Search Results (44)

Perfluorooctanoic acid (PFOA) and perfluorooctanesulfonic acid (PFOS) are emerging contaminants of concern as they persist in natural environments due to their unique chemical structures. This paper critically reviewed the adsorption of PFOA and PFOS, depending on their chemical structure, by different adsorbents as well as soil. Adsorption of PFOS generally surpasses that of PFOA across various adsorbents. Despite having the same number of carbons, PFOS exhibits greater hydrophobicity due to two major structural differences: firstly, it has one extra CF₂ unit and secondly, the sulfonate group in PFOS, being a relatively hard base, readily adsorbs on oxide surfaces, enhancing its adsorption compared to the carboxylate group in PFOA. While comparing activated carbon (AC) adsorption performance, powdered activated carbon (PAC) demonstrates higher adsorption capacity than granular activated carbon (GAC) for PFOS and PFOA. Anion exchange resin (AER) outperforms other adsorbents, with a maximum adsorption capacity for PFOS twice that of PFOA. Carbon nanotubes (CNTs) exhibit two-fold higher adsorption for PFOS compared to PFOA, with single-walled CNTs showing a distinct advantage. Overall, the removal of PFOS and PFOA under similar conditions on different adsorbents is observed to be in the following order: AER > single-walled CNTs > AC. Moreover, AER, single-walled CNTs, and AC exhibited higher adsorption capacities for PFOS than PFOA. In situ remediation studies of PFOA/S-contaminated soil using colloidal activated carbon show a reduction in concentration to below acceptable limits within 12–24 months. The theoretical and experimental studies cited in this review highlight the role of air–water interfacial adsorption in retaining PFOA and PFOS as a function of their charged head groups during their transport in unsaturated porous media. Full article

Groundwater is one of the major sources of water supply for human needs. But anthropic activities such as agriculture are causing significant volume depletion and quality deterioration, favoring microbial contamination that has a negative impact on human health. The geological characteristics of the ground can influence the transport of microorganisms, especially if made of permeable rock. Furthermore, irrigation with untreated or partially treated wastewater can represent an additional health risk due to the potential transmission of pathogens to food. The aim of our research is to provide an interdisciplinary perspective on this issue by integrating hygienic, geological, and agronomic skills. Water samplings are scheduled seasonally by four monitoring campaigns in five sampling points placed in two Southern Italy regions, Apulia (one point at the outlet and two wells near the wastewater plant at Carpignano Salentino, Lecce province, Italy) and Sicily (two wells at Scicli and Pozzallo, Ragusa province, Italy) Laboratory experiments of microorganism transport in permeable rocks will be carried out under saturated and unsaturated conditions. A mathematical model of transport through porous media will be implemented and validated with laboratory measurements. The model will be used to develop a monitoring tool to control sites in Apulia and Sicily where periodic cultural and molecular detection of pathogenic bacteria, viruses, and protozoa will also be taken. In addition, an analysis of the microbiological contamination of herbaceous crops due to the use of low-quality water will be conducted to assess the Quantitative Microbial Risk Assessment (QMRA). The project will provide methodological tools to evaluate anthropogenic pressures and their impact on environmental matrices. The results will allow these pressures to be modulated to minimize environmental and agri-food microbiological contamination and protect public health. Full article

Most previous investigations for consolidation-induced solute transport models have been limited to one-dimensional studies in unsaturated porous media and lack systematic parameter sensitivity analysis. This study addresses these gaps by analyzing the effects of hydraulic conductivity (K), shear modulus (G), saturation ($S_r$), Poisson’s ratio ($\nu$), partitioning coefficient ($K_d$), and anisotropy ratio (${\displaystyle \frac{K_x}{K_z}}$ and ${\displaystyle \frac{K_y}{K_z}}$) on pore water pressure, soil deformation, and solute transport. The findings reveal that higher $K_d$ values significantly hinder solute migration through enhanced adsorption and reduced vertical transport to deeper layers, while increasing anisotropy ratios primarily enhance horizontal migration, with their effects diminishing beyond a threshold. Additionally, a higher K accelerates pressure dissipation and solute movement, while a lower G increases soil deformation and speeds up solute migration. Saturation has a minor effect on solute concentration, with slight increases under higher $S_r$. The Poisson ratio significantly impacts the transport of the solute, with smaller $\nu$ accelerating and larger $\nu$ slowing migration. These insights offer valuable theoretical support for optimizing models in unsaturated porous media. Full article

The stiffened deep cement mixing (SDCM) pile, as a new type of rigid–flexible composite pile, significantly enhances the vertical bearing capacity of traditional precast piles, thus holding broad application prospects in the substructure construction of nearshore bridges and marine energy structures. This paper investigates the vertical dynamic response of SDCM piles through theoretical derivation and parameter analysis. Firstly, based on elastic dynamics theory and the three-phase porous media model, vertical vibration control equations for both SDCM piles and fractional-order viscoelastic unsaturated soils are established. Secondly, theoretical derivations yield exact analytical solutions for the surrounding dynamic impedance, top dynamic stiffness, and dynamic damping of the SDCM pile. Finally, through numerical examples and parameter studies, the impact mechanisms of physical parameters in the SDCM pile–unsaturated soil dynamic coupling system on the top dynamic stiffness and dynamic damping of the SDCM pile are analyzed. The research results presented in this paper indicate that reducing the radius of the rigid core pile while increasing the thickness of the exterior pile has a positive effect on enhancing its vibration resistance. Additionally, increasing the length of SDCM piles contributes to improved vibration performance. However, an increase in the elastic modulus of the cement–soil exterior pile is detrimental to the vibration resistance of the rigid composite pile. On the other hand, an increase in the elastic modulus of the concrete core pile only enhances its ability to resist vibration under low-frequency load excitation. Furthermore, enlarging the soil saturation, decreasing the intrinsic permeability, and enlarging the soil relaxation shear modulus have a significant positive impact on improving the vibration resistance of SDCM piles. In contrast, changes in porosity have a negligible effect on the ability to resist vertical vibrations of SDCM piles. Full article

This paper studies constrained Newtonian fluid flows through porous media, accounting for the drag effect on the fluid, modeled using a Mixture Theory perspective and a constitutive relation for the pressure—namely, a continuous and differentiable function of the saturation that ensures always preserving the problem hyperbolicity. The pressure equation also permits an ultra-small porous matrix supersaturation (that is controlled) and the transition from unsaturated to saturated flow (and vice versa). The mathematical model gives rise to a nonlinear, non-homogeneous hyperbolic system. Its numerical simulation combines Glimm’s method with an operator-splitting strategy to account for the Darcy and Forchheimer terms that cause the system’s non-homogeneity. Despite the Glimm method’s proven convergence, it is not adequate to approximate non-homogeneous hyperbolic systems unless combined with an operator-splitting technique. Although other approaches have already addressed this problem, the novelty is combining Glimm’s method with operator-splitting to account for linear and nonlinear drag effects. Glimm’s scheme marches in time using a formerly selected number of associated Riemann problems. The constitutive relation for the pressure—an increasing function of the saturation, with the first derivative also increasing, convex, and positive, enables us to obtain explicit expressions for the Riemann invariants. The results show the influence of the Darcy and Forchheimer drag terms on the flow. Full article

Backward erosion piping, a soil erosion phenomenon induced by seepage, compromises the stability of water-retaining structures such as dikes. During floods, the seepage in the dike body increases due to high water levels, which directly affects the progression of the piping channel. The formation of the piping channel then impacts the stability of the dike. In this paper, an improved piping model that considers the impact of seepage in the dike body is proposed based on Wewer’s model. Specifically, we added a seepage field of the dike body to the original model to account for the impact of dike-body seepage on the evolution of piping. The seepage field of the dike body is solved using Darcy’s law and the continuity equation for unsaturated porous media. In addition, this approach also incorporates the coupling effect of seepage stress. The accuracy of the model was verified through comparing the calculated results with the IJkdijk experiment and Wewer’s results. The effects of BEP on dike stability were investigated using the proposed improved piping model. The two major conclusions of the study are that (1) the incorporation of unsaturated seepage enhanced the performance of the piping model, allowing it to more accurately simulate the development of pipe length and the changing of pore pressure; and (2) the formation of the pipe impacted dike stability, leading to a substantial reduction in the safety factor of the dike slope. Full article

The necessity of understanding and simulating hydrological phenomena as well as their interactions and the effect of anthropogenic and climate conditions on the ecosystem have encouraged researchers for years to investigate the moisture transfer in soil. Considering the moisture transfer as an isothermal phenomenon might cause a wrong estimation due to the non-isothermal nature of the moisture movement in porous media. Hygrothermal (coupled heat and moisture transfer) models are quite diverse and are the engine of the various hygrothermal software tools used to analyze the heat and moisture in building envelopes, drying technologies, and many other applications. This paper is a literature survey conducted to provide an overview on the classical hygrothermal models to address the historical perspectives on these models. First, it investigated, from a historical point of view, the challenges behind the development of hygrothermal models as unsaturated flow theories, beginning with Buckingham theory. The non-isothermal nature of moisture was the starting point for researchers to deal with new challenges during mathematical modeling and experimental analysis. In general, the theory of coupled heat and moisture transfer first developed by J.R. Philip and De Vries and the authors in the mid-1950s inspired the novel hygrothermal models, including Sophocleous and Milly’s model, Rode’s model, Künzel’s model, and Grunewal’s model. In a parallel of hygrothermal model developments, the models of Whitaker and Luikov can also be classified as hygrothermal models; they were mostly applied in modeling the phenomenon of drying. The study highlights the application of hygrothermal models in building physics and gathered a summary of international efforts such as Annex 24, Annex 41, and the HAMSTAD project and advancements performed from the classical dew point or steady-state Glaser method. Moreover, this study emphasizes the advantages of the standard of EN 15026 and limitations of the Glaser method. To sum up, hygrothermal models are still under development based on various assumptions of moisture driving potentials and transfer coefficients. Full article

The mechanical behavior of unsaturated porous media under non-isothermal conditions plays a vital role in geo-hazards and geo-energy engineering (e.g., landslides triggered by fire and geothermal energy harvest and foundations). Temperature increase can trigger localized failure and cracking in unsaturated porous media. This article investigates the shear banding and cracking in unsaturated porous media under non-isothermal conditions through a thermo–hydro–mechanical (THM) periporomechanics (PPM) paradigm. PPM is a nonlocal formulation of classical poromechanics using integral equations, which is robust in simulating continuous and discontinuous deformation in porous media. As a new contribution, we formulate a nonlocal THM constitutive model for unsaturated porous media in the PPM paradigm in this study. The THM meshfree paradigm is implemented through an explicit Lagrangian meshfree algorithm. The return mapping algorithm is used to implement the nonlocal THM constitutive model numerically. Numerical examples are presented to assess the capability of the proposed THM mesh-free paradigm for modeling shear banding and cracking in unsaturated porous media under non-isothermal conditions. The numerical results are examined to study the effect of temperature variations on the formation of shear banding and cracking in unsaturated porous media. Full article

Data assimilation for unconfined seepage analysis has faced significant challenges due to hybrid causes, such as sparse measurements, heterogeneity of porous media, and computationally expensive forward models. To address these bottlenecks, this paper introduces a physics-informed neural network (PINN) model to resolve the data assimilation problem for seepage analysis of unsaturated earth–rockfill dams. This strategy offers a solution that decreases the reliance on numerical models and enables an accurate and efficient prediction of seepage parameters for complex models in the case of sparse observational data. For the first attempt in this study, the observed values are obtained by random sampling of numerical solutions, which are then contributed to the synchronous constraints in the loss function by informing both the seepage control equations and boundary conditions. To minimize the effects of sharp gradient shifts in seepage parameters within the research domain, a residual adaptive refinement (RAR) constraint is introduced to strategically allocate training points around positions with significant residuals in partial differential equations (PDEs), which could facilitate enhancing the prediction accuracy. The model’s effectiveness and precision are evaluated by analyzing the proposed strategy against the numerical solutions. The results indicate that even with limited sparse data, the PINN model has great potential to predict seepage data and identify complex structures and anomalies inside the dam. By incorporating coupling constraints, the validity of our PINN model could lead to theoretically viable applications of hydrogeophysical inversion or multi-parameter seepage inversion. The results show that the proposed framework can predict the seepage parameters for the entire research domain with only a small amount of observation data. Furthermore, with a small amount of observation data, PINNs are able to obtain more accurate results than purely data-driven DNNs. Full article

Contrary to the continuum hypothesis, which averages water flow across the entire domain, including both grains and pores, the line-element model concentrates unsaturated flow in the pore space in the intermediate region of horizontal and vertical channels. The flux equivalent principle is used to deduce the equivalent unsaturated hydraulic conductivity, the flow velocity and the continuity equations. It is found that the relative hydraulic conductivities derived from the line-element model and the continuum model are identical. The continuity equations in the two models are also similar, except that the coefficient in the water content term is half that in the line-element model. Thus, the unsaturated flow problem in porous media is transformed into a one-dimensional problem. A dimension-reduced finite line-element method is proposed that includes a complementary algorithm for Signorini’s-type boundary conditions involving the seepage-face boundary and the infiltration boundary. The validity of the proposed model is then proved by good agreement with analytical, experimental and simulated results for one-dimensional infiltration in a vertical soil column, unsaturated flow in a sand flume with drainage tunnels, and transient unsaturated flow water-table recharge in a soil slab, respectively. In general, the proposed method has good computational efficiency, especially for smaller mesh sizes and short time intervals. Full article

The sustainable exploitation of groundwater resources is a multifaceted and complex problem, which is controlled, among many other factors and processes, by water flow in porous soils and sediments. Modeling water flow in unsaturated, non-deformable porous media is commonly based on a partial differential equation, which translates the mass conservation principle into mathematical terms. Such an equation assumes that the variation of the volumetric water content ($\theta$) in the medium is balanced by the net flux of water flow, i.e., the divergence of specific discharge, if source/sink terms are negligible. Specific discharge is in turn related to the matric potential (h), through the non-linear Darcy–Buckingham law. The resulting equation can be rewritten in different ways, in order to express it as a partial differential equation where a single physical quantity is considered to be a dependent variable. Namely, the most common instances are the Fokker–Planck Equation (for $\theta$), and the Richards Equation (for h). The other two forms can be given for generalized matric flux potential ($\Phi$) and for hydraulic conductivity (K). The latter two cases are shown to limit the non-linearity to multiplicative terms for an exponential K-to-h relationship. Different types of boundary conditions are examined for the four different formalisms. Moreover, remarks given on the physico-mathematical properties of the relationships between K, h, and $\theta$ could be useful for further theoretical and practical studies. Full article

This work uses a mixture theory approach to describe kinematically constrained flows through porous media using an adequate constitutive relation for pressure that preserves the problem hyperbolicity even when the flow becomes saturated. This feature allows using the same mathematical tool for handling unsaturated and saturated flows. The mechanical model can represent the saturated–unsaturated transition and vice-versa. The constitutive relation for pressure is a continuous and differentiable function of saturation: an increasing function with a strictly convex, increasing, and positive first derivative. This significant characteristic permits the fluid to establish a tiny controlled supersaturation of the porous matrix. The associated Riemann problem’s complete solution is addressed in detail, with explicit expressions for the Riemann invariants. Glimm’s semi-analytical scheme advances from a given instant to a subsequent one, employing the associated Riemann problem solution for each two consecutive time steps. The simulations employ a variation in Glimm’s scheme, which uses the mean of four independent sequences for each considered time, ensuring computational solutions with reliable positions of rarefaction and shock waves. The results permit verifying this significant characteristic. Full article

In order to reduce the numerical difficulty of the 3D transient free surface flow problems in porous media, a line element method is proposed by dimension reduction. Different from the classical continuum-based methods, homogeneous permeable pores in the control volume are conceptualized by a 3D orthogonal network of tubes. To obtain the same hydraulic solution with the continuum model, the equivalent formulas of flow velocity, continuity equation and transient free surface boundary are derivable from the principle of flow balance. In the solution space of transient free surface flow, the 3D problem is transformed into 1D condition, and then a finite element algorithm is simply deduced. The greatest advantage of the line element method is line integration instead of volume/surface integration, which has dramatically decreased the integration difficulty across the jump free surface. Through the analysis of transient free surface flow in the unconfined aquifer, trapezoidal dam, sand flume and wells, the transient free surface locations predicted from the proposed line element method generally agree well with the analytical, experimental and other numerical data in the available literatures, the numerical efficiency can also be well guaranteed. Furthermore, the hydraulic anisotropy has significant effect on the evolution of free surface locations and the shape of depression cones in spatial. The line element method can be expanded to model the 3D unsaturated seepage flow, two-phase flow and thermos problems in porous media because of the similarity between the similarity of Darcy’s law, Buckingham Law and Fourier’s law. Full article

The computational cost of approximating the Richards equation for water flow in unsaturated porous media is a major challenge, especially for tasks that require repetitive simulations. Data-driven modeling offers a faster and more efficient way to estimate soil moisture dynamics, significantly reducing computational costs. Typically, data-driven models use one-dimensional vectors to represent soil moisture at specific points or as a time series. However, an alternative approach is to use images that capture the distribution of porous media characteristics as input, allowing for the estimation of the two-dimensional soil moisture distribution using a single model. This approach, known as image-to-image regression, provides a more explicit consideration of heterogeneity in the porous domain but faces challenges due to increased input–output dimensionality. Deep neural networks (DNNs) provide a solution to tackle the challenge of high dimensionality. Particularly, encoder–decoder convolutional neural networks (ED-CNNs) are highly suitable for addressing this problem. In this study, we aim to assess the precision of ED-CNNs in predicting soil moisture distribution based on porous media characteristics and also investigate their effectiveness as an optimizer for inverse modeling. The study introduces several novelties, including the application of ED-CNNs to forward and inverse modeling of water flow in unsaturated porous media, performance evaluation using numerical model-generated and laboratory experimental data, and the incorporation of image stacking to account for transient moisture distribution. A drainage experiment conducted on a sandbox flow tank filled with monodisperse quartz sand was employed as the test case. Monte Carlo simulation with a numerical model was employed to generate data for training and validation of the ED-CNN. Additionally, the ED-CNN optimizer was validated using images obtained through non-intrusive photographic imaging. The results show that the developed ED-CNN model provides accurate approximations, addressing the high-dimensionality problem of image-to-image regression. The data-driven model predicted soil moisture with an R² score of over 91%, while the ED-CNN optimizer achieved an R² score of over 89%. The study highlights the potential of ED-CNNs as reliable and efficient tools for both forward and inverse modeling in the analysis of unsaturated flow. Full article

Understanding the displacement of the resident wetting fluid in porous media is crucial to the remediation strategy. When pollutants or nutrients are dissolved in the surface wetting fluid and enter the unsaturated zone, the resident wetting fluid in the porous system may remain or be easily flushed out and finally arrive in the groundwater. The fate and transport of the resident wetting fluid determine the policy priorities on soil or groundwater. In this study, the displacement of the resident wetting fluid by the invading wetting fluid in porous media was simulated using direct numerical simulation (DNS). Based on the simulations of the displacements in porous media, the effect of the non-wetting fluid on the displacement was evaluated by observation and quantification, which were difficult to achieve in laboratory experiments. The result can also explain the unknown phenomenon in previous column experiments, namely that the old water is continuously released from the unsaturated porous media even after a long period of flushing with the new water. The effects of the interfacial tension, contact angle, and injection rate, which affected the immiscible fluid–fluid flow pattern, were also evaluated. Since pollutants dissolved in the wetting fluid could change the physical properties of the wetting fluid, the interfacial tensions of the resident wetting fluid and the invading wetting fluid were set separately in the simulation. Moreover, our simulation demonstrated that the consecutive drainage–imbibition cycles could improve the displacement of the resident wetting fluid in porous media. The successful simulation in this study implied that this method can be applied to predict other immiscible fluid–fluid flow in natural or industrial processes. Full article