Theory Of Porous Media Research Articles

Modelling of time‐dependent fatigue crack growth of hydrogels

AbstractThe service life of hydrogel‐based devices is strongly influenced by the anti‐fatigue capability of hydrogels. While recent advancements in the synthesis of hydrogels have improved their fatigue resistance, the underlying mechanisms that dominate the time‐dependent fatigue crack growth of hydrogels are still poorly understood. In this study, a computational method is developed to predict the fatigue crack of hydrogels. A physics‐based poro‐visco‐hyperelastic model is developed within the framework of the Theory of Porous Media at finite strains to describe the mechanical behaviour of hydrogels. A Bell model‐based chain evolution law is adopted to describe the time‐dependent breaking/reforming kinetics of physical chains. An energy‐based fatigue crack growth model is proposed to predict the fatigue crack growth of hydrogels. The averaged elastic energy density surrounding the crack tip is calculated as the driving force of fatigue crack growth. The effects of viscoelasticity, physical chain kinetics and fluid transport on the fatigue crack growth are analysed. The results indicate that these time‐dependent mechanisms cannot be ignored in predicting the fatigue crack behaviour of hydrogels.

Pressure Drop and Gas Flow in an Oxygen Blast Furnace Analyzed by a Combination of Experimentation and a Porous Model

As a modification of the conventional blast furnace (BF), the top gas recycling-oxygen blast furnace (TGR-OBF) has been continuously studied in the context of the technological transformation of low-carbon metallurgy. As it has a set of new gas inlets in the stack and changes the blast operation system in the hearth, the pressure drop and the in-furnace gas flow are the primary problems to be solved in the TGR-OBF’s industrialization. In this paper, a two-dimensional model of a whole blast furnace, based on a softening-and-melting experiment and porous-medium theory, is established. The in-furnace pressure drop and the gas velocity with different oxygen concentrations and tuyere heights are studied. The results show that the suitable height of the stack tuyere is the same as that of the elevation as the cohesive zone inside the furnace. With the gradual increase in oxygen enrichment, the permeability of the cohesive ore layer (COL) increases, while the gas flow through the coke layer (CL) decreases gradually up to 10%. The simulation results provide a theoretical basis for the TGR-OBF to reduce the coke rate and keep the pressure drop from increasing, or even to enable it to decrease.

A theory of porous media for unsaturated soils with immobile air

The Theory of Porous Media (TPM) has served as a reliable theory to deduce governing equations for unsaturated soils. In most works, the unsaturated soil is considered as a three-phase medium composed of air, water and solid. This neglects effects caused by the presence of residual water and/or entrapped (immobile) air attached to the particles. In this work, a set of governing equations for unsaturated soils with residual water and entrapped air is deduced. A mass transfer mechanism between the free air and the entrapped air is considered. The present work focuses only on the entrapped air attached to the particles (immobile air), and therefore it is assumed to have the same intrinsic velocity as the solid. This assumption allows to keep the same number of independent kinematic variables as in conventional three-phase theories. The performance of the theory is examined in simulations of water retention curves subjected to suction cycles, as well as in the dynamic analysis of a centrifuge test on a dam subjected to earthquake loading.

A reinterpretation of the gap fraction of tree crowns from the perspectives of computer graphics and porous media theory.

The gap fraction (GF) of vegetative canopies is an important property related to the contained bulk of reproductive elements and woody facets within the tree crown volume. This work was developed from the perspectives of porous media theory and computer graphics techniques, considering the vegetative elements in the canopy as a solid matrix and treating the gaps between them as pores to guide volume-based GFvol calculations. Woody components and individual leaves were extracted from terrestrial laser scanning data. The concept of equivalent leaf thickness describing the degrees of leaf curling and drooping was proposed to construct hexagonal prisms properly enclosing the scanned points of each leaf, and cylinder models were adopted to fit each branch segment, enabling the calculation of the equivalent leaf and branch volumes within the crown. Finally, the volume-based GFvol of the tree crown following the definition of the void fraction in porous media theory was calculated as one minus the ratio of the total plant leaf and branch volume to the canopy volume. This approach was tested on five tree species and a forest plot with variable canopy architecture, yielding an estimated maximum volume-based GFvol of 0.985 for a small crepe myrtle and a minimal volume-based GFvol of 0.953 for a sakura tree. The 3D morphology of each compositional element in the tree canopy was geometrically defined and the canopy was considered a porous structure to conduct GFvol calculations based on multidisciplinary theory.

Permeation grouting mechanism of viscous time-varying fluid considering diffusion path

Due to the hidden nature of the grouting project, it has not been possible to get a clear picture of the slurry transport law, and most of the existing permeation grouting theories have ignored the tortuous characteristics of the pore channels of porous media. Based on the fractal theory of porous media and the equation of seepage motion of viscous time-varying Bingham fluid, a theoretical model of permeation grouting with viscous time-varying Bingham fluid is established, and viscosity tests are carried out for C-S slurry to obtain the time-varying equation of viscosity of C-S slurry. A set of permeation grouting simulation experiment device was designed, and the permeation grouting simulation experiment of C-S slurry was carried out to obtain the variation curve of grouting pressure with time under different injection media and different grouting rates. The results show that the grouting pressure considering the diffusion path of the slurry is 0.9–1.1 times of the experimental results, the grouting pressure obtained from the experimental is 0.7–1.2 times of the theoretical value considering the diffusion path, and the calculated value considering the diffusion path agrees well with the experimental value. The theoretical model can provide scientific guidance for field grouting construction.

Semi-Analytical Solution for the Vertical Vibration of a Single Pile Embedded in a Frozen Poroelastic Half-Space

The theory of vertical pile vibration is the essential basis for pile integrity determination and dynamic analysis. The pile vibration characteristics are inevitably affected when the surrounding soil is frozen due to the low environmental temperature. Therefore, the investigation of pile vibration considering the surrounding soil as a saturated frozen porous medium is of great importance. In this paper, an analytical model for vertical pile vibration was established by employing the theory of composite saturated porous media, that is, by simplifying the upper frozen soil layer as a homogeneous isotropic saturated frozen porous medium and the foundation soil beneath the pile as an elastic half-space subjected to the motion of a rigid disk. By employing the integral transform and variable separation method, analytical solutions for the proposed model were derived under the three-dimensional axisymmetric condition. The analytical model and its solutions were verified by comparing them with the existing solutions for an end-bearing pile embedded in a homogeneously frozen soil layer as well as for a saturated half-space. A parametric study was conducted by utilizing the proposed solutions, and the results indicated that the pile bottom stiffness, the freezing temperature, the shear modulus of the unfrozen soil, etc., had a significant influence on the dynamic responses of the vertical pile vibration in both the frequency and the time domains.

Simulation of Contaminant Transport through the Vadose Zone: A Continuum Mechanical Approach within the Framework of the Extended Theory of Porous Media (eTPM)

The simulation of contaminant transport through the vadose zone enjoys high significance for decision makers and contaminated site planners since the vadose zone can serve as a filter, but many contaminants can be transported from this region to aquifers. The intention of this paper is to utilize the extended Theory of Porous Media (eTPM) to develop a ternary model for the simulation of contaminant transport in the vadose zone whose application is subsequently shown via a numerical example. The simulation was conducted for 140 days, during which the contamination source was removed after 25 days. The results indicate that the contaminant reached the water table after 76 days. The concentration of the contaminant reaching the groundwater was 17% less than that of the contaminant source.

Propagation of acoustic wave and analysis of borehole acoustic field in porous medium of heterogeneous viscous fluid

Sound field in fluid-saturated porous medium is closely related to the viscosity of fluid and the heterogeneity of porous medium. In order to improve the physical mechanism of wave propagation in porous medium and expand its application in borehole acoustic field, the shear stress of porous fluid and the heterogeneity of pore structure are considered. The wave theory in porous medium containing viscous fluid is deduced based on the Biot theory. The influence of porous medium parameters on slow shear wave is analyzed, and the dispersion and attenuation of elastic wave caused by shear stress balance in porous fluid under the influence of inhomogeneous pore structure are studied. The analytical solution of borehole acoustic field in porous medium containing viscous fluid is further derived. The phase velocity and attenuation of borehole mode waves in heterogeneous porous medium, and the waveform of borehole full wave are calculated. The influence of pore fluid viscosity on borehole full wave is analyzed. The results show that there are slow shear waves in the porous medium containing viscous fluid. The slow shear wave is characterized by low velocity and large attenuation. In heterogeneous porous medium, the balance process of shear stress related to slow shear wave not only leads to the dispersion and attenuation of fast P-wave, but also affects the propagation characteristics of borehole pseudo Rayleigh wave and Stoneley wave. In addition, the pore fluid viscosity has a great influence on the borehole Stoneley wave. The present work improves the physical mechanism of acoustic wave propagation in porous medium and provides theoretical guidance for the explanation and application of borehole acoustic waves in porous formations.

Study on vibration isolation performance of composite multilayer wave impeding block based on wave impedance ratio under an underground dynamic load

Based on the theory of single-phase elastic medium and unsaturated porous medium, the vibration isolation effect of composite multilayer wave impeding block (WIB) in the unsaturated ground under an underground dynamic load is investigated. The results show that the best vibration isolation effect can be obtained by designing the wave impedance ratio between the composite multilayer WIB and unsaturated ground. The composite multilayer WIB improves the vibration-damping bandwidth compared with the homogeneous WIB. The vibration isolation effect is better the closer the embedded depth of the composite multilayer WIB is to the vibration source, and its vibration isolation effect increases significantly with the increase of thickness, but when the thickness of the WIB exceeds a certain critical thickness, its vibration isolation effect decreases with the increase of thickness. Soil saturation has a significant effect on the vibration isolation effect of composite multilayer WIB in the unsaturated ground, and the composite multilayer WIB can achieve a better vibration isolation effect at low saturation.

A PERMEABILITY HYSTERESIS MODEL FOR FRACTAL POROUS MEDIA BASED ON ELASTIC-STRUCTURAL DEFORMATION OF CAPILLARY CROSS SECTION

Permeability hysteresis under cyclic pressure loading and unloading has received a lot of attention in both science and engineering. But most of the existing model is only for a one-time pressure cycle. Therefore, a permeability hysteresis model is established based on the theory of elastic-structural deformation of capillary cross section and the fractal theory of porous media. Both the triangular and quadrilateral structures are considered. The stress sensitivity of structural deformation decreases with the increase in the cycle. The porosity hysteresis can also be predicted by the proposed model. Compared with experimental data with different permeability hysteresis, the prediction of the proposed model is consistent with the experimental results. Compared with other models, the proposed model has a smaller average error and a better agreement with experimental data. The proposed model can predict the permeability hysteresis under not only a one-time pressure cycle like the existing model but also multiple pressure cycles. The influence of parameters shows that the decrease in Young’s modulus and Poisson’s ratio of the solid cluster increases the permeability stress sensitivity but does not influence the permeability hysteresis. The increase in the proportion of quadrilateral structure and stress sensitivity of structural deformation increases the permeability hysteresis and stress sensitivity at the same time, while the capillary fractal dimension, tortuosity fractal dimension, and the decay rate of stress sensitivity of structural deformation during the cycles show the opposite. The proposed model has a significant meaning in underground resource mining and the study of permeability hysteresis mechanism.

Uncertainty with Varying Subsurface Permeabilities Reduced Using Coupled Random Field and Extended Theory of Porous Media Contaminant Transport Models

To maximize the usefulness of groundwater flow models for the protection of aquifers and abstraction wells, it is necessary to identify and decrease the uncertainty associated with the major parameters such as permeability. To do this, there is a need to develop set of estimates representing subsurface heterogeneity or representative soil permeability estimates. Here, we use a coupled Random Field and extended Theory of Porous Media (eTPM) simulation to develop a robust model with a good predictive ability that reduces uncertainty. The coupled model is then validated with a physical sandbox experiment. Uncertainty is reduced by using 500 realisations of the permeability parameter using the eTPM approach. A multi-layer contaminant transport scenario with varying permeabilities, similar to what could be expected with shallow alluvial sediments, is simulated. The results show that the contaminant arrival time could be strongly affected by random field realizations of permeability compared with a modelled homogenous permeability parameter. The breakthrough time for heterogeneous permeabilities is shorter than the homogeneous condition. Using the 75% confidence interval (CI), the average contaminant concentration shows 4.4% variation from the average values of the considered area and 8.9% variation in the case of a 95% confidence interval.

Effects of the fluid-solid interface conditions on the dynamic responses of the saturated seabed during earthquakes

In this paper, the effects of the fluid-solid interface conditions between seawater and seabed on the dynamic responses of the seabed during earthquakes are investigated. Based on Biot's porous media theory, a semi-analytical solution of the 1D transient response and an analytical solution of the 1D steady-state response of the saturated seabed under different fluid-solid interface conditions are given, respectively. Based on the transient response solution, it is found that the fluid-solid interface conditions have a significant effect on slow waves and a small effect on fast waves. Based on the steady-state response solution, it is found that the effects of the fluid-solid interface conditions on the displacement amplification factor and pore-water pressure vary under different incident wave frequencies. In the low-frequency region, the lower the interface permeability, the smaller the displacement amplification factor. In the high-frequency region, the lower the interface permeability, the larger the displacement amplification factor. Moreover, the fluid-solid interface conditions affect the dynamic response of the seabed with different permeability coefficients to different degrees. As the seabed permeability coefficient decreases, the effects of the fluid-solid interface conditions on the dynamic responses of the seabed gradually decrease.

Quantitative evaluation on the suitable flow region inside the shielding device of submersible aquaculture facility

The primary purpose of the aquaculture facility is to provide a comfortable living environment and achieve welfare aquaculture for cultured fish in the open sea. Nevertheless, it has been a challenge to accurately assess the suitable flow region of the cultured fish inside the aquaculture facility for the severe ocean environment, which is a pressing concern for aquaculture farmers. First, the maximum domed swimming speed (MDSS) is used as an indicator to assess the swimming ability of Sciaenops ocellatus in this study, which can be measured through a vertical circulation water channel. Subsequently, the porous media theory is adopted and applied to predict the flow field inside the shielding device of the submersible aquaculture facility based on the shear stress transport k-omega turbulence model using the computational fluid dynamics (CFD) approach. In addition, combining the swimming ability of Sciaenops ocellatus and current speed distribution inside the shielding device of a submersible aquaculture facility, the suitable flow region is quantitatively assessed. The results indicate that when middle height, the inclined angle and net solidity are 0.4 m, 3π/12 and 0.65, respectively, the current speed inside the shielding device attenuates below the maximum domed swimming speed of Sciaenops ocellatus - 0.76 m/s and meets the survival of Sciaenops ocellatus for the actual sea condition with an incident current speed of 1.5 m/s. In addition, a suitable flow region for Sciaenops ocellatus, which is 204.512 m3 and accounts for 17.76% of the total aquaculture volume, is formed and located inside the shielding device, close to the downstream sides, and gradually extends towards the middle of the shielding device. Based on the swimming ability of Sciaenops ocellatus, using numerical means to describe the suitable flow region in detail is to provide clear and macroscopic guidance for aquaculture farmers.

A Leakage Rate Model for Metal-to-Metal Seals Based on the Fractal Theory of Porous Medium

Due to the complexity of sealing surface topography, it is difficult to take the surface topography into consideration when building a leakage rate model theoretically. Therefore, a theoretical model for estimating the leakage rate of metal-to-metal seals based on the fractal theory of porous medium, which can objectively reflect the influence of sealing surface topography from a microscopic perspective, is proposed in the present work. In the approach, fractal parameters are adopted to characterize the sealing surface. The sealing interface is supposed to be a porous medium space and the intrinsic parameters are obtained through rigorous theoretical derivation. The results show that the topography parameters of the sealing surface have a significant effect on the intrinsic parameters of the pore space and lead to a significant influence on the leakage rate of metal-to-metal seals. Specifically, the smoother the sealing surface, the lower the leakage rate of the metal-to-metal seal. Moreover, the leakage rate decreases with an increase in the contact pressure, and, if the fluid pressure difference is too large, the sealing performance will be seriously reduced. The proposed model provides a novel way to calculate the leakage rate of metal-to-metal seals.

Two‐phase model for the excavation analysis in partially saturated soft soils using the particle finite element method

AbstractA two‐phase velocity‐pressure stabilized formulation is proposed for the numerical analysis of mechanized excavations in partially saturated soft soils using the Particle Finite Element Method (PFEM). The fully coupled formulation is based on the theory of porous media in association with the Soil Water Characteristic Curve and the porosity‐dependent Kozeni‐Carman model for the realistic estimation of the soil permeability. The combination of the PFEM methodology, characterized by a global re‐meshing strategy equipped with a new adaptive mesh refinement scheme for the resolution of strain localization zones in the ground, with a hypoplastic constitutive model for the description of the non‐linear behavior of the deformable soil skeleton, allows for the modeling of very large deformations, as required for excavation simulations. The PFEM model is validated based on selected geotechnical benchmark problems concerned with fully and partially saturated soil specimens. The model is further applied to computational re‐analyses of excavation tests involving a single cutting tool moving in a sandbox. The reaction force‐tool displacement curve for the excavation tool as well as the evolution of the deformed topology of the sand including the formation of shear zones obtained from the computational model are compared with respective experimental observations. Parametric investigations aimed at elucidating the influence of selected geotechnical parameters on the excavation process are also carried out. Finally, the suitability of the proposed PFEM‐based numerical strategy for the modeling of 3D excavation problems is demonstrated by means of 3D PFEM simulations in fully saturated sand.

Multifield Modeling and Simulation of Nutrient Transport in Mechanically Stressed Meniscus Tissue.

Insights into the transport mechanisms of nutrients are essential for understanding the pathophysiology of menisci. In the present work, we focus on the modeling and numerical simulation of the transport of glucose molecules in mechanically stressed meniscus tissue. Therefore, a multifield model based on the theory of porous media is created. Due to a biphasic approach, the major phases of the solid and the fluid are represented. The description of the transport processes of the uncharged nutrient molecules, such as convection and diffusion, is given by three coupled partial differential equations valid for large deformations. Numerical simulations are performed for everyday types of stress such as (I) lying, (II) two-legged stance, (III) one-legged stance, (IV) level walking, and (V) stair descending using the finite element method. The results show that diffusion is the dominant process. However, in parts of the meniscus, the delivery of glucose can be improved by convection due to mechanical loading. Based on these basic insights, the model can now be adapted to individual patient's meniscus geometries. The model can thus give insights into the suitability of loading scenarios for rehabilitation after meniscus damage.

Salinity, force chains, and creep in muddy sediments

The salinity of sediments is not usually measured. Experience with sandy sediments shows that it has no significant effect on the acoustic properties. In muddy sediments, salinity is critical to the skeletal frame, because it causes the clay particles to flocculate, forming an aggregate of larger particles with significant water fraction. It behaves like a granular medium, in which stress is transmitted along random force chains. Mud is known to suffer from creep, and the force chain model fits neatly into creep theory. It may be modeled as a form of stationary creep, which is linear in many respects. No net strain-hardening is involved. The result is a creep model of the skeletal frame that naturally couples into the Biot theory of porous media. It predicts an attenuation that increases linearly with frequency at low frequencies, which is overtaken by viscous attenuation that increases as the second power of frequency and high frequencies. [Work supported by ONR, Ocean Acoustics Program.]

Numerical simulation of anti-sloshing performance in a 2D rectangular tank with random porous layer

The porous media theory is extensively used to simulate the porous structures due to the complexity of the shape and grain configuration. In this study, The open-source code OpenFOAM was firstly extended to solve the interaction between the sloshing flow and the random porous structure, and the accuracy of the extension was validated by comparing the numerical results with experimental data. In addition, the effect of porosity, average diameter of the porous structure was analyzed, and then the anti-sloshing performance of rectangular tank for different excitation frequencies and distances between the random porous structure and the nodal line of eigenmode (m = 1) was also discussed. After that, a comparison of the wave-damping performance between the random porous layer and the traditional perforated baffle was conducted. Results indicated that the random porous structure with porosity (n) of 0.2 and average diameter (d50/b) of 0.85 has the best anti-sloshing performance, and the anti-sloshing performance of random porous layer is generally decreased when the excitation frequency moves close to the first-order natural frequency, and it is decreased with the increasing distance. A better wave-damping performance of the present random porous structure can be observed when compared with traditional perforated baffle.

On robust discretization methods for poroelastic problems: Numerical examples and counter-examples

Finite element approximations of poroelastic materials are nowadays used within multiple applications. Due to wide variation of possible material parameters, robustness of the considered discretization is important. Within this contribution robust of discretization schemes, initially developed for Biot’s theory, will be applied within the Theory of Porous Media. Selected numerical test-cases, special attention will be paid to incompressible and impermeable regimes, are conducted.

Influence of surfactant on the permeability at different positions of a leaching column.

To solve the problems of poor permeability and low leaching rate in ore heap leaching, solid surface physical chemistry, seepage mechanics theory for porous media, CT scanning and SEM were used to carry out column leaching tests with a homemade segmented removable plexiglass column; the variation law for the permeability coefficients of each segment of the leaching column before and after leaching was analyzed. The experimental results showed that there was little difference in the permeability coefficient of ore at different heights before leaching. After leaching, the permeability coefficients were unevenly distributed along the column height, and the lowest value was located at the bottom of the leaching column. The addition of surfactant provided an obvious improvement in the permeability of the leaching column. The permeability coefficient at the bottom of the leaching column was 6% higher than that of the control group. At the same time, the addition of surfactant increased the leaching rate of ore by nearly 10%. A theoretical analysis showed that the surfactant improved the permeability of ore heaps mainly by preventing physical blockage by fine particles and inhibiting deposition of chemical products.