions, and the impact of various factors on the efficiency of parallel computing is analyzed. The results indicate that the parallel approach enhances computational efficiency, while the homotopy inversion technique exhibits broad convergence characteristics.

Poroelastic model of the lungs at low frequencies predicted by Biot's theory

Biot's theory of poroelastic wave propagation inherently lends itself to elucidate the characteristics of a biphasic medium comprising solid and fluid components, such as biological tissues. One of the intricately complex biological tissues that remains poorly understood is the lungs since their properties diversify significantly through their pore geometries affected by inspiratory positive airway pressure (IPAP) and applied frequency range. One hypothesizes that the vibroacoustic behaviour of the lungs can be predicted by Biot's theory, as the nature of the lungs aligns with the principles of the theory at low frequencies. This study aims to analytically investigate the vibroacoustic behaviour of the lungs, considering 10 and 20-cm H;2O IPAP. Utilizing a fractional derivative formulation, one predicts the complex-valued shear wave speed, as well as the fast and slow compression wave speeds, for frequencies ranging from 5 to 100 Hz. A 3D digital thorax twin study using these predicted wave speeds, particularly at 28 Hz and 20 cm H;2O IPAP, is validated against experimental data from the literature. Consequently, applying Biot's theory provides a valuable framework for understanding the dynamic vibroacoustic behaviour of the lung tissues in response to varying IPAP and low frequencies.

Measurements of the frequency dependence of geo-alpha in clayey silt at low frequencies

Transmission loss (TL) measurements in the Santa Barbara Channel, together with co-located chirp measurements, show that geo-alpha (dB/l) in clayey silt increases approximately linearly with frequency (f) at f < 3 kHz. TL was measured between a fixed source and fixed vertical array at 3.7 km at 0.3 < f < 5 kHz. Geo-alpha was inverted from the TL data at 0.3, 1.1 and 1.9 kHz. Inversion calculations at 1.1 and 1.9 kHz considered both geo-alpha and bio-alpha due to layer of anchovies at 12 m. Inversion calculations at 0.3 kHz considered only the effect of geo-alpha; the effect bio-alpha on TL was small. Geo-alpha was also inferred from chirp sonar measurements at 3.2 and 6.2 kHz at the ends and middle of the TL track. Chirp sonar showed that the bottom consisted of a layer of unconsolidated sediments overlying a layer of sand. Co-located cores revealed that the unconsolidated layer consisted of clayey silt. Bio-alpha data were compared to Biot and VGS theories and the theory of attenuation in suspended sediments (Pierce et al., 2017). The measured frequency dependence is consistent with Pierce et al.’s theory. This research was supported by The Office of Naval Research Ocean Acoustics Program.

Biogeoacoustic variability in muddy ocean bottom sediment

Both physical and biological benthic processes can influence seabed heterogeneity and contribute to spatiotemporal variability in geoacoustic properties. In particular, how biological processes affect both sediment acoustic properties and their variability is poorly understood. To address this deficiency, recent measurements investigated spatial variability in the upper few decimeters of sediment near the water-seabed interface within a fine-grained sediment deposit on the New England shelf. At each measurement location, acoustic probes were inserted into the sediment to collect direct in situ measurements of sediment sound speed and attenuation at near-ambient conditions, after which cores were collected from the inter-probe propagation paths for ex situ analysis of sediment physical, biological, and acoustic properties. Relationships among sediment properties, such as bulk density, porosity, grain size distribution, organic matter composition, infaunal community composition, and acoustic measurements spanning several frequency decades (10–1000 kHz) will be explored in this paper. Frequency dependence of sediment acoustic properties will also be discussed in the context of sediment acoustics models for mud based on the viscous grain shearing and extended Biot theories. [Sponsored by ONR.]

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

AbstractThis study investigates the localized wave propagation at the free edge of a thin semi‐infinite Magneto‐Electro‐Elastic (MEE) plate. The plate is supported by a two‐parameters elastic foundation. Biot's porosity theory is considered to formulate the porosity in the model, and the pore structure is saturated with an incompressible fluid. The Kirchhoff–Love plate theory determines the plate displacement field. A non‐homogeneity in the material parameters is considered, which varies with the spatial coordinate along the thickness direction of the plate. In order to illustrate the impacts of the surface elements on bending wave propagation, the model incorporates the surface elasticity theory. The short circuit boundary conditions are implemented to derive the general form of the potential function connected with the electric and magnetic fields, respectively. The dispersion relation for bending edge wave on a MEE fluid‐saturated porous plate is obtained by considering a sinusoidal waveform, which propagates along the free edge of the plate. A numerical method named Finite Difference (FD) scheme is employed to analyze the stability of the numerical scheme and also extract the expression of the velocity profiles of the bending edge wave in the absence of the pore structure. The impacts of the various parameters included in the considered model are examined using a numerical example, from which conclusions regarding their sensitivity are derived.

Introduction to Biot's theory of poroelastic wave propagation

Introduction to Biot's theory of poroelastic wave propagation

Численное моделирование цунами оползневого типа

The article proposes mathematical models and stable numerical algorithms for solving problems of deformation and flow of water-saturated porous materials. This class of problems arises in many engineering and applied fields, from field development to biomechanics. Of particular interest are the problems of the collapse of the banks of rivers, lakes and bays of the seas due to their catastrophic impact on possible consequences, for example, blocking the riverbed, the occurrence of a tsunami on the water surface of a reservoir, etc. For the mathematical description of the stress-strain state of saturated porous media, the Biot theory of three-dimensional consolidation is used, supplemented by the kinetics of damage accumulation in the medium and the Drucker-Prager yield conditions. After the formation of the main yield surface (or crack) in the material at the moment of the beginning of the collapse, its rheological properties are presented in the form of a Bingham model with a mathematical description similar to the Navier-Stokes equations with effective viscosity. A characteristic hydrodynamic feature of the problem under consideration is the presence of a free surface. Numerical modeling of the considered problems is carried out by the finite element method. The evolution of the free surface and the occurrence of a tsunami generated by a landslide are investigated.

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.

Opening-dependent phase field model of hydraulic fracture evolution in porous medium under seepage-stress coupling

In this paper, a seepage-stress coupling numerical analysis method is developed to simulate complex hydraulic fracturing in porous medium, in which the characteristics of hydraulic fracture evolution in porous medium under seepage-stress coupling are revealed. The classical Biot's poroelasticity theory is applied to couple the stress and fluid fields, and the crack propagation path of hydraulic fracturing is described by an opening-dependent phase field model. Potential energy caused by fluid pressure is also coupled into the governing equation of phase field evolution. The system of fracture opening affecting fluid flow is established. Staggered iterative scheme is applied to solve the above three-field coupled problem based on Newton–Raphson iterative algorithm. Three classical cases are presented to validate the proposed method: the first one is an analytical solution of pressure distribution in a fixed opening crack and the second one is a benchmark case of Sneddon analytical solution for a pressurized pre-crack and the third one is the KGD problem for hydraulic fracture propagation. Moreover, numerical simulations of hydraulic fracturing in shale block, multi-layer and natural fractures are also investigated. The numerical results agree well with the results in published literatures. It is indicated that hydraulic fracture evolution under seepage-stress coupling can be forecasted by the proposed method. The proposed method not only provides a powerful analytical tool for the oil or gas production, but also provides assessment tools for the stability of geotechnical engineering in water rich environments.

Programmable sound absorption performance enabled by 3D printed fibers

Design of acoustic materials can be achieved through the connection between their geometry and acoustical performance. Here, we propose 3D-printing as an enabling technology that allows us to precisely control an acoustic material's micro-geometry and orientation, which then eliminates microscopic geometry bias due to conventional manufacturing process, thus realizing precise material characterization at the 3D-printing CAD programming stage. This concept was practiced in the current study focusing on 3D-printing fibrous sound absorbing layers. A fused deposition modeling (FDM) method was applied to produce the fibers. A Tarnow-based airflow resistivity model was implemented together with Johnson-Champoux-Allard and Biot theories for modeling the geometry-performance connection for the fibers. The sound absorption prediction accuracy of the model was validated by E-1050 standing wave tube measurements on the printed sample.

A FEM for three‐field u–p–η poroelasticity with nonreciprocal interactions

AbstractThe de la Cruz and Spanos (dCS) theory of poroelasticity is a pore‐scale volume averaged formulation and differs from the widely used Biot (BT) theory. A novel Finite Element Method (FEM) is developed for dCS theory to enable the study of nonreciprocal solid–fluid interactions, which are omitted from BT model. Solid deformations are quasi‐static and pore fluid flow is transient; dynamic effects are neglected. The form of the dCS theory chosen includes BT theory as a special case. The governing equations are written in terms of three fields: solid displacement u, fluid pressure p, and porosity η. Fully implicit time integration and a mixed‐element formulation are employed to ensure stability. The convergence rate of the FEM dCS model is shown to be optimal in a one‐dimensional consolidation problem. Examples of a footing and subsurface injection problems in two dimensions further attest the robustness of the implementation and are shown to reproduce BT model results as a special case. The effect of nonreciprocal solid–fluid interactions is studied in all examples and shows a wide range of importance depending on the properties of the porous media (e.g., permeability) and problem‐specific constraints. The developed FEM provides a tool to enable further comparisons between dCS and BT theories and validation in practical applications.

Quantitative osteoporosis diagnosis of porous cancellous bone using poroelastodynamic modal analysis.

Osteoporosis is a skeletal disease characterized by reduced bone mass and microarchitectural deterioration, leading to increased fragility. This study presents a novel three-dimensional poroelastodynamic model for analyzing cancellous bone free vibration responses. The model incorporates the Navier-Stokes equations of linear elasticity and the Biot theory of porous media, allowing the investigation of osteoporosis-related changes. The analysis considers parameters like porosity, density, elasticity, Poisson ratio, and viscosity of bone marrow within the porous medium. Our findings indicate that natural frequencies of cancellous bone play a crucial role in osteoporosis prediction. By incorporating experimental data from 12 mouse femurs, we unveil insights into osteoporosis prediction. Increased porosity reduces bone stiffness, lowering natural frequencies. However, it also increases bone mass loss relative to stiffness, leading to higher frequencies. Therefore, the natural frequencies of osteoporotic bone are always higher than the natural frequencies of normal bone. Additionally, an increase in bone marrow within the pores, while increasing damping effects, also increases natural frequencies, which is another indication of osteoporosis growth in bone. The presence of bone marrow within the pores further influences natural frequencies, providing additional insights into osteoporosis growth. Thinner and smaller bones are found to be more susceptible to osteoporosis compared to larger and bigger bones due to their higher natural frequencies at equivalent porosity levels.

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.

Biot's theory-based dynamic equation modeling using a machine learning auxiliary approach

Abstract Characterizing seismic wave propagation in a fluid-saturated porous media well enhances the precision of interpreting seismic data, bringing benefits to understanding reservoir properties better. Some important indicators, including wave dispersion and attenuation, along with the wavefield, are widely used for interpreting the reservoir, and they can be obtained from a rock physics model. In existing models, some of them are limited in scope due to their complexity, for example, numerical solutions are difficult or costly. In view of this, this study proposes an approach of establishing equivalent dynamic equations of existing models. First, the framework of the equivalent model is derived based on Biot's theory, while the elastic coefficients are set as unknown factors. The next step is to use deep neural networks (DNNs) to predict these coefficients, and surrogate models of unknowns are established after training DNNs. The training data is naturally generated from the original model. The simplicity of the equation forms, compared to the original complex model and some other equivalents such as the viscoelastic model, enables the framework to perform wavefield simulation easier. Numerical examples show that the established equivalent model can not only predict similar dispersion and attenuation, but also obtain wavefields with small differences. This also indicates that it may be sufficient to establish an equivalent model only according to dispersion and attenuation, and the cost of generating such data is very small compared to simulating the wavefield. Therefore, the proposed approach is expected to effectively improve the computational difficulty of some existing models.

Lateral dynamic responses of coastal group piles considering pile‒water‒soil interactions

In this paper, an analytical framework is developed to investigate the dynamic impedance of pile groups comprising an arbitrary number of cylindrical piles connected with a rigid cap. The solution considers the combination of the secondary ground wave effects transferred by the pile‒soil vibration and the hydrodynamic pressure from the pile‒water interaction. A displacement attenuation function is introduced to define the pile‒to‒pile interaction factor, which describes the relationship between the active and passive piles based on the soil reaction development. The pile is modeled as a Euler‒Bernoulli (EB) beam, and the hydrodynamic pressure is calculated using radiation wave theory. Biot's dynamic poroelastic theory describes the saturated soil around the piles. The rationality and correctness of the proposed theoretical model are verified by degenerating the solution to the existing research results. An extensive parametric analysis is conducted to investigate the effect of various factors on the lateral dynamic impedance of the group pile. Moreover, some interesting findings and meaningful conclusions are obtained.