Unsaturated Porous Materials Research Articles

Sound Absorption Characteristics of Unsaturated Porous Material Calculated by Modified Transfer Matrix Method

Porous materials have emerged as one of the most widely employed sound-absorbing materials in practical applications, owing to their excellent sound absorption properties and lightweight nature. Unsaturated porous materials have the potential to achieve superior sound absorption effects and significantly reduce mass. However, current research on the sound absorption performance of unsaturated porous materials is limited. This paper used a modified transfer matrix method (MTMM), which relies on matrix dimensionality reduction, to analyze the sound absorption characteristics of unsaturated porous materials under various boundary conditions. The study also examines the impact of different parameters, such as material thickness and saturation, on sound absorption performance and compares the results. The findings indicate that when a solid elastic plate is attached to an unsaturated porous elastic plate, the absorption coefficient decreases while the transmission loss increases. Additionally, reducing the thickness of the plate and increasing its porosity and saturation levels lead to an increase in the absorption coefficient and a decrease in the transmission loss.

A machine‐learning supported multi‐scale LBM‐TPM model of unsaturated, anisotropic, and deformable porous materials

AbstractThe purpose of this paper is to investigate the utilization of artificial neural networks (ANNs) in learning models that address the nonlinear anisotropic flow and hysteresis retention behavior of deformable porous materials. Herein, the micro‐geometries of various networks of porous Bentheimer Sandstones subjected to several degrees of strain from the literature are considered. For the generation of the database required for the training, validation, and testing of the machine learning (ML) models, single‐phase and biphasic lattice Boltzmann (LB) simulations are performed. The anisotropic nature of the intrinsic permeability is investigated for the single‐phase LB simulations. Thereafter, the database contains the computed average fluid velocities versus the pressure gradients. In this database, the range of applied fluid pressure gradients includes Darcy as well as non‐Darcy flows. The generated output from the single‐phase flow simulations is implemented in a feed‐forward neural network, representing a path‐independent informed graph‐based model. Concerning the two‐phase LB simulations, the Shan‐Chen multiphase LB model is used to generate the retention curves of the cyclic drying/wetting processes in the deformed porous networks. Consequently, two different ML path‐dependent approaches, that is, 1D convolutional neural network and the recurrent neural network, are used to model the biphasic flow through the deformable porous materials. A comparison in terms of accuracy and speed of training between the two approaches is presented. Conclusively, the outcomes of the papers show the capability of the ML models in representing constitutive relations for permeability and hysteretic retention curves accurately and efficiently.

A multi-scale model for impingement drying of porous slab

Air impingement drying of a planar sheets of porous materials offers advantages of high and controllable heat and mass transfer rates. The governing heat and mass transfer phenomena involve multi-scale physical mechanisms ranging from mesoscopic pore scale to macroscopic jet scale. This work presents a pore-scale heat and mass transfer model of an unsaturated porous material based on statistically self-similar fractal scaling laws of pore structures. Furthermore, the effective transport coefficients are derived and applied to develop a cross-scale mathematical model for hot air impingement drying of a slab made of an unsaturated porous material. The flow and thermal fields of jet impingement and drying characteristics of unsaturated porous material are modeled numerically. The quantitative correlations between the mesoscopic pore structure and macroscopic heat and mass transfer properties are explored. The proposed fractal pore-scale model of porous material and cross-scale mathematical model of jet impingement show good agreement with experimental data. The effects of jet velocity, porosity as well as pore and tortuosity fractal dimensions on drying rate are discussed in detail. The computational results show that the mesoscopic pore structures indicate significant effect on the drying rate during later stage of drying. Results of this study provide useful guidance for efficient design of impingement of porous materials. • Meso-scale heat and mass transfer model of unsaturated porous material is proposed. • Multi-scale model for laminar impingement drying of porous slab is developed. • Impingement drying performance of porous slab is predicted. • Effect of mesoscopic structure on drying kinetics of porous material is explored.

Study on influence of geometric characteristics of cracks on HAM coupling transfer and thermal performance of multi-layer cellular concrete wall

The effect of concrete cracks on the evaluation of the thermal performance of walls has not been effectively considered within the assessment of the thermal and hygroscopic performance of buildings. Based on the dual permeability model, a conjugate method is proposed to reconstruct the PDE equation of unsaturated porous materials with cracks. The reliability of the model is verified from three angles: the heat-moisture coupling benchmark of matrix material, the analytical solution of two-dimensional single fracture heat flow coupling problem and the moisture absorption problem of unsaturated cracks. The reliability of the model is verified from three perspectives: the benchmark of thermal and hygroscopic coupling of matrix materials, the analytical solution to the two-dimensional single-break thermal flow coupling problem, and the hygroscopic problem of unsaturated cracks. The effect of heat and moisture transfer in cracked concrete was quantified by detailed modeling of cracks in terms of the probability of over-penetration, crack roughness, crack density, length, and angle of a two-dimensional discrete crack network, showing that cracks contribute to moisture transfer. This is followed by a 10 day experimental simulation of the meteorological environment, comparing the quantities of moisture accumulation, thermal performance, internal surface temperature and humidity within the fractured and non-fractured wall structures, illustrating the potential adverse effects of cracks on thermal performance and moisture transfer in walls under characteristic conditions. Finally, the necessity of applying moisture-proof layer to the damaged wall is demonstrated by comparing the results before and after the application of the moisture-proof layer.

Cryosuction‐induced fracturing in multiphase porous materials: Numerical modeling and experimental validation

AbstractWhether naturally‐ or artificially‐induced due to human activities, decreasing or increasing the suction in multiphase‐fluid‐saturated porous materials can lead to enormous changes in their thermo‐hydromechanical properties. In this, both the mathematical description and the numerical modeling of the coupled problem present a challenging task. The following contribution considers the instance related to micro‐cryosuction‐induced fractures, which can be observed in saturated and unsaturated porous materials under freezing conditions. This research focuses on continuum porous media mechanics extended by a diffusive phase‐field fracture method. For the cryosuction‐induced fractures in saturated porous media, the water freezing is treated as a phase‐change process. This is modeled using a phase‐field approach, in which the thermal energy derives the phase change and, thus, leads to the occurrence of micro‐cryosuction due to the formation of the ice phase.

Effect of Water Saturation on the Electrical Conductivity of Microporous Silica Glass

The electrical conductivity of porous dielectric materials saturated with water is usually determined by the bulk water conduction. However, the unsaturated state can be affected by a water film covering the unsaturated grain surface. Thus far, a few studies have been conducted on the study of the electrical conductivity with respect to water film covering the grain surface. In this study, the electrical conductivities of the Shirasu porous glass with three different uniform pore sizes (1.0, 0.5, and 0.2 $$\upmu \mathrm{m}$$ ) soaked in various NaCl solutions (0.001, 0.01, and 0.1 $$\mathrm{mol} {\mathrm{L}}^{-1}$$ ) were measured using an impedance meter while being dried at different water saturations. The resulting complex conductivities were fitted by a three-component Cole–Cole model to obtain Cole–Cole parameters. The conductivity values in these parameters were compared with the calculated conductivity values using tortuosities of surface and bulk conduction obtained from two different circuit models. The parallel model of bulk and surface water conduction could not reproduce accurate experimental results; however, the parallel plus series model, including the series connection of water film and bulk water around the meniscus, produced better results. This new model is expected to provide an improved quantitative evaluation of the electrical conductivity of unsaturated porous materials.

Advancements in multi‐phase unsaturated porous media fracture

AbstractThe focus in this research is on introducing an accurate and stable numerical modeling framework and to compare the numerical results with experimental data from the literature for desiccation‐induced fracturing of unsaturated porous materials. The macroscopic modeling approach is based on combined continuum porous media mechanics and a diffusive phase‐field method (PFM). In the case of unsaturated porous media, one has to deal with more than one pore fluid (e.g. water and air). In this, the mechanical behavior can be expressed via using the Bishop's effective stress principle, which considers the total stress, the capillary pressure (air pressure minus water pressure), and saturation degree. The onset of desiccation‐induced fracturing is driven by the capillary pressure, which leads to degradation not only in the effective stresses but also in the capillary pressure itself. In this contribution, we discuss via a numerical example the effect of considering the air pressure variation on the cracking process and numerical stability. Besides, we briefly discuss the potential inclusion of machine‐learning material laws, such as for retention curves and anisotropic permeability, using, e.g., deep recurrent neural networks (RNN) to improve the model accuracy.

Freezing behavior of unsaturated porous materials

The freezing/thawing behavior and the frost-resistance of unsaturated porous materials are quite different from those in water saturated condition. Most previously studies have focused on the water saturated porous systems, however, the effect of moisture content on the freezing behavior of unsaturated porous materials is not well understood. Cement paste is a porous material whose pores ranging from nanometers to micrometers. Herein, low-temperature calorimeter (LTC) measurements on porous hardened cement paste of various saturation degrees SL are performed. It is found that the decrease of moisture content leads to multiple nucleation of ice crystals due to the discontinuity of liquid pores. At the lowest temperature, a large portion of water remains unfrozen because of the block effect of air pores where the propagation of ice crystals into unfrozen pores is cut off. The nucleation temperature decreases with the decreasing SL due to the small probability of finding appropriate nucleation sites. Ice formed in pores varies from the smallest pore size it can be frozen to a certain big size, and cryo-suction into air pores is limited. This study advances the fundamental knowledge of the influences of moisture content on the freezing nature of unsaturated porous materials.

Direct characterization of solute transport in unsaturated porous media using fast X-ray synchrotron microtomography

Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 μm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids' topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.

A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking

This manuscript introduces a unified mathematical framework to replicate both desiccation-induced and hydraulic fracturing in low-permeable unsaturated porous materials observed in experiments. The unsaturated porous medium is considered as a three-phase solid–liquid–gas effective medium of which each constituent occupies a fraction of the representative elementary volume. As such, an energy-minimization-based phase-field model (PFM) is formulated along with the Biot’s poroelasticity theory to replicate the sub-critical crack growth in the brittle regime. Unlike hydraulic fracturing where the excess pore liquid pressure plays an important role at the onset and propagation of cracks, desiccation cracks are mainly driven by deformation induced by water retention. Therefore, the wettability of the solid skeleton may affect the evolution of the capillary pressure (suction) and change the path-dependent responses of the porous media. This air–water–solid interaction may either hinder or enhance the cracking occurrence. This difference of capillary effect on crack growth during wetting and drying is replicated by introducing retention-sensitive degradation mechanisms in our phase field fracture approach. To replicate the hydraulic behaviors of the pore space inside the host matrix and that of the cracks, the path-dependent changes of the intrinsic permeability due to crack growth and porosity changes are introduced to model the flow conduit in open and closed cracks. Numerical examples of drying-induced and hydraulic fracturing demonstrate the capability of the proposed model to capture different fracture patterns, which qualitatively agrees with the fracture mechanisms of related experiments documented in the literature.

Macroscopic description of quasi-static and quasi-stationary processes in unsaturated porous materials

The main aim of this work is to derive equations describing quasi-static and quasi-stationary processes of capillary transport of liquid and gas in unsaturated porous materials. Considerations are based on the new macroscopic model of the capillary transport in porous media, proposed in the paper (Cieszko, 2016). This model has been formulated in the spirit of the theory of interacting continua and shows that the capillary processes of transport in porous materials take place in five-dimensional pressure-time-space. This means that the equations for quasi-static and quasi-stationary processes are not a simple consequence of reduction of the general system of equations. An extended definition of quasi-static processes is proposed, allowing such processes to be analysed as a special case of the general description. A nonlinear first-order evolution equation is obtained for pore saturation with mobile liquid in quasi-static processes; it simultaneously describes the non-stationary processes of saturation evolution taking place in the pressure-space continuum. A new class of processes of capillary transport in unsaturated porous materials is proposed, called quasi-stationary, and a system of strongly coupled nonlinear equations describing these processes is derived. It is shown that even the geometrically very simple boundary value problem of non-wetting liquid flow through an unsaturated porous layer is described by a system of three nonlinear coupled equations for the saturation, pressure and velocity of the liquid.

A Noninvasive TDR Sensor to Measure the Moisture Content of Rigid Porous Materials.

The article presents the potential application of the time domain reflectometry (TDR) technique to measure moisture transport in unsaturated porous materials. The research of the capillary uptake phenomenon in a sample of autoclaved aerated concrete (AAC) was conducted using a TDR sensor with the modified construction for non-invasive testing. In the paper the basic principles of the TDR method as a technique applied in metrology, and its potential for measurement of moisture in porous materials, including soils and porous building materials are presented. The second part of the article presents the experiment of capillary rise process in the AAC sample. Application of the custom sensor required its individual calibration, thus a unique model of regression between the readouts of apparent permittivity of the tested material and its moisture was developed. During the experiment moisture content was monitored in the sample exposed to water influence. Monitoring was conducted using the modified TDR sensor. The process was additionally measured using the standard frequency domain (FD) capacitive sensor in order to compare the readouts with traditional techniques of moisture detection. The uncertainty for testing AAC moisture, was expressed as RMSE (0.013 cm3/cm3) and expanded uncertainty (0.01–0.02 cm3/cm3 depending on moisture) was established along with calibration of the applied sensor. The obtained values are comparable to, or even better than, the features of the traditional invasive sensors utilizing universal calibration models. Both, the TDR and capacitive (FD) sensor enabled monitoring of capillary uptake phenomenon progress. It was noticed that at the end of the experiment the TDR readouts were 4.4% underestimated and the FD readouts were overestimated for 12.6% comparing to the reference gravimetric evaluation.

Influence of frozen conditions on the oxygen diffusion coefficient in unsaturated porous materials

The efficiency of soil covers used as oxygen barriers to control the generation of acid drainage from sulfidic mine wastes can be evaluated in terms of the diffusive oxygen flux reaching the underlying wastes. Oxygen diffusion has been extensively investigated over the last few decades for unsaturated porous materials that are not frozen. However, little attention has been paid to materials that are fully or partially frozen, and thus, the diffusion of oxygen through soil covers during the winter freezing period has been generally neglected. This paper presents a laboratory method developed to evaluate the effective diffusion coefficient of oxygen (De) in frozen, inert materials. The method is a modified version of the conventional double-chamber cell in which the temperature and unfrozen volumetric water content of the sample are measured in addition to the more commonly monitored change in oxygen concentration. Several tests were conducted on non-reactive materials: that is, a sand at multiple degrees of saturation (Sr = 20, 30, 39, and 42%), a silt (Sr = 47%), and a mixture of the two (Sr = 90%). Experimental data were interpreted using the POLLUTE code. Values of De for frozen materials were slightly lower than those obtained at ambient laboratory temperatures. In addition to the development of an empirical method for determining De, a preliminary model based on the model proposed by Aachib et al. (Water Air Soil Pollut 156:163–193, 2004) was created for the prediction of De in frozen materials by defining the involved parameters as temperature-dependent. The results indicate that predicated values of De are slightly higher than experimental values, suggesting that there remains room for improvement in the model.

Convective and conductive thermal homogenization for non-saturated porous building materials: Application on the thermal conductivity tensor

Porous materials possess a complex structure on a microscopic scale and present strong heterogeneities, which makes their precise study extremely complex. In fact, the macroscopic behavior of these materials is strongly dependent on mechanisms that act to the scale of their components. The present work focus on the development of a macroscopic conductive and convective fluid heat transfer model, with a heat source in the unsaturated porous materials. This model is established by periodic homogenization of energy conservation equations written on a microscopic scale in each phase (solid, liquid and gas). The resulting input parameters formulations of the submodel were explicitly identified. Numerical calculations of the homogenized thermal conductivity tensor are performed on a representative 3-D elementary cell of the porous medium. Finally, a sensitivity study of this tensor depending of the variation of the water content and porosity of the concerned elementary cell has been performed. This sensitivity is required to be considered in simulations to better understand the behavior of building materials and improve the prediction of energy performance.

2-D hydro-viscoelastic model for convective drying of deformable and unsaturated porous material

The aim of this work was to simulate in two dimensions the spatio-temporal evolution of the moisture content, the temperature, the solid (dry matter) concentration, the dry product total porosity, the gas porosity, and the mechanical stress within a deformable and unsaturated product during convective drying. The material under study was an elongated cellulose–clay composite sample with a square section placed in hot air flow. Currently, this innovative composite is used in the processing of boxes devoted to the preservation of heritage and precious objects against fire damage and other degradation (moisture, insects, etc.). A comprehensive and rigorous hydrothermal model had been merged with a dynamic linear viscoelasticity model based on Bishop's effective stress theory, assuming that the stress tensor is the sum of solid, liquid, and gas stresses. The material viscoelastic properties were measured by means of stress relaxation tests for different water contents. The viscoelastic behaviour was described by a generalized Maxwell model whose parameters were correlated to the water content. The equations of our model were solved by means of the ‘COMSOL Multiphysics’ software. The hydrothermal part of the model was validated by comparison with experimental drying curves obtained in a laboratory hot-air dryer. The simulations of the spatio-temporal distributions of mechanical stress were performed and interpreted in terms of material potential damage. The sample shape was also predicted all over the drying process.

A semi-analytical solution for the transient response of one-dimensional unsaturated single-layer poroviscoelastic media

This paper develops a semi-analytical solution for the transient response of an unsaturated single-layer poroviscoelastic medium with two immiscible fluids by using the Laplace transformation and the state-space method. Using the elastic–viscoelastic correspondence principle, we first introduce the Kelvin–Voigt model into Zienkiewicz’s unsaturated poroelastic model. The vibrational response for unsaturated porous material can be obtained by combining these two models and assuming that the wetting and non-wetting fluids are compressible, the solid skeleton and solid particles are viscoelastic, and the inertial and mechanical couplings are taken into account. The Laplace transformation and state-space method are used to solve the basic equations with the associated initial and boundary conditions, and the analytical solution in the Laplace domain is developed. To evaluate the responses in the time domain, Durbin’s numerical inverse Laplace transform method is used to obtain the semi-analytical solution. There are three compressional waves in porous media with two immiscible fluids. Moreover, to observe the three compressional waves clearly, we assume the two immiscible fluids are water and oil. Finally, several examples are provided to show the validity of the semi-analytical solution and to assess the influences of the viscosity coefficients and dynamic permeability coefficients on the behavior of the three compressional waves.

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

A new macroscopic description of capillary transport of liquid and gas in porous materials is presented within the framework of multiphase continuum mechanics. It is assumed that unsaturated porous material form a macroscopic continuum composed of three constituents: gas, mobile liquid and capillary liquid, while the skeleton is rigid with an isotropic pore space structure. The capillary liquid forms a thin layer on the internal contact surface with the skeleton, is immoveable and contains the whole capillary energy. The remaining part of the liquid, surrounded by the layer of the capillary liquid and menisci, forms the constituent called mobile liquid. Both liquids exchange mass, momentum and energy in the vicinity of menisci surfaces during their motion, which is described by an additional macroscopic velocity field. A macroscopic scalar quantity is introduced, parametrizing changes of saturations, which for quasi static and stationary processes is equal to the capillary pressure. This quantity extends the dimensionality of the description of mechanical processes taking place in unsaturated porous materials. For the three fluid constituents of the medium, balance equations of mass and linear momentum and evolution equations for saturations are formulated. The constitutive relations for quantities describing mechanical processes in such a medium are proposed based on the dissipation inequality of mechanical energy for the whole system. A new approach is proposed, similar to that used in rational thermodynamics, based on entropy inequality analysis and the Lagrange multipliers method.

Network modelling of fluid retention behaviour in unsaturated soils

The paper describes discrete modelling of the retention behaviour of unsaturated porous materials. A network approach is used within a statistical volume element (SVE), suitable for subsequent use in hydro-mechanical analysis and incorporation within multi-scale numerical modelling. The soil pore structure is modelled by a network of cylindrical pipes connecting spheres, with the spheres representing soil voids and the pipes representing inter-connecting throats. The locations of pipes and spheres are determined by a Voronoi tessellation of the domain. Original aspects of the modelling include a form of periodic boundary condition implementation applied for the first time to this type of network, a new pore volume scaling technique to provide more realistic modelling and a new procedure for initiating drying or wetting paths in a network model employing periodic boundary conditions. Model simulations, employing two linear cumulative probability distributions to represent the distributions of sphere and pipe radii, are presented for the retention behaviour reported from a mercury porosimetry test on a sandstone.

Investigation of the Consolidation Drainage of High Water Content Clay by Siphon Method through Unsaturated Filter

Recently, the disposal of dredged soil has become a worldwide problem. In order to utilize high water content soil material, it is essential to dewater and increase the soil strength. There are urgent demands for developing an alternative new method to dewater the dredged soils in more economical and environment friendly standpoint. Furthermore, by using adsorption effect of porous material such as granular blast furnace slag, there is possibility to establish purification technology of contaminated soil.In this paper, the siphon method is proposed to dewater the high water content dredged soil with horizontally installed plastic board drain and filter material. In order to investigate the availability and effectiveness of this method, series of tests were conducted to investigate the dewatering behaviour and strength of dredged soil with vacuum and siphon methods by using different materials as filter, such as Toyoura sand, zeolite, granular blast furnace slag. High water content dredged soil can be consolidated by using siphon method with saturated filter material such as Toyoura sand. However, it was impossible to dewater dredged soil by using siphon method with unsaturated porous filter material. The water retention tests of soil by using centrifuge method was performed to clarify the mechanism of preventing consolidation dredged soil. The test cannot find an accurate soil-water retention curve of dredged soil because of volume change.The water retention test by suction method was performed and clarify the mechanism that prevents consolidation dredged soil. The cause that prevents consolidation of dredged soil has been presumes by clarifying the air entry value. In addition, degree of saturation and suction in dredged soil and filter material has been clarified by using aquameters. The examination whether consolidation of dredged soil on various conditions focused on height of dredged soil and filter material is performed based on the revealed mechanism.

Methodology of Moisture Measurement in Porous Materials Using Time Domain Reflectometry / Metodyka Prowadzenia Badań Wilgotności W Ośrodkach Porowatych Za Pomocą Reflektometrii W Domenie Czasu

Abstract The article presents the description of measurement methodology of moisture transport in unsaturated porous materials using Time Domain Reflectometry (TDR) technique on the example of measurement of capillary uptake phenomenon in the sample of autoclaved aerated concrete (AAC). In the paper there are presented basic principles of the TDR method as a technique applied in metrology, its potential for measurement of moisture in porous materials like soils and porous building materials. Second part of the article presents the experiment of capillary rise process in the sample of AAC. Within the experiment moisture content was monitored in the sample exposed on water influence. Monitoring was conducted using TDR FP/mts probes. Preparation of the measuring setup was presented in detail. The TDR readouts post-processing, graphical presentations of the obtained results, short discussion and comparison of TDR readouts to gravimetric measurement were also presented.