Elsevier

Geoderma Regional

Volume 27, December 2021, e00434
Geoderma Regional

Relationship of soil moisture characteristic curve and mechanical properties in Entisols and Inceptisols of Iran

https://doi.org/10.1016/j.geodrs.2021.e00434Get rights and content

Highlights

  • The confined compression curve (CCC) and soil moisture characteristic curve (SMCC) are strongly correlated.

  • SMCC has been predicted reliably using CCC parameters as predictors.

  • Gardner model could describe both SMCC and CCC accurately.

Abstract

The objective of this research was to investigate the relationship between soil moisture characteristic curve (SMCC) and confined compression curve (CCC), and the ability to estimate the SMCC from the CCC. Five provinces of Iran have been chosen as sampling sites and soil samples (150) were collected from these areas, and some properties of the soil samples were determined. The Gardner model has been fitted to the measured SMCC and CCC. The Gardner model's stress-void ratio coefficients, as well as the CCC properties, were used to estimate the soil moisture at five levels (five classes of variables) through the Gardner model using artificial neural networks (ANNs). A more accurate estimation of the water content was obtained by combining the basic soil properties, and three key properties of soil compression. In addition, the integral root mean square error (IRMSE) in the training and testing steps was reduced from 0.107 and 0.111 to 0.095 and 0.096, respectively. In conclusion, the use of CCC data to estimate the SMCC at all levels of the input variables indicated very favorable results with an increase in the accuracy of the water content estimation between 4% and 16% in both training and testing steps.

Introduction

Soil moisture characteristic curve (SMCC) describes the relationship between soil moisture content and matric potential (Dexter et al., 2008). For the coefficient of permeability, shear strength parameter, and volume change, the SMCC consists of crucial information for deriving unsaturated soil characteristic functions. This provides key information relating to the moisture content at various potentials, the pore size distribution, and the soil stress status (Sillers et al., 2001; Toll et al., 2013). Because the direct determination of the SMCC in field or laboratory conditions is somewhat expensive requiring considerable effort and time, indirect approaches including pedotransfer functions (PTFs) were widely used to estimate the SMCC using easily available soil properties.

So far different variables have been used to predict SMCC in PTFs, and there are lots of PTFs which have been developed to estimate SMCC, but finding new appropriate input variables to be included in the PTFs to improve their performance in the estimation of the SMCC is challenging because good estimates can be accurate and reliable enough for use in many applications rather than direct measurements. Scheinost et al. (1997) proposed that the relationship between input variables and the SMCC model parameter should first be explored in developing parametric PTFs. The researchers should then search for new input variables that correlate with the parameters of the SMCC model.

Confined compression curve (CCC) parameters potentially may be new inputs in the estimation of the SMCC. Several researchers (Baumgartl and Koeck, 2004; Zeng et al., 2017) reported that variation in the void ratio (e) to the logarithm of stress (logσ) is used to show CCC in the unsaturated soils. There are many similarities between the CCC and the SMCC. Both curves are highly dependent on the soil pore size distribution, soil texture, and structure (Wang et al., 2017; Zeng et al., 2017). These curves start from the maximum and then reduce by increasing stress or matric suction (Chan et al., 2006; Dexter et al., 2008). The measurement of the SMCC is costly and time-consuming, while the determination of the CCC (stress-void ratio) is easy and cost-effective. However, the authors confirm that the measurement of the CCC is not so easy and routine and it does still require specialized laboratory apparatus that can accurately measure force and displacement. But, it is certainly more routine than measuring the SMCC. To measure SMCC, it is necessary to measure water content at different matric suctions, and measuring the moisture content at each suction requires pressure plate apparatus, this device costs a lot. On the other hand, the time required to measure the moisture at each suction often takes more than a month due to its texture. Considering the price of the device and the time required to achieve moisture balance in the device, this method is somewhat difficult to be used, and it is better to obtain SMCC with an alternative approach including modeling and different methods, as presented in the current article.

Therefore, the use of the CCC properties as predictors will probably improve the estimation of the SMCC, which could be a step forward in developing the PTFs, and also would be a response to demand for newly related inputs. Bayat et al. (2018a) estimated the SMCC using the CCC properties as predictors. They applied the Dexter et al. (2008) model to acquire parametric PTFs, but they could not prove the mathematical relationship between the SMCC and the CCC. Since the impact of the soil texture and structure on the SMCC was not the objective of this study, it has not been directly addressed. However, the soil texture and structure, as shown in this research, have a direct effect on the characteristics of the CCC including pre-compression stress (Pc), the swelling index (Cs), and the compression index (Cc).

The relationship between applied stress and volume change can be used in soil physics and mechanics to describe the mechanical properties of the soil. Considering the relationship between volume changes and stress, the four types of line slope in Fig. 1 can be defined for void ratio (e) or moisture ratio (θ) as a function of mechanical stress (σ) or hydraulic stress (matric suction) (ψ) as follows (Fig. 1):e,ψ=eψe,σ=eσθ,ψ=θψθ,σ=θσ

According to the hypotheses given above, changes in water content due to hydraulic stress (ψ) can be referred to volume change as a result of mechanical stress (σ). Mechanical stress (σ) will first decrease the size of less stable coarse pores, which is comparable to draining coarse pores of water-saturated soil by increasing hydraulic stress. The combination of these concepts forms the basis for modeling the void ratio using a hydraulic model. The SMCC model of Gardner has been extended to fit the data of the compression curve. The extension and assumptions were the same as the extension of the van Genuchten (1980) SMCC model in describing consolidation data based on the mechanical parameters (Baumgartl and Koeck (2004).

Water content-matric suctionθθrθsθr=1+αθψhnθψmθψ

Void ratio-matric suctioneereser=1+αhnm

Void ratio- effective stresseereser=1+ασnmwhere θs and es are the saturated water content and initial void ratio, respectively, before applying the stress. θr represents residual water content(fitting parameter). α, n, and m are the coefficients or parameters of the van Genuchten model. σ is the mechanical stress or hydraulic stress. In these equations (Eqs. (2), (3), (4)), er also represents the lowest soil void ratio, which is equal to 0.27 (Baumgartl and Koeck, 2004).

The consolidation curve of 10 types of soils was described by Baumgartl and Koeck (2004) via changing the van Genuchten (1980) model from the water content-matric suction form to the void ratio-stress one. The consolidation curve and CCC are the same, only with the difference that the consolidation curve is for the saturated soil, whereas the CCC is for the unsaturated soil.

On the other hand, several equations have been introduced for the SMCC, and one of the oldest models is the Gardner (1958) model, which is very similar to the van Genuchten (1980) model. Also, the Gardner model has a more simple form than the van Genuchten model.

The objectives of this research were therefore to (1) investigate the possibility of extending Gardner (1958) SMCC model to fit the CCC data for a wide range of soils, and (2) to study the effect of using extended Gardner (1958) CCC model parameters and other mechanical properties of CCC as predictors for improving the SMCC estimate.

The advantage of the hypothesis in Eq. (1) is that it allows a simple and continuous function such as the van Genuchten (1980) or Gardner (1958) model to define volume change. The Gardner model, with a limited number of parameters, was therefore preferred to the van Genuchten model.

The Gardner (1958) SMCC model is an empirical model with a continuous curve:θ=θr+θsθr11+αhnwhere, θs and θr are the saturated and residual water contents, correspondingly; h is the matric suction; the parameters α and n are the fitting parameters that are associated with the air entry suction, and the soil pore size distribution, respectively.

Based on the stress-void ratio, the Gardner equation was extended according to the suggestion of Baumgartl and Koeck (2004). Eq. (6) is obtained by replacing the initial void ratio, es and final void ratio, er by the saturated and residual water contents in Eq. (4), respectively:eereser=1+αhn1

At this step, the replacement is done between the suction and stress, and Eq. (6) is changed to Eq. (7):eereser=1+ασn1where, α and n are the Gardner model parameters determined from fitting to the stress-void ratio data. The er, void ratio at the end of the test, es, void ratio before applying stress to the soil.

Pre-compression stress (Pc) is usually obtained by plotting the void ratio (e) or the vertical strain (ε) of the soil versus the logarithm of the vertical stress (Fig. 2). This curve has two distinct regions exhibiting the elastic and plastic behavior at low stresses (called swelling line or recompression line: RL) and higher stresses (called virgin compression line: VCL), respectively.

The point of the curve (stress), which indicates the change in the elastic behavior to the permanent deformation, is considered to be Pc (Cavalieri et al., 2008). The use of pre-compaction stress as a criterion of threshold load, beyond which further compaction is substantial and leads to permanent soil deformation, was widely accepted (Vossbrink and Horn, 2004).

The Cc as the absolute value of the gradient of the virgin compression line is considered to be an index of soil stability and its resistance to compression as well as a standard for measuring soil compressibility behavior (Larson et al., 1980). With increasing clay content (up to 33% clay content), the Cc increases linearly, while it remains constant afterward. Soils with kaolinite clay and iron oxides have a lower Cc. Soils with the 2:1 clay minerals, however, have a higher Cc and are thus more likely to be compacted (Larson et al., 1980). The Cs displays the absolute value of the slope of the swelling line, which is remarkably lower than the Cc value. The higher value of this index indicates the higher elasticity of the soil.

hi and hmc are the stress at the inflection point of the CCC and the maximum curvature of the CCC, respectively, which were used as input variables and obtained by several mathematical operations on Eq. (7).

Existing stresses are divided into two categories; external stresses and internal stresses, which are called mechanical stress and hydraulic stress, respectively. The liquid phase affecting the shear resistance is affected by hydraulic or internal stresses. Therefore, there is a strong relationship between water content and hydraulic stress. Changes in hydraulic or internal stresses under drying-wetting cycles may reduce the volume of soil under unsaturated conditions. Terzaghi combined both internal and external stresses in a formula to present a complete definition of stress.σ´=σua+χuauw

Stresses are expressed in this equation in terms of the soil matric potential. The factor χ is based on the volume of pores filled by water, which depends on the matric potential, and is equal to one, under saturation conditions. σʹ is effective stress; σ is total stress; ua is pore-air pressure and uw is pore-water pressure. This equation clearly shows the relationship between soil water retention (which is a function of the soil matric potential) and soil behavior under stress. There is a strong correlation between soil stress, soil volume, and soil moisture content (such as Dıaz-Zorita and Grosso (2000)).

In the following, the derivations of the Gardner model are explained in detail. The Gardner model is rewritten in Eq. (9) to simplify notations. Therefore, f (h) is replaced by the following function to take account of the logarithmic stress.fh=θsθr1+αhn1+θrgx=f10x=θsθr1+α10xn1+θr

Eq. (11) is obtained from derivation of Eq. (10) (first derivative, gʹ(x)), andk = α10x with regard to kʹ (x) = k (x) ln(10), the chain rule was used:g'x=θsθr1+kn2nkn1kln10=ckn1+kn2

When c is constant, c = −n(θsr)ln(10) then the second, g''(x), and third derivative, g'''(x), of g(x) can be calculated as follows:g''x=cnkn1kln101+kn2+ckn21+kn12nkn1kln10=cnln10kn1+kn31+kn1+1kn=c'kn1k2n1+kn3where cʹ = cn ln (10).

Also by deriving from Eqs. (12), (13) is achieved. In general, Eq. (13) is the third derivative of g(x):g'''x=c'nkn1kln102nk2n1kln101+kn3+c'kn1k2n31+kn4nkn1kln10=c'nln10kn1+kn412kn1+kn3knk2n=c'nln10kn1+kn412kn+kn2k2n3kn+3k2n=c'nln10kn1+kn414kn+k2n

Therefore, stress at the inflection point (hi) or zero point of the gʹʹ(x), can be calculated by:hi=10xi=1/α

In the second derivative, g″ (x), 1-kn is the inflection point of g(x). Zero point of gʹʹʹ(x) can be computed by solving the quadratic polynomial equation (Eq. (15)).

The third derivative is equal to zero and in this eq. Y = kn = αn(10×)n = αnhn.14Y+Y2Eq. (16) is used to obtain maximum curvature (1st zero-point of the 3rd derivation) of g(x):Ymc=0.268hmc=1αYmc1/n=1α0.2681/ngxmc+1/2g'xmcxpxmc=gxi+g'xixpxi

Hencexp=gxigxmc+12g'xmcxmcg'xixi12g'xmcg'xiwhere xp is the logarithm of the Pc, xmc is the logarithm of the stress at the maximum curvature, and the variables g(xi) and gʹ (xi) are given by.gxi=fhi=θsθr1+αhin1+θrg'xi=nθsθrln10αhin1+αhin2and the variables g (xmc) and g' (xmc) are given analogously.

Section snippets

Sampling

For this research, the number of 150 undisturbed and 150 disturbed samples of soil were collected from five provinces of Iran, including Mazandaran, West Azarbaijan, East Azarbaijan, Kermanshah, and Hamedan (thirty samples from each province). These samples have been collected from the depth of 0–30 cm. Stainless steel cylinders with a diameter of 5.3 cm and a height of 4.5 cm were used to take the undisturbed soil samples. Also, disturbed soil samples were taken from the undisturbed sample

Results and discussion

Table 2 shows the statistical properties of the input variables and the Gardner model parameters determined by fitting to the water content-matric potential and stress-void ratio data in addition to the parameters of the Gompertz model.

At first, both of the van Genuchten and the Gardner models were fitted to the SMCC measured data, and the results showed the superiority of the Gardner model with higher R2 and lower RMSE compared to the van Genuchten SMCC model (Table 3).

Table 3 represents the

Conclusion

In this research, the Gardner model was used as a basic model to estimate the soil water content. There are many similarities between the CCC and SMCC, which have a lot in common physically. The SMCC is likely to be estimated using the CCC according to the similarities between these two curves. The Gardner model was rewritten using the stress parameter and void ratio instead of suction and water content, respectively. The rewriting of the model did not change its mathematical form, but as

Declaration of Competing Interest

None.

Acknowledgements

This work was funded by Bu-Ali Sina University, Hamedan, Iran.

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  • Cited by (3)

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    Postal Address: Department of Soil Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Iran.

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