Estimating the Soil-Water Retention Curve of Arsenic-Contaminated Soil by Fitting Fuentes’ Model and Their Comparison with the Filter Paper Method

Abstract

Arsenic is a metalloid frequently found in contaminated sites, especially in the soil. In this regard, soil contamination has attracted researchers’ attention because it affects soil suction, which is essential in unsaturated soil mechanics. Due to its reliability and low cost, the filter paper method is frequently used to evaluate soil suction. However, it is laborious and time consuming. As an alternative, different mathematical models have been developed to estimate natural soil’s suction. The objective of this study was to elucidate if Fuentes’ model (using fractal, Mualem, and Burdine restrictions) can be used to estimate the soil-water retention curve of an arsenic-contaminated soil by comparing it with the filter paper method data already reported. The results showed that under natural conditions, Fuentes’ model provided similar results to those obtained by the filter paper method. The model also suggested modification of the soil’s structure, observed by the increase in the soil’s particle diameter after contamination. However, Fuentes’ model was observed to overestimate the suction values for contaminated soils. This observation highlights the necessity to use a soil stabilization method to control the soil’s volume variations. The data also showed that Fuentes’ model overestimated the hydraulic conductivity function of the contaminated soil. Hence, the retention potential does not reflect the behavior of the contaminated soils and can induce misinterpretation of contaminant transport evaluation in soil. Nevertheless, further analyses should be performed to investigate the direct applicability of this model to soils contaminated with other substances.

1. Introduction

Soil is a critical environment that acts as filters, absorbers, and transformer elements that can retain different substances [1]. To perform such functions, the soil’s biological activity and cation exchange capacity must be conserved [2]. Given these characteristics, it is capable of protecting groundwater and surface water against contamination [1]. However, the accidental introduction of contaminants into the environment may exceed the self-decontamination capacity of the soils, increasing the number of contaminated sites over time. The present study’s researchers found this noteworthy because contaminants modify the geotechnical properties of natural or non-contaminated soils.

Heavy metals contamination relates to industrial and urban sites, which have received attention to study the spatial distribution pattern (i.e., geostatistical models) [3], and the contaminant transport (which depends on the water content, but not on the degree of soil contamination) [4]. Unlike various contaminants in the environment (i.e., organic materials), metals need to be reduced, removed, or immobilize from the soil by transformation techniques such as phytoremediation. Although plant roots can absorb heavy metals via soil solution, depending on their phytoavailability [5], the phytoremediation time is relatively long [6]. Nevertheless, other remediation techniques are available to remove heavy metals from soils [7,8].

Among the various contaminants present in the environment, arsenic is one of the heavy metals that are more frequently found in contaminated sites [9,10]. Arsenic is considered a metalloid since it exhibits both properties of metals and non-metals [2]. Arsenic contamination is distributed unevenly, worldwide. It happens due to natural and anthropogenic processes [11], such as volcanic eruptions, rock mineralization, and industrial and mining activities [12,13]. Arsenic can be introduced into the soil by the discharge of industrial wastewaters that contain different heavy metals [7]. Moreover, fertilizers, pesticides, manure, and sludge are significant sources of arsenic in agricultural soils [2]. Arsenic is one of the most toxic and carcinogenic elements associated with various chronic disorders [14,15,16]. Although Jiménez et al. [17] reported the presence of arsenic in the liver of ground doves (Columbina passerine, 0.046 mg/kg) and house sparrows (Passer domesticus, 0.025 mg/kg), it did not reach the toxic thresholds. Nevertheless, Howell and Hill [18] reported a decrease in chicks’ growth due to a 50 mg/kg arsenic content in their diet.

According to the prevailing environmental conditions, arsenic species are classified as organic and inorganic. However, arsenate (As⁺⁵)—an inorganic arsenic species—is more frequently found in aerobic environments, such as the aerated or unsaturated zone of the soil, compared to organic arsenic species [11]. Despite the efforts made to study the effects of heavy metal contamination on soil properties, there is scarce information about the impact of arsenic contamination on the mechanical and hydraulic properties of the soil. Therefore, it remains a problem in environmental geotechnics due to the uncertainty in the mechanical behavior of civil structures founded on such soils.

Unsaturated soils experience negative pressures called suction. Soil suction (${\psi }_t$) is measured through its components, known as matric (${\psi }_m$) and osmotic suctions (${\psi }_o$). The ${\psi }_o$ depends on the effect the dissolved salts and contaminants can create in the pore water. Nevertheless, its contribution to ${\psi }_t$ is negligible in natural soils. In contrast, the ${\psi }_m$ is developed by capillary forces and adsorption due to the soil’s structure [19] and is determined by the soil’s particle size [20].

Soil suction varies according to the structure and moisture content of the soil. The curve that describes such variations is known as the soil-water retention curve (SWRC). This curve is used to evaluate the essential aspects of unsaturated soil mechanics because of its hydromechanical coupling [21] that has diverse applications on contaminated soils, protective barriers for excavations, and the remediation of contaminated sites [22]. Moreover, the reactions between soils and contaminants have a coordinated effect on the ${\psi }_o$, which, in turn, affects the mechanical properties of contaminated soils [23] and the liquid’s movement regulation through the soil mass due to the subsequent changes in its geotechnical properties [23,24,25].

A frequently used method to evaluate soil suction is the filter paper method due to its reliability [26,27,28,29] and the suction range it covers (from 0 to 1 × 10⁶ kPa and from 1000 to 500,000 kPa for the total and matric suction, respectively) [27]. This test method is described by the ASTM D5298 standard [30]. It uses a calibration curve to calculate the corresponding soil suction component (allowing to measure the ${\psi }_t$ using a non-contact procedure and ${\psi }_m$ via a contact procedure). Its calibration is based on the relationship between soil suction and relative humidity. However, this method’s obtention of the SWRC is laborious and time consuming.

Nevertheless, researchers have developed mathematical models such as the one proposed by Fuentes [31]. A model like this requires simple parameters, such as the grain-size distribution, to estimate the van Genuchten parameters and, consequently, the obtention of the ${\psi }_m$ of natural soils. Moreover, Fuentes’ model provides a fast way to evaluate the SWRC of the soil. The van Genuchten model (Equation (1)) is also a frequently used model to predict the SWRC. Its parameters are obtained by performing a non-linear least-squares process:

$$\frac{\theta -{\theta }_r}{{\theta }_s-{\theta }_r}={\left[1+{\left(\alpha {\psi }_m\right)}^n\right]}^{-m}$$

(1)

where ${\theta }_r$ is the residual volumetric water content, ${\theta }_s$ is the saturated volumetric water content, ${\psi }_m$ is the matric suction, $\alpha$ is calculated as $1/{\psi }_d$ and indirectly describes the pore-size distribution (PSD), ${\psi }_d$ is the inverse of the air entry value, and $m$ and $n$ are fitting parameters that affect the shape of the retention curve [32]. Moreover, the parameter $n$ describes the dispersion of both the largest and smallest pores [33].

The most common fitting parameters used for the van Genuchten model are $n=1/\left(1-m\right)$ and $n=2/\left(1-m\right)$, which correspond to the Mualem and Burdine restrictions, respectively, and are obtained from a probabilistic approach. Mualem [34] considers a radius to evaluate the hydraulic conductivity; that is, the geometric mean of the radii of two capillary elements. In contrast, Burdine only considers the radius of the largest pore [35].

The SWRC induces a porosimetry curve because the water pressure in the soil is associated with an equivalent pore diameter, using the Laplace equation (Equation (2)):

$${\psi }_m=\frac{2Ts}{R}$$

(2)

where $Ts$ is the superficial tension, and $R$ corresponds to the radius of the pore.

The model by Fuentes [36] helps establish a relationship between the particle size distribution and porosimetry curve, where the physical volume of the soil is characterized by spheres of equivalent diameter, as indicated in Equation (3):

$$F\left(D\right)=1/{\left[1+{\left(\frac{D_g}{D}\right)}^n\right]}^m$$

(3)

where $D_g$ is the geometrical diameter, $D$ is the diameter of the particle size distribution, and $n$ and $m$ are the fitting parameters of the SWRC. It is possible to obtain the SWRC path by introducing the $\alpha$ value into Equation (1) when the $m$ and $n$ values are obtained. However, an essential limitation of this model is that it only considers the porosimetry curve and, consequently, the ${\psi }_m$ value.

Soil structure relates to physical (i.e., solid density or porosity), chemical, and biological processes that are dependent either on the size of the soil core or the resolution of the measuring device. Given this context, it often causes a predicament when it comes to introducing measurable parameters of soil structure. In the case of the transport processes in soils, it occurs at two time scales: the first one is associated with macropore transport (packing of solid elements that generate pores), and the second is associated with micropore transport (network of connected pores surrounded by solid elements) [37]. To avoid working with different scales, a fractal dimension would be quite valuable for describing the heterogeneous soil structure on different scales, assuming that the properties are the same across the range of these scales [38].

To reduce the number of unknown functions in the aerated soil zone, Fuentes [36] introduced the fractal relation to the common parameters. This was performed by hypothesizing the flow resistance, which is a function of capillary pore size. In addition, Fuentes considered the soil as a collection of Lebesgue measures that deviate from zero. Moreover, sets whose porosity was a unit were not considered since they might not accurately model the natural soil. The resulting models were defined as the neutral pore, geometric pore, and large pore. Equation (4) is the integral relation for Burdine’s model with a correction factor, this factor being the volumetric porosity. On the other hand, the second model (Equation (5)) adds a correction factor to Mualem’s model, and Equation (6) is a new model established by Zavala et al. [35].

$$0<sm=1-\frac{4s}{n}<1$$

(4)

$$0<sm=1-\frac{2s}{n}<1$$

(5)

$$0<2sm=1-\frac{4s}{n}<1$$

(6)

where $m$ and $n$ are fitting parameters that affect the shape of the retention curve and $s$ is the relative dimension, which is the relationship between the fractal (D) and Euclidean (E) dimensions that satisfies Equation (7) [39].

$${\left(1-\varphi \right)}^s+{\varphi }^{2s}=1$$

(7)

where $\varphi$ is volumetric porosity (0 ≤ $\varphi$ ≤ 1).

Nonetheless, after the literature review, no available evidence was obtained on the applicability of such models to evaluate the SWRC of the contaminated soils. When assessed through the filter paper method, it has been reported that the SWRC tends to change its position and retention potential once the soil becomes contaminated [23,29]. Hence, there is uncertainty about whether such models can be directly used to evaluate the SWRC of the contaminated soils. Thus, the objective of the present study was to elucidate if Fuentes’ model [36] can be used to estimate the SWRC of arsenic-contaminated soil, by comparing it with the reported filter paper method data [29] at the wetting path.

2. Materials and Methods

Experimental Procedure

The methodology used to achieve the objective of the present study was performed in two stages: (i) estimation and comparison of the SWRC using Fuentes’ model (including the fractal, Burdine, and Mualem restrictions) and (ii) evaluation of the hydraulic conductivity function (HCF) using the van Genuchten equation via the Mualem model. In the first stage, it was necessary to use Equation (1) to adjust the ${\psi }_m$ data previously reported in [29] to compare it with the SWRC obtained by Fuentes’ model. This allowed the researchers to collate the ${\psi }_m$ with the SWRC using Fuentes’ model. Following this, using Equation (3), the adjustment of the grain-size distribution was performed using MATLAB software in the following manner:

• The model to be used (Mualem or Burdine) was defined. For fractal analysis, the relation s = D/E that satisfies Equation (7) was obtained;
• The $m$, $n,$ and $s$ parameter values for every model to be evaluated (i.e., geometrical pore, larger pore, neutral pore, Mualem, and Burdine), were selected;
• Diameter increments of 5.5 µm, $m$ increments of 0.001 (a conditional of the loop during each iteration through the first stage), and an error of 0.03 (which means a coefficient of determination of 0.97) were established;
• The grain-size data for each contaminant concentration (i.e., 0 mg/kg, 25 mg/kg, and 50 mg/kg), which corresponds to experimental frequency (0 to 1) and diameter (µm), was introduced;
• For the first iteration, an initial diameter of 1 µm and an initial value of 0.001 for the parameter $m$ were used. Then, those parameters are evaluated in Equation (3) for the entire data of the grain size analysis, obtaining a proposed frequency;
• If the error is less than or equal to 0.03 (as previously defined), the parameters $m$ and $n$ are obtained to evaluate Equation (1), assuming ${\psi }_m$ as the unknown value. In other cases, a new diameter (Diameter = diameter + increment) and parameter $m$ value ($m$ = $m$ + increment) are proposed, and the process is repeated from step 5.

Once the parameters $m$ and $n$ were obtained, they were optimized by minimizing the sum of squared errors ($SSE$). The coefficient of determination ($R^2$) was obtained by applying Equation (8) as an index to evaluate the linear relationship between the frequency of the grain-size analysis and the frequency of Equation (1). Its value varies from 0 to 1 (1 is a perfect linear adjustment, while 0 means that the model represents none of the data) [40].

$$R^2=1-SSE/SST=1-\left[\mathsf{\Sigma }{\left(Y-\widehat{Y}\right)}^2/\mathsf{\Sigma }{\left(Y-\overline{Y}\right)}^2\right]$$

(8)

where $SST$ is the total sum of squares, $Y$ is the dependent variable, $\widehat{Y}$ is the estimated dependent variable, and $\overline{Y}$ is the mean of the dependent variable.

In the second stage, the HCF was evaluated using the van Genuchten method since the flow of contaminants is a constant concern in soil mechanics. In this regard, the HCF should be evaluated because contaminants travel along the flow paths at different velocities; it depends not only on the saturation rate but also on the stress state of the soil.

3. Results

3.1. Evaluation of the SWRC Using Fuentes’ Model

Table 1. The equivalent particle’s diameter of natural and arsenic-contaminated soils, as obtained by the evaluated models.

Model Restriction	Equivalent Particle Diameter (µm)
	As 1: 0 mg/kg 2	As: 25 mg/kg	As: 50 mg/kg
Burdine	2264.30 ± 21.40 (0.971) 3	2580.00 ± 305.40 (0.970)	2298.50 ± 78.10 (0.971)
Mualem	2267.70 ± 33.30 (0.970)	2238.20 ± 50.80 (0.970)	2336.00 ± 57.70 (0.971)
Geometric pore	2181.00 ± 43.60 (0.970)	2230.00 ± 171.70 (0.970)	2408.20 ± 74.90 (0.970)
Neutral pore	2527.70 ± 30.60 (0.970)	2589.70 ± 233.40 (0.970)	2524.30 ± 30.60 (0.970)
Larger pore	2630.20 ± 40.20 (0.972)	2838.50 ± 412.70 (0.971)	2646.80 ± 83.20 (0.971)

¹ Arsenic concentration. ² Natural soil. ³ Data between parenthesis denote the value of the coefficient of determination.

presents the data values obtained from the simulation of the SWRC. As observed, the soil’s equivalent particle diameter increased after contamination in almost all the models used to describe the SWRC by simulation. From these results, a decrease in ${\psi }_m$ (evaluated with Equation (2)) can be expected. It helps to partially explain the change in the shape of the SWRC as well (Figure 1). The equivalent particle diameter reaches its maximum value with the larger pore model in all arsenic concentrations, which is 15% bigger than the minimum value obtained with the other models. After its contamination with an arsenic concentration of 25 mg/kg and 50 mg/kg, the particle diameter increased its size by 2–14% and 0.6–9%, respectively, compared to the natural soil. The physical changes attributed to chemical reactions between the arsenic and the soil elements that resulted in the formation of larger particles were verified using Fuentes’ model by comparing these results with those reported in Table 1.

Upon comparing the SWRCs (0 mg/kg, 25 mg/kg, and 50 mg/kg) resulting from simulation (Figure 1), it was observed that the SWRC modifies its shape at a high saturation rate ($s_r$ > 70%), aside from the model restriction used. Under $s_r$ = 70% the curve did not suffer a significant variation. These results agree with the conclusion of Fuentes and Rendon [39], which remarks that the SWRC obtained from Fuentes’ model behaves similarly, aside from the restriction used (Burdine, Mualem, geometric pore, neutral pore, and larger pore).

3.2. Comparison of the Simulated and Filter Paper Method SWRC

Table 2. Values of the parameter $n$ for the van Genuchten data fitting.

Arsenic Concentration	$\mathbf{Value}\mathbf{of}\mathbf{the}\mathbf{Parameter}\mathit{n}$
	Filter-Paper SWRC	Burdine	Mualem	Geometric Pore	Neutral Pore	Larger Pore
0 mg/kg	1.44 ± 0.03	2.96 ± 0.01	1.83 ± 0.02	1.96 ± 0.02	3.33 ± 0.08	3.87 ± 0.02
25 mg/kg	1.19 ± 0.00	2.78 ± 0.06	1.77 ± 0.08	1.89 ± 0.06	3.26 ± 0.06	3.83 ± 0.08
50 mg/kg	1.18 ± 0.01	2.88 ± 0.04	1.88 ± 0.04	1.96 ± 0.03	3.31 ± 0.02	3.86 ± 0.05

shows the parameter $n$ values for the van Genuchten model. Comparing the natural state of both the simulated restrictions and laboratory results, the most striking effect is the substantial increase in the parameter $n$ value when the simulation is considered aside from the model. The value of the parameter $n$, which used Mualem’s approximation, was the closest to the filter paper method data, which also uses the Mualem restriction. However, the increase in the value of the parameter $n$ was about 27%.

Similarly, the arsenic-contaminated condition increased the value of the parameter $n$ on all the simulations. The difference was about 49% and 59% for the 25 mg/kg and 50 mg/kg arsenic concentration, respectively, compared to Mualem’s restriction. This resulted in a change in the SWRCs’ slope. Such a difference can be explained through the correlation between the value of the parameter $n$ and the pore-size distribution because the parameter $n$ is a slope function [32,41]. The comparison of the simulated SWRC and the filter paper SWRC is shown in Figure 2 for the three arsenic concentrations with Mualem’s restriction.

Upon analyzing the SWRC obtained by the filter paper method (Figure 2), for the same saturation rate ($s_r$ = 1%), it was observed that the natural soil reached its maximum ${\psi }_m$ value at 1.30 × 10⁸ kPa, while the estimated SWRC reached it at 4.13 × 10⁵ kPa, indicating a difference of about three orders of magnitude (log scale). Moreover, at high saturation rates ($s_r$ ≥ 70%), the estimated curves provided the suction values provided by the estimated curves were almost two times higher than those of the filter paper method curve, which was particularly notable in the shape of the SWRCs (Figure 1).

In the case of the SWRC of the 25 mg/kg arsenic-contaminated soil, for $s_r$ < 45%, the simulated SWRC provided smaller ${\psi }_m$ values than those obtained by the filter paper method curve. In contrast, for $s_r$ > 45%, the simulated SWRCs tended to overestimate the ${\psi }_m$ of the contaminated soil. The simulated SWRC provided a ${\psi }_m$ value as high as eight times bigger (log scale) than the one obtained by the filter paper method SWRC for $s_r$ = 99%. A similar tendency was observed for the SWRC of the 50 mg/kg arsenic-contaminated soil. The simulated curves overestimated the ${\psi }_m$ for $s_r$ > 65% in this case. The most significant ${\psi }_m$ value difference was obtained at $s_r$ = 99%, corresponding to three times the ${\psi }_m$ obtained by the filter paper SWRC.

The ${\psi }_m$ decrease can be partially explained by the number of points used for the van Genuchten fitting at a low saturation rate in the filter paper curves. The variations in the parameter $n$ value also contributed to the ${\psi }_m$ decrease since it modifies the slope of the SWRC. Therefore, the rise in this parameter on the simulated SWRC results in smaller ${\psi }_m$ values. Hence, according to the results provided by Fuentes’ model, it would be necessary to use a stabilization method to control the volume changes (due to soil suction) of the arsenic-contaminated soil; although, it would not be necessary.

The variation in the shape of the SWRC follows the soil’s particle size change. According to the Laplace equation, the bigger the particle size, the smaller the ${\psi }_m$ value. This is explained by the inverse relationship between the ${\psi }_m$ and the radius of curvature. In other words, when the suction decreases, the radius of curvature increases. However, this increase in the estimated particle’s diameter and the modification of the value of the parameters $m$ and $n$ do not decrease the difference between the simulated and the filter paper method curves.

As an alternative, using diverse methods to predict the SWRC on contaminated soil samples might provide a fast and initial approximation. An example of such a simple method is the grain-size analysis. However, these SWRCs should be interpreted with caution since they may induce incorrect estimates of the ${\psi }_m$ and, consequently, the hydraulic conductivity since the ${\psi }_d$ value is required to obtain the SWRC from Equation (1). Therefore, the ${\psi }_d$ value can be obtained using the reference values of a similar soil or by using the filter paper method at a high saturation rate.

3.3. Comparison of the HCF Obtained by the Simulated and the Filter Paper Method

The ${\psi }_d$ used to adjust the SWRC with Fuentes’ model was obtained by using the filter paper method at a high saturation rate (i.e., ${\psi }_d$ = 4000 kPa). The saturated hydraulic conductivity used were 5.3 × 10⁻¹⁰ m/s ± 6.2 × 10⁻¹¹ m/s for the natural soil, 2.5 × 10⁻⁸ m/s ± 4.7 × 10⁻⁹ m/s for the 25 mg/kg arsenic-concentration, and 1.2 × 10⁻⁸ m/s ± 1.4 × 10⁻⁷ m/s for the 50 mg/kg arsenic-concentration. Figure 3 shows the HCF of the arsenic-contaminated soils for the filter paper and the simulated conditions. It is worth noting that both of these methods used Mualem’s restrictions. For clarity, the analysis was divided into two phases: (i) the SWRC of the natural soil and (ii) the comparison of the simulated SWRC with the filter paper SWRC.

In the first phase, the comparison of the HCF shows that there was no significant variation between the simulated SWRC and those of the filter paper SWRC under natural conditions with the Mualem model. However, at high suction values, the hydraulic conductivity value ($k$) of the simulated SWRC does not correspond to that of the filter paper due to the van Genuchten fit, where the parameter $n$ value controls the slope of the SWRC and, therefore, the ${\psi }_m$ value.

In the second phase, the comparison of the HCF for the 25 mg/kg shows a great variation in the shape of the HCF curve, which is affected by the parameter value in the van Genuchten method ($m$ = 0.43 ± 0.03 and $m$ = 0.16 ± 0.00 for the simulated and the filter paper method curves, respectively). Even when the results are in the same order of magnitude, the simulated curves give higher $k$ values than those of the filter paper method. At $s_r$ = 90%, the $k$ value for the simulated SWRC is about 18 times smaller than that of the filter paper method. For the 50 mg/kg condition, similar results were obtained ($m$ = 0.47 ± 0.01 and $m$ = 0.15 ± 0.01 for the simulated and the filter paper method curves, respectively).

Both methods (simulated and filter paper) provided similar HCF curves. However, the estimated data are higher than those obtained through the filter paper. This indicates that the retention potential does not reflect the behavior of the evaluated soils. Specifically, the HCF of the soil is modified due to the arsenic contamination, which, in turn, increases the permeability coefficient by increasing the specific surface and pore-size distribution [29], indicating a modification of the soil’s structure. In contrast, the simulated HCF for the contaminated soils does not reflect that change either by the SWRC or the HCF.

The available SWRCs of the contaminated soils [24,29] showed an oddly shaped curve when evaluated using the filter paper method. This has significant repercussions when the data are fitted to van Genuchten’s model. Consequently, its use may result in inadequate hydraulic analysis, that is, HCF. Furthermore, although it would be risky to indicate that Fuentes’ model does not represent the contaminated soil condition, the results provided by this model should be interpreted with caution, nevertheless. Thus, further investigation needs to be conducted to verify the applicability of such models to other contaminated soils.

4. Conclusions

The SWRC is a critical soil hydraulic property for studying unsaturated soil mechanics, contaminant transport simulation in the aerated zone of the soil, irrigation and drainage scheduling, predicting nutrients leaching, and other soil conservation activities. The results obtained in this study showed that Fuentes’ model adequately represented the SWRC and HCF of the natural soil. However, when the model was applied to the contaminated soil, an increase in the equivalent soil´s particle diameter was observed, suggesting a change in the soil’s structure. This resulted in the modification of the hydraulic properties of the contaminated soil because it is related to the porous system of the soil (i.e., geometry and size).

The values of the parameter $n$ increased when using the simulation for either the contaminated or natural conditions and modified the slope of the SWRCs. In the wetting path and for $s_r$ < 45%, the suction values of the arsenic-contaminated soils obtained by Fuentes’ model were higher than those obtained by the filter paper method. Even if fractal analyses were used (geometrical pore, neutral pore, and larger pore), the estimated SWRC did not represent the hydraulic and mechanical behavior of the arsenic-contaminated soils, especially at low saturation degrees. Hence, the use of this model to estimate the SWRC of contaminated soil from the unsaturated soil mechanics perspective must be considered carefully because the results highlight the necessity to use a soil stabilization method to control the soil’s volume variations. Although Fuentes’ model provides an initial and fast approximation for the SWRC, compared to the filter paper method, additional analyses should be performed to ensure this model adequately represents the contaminated soil behavior.

Fuentes’ model does not consider the soil-contaminant interaction, which is essential to evaluate the distribution and accumulation of heavy metals in soil. Knowing how the contaminant modifies the SWRC should allow a better parametrization of the Richards equation. Consequently, a better prediction of solute transport in the aerated zone of the soil can be obtained. Since the Fuentes model provided higher hydraulic conductivity values for the contaminated soil, it can result in the misinterpretation of contaminant transport in soil. Therefore, the time and costs associated with soil remediation can vary significantly. Moreover, the results obtained using this model may suggest the development of a soil erosion process, which has important repercussions on civil works and soil mechanical and hydraulic behavior.