SSSAJ Grow Your Career with SSSA
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published online 23 May 2006
Published in Soil Sci Soc Am J 70:1082-1093 (2006)
DOI: 10.2136/sssaj2005.0218
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via ISI Web of Science (1)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Boivin, P.
Right arrow Articles by Vauclin, M.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Boivin, P.
Right arrow Articles by Vauclin, M.
Agricola
Right arrow Articles by Boivin, P.
Right arrow Articles by Vauclin, M.
Related Collections
Right arrow Structure and Properties
Right arrow Soil Physics
Right arrow Soil Hydrology

Soil Physics

Modeling the Soil Shrinkage and Water Retention Curves with the Same Equations

Pascal Boivina,*, Patricia Garnierb and Michel Vauclinc

a Institute of Research for Development (IRD), LTHE, Universite J. Fourier, B.P. 53, 38041 Grenoble Cedex 9, France
b INRA, rue Fernand Christ, 02000 Laon, France
c Laboratoire d'étude des Transferts en Hydrologie et Environnement, LTHE, UMR 5564 (CNRS, INPG, IRD, UJF)- BP 53, 38041 Grenoble Cedex 9, France

* Corresponding author (Pascal.Boivin{at}ird.fr)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Recent studies underlined the likeness of soil water retention (WRC) and shrinkage curves (ShC) with respect to their shapes. This paper aims at experimentally discussing the possible use of the same equations to fit them. The WRC (on the tensiometric range) and ShC were simultaneously determined on a series made of 28 undisturbed soil cores collected in surface horizons from a wide variety of soil types, with clay content ranging from 8.5 to 65% and of 30 repacked soil samples of various clay contents and mineralogies. The van Genuchten (VG) closed-form equation of WRC and the VG modified equation of ShC, with five and three parameters, respectively, were found to fit well to both curves, but they did not properly reproduce the observed linear parts and sloping ends of both curves, and the dissymmetric shapes of the ShC as well. The exponential shrinkage model XP fitted significantly better to both the WRC with five parameters and the ShC with eight parameters. It is shown that the transition points of the XP equations independently fitted on the ShC and WRC curves occur at the same gravimetric water content, thus illustrating the likeness of the curves with respect to their shape. The WRC was estimated with a reasonable accuracy from the water content of the ShC transition points plus some measured suction values.

Abbreviations: AE, air-entry point • C, cambisol samples • F, fluvisol samples • ML, macroporosity limit point • MS, maximum swelling point • PS, pedostructure model • SC, swelling capacity • ShC, shrinkage curve • SL, shrinkage limit point • V, vertisol samples • VG, van Genuchten closed-form equation • WRC, water retention curve • XP, exponential model


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
THE SOIL SHRINKAGE was defined as the specific volume change of soil in relation to its water content (Haines, 1923; Stirk, 1954), and shrinkage properties were first considered as an indicator of soil structure and soil stability (e.g., Tempany, 1917; Haines, 1923; Lauritzen and Stewart, 1941). Recently, the use of soil shrinkage properties was proposed for determining the volume of soil pore systems (Boivin et al., 2004), for modeling the WRC (Braudeau and Mohtar, 2004), for assessing soil compaction (Boivin et al., 2006), and for determining soil mechanical properties (Baumgartl and Kock, 2004).

The experimental determination of the ShC was greatly improved with the ability to carry out quasi-continuous measurement of both soil volume and water content with time (e.g., Tariq and Durnford, 1993b; Braudeau et al., 1999). These studies, among others, showed that most structured-soils have S-shape ShC. As reviewed in Boivin et al. (2004) and Peng and Horn (2005), several modeling approaches of shrinkage were developed, for pure clay pastes (Sposito, 1973) and structured soils (e.g., Giraldez et al., 1983; McGarry and Malafant, 1987; Tariq and Durnford, 1993a; Braudeau et al., 1999). The XP model introduced by Braudeau et al. (1999), was shown to fit well to most of the ShCs. The XP model parameters are water content and bulk specific volume coordinates of four points of the ShC. Moreover, this model is based on conceptual assumptions on the relation between soil structure and soil shrinkage (Braudeau, 1988). If the conceptual assumptions were valid these parameters would allow calculating other soil characteristics such as porosity of the soil plasma, as defined in Fies and Bruand (1998), and the complementary porosity called macroporosity, at any water content. In the studies of Braudeau and Bruand (1993), and Boivin et al. (2004), these assumptions were verified against experimental data. Braudeau et al. (2004) proposed the pedostructure (PS) model as another physically based approach of the shrinkage, which makes distinction between several water pools in soils, according to their relation with the pedostructure. The PS model is compatible with XP model and the parameters for the calibration of one of the models can be calculated with the parameters of the other. Braudeau and Mohtar (2004) proposed to take into account the shrinkage properties, which they call pedostructure, in a new modeling approach of the WRC. Another approach is to model the ShC with a modified VG closed-form equation (van Genuchten, 1980) of WRC (Peng and Horn, 2005). This approach does not make any assumption on the shrinkage process and allowed to fit different ShCs with three parameters only.

The use of the same model (namely VG equation) to fit either the WRC or the ShC relies on the observation of a likeness between the shape of the two curves, which was underlined by Baumgartl and Kock (2004). The VG equation parameters have no physical meaning that might represent a limitation for the fitting of ShCs compared with the possible applications of XP model (e.g., Braudeau and Bruand, 1993; Boivin et al., 2006). Alternatively, the use of XP equations to fit the WRC was, however, not discussed. The objectives of this paper are (i) to test the shape likeness of WRCs and ShCs measured simultaneously on a series of different soil samples from different soil types, clay content, and clay mineral composition, thus presenting a variety as broad as possible of shrinkage and water retention properties, and (ii) to compare the ability of XP model and VG equation to fit both experimental curves.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Soil Samples
To analyze a variety of shrinkage and water retention properties as broad as possible, we considered a series of ShCs and WRCs simultaneously measured on different undisturbed soil cores collected within surface horizons (0- to 30-cm depth) originated from different geographical locations and soil types: (1) A vertisol following the FAO (1998) classification, from northern Senegal (three samples) described in Favre et al. (2002). The vertisol samples are denoted "V" in the following. (2) A loamy soil from Switzerland (12 samples). This soil is termed Cambisol in the FAO (1998) classification, and the samples are denoted "C." (3) A Fluvisol (FAO classification) from south Senegal (13 samples). These samples are denoted "F." The clay content and clay mineralogy of the samples are reported in Table 1.


View this table:
[in this window]
[in a new window]
  		Table 1. Selected properties of the investigated soils. Undisturbed samples were collected in the surface horizons (0- to 30-cm depth).

 
In addition, we included in the study the results of experiments presented in Boivin et al. (2004), that is, ShC and WRC measured on two sets of 15 repacked soil samples each, with two different ratios of smectite/kaolinite, various clay contents, and a dry bulk density of 1.7 g cm–3. The same nomenclature as in Boivin et al. (2004) was used.

Each soil sample was denoted with the soil sample origin (namely V, C, F, 1 or 2) followed by its clay content (for instance 1–18 is a soil sample from set 1 with 18% clay content).

Experimental Device
The ShCs and WRCs were simultaneously measured, from saturation to air-dry, on undisturbed soil cores of approximately 100 cm3 volume (5 cm high and 5 cm diameter approximately) with the experimental setup described in Boivin et al. (2004), except that at the end of the experiment the C samples were carefully disassembled or reduced into pieces to separate gravel (>2 mm) from finer soil particles (<2 mm) and the mass and volume of particle size > 2 mm (coarse fraction) was measured. These values were subtracted from the mass and volume of the sample to obtain the ShC of the fine soil (<2-mm particle size), thus allowing comparison of the curves regardless of heterogeneities in the coarse fraction. The coarse fraction in the C samples represented, however, <5% of the dry weight of the samples. The effect of the gravel, which was mostly in the <5-mm size, was assumed to be negligible for the shape of the ShC and limited to a shift in the bulk volume and gravimetric water content.

The swelling capacity (SC) of the soil was calculated as (Braudeau and Bruand, 1993):

Formula 1[1]
where Vb(MS) and Vb(SL) are the values of the sample bulk volume at the MS (maximum swelling) and SL (shrinkage limit) points respectively (see Fig. 1 ).


Figure 1
View larger version (16K):
[in this window]
[in a new window]
  		Fig. 1. Example of an experimental shrinkage curve (solid line) with the location of the transition points of the XP model: shrinkage limit (SL), air entry (AE), macroporosity limit (ML), and maximum swelling of plasma (MS), and the structural, basic, and residual shrinkage domains. Dashed line: theoretical 1:1 saturation line.

 
The accuracy of the results can be estimated according to the experimental errors. The volume calibration introduces the main source of uncertainty in the ShC determination, estimated at 1% in Boivin et al. (1991). This affects the volume estimation only, but neither the water content nor the suction, which were estimated with a precision of 0.01 g and 0.1 cm of water, respectively, The specific volume of the sample was measured before and after the experiment; the errors affecting the ends of the ShC were, therefore, limited to that made on the volume calibration estimated at 1%.

Models
The XP model was described in Braudeau et al. (1999), and discussed in Boivin et al. (2004). The XP model is continuous and combines three linear parts and two curvilinear ones separated by four transition points (Fig. 1). By exploring the full range of water content from saturation to maximum drying, the linear parts are successively associated with the structural, the basic, and the residual shrinkage, respectively. The transition points correspond to the MS, the ML, the air entry (AE) and the S). The SL and AE points are assumed to be respectively the shrinkage limit and the air entry point of the soil plasma (also called microporosity or soil clay matrix, see below) (see for example Sposito, 1973 or Chertkov, 2000). The ML point is assumed to be the dry point of the macroporosity by Braudeau (1988), and the MS point is considered as the maximum swelling of the soil plasma, also called swelling limit in Tariq and Durnford (1993a), or swelling point in McGarry and Malafant (1987).

In Braudeau et al. (2004), interpedal swelling is an additional part of the ShC close to water saturation. We observed this in some samples when the suction was smaller than –10 cm of water and shall not consider it in the following.

Without taking into account the interpedal swelling, the XP model has formally eight parameters, the water content and specific volume coordinates of the SL, AE, ML, and MS transition points, which must be fitted on experimental observations. The slope of the linear parts can be used instead of some of the parameters. The corresponding equations are presented in Table 2.


View this table:
[in this window]
[in a new window]
  		Table 2. Equations of the exponential (XP) model used. AE, air entry; ML, macroporosity limit; MS, maximum swelling; SL, shrinkage limit; Wn normalized water content. The table is given for the calculation of the specific bulk volume V. One must replace the variable V by the variable h for calculation of the water suction. The values of KBs and KStr are thus changed, and the corresponding slopes of the WRC are denoted KhBs and KhStr in the text.

 
The WRC was fitted with the VG closed-form equation written as:

Formula 2[2]
where W is the gravimetric water content, Wr and Ws are the fitted residual and saturated values of W, {alpha}, m, and n are fitted parameters, and the dimension of {alpha} is cm–1. For ShC modeling, the VG equation was modified following Peng and Horn (2005). These authors expressed the ShC as void ratio e as a function of moisture ratio {upsilon}:

Formula 3[3]
where {alpha}, n, and m are fitting parameters, es and er are the maximum and minimum recorded void ratio respectively, and {alpha} has no dimension. By using e = V/Vs; es = Vsat/Vs; er = Vr/Vs; {upsilon} = Vw/Vs; Vw = W/{rho}w where V is the specific volume of the soil sample, Vs is the specific volume of the solid phase (taken as 1/2.65), Vsat and Vr are the maximum and the minimum specific volume of the sample, Vw is the volume of the water, and {rho}w is the density of the water (taken as 1) respectively, Eq. [3] transforms in:

Formula 4[4]

Curve-Fitting Procedure
The data were treated as follows:

The tensiometer readings were stopped when desaturation of the capillary tube was visually observed. The ShCs were fitted on the full range of measured gravimetric water content (i.e., from saturation to air-dry at the end of the experiment). The WRCs were fitted on the data sets limited to the obtained tensiometric working range, that is, in a range of 0 to 650 to 0 to 950 cm of water depending on the samples. The fittings were achieved by the Simplex optimization algorithm proposed by Chen et al. (1986).
The ShC data were fitted with XP model, which required eight parameters namely coordinates of the SL, AE, ML, and MS points, and with the modified VG Eq. [4] following Peng and Horn (2005), which required three parameters namely n, m, and {alpha}, Vsat and Vr being the maximum and minimum recorded specific volumes, respectively.
Within the range of water content corresponding to the recorded suction values, WRCs were fitted by the van Genuchten closed-form Eq. [2], which needs five parameters (namely Wr, Ws, {alpha}, m, and n). Because they are fitting parameters, the saturated and residual water contents may significantly differ from the W values at the largest and lowest recorded water contents, respectively.
The XP model was fitted on the WRC data as well. In that case, the h(W) data were fitted (see equations in Table 2), and the coordinates of the transition points are W (abscissa) and h (ordinate). Note that fitting the WRC with XP equations is empirical. Therefore there is no assumption on the meaning of the transition points but for the sake of legibility we used the same denotation with the addition of subscript h for the transition points (i.e., MSh, MLh). Because the range of recorded suction values covers only the structural and basic shrinkage parts, the XP equations were fitted on these domains, which required five parameters only to be determined: the four coordinates of MLh and MSh points, plus one of the slopes of the linear parts because of the relation between KBs and KStr ([a-2] or [b-2] in Table 2). Conversely to the VG equation, the XP model is defined on segments, and can be fitted on a part of the full curve without influence of the discarded or missing data on the determined parameters, provided that the transition points of the missing part were not fitted.
The likeness between ShCs and WRCs was analyzed by comparing the water content values (abscissa) at either the ML and MLh or MS and MSh transition points as independently fitted on both curves.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 APPENDIX
 REFERENCES
 
Shrinkage and Water Retention Curves
For the sake of brevity and legibility, results obtained on six samples and representative of the whole data set are reported in Fig. 2 , 4, and 5, while Fig. 3 and 6 and statistical results deal with the whole data set. Examples of simultaneously measured ShCs and WRCs are presented in Fig. 2, with the XP model fitted on the ShCs. The S-shape of the ShCs was observed for all samples, though the amplitude of the volume change was considerably different between the soils (see for example samples V-51 and F-9). All the curves departed largely from the saturation line, contrarily to the ShC of clay pastes, whatever is the clay content of the samples. The relative length of the different shrinkage parts also varied sharply with clay content and soil type. The longer part could be either the structural (F-9), the basic (V-46), or the residual one (C-17). The sandy fluvisol F-9 had the smallest clay content of the experimented samples with 9% of clay. In this case, the changes in sample height between two successive records were close to the resolution of the experimental setup, resulting in a scattered ShC (Fig. 2e). Moreover, after reaching a shrinkage threshold, the sample volume was increasing. This particular behavior was interpreted as an effect of the breaking of water meniscus between sand particles on drying. The corresponding data (release of the sample after reaching of a minimum volume) cannot be interpreted in the frame of the studied ShC models and was not considered.


Figure 2
View larger version (28K):
[in this window]
[in a new window]
  		Fig. 2. Examples of simultaneously measured shrinkage (ShC) and water retention (WRC) curves with the fitted XP equations, for Cambisols with (a) 17% and (b) 14% of clay, Vertisols with (c) 46% and (d) 51% of clay, and Fluvisols with (e) 8.5% and (f) 42% of clay. Abscissa: gravimetric water content W. Ordinates: specific bulk volume V (solid line), fitted XP model (dashed line), saturation line (dotted line) and suction h (black dots).

 

Figure 4
View larger version (27K):
[in this window]
[in a new window]
  		Fig. 4. Examples of shrinkage (ShC) and water retention curves (WRC) measured simultaneously with the fitted VG equations, for Cambisols with (a) 17% and (b) 14% of clay, Vertisols with (c) 46% and (d) 51% of clay, and Fluvisols with (e) 8.5% and (f) 42% of clay. Abscissa: gravimetric water content W. Ordinates: specific bulk volume V (black solid line), fitted VG-modified equation (black dashed line), suction (gray solid line), and fitted VG equation (gray dashed line).

 

Figure 5
View larger version (18K):
[in this window]
[in a new window]
  		Fig. 5. Examples of problems faced when fitting the VG modified equation on experimental shrinkage curves with linear phases, sloping ends, or dissymmetric parts. Experimental shrinkage (ShC) and water retention (WRC) curves (solid line), fitted VG modified and VG equations (bold dashed gray line) compared to fitted XP models (black dotted line) for sample C-15 (top) and sample F-17 (bottom) different from the ones presented before.

 

Figure 3
View larger version (13K):
[in this window]
[in a new window]
  		Fig. 3. Calculated structural (KStr–triangle) and basic (KBs–square) slopes of the shrinkage curves as a function of swelling capacity (SC) for the whole set of data. Thirty repacked soil samples (open) and 28 undisturbed soil samples (black). F: Clayey fluvisol. V: Vertisol.

 

Figure 6
View larger version (20K):
[in this window]
[in a new window]
  		Fig. 6. Examples of estimation of the water retention curve using shrinkage properties. Comparison between experimental data (solid line), direct fitting of the exponential model equations (dashed line), direct fitting of van Genuchten equation (gray dashed line), and estimation with the use of (i) macroporosity limit (ML) or maximum swelling (MS) water content fitted on the shrinkage curve, (ii) the slopes of the linear parts, and (iii) recorded suction at MS or ML (see prediction methods 2 and 3, Table 3, for the equations used). C-17 and C-14 are Cambisols, V-46 and V-51 are Vertisols, F-9 and F-42 are Fluvisols.

 
Modeling the Shrinkage Curves with the Exponential Model
Mean square errors (MSE) between the experimental ShC and the fitted XP model on the data presented in Fig. 2 are given in Table 3, together with the average and standard deviation values of MSE obtained when fitting XP model on the 58 experimental ShCs. The fitted XP model parameters of the samples presented in Fig. 2 are given in Table 4. It can be observed that the XP model fitted similarly well to all the ShCs regardless of the large differences between the various soil samples in terms of clay content, clay mineralogy, and structure. Except release of the sample at smaller water content (F-9) or interpedal swelling at higher water content range (C-17), it is difficult to show the model (dotted line) that is perfectly superposed to the experimental data (solid line) in Fig. 2. Representing the ShCs with a succession of linear and curvilinear parts gave, therefore, good fitting results. For the XP model, Fig. 3 presents for the whole data set (58 samples), the values of the structural (KStr) and basic (KBs) shrinkage slopes (see Table 2, Eq. [a-1] and [b-1], respectively) as a function of the swelling capacity, SC. The higher values of SC were observed for the vertisol samples and the clayey fluvisol samples. Unsurprisingly, there was a clear increasing trend of the slopes with SC. The KStr values ranged from 0 to 0.65, and the KBs values varied from <0.1 to 1 (Fig. 3) the latter corresponding to the theoretical slope for water and solid systems. The higher KBs slopes were observed with undisturbed vertisols, whose ShCs were, however, largely different from those of clay pastes, as KStr slopes are smaller than 0.5 and stood largely above the saturation line, corresponding to a stable pore network filled with air. The most clayey of the repacked soils (Boivin et al., 2004) had slopes up to 0.8, and their KStr values seem higher than those of the undisturbed vertisol samples, which reveals a less rigid structure compared with undisturbed samples in the structural shrinkage domain.


View this table:
[in this window]
[in a new window]
  		Table 3. Mean square errors (MSE) of the fitting of exponential (XP) and van Genuchten (VG) equations on the shrinkage and water retention curves (WRC) for the examples presented in Fig. 2, 4, and 5, as well as average and standard deviation values for the 58 samples. For the WRCs, the W (water content) and h (water suction) raw data were normalized after fitting and before MSE calculations.

 

View this table:
[in this window]
[in a new window]
  		Table 4. Parameters of the fitted models for the samples presented in Fig. 2, 4, and 6. Water contents W in g g–1, specific volumes V in cm3 g–1, {alpha} (VG) in cm–1, slopes KStr, KBs, KR in cm3 g–1, h in cm, slopes KhStr and KhBs in cm g–1, other parameters are dimensionless.

 
Some likeness in shape between WRC and ShC is observed on the examples given in Fig. 2. Both curves seem to be made of a succession of linear and curvilinear parts, and transitions between linear and curvilinear parts seem to occur on the same water content range, although the soil samples show very different shrinkage behavior.

Modeling the Water Retention Curves and Shrinkage Curves with the van Genuchten Closed-form Equation
Figure 4 presents WRCs and ShCs fitted with Eq. [2] and [4], respectively, and the corresponding fitted parameters are presented in Table 4. It can be observed that the VG equation fitted fairly well to both ShC and WRC in most cases (see Table 3 for the MSE values), thus supporting the conclusions of Peng and Horn (2005). However, the fitted VG model tended to cross the experimental curves in the linear parts of both curves, as can be seen for example with samples C-14, C-17, V-46, and V-51 (ShC) or V-46 and V-51 (WRC) on Fig. 4 and with samples C-15 and F-17 (ShCs) on Fig. 5 . The fit was almost perfect with the ShCs like that of F-42 (Fig. 4f) showing similar amplitude of the several parts and horizontal slopes at the end points (water saturation and dry end of the ShCs). The larger deviations between observed and fitted curves were noted when the ShCs presented a marked slope at the dry ends such as presented in Fig. 5, which was noted in most cases. Vr and Vsat are not fitted parameters in the approach of Peng and Horn (2005), and the slopes of the ShC are assumed to be equal to 0 at these end points. However, the slope of the structural shrinkage was null for three fluvisol samples only, and the slope of the residual shrinkage was null for fluvisols, but positive for most of the cambisol, vertisol, and repacked soil samples. The ShCs showing a large structural domain compared with the other parts, which was the case for many cambisols and fluvisols, were also poorly fitted (sample C-15, Fig. 5). We tried to fit Vr and Vsat, which gave estimated values out of the recorded range, but this only slightly improved some of the fittings (results not presented), and the problem of model crossing the experimental curves was still pending. This was not observed by Peng and Horn (2005), who worked on discrete ShC measurements with a smaller diversity in the shrinkage behavior than presented here.

The MSE values obtained with the modified VG equation fitted on the ShCs were found to be always larger than those obtained when fitting XP model, and were larger of one order of magnitude in average (Table 3). Assuming a normal distribution of the observations, the average MSE values for both models were significantly different at 95% confidence interval.

Modeling the Water Retention Curves with the Exponential Model
Exponential model fitted fairly well the WRCs on the tensiometric range of water content, as illustrated in Fig. 6 , which shows the experimental curves and fitted models. The corresponding parameters are presented in Table 4. Though it uses the same number of parameters (5) as the VG equation, XP gave a better goodness of fit than Eq. [2], as shown by the MSE values given in Table 3. Because VG equation was fitted on W(h) data while XP equations were fitted on h(W) data, the fitted and experimental WRC values were normalized as follows:

Formula 5[5]
to allow comparison of the goodness of fit. In Eq. [5] Y is either h or W, and Ymin and Ymax are the minimum and maximum recorded values, respectively. Therefore, the normalized variables range between 0 and 1.

The average MSE value obtained when fitting the WRCs of the 58 samples with XP model was significantly smaller than the MSE value obtained with the use of Eq. [2] at 90% confidence interval (Table 3). The improved goodness of fit with XP compared with VG seemed to be due to the linear parts of the curves. However, this conclusion is restricted to the tensiometric water content and suction range in the present study.

Degree of Likeness between Water Retention Curve and Shrinkage Curve
The degree of likeness of the WRCs and ShCs was estimated by comparing the gravimetric water content values W at the ML and MLh, and MS and MSh points independently fitted using XP equations on the experimental V(W) and h(W) curves, respectively. The results are presented in Fig. 7a for W(ML) and 7b for W(MS), where the linear regression and coefficient of determination (R2) are also reported. The intercepts of the regression lines being smaller than 0.02 g g–1, the correlations were forced through the origin on Fig. 7. The resulting slopes are very close to 1, indicating that the transition points occur at the same water content values on both curves for the whole set of data. Though they showed higher KStr values (Fig. 3), the repacked soil samples stand on the same regression than the undisturbed ones. To judge the quality of the agreement between MS or ML gravimetric water contents independently fitted on the ShC or WRC, the regression lines with correlations not forced through the origin were compared with the first bisector by calculating the following quantity (Saporta, 1978):

Formula 6[6]
where a and b are the intercept and slope, Formula 62 is the residual variance, n the number of points in the correlation (58), Formula 6 is the mean of the measured values {chi}i, a0 = 0 and b0 = 1 for the first bisector. F being a realization of a Fisher variable F(2, n – 2), the null hypothesis (i.e., the regression line can be assimilated to the first bisector) is rejected if F > 3.2 for 56 degrees of freedom at a Fisher test significance of 0.05. F was lower than 0.02 in both cases, showing that the regression lines can be assimilated to the first bisector with a high level of significance.


Figure 7
View larger version (17K):
[in this window]
[in a new window]
  		Fig. 7. Relation between macroporosity limit (a) and maximum swelling (b) gravimetric water content values, fitted independently on shrinkage curve (abscissa) and water retention curve (ordinates), respectively, for the whole set of data: 30 repacked samples (open) and 28 undisturbed samples (black). Linear regressions are forced through the origin; R2 is the coefficient of determination.

 
The gravimetric water contents W(ML) and W(MLh), and W(MS) and W(MSh), fitted on the experimental ShCs and WRCs respectively, can therefore be statistically considered as equal. This illustrates the likeness between the experimental curves for the whole data set (58 samples).

Modeling the Water Retention Curve with Exponential Model Equations and Shrinkage Parameters
Because of this likeness, the possibility for estimating the WRC from the XP equations, the water contents at the transition points of the ShC, and the recorded suctions at these points was empirically investigated. The considered methods used the water contents at ML and MS, the corresponding measured suctions, and one of the slopes of the WRC in the linear parts. These parts were delimited by fitting the XP model to the ShC. The slopes of the WRC were denoted KhBs and KhStr in the basic and structural shrinkage parts, respectively. KhBs and KhStr were determined with W(ML) and W(MS) fitted on the ShC, and corresponding h(ML) and h(MS), plus the maximum recorded suction and corresponding W value (Method 1). KhStr and KhBs are then calculated using Eq. [b-1] and [a-2] in Table 2, and the WRC is calculated using Eq. [d]GoGoGoGo through [h] (Table 2). The slopes KhBs and KhStr were also directly determined using two points recorded in each linear part as delimited by fitting the XP model to the ShC. In that case, only one transition point fitted on the ShC was required, either MS or ML (Methods 2 and 3, respectively), to use Eq. [d]GoGoGoGo through [h] (Table 2).

Using recorded water suctions at both ML and MS points, and KhStr, gave a very good fitting of the WRC from saturation to ML, but KhBs was generally underestimated (results not presented). Similarly, the use of KhBs led to poor estimations of KhStr. Though the ML and MS transition points were nearly identical when determined either on the ShC or WRC (Fig. 7), we observed that slight changes in the position of the transition points on the curves impacted the estimates of either KhBs from KhStr (Eq. [a-2] in Table 2) or KhStr from KhBs (Eq. [b-2] in Table 2). The dispersion of the points around the linear regressions in Fig. 7, though representing small changes in water content, are large enough to induce poor estimations of either KhBs or KhStr with Method 1. For undisturbed soil samples, the best results were obtained by using KhBs and KhStr combined with water content and suction measured at MS. For the repacked soil samples, the best results were obtained by using values of W and h at ML rather than MS (Methods 2 and 3, respectively). Examples of comparison between straightforward fitting of XP to experimental WRCs and their estimates by the two last methods are presented in Fig. 6. It can be seen that experimental and estimated curves are in good agreement in all cases, which can be considered as another illustration of the likeness between the WRCs and ShCs with respect to their shapes. Using the same parameters for the MS and ML abscissa in XP for the description of both WRC and ShC equations in the modeling of water transfer in a swelling soil would decrease the total number of parameter required.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
APPENDIX
 REFERENCES
 
The experimental results were obtained on a large variety of soil types and clay contents. Quasi continuous measurements in time allowed detailed analyses and comparisons of WRC and ShC models. In the tensiometric water content and suction range, the likeness in shape between the WRC and the ShC was, illustrated by representing both curves with a succession of linear and curvilinear parts, transition points occurring at the same gravimetric water content. The results suggest the use of a shrinkage model that account for soil pedostructure (Braudeau and Mohtar, 2004) for estimating water retention function. However, further research on the identification and physical interpretation of transition points is required. The results dealing with the repacked samples were similar to those obtained on undisturbed ones with respect to ShC and WRC properties, except that the structural shrinkage slope was larger, emphasizing a less rigid structure of the repacked samples in that shrinkage domain.

VG and XP equations were applied to the fitting of both ShC and WRC, supporting the conclusions of Peng and Horn (2005), although a better goodness of fit was obtained with XP than with VG equation, even when the same number of parameters was used in the case of WRC. Problems with the use of VG equation were related to the observed linear parts and sloping ends of both WRC and ShC, and possible dissymmetry of the ShC. In the case of the ShC, XP model needs five more parameters than VG equation to be calibrated. The choice of the appropriate model for fitting the ShC will, therefore, depend on the objective. If applications such as the assessment of soil compaction, with distinction between macropore and plasma pore compaction (Boivin et al., 2006) or the scaling of parameters with soil properties (Boivin et al., 2004) are envisaged, the use of XP is recommended, while the VG-modified equation (Peng and Horn, 2005) is easier to use in numerical modeling.

The description of the WRC with XP model equations and parameters may be relevant (i) because the MS and ML abscissa are water contents highly correlated with simple soil properties, such as clay content (Boivin, 1990, Boivin et al., 2004), and (ii) because of the significance of the XP parameters in terms of pedostructure (Braudeau, 1988, Braudeau and Mohtar, 2004). An important restriction to this approach is, however, that the present analysis was limited to the tensiometric range. The extension to the full range of water content should be further studied by, for instance, using additional experimental devices such as psychrometers to enlarge the range of water suction measurement. It might also be worthwhile to investigate the possible determination of the hydraulic conductivity curve from the WRC described by the XP equations. This point, which is out of the scope of this paper, would merit further experimental and theoretical studies.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
REFERENCES
 
Variables:

e: void ratio (volume of voids divided by volume of solid phase) (–)
er: van Genuchten parameter (residual void ratio) (–)
es: van Genuchten parameter (saturated void ratio) (–)
h: suction (cm of water)
KBs: slope of the basic shrinkage part (cm3 g–1)
KhBs: slope of the WRC in the basic shrinkage part (cm H2O g–1)
KStr: slope of the structural shrinkage part (cm3 g–1)
KhStr: slope of the WRC in the structural shrinkage part (cm H2O g–1)
KR: slope of the residual shrinkage part (cm3 g–1)
n: van Genuchten parameter (cm–1), and modified van Genuchten parameter (–)
m: van Genuchten and modified van Genuchten parameter (–)
SC: swelling capacity (%)
V: bulk specific volume (cm3 g–1)
Vb: bulk volume of the soil sample (cm3)
Vr: VG modified parameter, minimum (air-dry) specific volume of the soil sample (cm3 g–1)
Vsat: VG modified parameter, maximum specific volume of the soil sample (cm3 g–1)
Vs: specific volume of the solid phase (taken as 1/2.65)
Vw: specific volume of water in the soil sample (cm3 g–1)
VStr: a value of specific volume in the structural part (Table 1) (cm3 g–1)
W: gravimetric water content (g g–1)
Wn: water content normalized in the curvilinear parts (Table 1) (–)
WStr: a value of gravimetric water content in the structural part (Table 1) (g g–1)
{alpha}: van Genuchten and modified van Genuchten parameter (–)
{rho}w: density of water (g cm–3), taken as 1
{upsilon}: moisture ratio (volume of water divided by volume of solid phase) (–)
{upsilon}r: van Genuchten parameter (residual moisture ratio) (–)
{upsilon}s: van Genuchten parameter (saturated moisture ratio) (–)


   ACKNOWLEDGMENTS
 
The authors thank Dr. H. Gerke (Associate Editor), and anonymous reviewers for helpful comments to improve the manuscript. This research was partly funded by the Swiss Agency for Environment, Forest and Lanscape (SAEFL) of the Swiss Federal Department of Environment, Transport, Energy and Communications, and the authors are grateful to G. Bellier (Institute of Research for Development, Paris) for his technical assistance.

Received for publication July 7, 2005.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 





This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via ISI Web of Science (1)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Boivin, P.
Right arrow Articles by Vauclin, M.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Boivin, P.
Right arrow Articles by Vauclin, M.
Agricola
Right arrow Articles by Boivin, P.
Right arrow Articles by Vauclin, M.
Related Collections
Right arrow Structure and Properties
Right arrow Soil Physics
Right arrow Soil Hydrology

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
The SCI Journals Agronomy Journal Crop Science
Vadose Zone Journal Journal of Plant Registrations
Journal of Natural Resources
and Life Sciences Education		 Journal of
Environmental Quality