Transport In Unsaturated Soils Research Articles

Semi-implicit schemes for modeling water flow and solute transport in unsaturated soils

The coupled model of water flow and solute transport in unsaturated soils is addressed in this study. Building upon previous research findings by Keita, Beljadid, and Bourgault, we investigate a class of second-order time-stepping techniques where two free parameters are introduced, to identify the most stable and accurate scheme. The spatial discretization of the Richards equation is accomplished using the mixed finite element method. The proposed approach involves formulating noniterative schemes using an extrapolation formula and Taylor approximation in time to linearize nonlinear terms. Additionally, a specialized regularization technique is applied to ensure the convergence of the proposed numerical methods. Numerical simulations are conducted to determine the optimal scheme for solving the Richards equation, which is subsequently extended to the transport equation.Numerical simulations of water flow reveal the good accuracy of three schemes—SBDF, MSBDF, and Richards-M2 for homogeneous and heterogeneous soils. Notably, the SBDF scheme stands out for its computational efficiency and stability, especially when gravity forces dominate over capillary forces. Through numerical analysis of the coupled semi-implicit schemes, our results affirm the SBDF scheme’s superior robustness, establishing it as the optimal choice among the proposed numerical methods. Therefore, the SBDF scheme is employed to solve the coupled model of water flow and solute transport. We conducted various numerical experiments to solve the coupled model, addressing scenarios including single and multispecies nitrogen transport, pore water electrical conductivity, and nitrate transport. The SBDF scheme’s accuracy was rigorously verified through comparisons with reference solutions and experimental data. This establishes the SBDF scheme as an efficient alternative to traditional implicit methods for modeling water flow and solute transport in unsaturated soils.

Influence of Spatially Varying Boundary Conditions Based on Material Heterogeneity

When conducting numerical analyses, boundary conditions are generally applied homogeneously, neglecting the inherent heterogeneity of the material being represented. Whilst the heterogeneity is often considered within the medium, its influence on the response at the boundary should also be accounted for. In this study, A novel approach to applying heterogeneous boundary conditions in the simulation of physical systems is presented, particularly focusing on moisture transport in unsaturated soils. The proposed method divides the surface into blocks or “macro-elements” and scales the boundary conditions based on the variation of material properties within these blocks. The principle of using overlapping kernel functions allows local effects to be considered, impacting neighbouring regions. To demonstrate the efficacy of the approach, a set of analyses were conducted that considered infiltration into a body of unsaturated soil, with various configurations of material properties and boundary conditions. The numerical simulations indicate that the application of scaled boundary conditions leads to a more natural and realistic response in the system. The applied method is independent on the numerical techniques employed in the simulation process, making it adaptable to existing computational codes, offering flexibility in capturing complex behaviours, and providing insights into how heterogeneity influences the system’s overall response.

High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS)

Quantification of the soil hydraulic conductivity is key to the study of water flow and solute transport in unsaturated soils. Rapid advances in measurement technology have provided a large number of observations at different scales, offering unprecedented opportunities and challenges for the estimation of hydraulic parameters. This paper proposes an inverse estimation method for downscaling of observations on coarse scales to estimate hydraulic parameters on high-resolution scales. Due to the significant spatial heterogeneity, the inversion faces the problems of dynamics-based integration of data at different scales, model uncertainty due to hundreds and thousands of parameters, and computational consumption due to the large number of forward simulations. To overcome these problems, this paper uses an efficient Bayesian optimization DREAM(ZS) as an inverse framework, and incorporates an analytical upscaling method and Karhunen–Loève (KL) expansion to infer finer-scale saturated hydraulic conductivity distribution conditioned on coarse-scale measurements. The efficient upscaling method is used to link measurements and hydraulic parameters at different scales, and Karhunen–Loève (KL) expansion is incorporated to greatly reduce the dimension of the parameter to be estimated. To further improve the efficiency of the inversion, a locally one-dimensional (LOD) algorithm is used to solve the multidimensional water flow model at coarse scales. The proposed inverse model is applied in a series of numerical experiments to demonstrate its applicability and effectiveness under different flow boundary conditions, different levels of ratio between coarse- and fine-scale grids, different densities of observation points, and different degrees of statistic heterogeneity of soil mediums.

Non-local modelling of freezing and thawing of unsaturated soils

A large part of the earth’s surface is covered by seasonally or permanently frozen soils. Considering the negative impact of climate change, future development of such regions can be underpinned by mathematical methods for accurate analysis of heat and moisture transport in freezing and thawing soils. Reported in this paper is a novel non-local formulation of water and heat transport in unsaturated soils. The formulation uses bond-based peridynamics (PD) and consists of a set of integral–difference formulations of energy and mass conservation. Specific features of freezing/thawing soils are incorporated by a combination of van Genuthcen and Clausius–Clapeyron relations. Computational results are compared with four sets of laboratory experiments to demonstrate the efficiency of the developed approach. The model can be used to analyse the effect of water flow on heat transfer in soils during thawing of permafrost soils. Further, it can be applied in modelling climate change effects, and can be used for construction of coupled physically justified models of frost heave.

Modeling Water Flow and Solute Transport in Unsaturated Soils Using Physics‐Informed Neural Networks Trained With Geoelectrical Data

AbstractAccurate modeling of water flow and solute transport in unsaturated soils is of significant importance for precision agriculture, environmental protection and aquifer management. Traditional modeling approaches are considerably challenging since they require well‐defined boundaries and initial conditions. Physics‐informed neural networks (PINNs) have recently been developed to learn and solve forward and inverse problems also constrained to a set of partial differential equations and are more flexible than traditional modeling approaches. However, hydrological applications of PINNs used so far spatial measurements of hydraulic head, water content and/or solute concentrations, which were well distributed in the subsurface for training the system. Such measurements are hard to obtain in real‐world applications. Here, we propose to train PINNs with non‐invasive geoelectrical tools for simulating two‐dimensional water flow and solute transport during infiltration and redistribution processes with unknown initial conditions. Two‐dimensional flow and transport numerical simulations were used as benchmarks to examine the suitability of the described approach. Results have shown that the trained PINNs system was able to reproduce the spatiotemporal distribution of both water content and pore‐water salinity during both processes with high accuracy, using five time‐lapse geoelectrical measurements and matric head measurements at a single location. The trained PINNs system reconstructed the initial conditions of both state parameters at both processes. It was also able to separate the measured electrical signal into its two components, that is, water content and pore‐water salinity. The subsurface geoelectrical tomograms were significantly improved compared to those obtained from a classical inversion of the raw geoelectrical data.

A universal soil–water characteristic curve model based on the particle size distribution and fractal theory

A soil–water characteristic curve (SWCC) is a prerequisite relationship to study water transport in unsaturated soils and has significant applications in agriculture and engineering sciences. Therefore, many SWCC models were proposed and improved the understanding of water transport. Many of these models were obtained depending on the particle size distribution (PSD) because the water content is related to the sizes and distributions of particles and pores in soils. However, the continuous PSD was divided into many fractions to calculate the water content in these models. Moreover, the particles and pores were simplified as spheres and cylinders, respectively. These simplifications are idealistic and contrary to actual complex structures in soils. To solve the above limitations of these models, we considered the Weibull distribution and fractal theory and established a universal SWCC model called PF (PSD and fractal theory) based on the continuous PSD and irregularities of the pore structures. The new proposed PF model was verified by measured data in the UNSODA database. Furthermore, its accuracy was proven by comparison with two classical models widely used. The verification and comparison results show that the PF model can well describe the measured data of various types of soils and has fewer errors than the other two models. Meanwhile, the continuous PSD in this study overcomes the limitation of artificial discretization and is convenient for subsequent calculation. In addition, the actual irregular soil geometry is described by the fractal theory, which well matches complex soil structures. Therefore, the PF model based on the PSD and the fractal theory is reasonable and reliable in predicting SWCC. In addition, this study can provide a foundation and reference for subsequent studies on hydraulic behaviors.

Effects of hydrogen sulfide on grass traits and water-gas transport in grass-planted unsaturated soil

Vegetation has been found to improve the hydrological performance of landfill cover. However, existing studies ignore the effects of hydrogen sulfide (H2S), which forms the toxic odour generated from municipal solid wastes. Hydrogen sulfide is a potential signalling molecule in regulating plant-stomata aperture, but how the plant–hydrogen sulfide interaction affects the water–gas transport in soil remains unknown. This aim of this study was to investigate the effects of hydrogen sulfide on Bermuda grass growth and its influence on water–gas transport in unsaturated soils. Soil columns, with and without vegetation, were prepared and fumigated with different hydrogen sulfide concentrations. These columns were subjected to controlled drought and rainfall sequentially. The results showed that grass leaves almost wilted without hydrogen sulfide fumigation due to the Pythium diseases caused by the antecedent waterlogged conditions. In contrast, hydrogen sulfide fumigation promoted grass growth because of the fungicidal effects of hydrogen sulfide. In drought, hydrogen sulfide fumigation caused stomata closure, which resulted in a lower matric suction in the vegetated soil than that without hydrogen sulfide fumigation. Accordingly, hydrogen sulfide concentration reduced because of oxidation by metal oxides in soil. Upon subsequent rainfall, more infiltration but lower matric suction was observed in vegetated soils than was found in the bare case, whereas hydrogen sulfide concentration decreased continuously due to gas dissolution in the pore water. Direct application of laboratory findings herein to field cases should be used with caution, because the applied continuous lighting and low evapotranspiration rate of the soil column tests may not be representative of field conditions.

Influence of Soil Heterogeneity on Water Flow and Solute Transport Characterized by Dye Tracer Experiments

Soil heterogeneity is a key factor affecting horizontal water flow and solute transport in unsaturated soil, in which particle distribution, pore structure, and pore connectivity in the soil all present fractal characteristics. The initial water content of soil has significant influence in the resulting heterogeneity of the soil structure, which can affect the water flow and solute transport. In this study, through a series of horizontal transport laboratory simulation experiments in soil columns, the initial water content dependency of transport was elucidated using the fractal Richards’ equation (FRE) model. We first observed that water flows faster in soil columns with higher initial water content, but the law is opposite in the initial process of water flow. By analyzing the variation of parameter values in the FRE model, we speculated that the abnormal phenomenon of early diffusion is caused by the heterogeneity of the soil structure. To elucidate the mechanisms of the water content’s dependency of the solute transport process and to identify the circumstance of altering of flow regime, a series of dye tracer experiments were conducted. Results show that in soil columns with low water content, the inflow of external fluid leads to the agglomeration of soil particles. Combined with matric suction, the heterogeneity of the soil structure is enhanced, which affects the formation of water flow and solute transport paths. It even leads to preferential flow in unsaturated soil columns with low water content.

A METHOD FOR PREDICTING UNSATURATED SOIL PERMEABILITY COEFFICIENT BASED ON CLAY CONTENT

The unsaturated permeability coefficient is of importance to study the behavior of the water seepage and contaminant transport in unsaturated soils. The direct measurement of the unsaturated permeability coefficient is time consuming and laborious. Therefore, indirect approaches are usually applied to obtain the unsaturated permeability coefficient. However, indirect methods still have some drawbacks. An indirect method is usually fitted through the soil–water characteristic curve of a special type of soil, which also requires a large workload and its application is limited. To overcome these drawbacks, a fractal model of the relative permeability coefficient of unsaturated soils has been deduced in this study based on the relation between clay contents and fractal dimensions in terms of mass. A new fractal simple prediction method of unsaturated soil absolute permeability coefficient associated with the new fractal model has also been proposed by combining the simple relation between saturated permeability coefficient and air-entry value. The method is validated with the experimental data of existing literature, and the result shows that the proposed model has a higher prediction accuracy.

Pyrene and lead transport in unsaturated soil at two different water saturations

ABSTRACT In the present paper, we focus on the study of the transport of mixtures of inorganic and organic compounds (Pyrene and lead) on unsaturated soil at two different water saturations. The soil used is a mixture of sand, clay, and organic matter. The transport of solutes exhibiting different sorption characteristics under steady-state conditions at 0.3 and 0.21 volumetric water contents (VWC) of the porous medium was experimentally investigated in a column. The Thomas model and the two-site first-order approach were used for modeling the adsorption/desorption steps. As the first results, the adsorption and desorption of mono- compound show a strong fixation of the lead than for the pyrene. In addition, the coexisting pollutant tests show the decrease of the lead and pyrene adsorption on soil and the decrease in lead retention after the desorption step. Tests with lower VWC show enhancement of lead adsorption with the multipollutant condition. The model approach shows that the equilibrium condition is not appropriate for all tests even for the lead adsorption.

Effects of heat and moisture transfer on the transient dynamic of solute transport in unsaturated soil under isothermal and thermal conditions

Effects of heat and moisture transfer on the transient dynamic of solute transport in unsaturated soil under isothermal and thermal conditions

Enhancing solute transport by pressure-wave driven flow in unsaturated porous media

• Pressure waves in unsaturated porous media enhance solute transport. • Imbibition driven by pressure pulses creates a uniform wetting front. • Solute leaching driven by pressure waves is more efficient than with Darcy flow. Solutes and their limited mobilization in heterogeneous porous media may lead to subsurface salinization and contamination evident in various environmental settings. Previous studies showed that flow and transport driven by pressure waves in porous media under saturated conditions significantly enhance solute displacement compared to drag-dominant (Darcy) flow and transport, resulting in more thorough remediation. However, experimental evidence lacks demonstration of such transport under unsaturated conditions. We investigate solute leaching in a flow cell, experimentally modeling solute displacement from an unsaturated, saline, fine-textured soil region to the surrounding coarse-textured soil. The extent of mobilization efficiency is evaluated by comparing solute breakthrough measurements between two leaching treatments, with drag-dominant continuous flux (CF) and pressure-wave pulse flux (PPF). The results indicate that the PPF treatment provided an additional 75% solute mass that leached from the fine-textured region per unit volume of water compared to the CF. The effect is partly due to the impact of the pressure waves on water imbibition into the medium. The PPF induced relatively high pressure gradients at the wetting front compared to percolation during the CF, thus wetting the media in a more spatially uniform pattern. Consequently, the PPF treatment led to higher water content at and behind the front, which increased the continuity of the water phase across the fine-textured and coarse-textured soils and enhanced transport. The study is a proof of concept for pressure-wave driven flow to enhance local wetting and solute transport in unsaturated soil.

The Effect of Soil–Cement Barriers in Containing the LNAPL Contaminants Transport in Unsaturated Soil; A Physical Modeling

ABSTRACT In the current study, three Ng tests were performed to simulate the LNAPL contaminants’ transport and fate in the porous media. Through the tests, the efficacy of the soil–cement vertical barriers with a low permeability, which is among the most-used techniques in site remediations in practical projects, was assessed, and the results were compared to that of free field condition. Furthermore, extensive insight was achieved into the migration pattern of the LNAPL in unsaturated soil. All of the Ng tests were implemented at 40 g to simulate a voluminous spill of LNAPL in various timeframes. Consecutive imaging through the transparent front was used to gather data, and the LRV image processing technique was utilized to analyze these data. Reliable and effective performance of the barriers for containing the LNAPL spread was confirmed. Groundwater depression was observed in all three tests, particularly in the tests with using barriers. Nevertheless, using barriers restrained the contaminated soil and groundwater to the zones between the two barriers. Based on the observed LNAPL plume, the minimum depth of these barriers was recommended to account for the preferential flow. Three different methods were used for the validation of the image processing results. All in all, the accuracy of image processing was satisfactorily high.

Experimental study on migration of chloride ion and cadmium ion in unsaturated soil

This study aims at understanding the migration behaviours of heavy metals in unsaturated soils, especially the influences of soil water content. An unsaturated advection–diffusion column test apparatus was developed. The advection–diffusion tests were performed under steady states, and migration parameters corresponding to different soil water contents were obtained. First, a nonreactive solute, chloride, was used to reveal the mechanisms of unsaturated advection, diffusion and dispersion. Second, cadmium was selected as a reactive solute to reveal the mechanisms of heavy metal migration in unsaturated soils in which adsorption was involved. The test results of chloride and cadmium ions show that the effective diffusion coefficient decreases linearly with the decreasing dimensionless water content and that the dispersivity increases as water content decreases. The dispersion coefficient shows an exponential relationship with volumetric water content. Diffusion becomes a more dominant mechanism as water content decreases. The logarithmic hydraulic conductivity decreases linearly with the dimensionless water content. The test results of cadmium show that there is a linear relationship between the amount of adsorbed cadmium and water content. The relationships obtained or verified in this paper are helpful for parameter setting when modelling contaminant transport in unsaturated soils.

A modification to the van Genuchten model for improved prediction of relative hydraulic conductivity of unsaturated soils

AbstractModelling of flow and transport in unsaturated soils requires information on two fundamental hydraulic properties: the soil water retention curve and relative hydraulic conductivity. A soil's relative hydraulic conductivity is frequently predicted from the soil water retention curve. The most widely used combination is the van Genuchten model for the soil water retention curve and the Mualem model for relative hydraulic conductivity (VGM). Previous studies show that the VGM model underestimates measured relative hydraulic conductivity for soils with fine textures; a sharp drop in relative hydraulic conductivity can be seen near saturation. A new modification of the van Genuchten soil water retention model is proposed with the aim of improving the agreement between predicted and measured relative hydraulic conductivity. The Brooks and Corey‐Burdine model is used to predict relative hydraulic conductivity from the modified van Genuchten soil water retention curve (MVG‐BCB). The modified model assumes independent m and n in the van Genuchten model but with constraints n > 2 and 0 < m < 1. The MVG‐BCB model is evaluated by comparing calculated and measured data for 59 soils that have widely varying soil textures, ranging from sandstone to clay. The MVG‐BCB model improves the agreement between calculated and measured data for both the soil water retention curve and relative hydraulic conductivity. The MVG‐BCB model is closer to measured relative hydraulic conductivity data for most of the selected soils and the sharp drop near saturation is eliminated. Both the modified soil water retention curve and relative hydraulic conductivity functions are smooth curves and can easily be incorporated into vadose zone flow and transport modellings.Highlights A new modification to the van Genuchten soil water retention model. The model improves the fit to measured soil water retention data. The chosen model improves the prediction of relative hydraulic conductivity.

Numerical modeling of water–heat–vapor–salt transport in unsaturated soil under evaporation

Evaporation-induced soil salinization will threaten the durability of engineering buildings, and it is crucial to study the coupling effect of water–heat–vapor–salt (WHVS) for anticorrosion of porous materials. To analyze the coupled system, a modified and developed WHVS transport model is proposed under the conditions that the film water transport theory, surface tension affected by salt, the filling effect of precipitated salt on soil pores, the residual volumetric air content, the effect of salt on heat transport and storage and the effect of vapor flux and thermal radiation on thermal boundary are all taken into account. The predictions are validated and analyzed by the results obtained from evaporation experiments under different boundary conditions. The data of silica sand are from the literatures ([16,17,57]), and the data of silty clay are from our laboratory test. The results indicate that the calculated water content, solute concentration, temperature and evaporation rate are in good agreement with the experimental data, especially for silty clay. For silica sand, there are some deviations in concentration and temperature, and the overall agreement is satisfied. The consistency between the simulated and measured data shows the effectiveness of proposed model and that the model can be applied successfully in soil science and groundwater hydrology and can be extended to related disciplines.

Temperature Effects on the Hydraulic Properties of Unsaturated Sand and Their Influences on Water-Vapor Heat Transport

AbstractThermally driven moisture and vapor transport in unsaturated soil under a thermal loading applied by underground structures affects the magnitude and distribution of matric suction. There i...

Effects of different parameters on transient heat transfer surrounding energy piles in unsaturated soils

Energy piles are one of the best candidates to harvest shallow geothermal energy. Continuing harvesting and rejecting thermal energy from/to the ground may permanently change the soil temperature and consequently, may lead to different soil resistance parameters. Therefore, careful prediction of soil temperature variation close to energy geostructures is needed. This paper investigates the various parameters of heat source and soil media on transient heat transport in unsaturated soils. Green’s function and the method of separation of variables are employed to analytically analyze the transient heat transfer in the vicinity of energy piles. Results indicate that although higher heat flux increases the soil temperature surrounding a heat source, it has negligible effect on thermal influence zone where the soil temperature varies. In contrast, higher thermal diffusivity results in lower soil temperature close to a heat source while it increases the thermal influence zone.

Numerical Modelling of consolidation-induced solute transport in unsaturated soil with dynamic hydraulic conductivity and degree of saturation

The effects of the pore pressure related dynamic hydraulic conductivity and dynamic degree of saturation on the consolidation-induced solute transport in deformable unsaturated soils are investigated. The storage equation and solute transport equations are revised to account for the dependence of these two soil parameters on pore pressures. Three dynamic models were conducted for dynamic hydraulic conductivity, dynamic degree of saturation, and both. Compared with the conventional model, the simulation results showed that both hydraulic conductivity and degree of saturation increased near the soil surface where pore pressure exceeded air-entry value. Dynamic hydraulic conductivity results in a slightly slower solute transport while dynamic degree of saturation accelerates the migration of contaminants. Including both dynamic effects produced limited differences in solute concentration, while consolidation results were affected significantly. Although dynamic degree of saturation has some influences on consolidation-induced solute transport, the correlation of the dynamic path is less significant. The air-entry value is an important parameter to determine when soil parameters become dynamic, and it affects the soil consolidation process in certain extent. This study provides new methods to incorporate in-homogeneous soil parameters, which are not only spatiotemporal variables, but also dynamic variations with pore pressure.

Modelling microbial growth and biomass accumulation during methane oxidation in unsaturated soil

Microbial aerobic methane oxidation (MAMO) affects methane emissions through landfill covers by not only consuming methane, but also causing biomass accumulation associated with bacterial growth. Although the reduction of soil porosity by biomass accumulation has been well recognized, most existing models ignore this effect when estimating MAMO efficiency. The present study proposes a newly improved theoretical model that could consider the effects of both microbial growth and biomass accumulation on MAMO during coupled water–gas–heat reactive transport in unsaturated soil. Comprehensive batch incubation tests were performed to determine the input parameters required. Part of a set of published experimental data was used to validate the new model, while the remainder of the dataset was used to evaluate the model predictability of soil–microbe interaction (i.e., class B prediction). When ambient temperature is relatively high (30 °C), ignoring biomass accumulation would lead to an overestimation of MAMO efficiency by more than three times. As the biomass accumulated in soil pores, the water permeability, gas permeability, and gas diffusion in the unsaturated soil reduced, consequently limiting the supply of oxygen to the bacteria for MAMO to take place.