Estimation of the soil water retention curve using penetration resistance curve models

Highlights

• There are similarities between PR characteristic curve and SWRC.

• There are significant correlations between the parameters of PR and SWRC models.

• To and Kay (2005) model performed better than the other models in fitting to PR data.

• Using PR curve model parameters improved the estimation of soil water content.

• Parameters in model of Mielke et al. as water content predictors were recommended.

Abstract

In this study, pedotransfer functions (PTFs) were developed for estimating the gravimetric water content based on the model of Dexter et al. (2008) using feed-forward artificial neural networks. Soil samples were collected from 148 locations in the West Azarbaijan, Hamedan, Fars, and Kurdistan provinces of Iran. The cation exchange capacity (CEC), organic matter content, electrical conductivity and equivalent CaCO₃, bulk density, penetration resistance (PR) curve, soil water retention curve (SWRC), and particle size distributions of the soils were measured. Various PR models were fitted to the experimental PR data and the model parameters were then used to estimate the SWRC with nine versions via the model of Dexter et al. Among the two PR models that described the PR versus the water content, the parameters of the model proposed by Mielke et al. (1994) obtained more accurate PTFs and improved the water content estimates. In addition, using the parameters in the model of Stock and Downes (2008) based on suction and organic matter improved the water content estimates. Measuring the PR and water content is cheaper and requires less time than measuring the PR and matric suction, so we recommend using the parameters in model of Mielke et al. (1994) as water content predictors.

Introduction

The functional relationship between the matric suction of soil and the water content can be described by the SWRC (Hillel, 1998, Jury and Horton, 2004). Various physical and chemical properties of soil affect the shape of the SWRC, which are specific to each soil (Botula et al., 2012). The SWRC contains useful information about the water content present in the pores at a given soil suction and the pore size distribution that corresponds to the stress state of the soil (Fredlund et al., 2002). In general, the SWRC provides insights into the soil behavior during adsorption and desorption procedures, where the soil may be close to full saturation at the start of the drying procedure. As the drying proceeds, there is an increase in suction and air begins to enter the soil pores, thereby defining the air entry value for the soil. Above the air entry value, the desorption process stage enters the transition zone where most of the desaturation occurs. This stage is followed by residual suction, where the only water present in the soil is that bound closely to the soil particles (Au, 1998, Lourenço, 2008).

Due to the difficulties and labor costs incurred when measuring the SWRC, it is necessary to develop methods for describing this function using readily available data (Huang et al., 2006). The most widely used method for obtaining the SWRC is the application of pedotransfer functions (PTFs) (Bouma and Lanen, 1987) because of their capacity to obtain difficult and expensive to measure soil properties based on readily available or inexpensive data (Huang et al., 2006).

PTFs are empirical relationships that allow the hydraulic properties of a given soil to be predicted from widely available data, such as the texture (sand, silt, and clay contents), bulk density (BD), and organic carbon (OC) content (Hodnett and Tomasella, 2002). Previous studies have shown that it is also possible to empirically correlate the SWRC with other unsaturated soil properties such as hydraulic conductivity and shear strength (Fredlund et al., 1994, Lu and Griffiths, 2004, Mualem, 1976, Vanapalli et al., 1996).

The PR is an engineering parameter that has been used extensively to measure the relative soil strength, foundation bearing capacity, trafficability, and root penetration (Perumpral, 1987, Raper, 2005). The PR is defined as the force per unit cross-sectional area from a penetrating root or probe (Bengough and McKenzie, 1997). The PR has been used widely to evaluate the effects of different changes in soil pores and aggregate structures (Dexter et al., 2007, Perfect et al., 1990). The PR of a soil depends on soil parameters that remain relatively constant over time but it can exhibit significant spatial heterogeneity according to the soil type, distribution of particle sizes and shapes, clay mineralogy, amorphous oxide content, organic matter (OM) content, and the chemistry of the soil solution (Byrd and Cassel, 1980, Gerard, 1965, Stitt et al., 1982), as well as temporally and spatially due to highly dynamic soil properties such as the water content, matric potential, BD, or total porosity (Vaz et al., 2011).

Soil moisture (and consequently the matric suction) is a crucial factor that affects the PR of a soil (Franzen et al., 1994, Yasin et al., 1993). The correlation between soil PR and matric suction is known as the soil PR characteristic curve (Bengough et al., 2002). The SWRC and soil PR curve are related to the physical properties of soils such as the textural parameters (e.g., sand, silt, and clay contents), BD, and OM, as well as tillage practices (Camp and Lund, 1968, Perumpral, 1987, Taylor and Gardner, 1963).

Several studies have investigated the relationship between PR and the soil water content. In particular, Ayers and Perumpral (1982) concluded that there is a direct relationship between PR and BD, but an inverse relationship between PR and water content for different mixtures of sand and clay. By contrast, Ohu et al. (1988) found an exponential relationship between PR and the water content for loam and clay texture soils, where their equation considered the compaction pressure applied, shear strength, and overburden pressure. Ley et al. (1995) determined a linear relationship between PR and the water content, and a non-significant relationship between PR and BD. Martino and Shaykewich (1994) identified a relationship between PR and time as the water content varied in different tillage systems. Ley and Laryea (1994) used spatial statistics in order to represent a general relationship between the PR and water content, while Hummel et al. (2004) used the clay fraction of soil as a major variable for predicting PR.

Many laboratory and field studies have determined PR based on soil parameters such as the BD, porosity, water content, matric suction, soil texture, or plasticity via regression equations (Ayers and Bowen, 1987, Ayers and Perumpral, 1982, Busscher, 1990, Canarache, 1990, Dexter et al., 2007, Hernanz et al., 2000, Ohu et al., 1986, Whalley et al., 2007), thereby showing that there is a direct relationship between PR and matric suction (Bengough et al., 2002). Both the BD and matric suction affect the PR. The resistance behavior of soils is unpredictable but it is related to the soil BD and matric suction (Mirreh and Ketcheson, 1973). Most studies of the PR–matric suction relationship have demonstrated that the soil PR increases only with the matric suction (Barley et al., 1965, Barley and Greacen, 1967, Henry and McKibben, 1967, Taylor, 1968). Increases in the soil PR due to drying appear to depend on the current status of the soil BD (Mirreh and Ketcheson, 1972). At low BDs, PR is augmented by drying up to a maximum at a soil water matric suction of 400 kPa, but it then decreases with more drying. At high BDs, the maximum PR occurs at 800 kPa (Mirreh and Ketcheson, 1973). Camp and Lund, 1968 also extrapolated the increasing trend in the soil PR from 2 kPa to higher suctions. Several studies employed cone penetrometers to determine the water contents close to a standardized matric suction and they obtained similar results because of the strong positive correlation between PR and the matric suction (Busscher, 1990, Busscher et al., 1997, Smith et al., 1997). PR is affected least by texture at a matric suction of 10 kPa (Vaz et al., 2011).

It is not clear whether the resistance determined by a penetrometer is precisely comparable with the effective stress (Dexter et al., 2007). Whalley et al. (2005) showed that the effective stress alone can be employed to predict the penetrometer resistance in soils with low density, but not in those with high density. The effective stress expression considers the influence of the pore water on the soil strength, where the effective stress comprises two terms: a pore water pressure term and a term due to the surface tension in water menisci between soil mineral particles (Towner and Childs, 1972b). Moreover, matric suction has a mechanistic link with effective stress via the surface tension between the water films that hold soil particles together, and thus to soil strength (Bengough et al., 2002).

Various models have been proposed for predicting the SWRC and soil PR curve. These models, employed soil properties that are easy to measure and more readily available for predicting the SWRC and soil PR curve (Imhoff et al., 2006). The SWRC is a function of the pore size distribution, while the soil PR curve is related to the pore size distribution as well as the interaction between the soil water content and matric suction. The water content and matric suction affect the soil strength by determining the effective stress (Towner and Childs, 1972a, Williams and Shaykewich, 1970). Experiments have elucidated the relationships between the PR, BD, and gravimetric water content, where they focused on the shape of the PR curve, which is connected to the shape of the SWRC, soil pore size distribution, and variations in the effective stress (Vepraskas, 1984).

The PR curve can be measured in about 2 to 3 days, where soil core samples can be saturated and dried in the air until they reach the desired moisture levels to measure their PR. Moreover, the types of equipment used for obtaining PR measurements are cheaper than SWRC measurement tools.

Many studies have attempted to estimate the SWRC using various SWRC models. However, the SWRC model proposed by Dexter et al. (2008) has not been employed for predicting the parameters of PR models. Therefore, the aim of the present study was to examine the possibility of improving the water content estimates obtained by the model of Dexter et al. (2008) by using the parameters of PR models as predictors.

It is considered that the van Genuchten model has several advantages. The Van Genuchten (1980) model is a unimodal model for soils with a homogeneous pore structure. This model is highly flexible and it provides a good fit to SWRC data for various soil types. In addition, the model parameters have physical meanings (but not distinct physical meanings, where the van Genuchten model parameters are highly inter-dependent (Dexter et al., 2008)) and the effects of its parameters on the shape and position of the SWRC are distinguishable (Sillers et al., 2001). However, the van Genuchten model also has several disadvantages because it is a unimodal equation and it is not possible to accurately describe the SWRC for bimodal soils (Omuto, 2009). Thus, this model does not describe the measured SWRC very well for some soils with a heterogeneous pore size distribution. Well aggregated soils contain two pore size distribution peaks for the large pores and small pores, but both peaks cannot be represented by models with a unimodal pore size distribution (Seki, 2007). Frequently, it is necessary to set the residual water content in the van Genuchten equation as equal to zero in order to prevent the production of negative fitted values, especially for soils with high clay contents (e.g., Grunwald et al. (2001) and Groenevelt and Grant (2004)). The magnitudes of the n and m values with the best fit depend on the convergence procedure employed and they may vary slightly (Sillers et al., 2001). The model proposed by Dexter et al. (2008) is a user friendly double-exponential water retention equation, where its exponential terms are connected to the matrix and structural pore spaces. This model is a bimodal equation with the five adjustable parameters have distinct physical meanings (Dexter et al., 2008). The parameters in the Dexter et al. (2008) model are related to the physical properties of soil. Thus, these parameters can vary under different soil physical conditions (Omuto, 2009).

Dexter et al. (2008) introduced the following double exponential model in order to describe the matrix (pore spaces between individual soil mineral particles) and the structural (pore spaces between micro-aggregates and between primary aggregates) pore spaces:

$${\mathrm{\theta }}_{\text{m}}={\text{C}}_{\text{D}}+{\text{A}}_{1\text{D}}{\text{e}}^{\left(\frac{-\text{h}}{{\text{h}}_{1\text{D}}}\right)}+{\text{A}}_{2\text{D}}{\text{e}}^{\left(\frac{-\text{h}}{{\text{h}}_{2\text{D}}}\right)}\text{,}$$

where θ_m is the gravimetric water content and C_D is the asymptote of the equation, which is the residual water content (i.e., the water content as h → ∞). When h_1D > h_2D, we identify the second term as the emptying of the matrix pore space and the third term as the emptying of the structural pore space. The amounts of matrix and structural pore spaces are proportional to A_1D and A_2D, respectively. The values of h_1D and h_2D are the characteristic pore water suctions at which the matrix and structural pore spaces empty, respectively. This model is a double-exponential water retention equation with five adjustable parameters and it provides a user-friendly equation where all the terms have distinct physical meanings (Dexter et al., 2008). The parameters in the Dexter et al. (2008) model are related to the physical properties of soil, where these parameters can describe different physical conditions of soil (Omuto, 2009). In addition, the parameters in the Dexter et al. (2008) model directly represent the pore size distribution in soil (Seki, 2007), so this model was used in the present study.

The PR is a measurable variable related to soil structure, which can be used to estimate the hydraulic properties of soil (Pachepsky et al., 1998, Wösten et al., 2001). The significance of the soil structure when estimating the SWRC has been shown in many studies (Abbaspour and Moon, 1992, Kay and Angers, 2002, Nguyen et al., 2014, Pachepsky et al., 2006). However, PR models have rarely been used as predictors of the SWRC. The development of PR models could provide useful new soil structure parameters for estimating soil hydraulic properties. PR models can quantify the soil structure and describe it numerically, which is an important feature of the PR models used in this study for estimating the SWRC.

The models proposed by Stock and Downes (2008) (Eq. (2)), Mielke et al. (1994) (Eq. (3)), and To and Kay (2005) (Eq. (4)) described the relationships between the soil PR and soil moisture or matric suction.

Stock and Downes (2008) defined the effect of supplementation with OM on the PR of a hardsetting soil for the entire matric suction range, where they used a sigmoidal equation to model the relationship between matric suction and PR. Regression curves were fitted using the hydraulic model of van Genuchten (1980). The models obtained by Stock and Downes (2008) were highly consistent with the experimental data.

The hydraulic model of van Genuchten (1980) in the following modified form was fitted to PR–matric suction data by Stock and Downes (2008):

$$\text{Q}={\text{Q}}_{\text{drySS}}+({\text{Q}}_{\text{satSS}}-{\text{Q}}_{\text{drySS}}){[1+{({\mathrm{\alpha }}_{\text{SS}}\text{h})}^{{\text{n}}_{\text{SS}}}]}^{-{\text{m}}_{\text{SS}}}\text{,}$$

where Q is PR (MPa), Q_satSS and Q_drySS are the PR (MPa) at matric suctions of 0.0001 and 10³ MPa, respectively, h defines the matric suction (MPa), and α_SS, n_SS, and m_SS are empirical parameters. The Q_satSS, Q_drySS, α_SS, n_SS, and m_SS parameters were determined by fitting.

Mielke et al. (1994) used the PR as an indicator to evaluate the soil water content, where they employed a flat tip and cone penetrometer in the laboratory to measure the soil strength. They used nonlinear regression techniques to fit the equation to the plots of the gravimetric water content versus soil strength. The equation is a power function equation:

$$\text{PR}={\text{a}}_{\text{M}}{\mathrm{\theta }}_{\text{m}}^{{\text{b}}_{\text{M}}}\text{,}$$

where PR is the PR (MPa), θ_m, is the gravimetric water content, and a_M and b_M are adjustable parameters.

To and Kay (2005) developed and evaluated a function containing suitable terms for determining the effective stress, where they measured the PR with different ranges for the soil texture, OC content, and BD at different matric suctions using disturbed and undisturbed soil samples. Their results showed that decreasing the soil mechanical resistance by decreasing the matric suction in coarse textured soils and medium-textured soils with high compaction led to decreases in the effective stress. Their function is the most successful for characterizing the soil mechanical resistance in both disturbed and undisturbed soils.

Measurements of the PR in disturbed and undisturbed soil cores indicate that the PR curve is described more accurately by a function including two terms related to the magnitude of the matric suction (MPa) rather than by a function with a single term. The function with the smallest prediction errors and the fewest variables has the following form (To and Kay, 2005):

$$\text{PR}={\text{a}}_{\text{T}}{\text{h}}^{{\text{b}}_{\text{T}}}-{\text{c}}_{\text{T}}\text{h,}$$

where a_T, b_T, and c_T are fitting parameters, which are functions of the sand or clay contents, OC content, and BD respectively.