New device and method for soil shrinkage curve measurement

Reprinted from the Soil Scieiice Sociefy of Aiirerica Jounial Volume 63, no. 3, May-June 1999

677 South Segoe Rd., Madison, WI 5371 1 USA

New Device and Method for Soil Shrinkage Curve Measurement and Characterization E. Braudeau," J. M. Costantini, G. Bellier, and H. Colleuille

ABSTRACT There is a need for a conceptual and analytical model to describe

and interpret the common shrinkage curves of structured soil samples. In this work, we propose a new device for direct shrinkage measurement of unconfined structured soil samples and discuss the relevance of parametric models of the shrinkage curve to fit the experimental data.The experimental procedure consists of simultaneous and continuous measurements of the diameter, height, and weight of an initially saturated soil sample as it dries. The shrinkage measurement can be completed for the full moisture range in a short time (2-3 d), and all shrinkage phases can be established easily and accurately identified. The points of transition between the differeut shrinkage zones of the shrinkage curve are considered as characteristics of the shrinkage process. They are used as parameters to model the experimental shrinkage curves by lmear shrinkage zones separated by cunilinear transition ones. The efficiency of two parametric models to fit the experimental data and to provide the characteristic points of the curve are compared and discussed. A new procedure for fitting the shrinkage curves of structured soil samples and for determining the best position of the characteristic points on the curves is proposed.

OIL STRUCTURE, the arrangement of particles and ag- S gregates and the ensuing porosity, influences the movement and storage of fluids, gases, and nutrients in the soil, and hence most of the soil's hydrological, physical, and agronomical processes. Soil structure de- cline is also regarded as one of the most important single issues in soil degradation and declining crop production. It is therefore essential that soil structure is accurately represented in models to simulate its hydrostructural behavior of soil. Shrinkage curve analysis is one of the few methods allowing an accurate quantitative assessment of soil structure (Coughlan et al., 1991) and hydrostructural properties (Braudeau and Bruand, 1993). A shrinkage curve represents the specific volume change of a soil relative to its water content (Haines, 1923; Stirk, 1954), which may be interpreted as soil pore changes on drying. Shrinkage curve analysis provides pertinent indices of soil structure and soil behavior (McGarry and Daniells, 1987; Braudeau, 1988b) and has been success- fully applied to investigate soil structure degradation under crops (Chan, 1982; Reeve and Halls, 1978; McGarry, 1988; McGarry and Smith, 1988). However, the use of shrinkage curves as a measure of soil structure depends first on the development of an accurate method of measurement and modeling of the shrinkage curve. Thus, we present an improvement of the method for continuous and automated measurement of soil shrinkage curves suggested by Braudeau (1987), and the rele-

E. Braudeau, IRD, BP 434,1004 Tunis-el-Menzah, Tunisia; J.M. Cos- tantini, Geodit, 29 Grande Rue, 13002 Marseille, France; G. Bellier, IRD, Lab Hydrophysique, 32 Av. Henri Varagnat, 93143, Bondy, France; H. Colleuille, NVE, Hydrology Dep., Middlelthunsgate 29, P.O. Box5091 Maj, Oslo, Sweden. Received 6May 1997. *Correspond- ing author ([email protected]).

Published in Soil Sci. Soc. Am. J.] 63525-535 (1999).

vance of existing models of parametric equations to fit the experimental data for different kinds of soil structure is tested and discussed.

THEORY Presentation of the Shrinkage Curve

Shrinkage data plotted as specific volume, v, against water content is commonly termed a shrinkage curve (McGarry and Malafant, 1987). On such a plot (Fig. l), the location of experimental data is generally referred to the 1:l saturation line, also called the load line (Sposito and Giraldez, 1976), which is characterized by an intercept equal to the specific volume of the solids, vs, and by a slope equal to Upw, pw being the bulk density of water (1 kg m-'). This 1:l line represents the shrinkage curve of a theoretical two-component (solid and water) saturated system where the water removal is not re- placed by air entry throughout the full moisture range (McGarry and Malafant, 1987). The point of intersection between the shrinkage curve and the 1:l saturation line defines the water content of the saturated soil sample Os.

Shrinkage data may be also plotted as void ratio e against moisture ratio 6, where e and 6 relate the volume of voids and water to the volume of solid, respectively (Groenvelt and Bolt, 1972; Tariq and Durnford, 1993). They are related to the variables used in this work by the following equations:

v = (e + 1) v, and 0 = 6 v, pw Pl Three distinct shrinkage zones are generally distinguished

in a typical shrinkage characteristic curve (Fig. l), although there exist different terminologies and more than three zones may be noticed. These zones are referred to as: (i) structural, (ii) normal, (E) residual (Haines, 1923; Lauritzen and Stewart, 1941; Stirk, 1954; Reeve and Hall, 1978). The points of transition between these different shrinkage zones are generally considered as characteristic parameters of the soil samples (Coughlan et al., 1991). According to the literature, the structural and the residual shrinkage zones correspond with a volumetric change smaller than in the normal shrinkage zone where it is maximum. A zero shrinkage zone, corresponding with a loss of water without volumetric change, is sometimes recognized (Bronswijk, 1988). In the normal zone, or basic zone, as suggested by Mitchell (1992), the volumetric change is often assumed to be equal to the water loss (Kbs = dvldO = 1) (McGany and Malafafit, 1987; Tariq and Durnford, 1993b). However, this assumption is only valid for a structureless clay paste (Sposito and Giraldez, 1976; Chan, 1982). Generally, the slope of the shrinkage curve in this zone does not correspond with a unitary shrinkage (Lauritzen and Stewart, 1941; Croney and Coleman, 1954; Bruand and Prost, 1987; Mac- Garry and Daniells, 1987) and may be very low, near 0.1 (Braudeau, 1987).

In fact there are actually two conceptions for modeling a shrinkage curve (Fig. Z), depending on the number of measured points of the curve: either by three straight lines corresponding with the three structural, normal, and residual shrinkage zones (McGarry and Malafant, 1987; Coughlan et

~

Abbreviations: PL, polynomial model; XP, exponential model; SL, straight lines model; TSL, three straight lines model.

l a

525

526 SOIL SCI. SOC. AM. J., VOL. 63, MAY-JUNE 1999

al., 1991; Mitchell, 1992), or by a sigmoidal curve divided alternatively by linear and curvilinear zones (Lauritzen, 1948; Braudeau, 1988a; Tariq and Durnford, 1993b).

Our study addresses the second type of modeling, where all the shrinkage zones are distinguished. These zones are referred to as linear and curvilinear residual shrinkage, basic shrinkage, and linear and curvilinear structural shrinkage zones. Assuming that each zone corresponds with a different stage of the shrinkage process, the endpoint of these zones (O, A, B, C, D, S in Fig. 1) are points of transition between two kinds of hydrostructural states of the soil (Braudeau, 1988b), such as the well-known air entry point (Sposito and Giraldez, 1976). These transition points are thus considered as characteristic parameters of the soil’s hydrostructural behavior. They may be determined using fitting parametric models on measured shrinkage curves. By this way, Sposito and Giraldez (1976) determined the air entry point AE, while MacGarry and Daniells (1987) determined the air entry point, the swelling limit MS, and the saturated point S; then Braudeau (1988b) and Braudeau and Bruand (1993) identified the shrinkage limit SL, the air entry point in primary aggregates AE, the friability point C, and the swelling limit of primary aggregates MS (Fig. 2).

Measure of the Shrinkage Curve Numerous methods for soil volumetric shrinkage measure-

ment have been suggested. Two approaches may be distinguished. The first one is a direct assessment of a soil sample’s volume by measuring its displacement in fluid commonly using the Archimedes’ principle. Some authors have measured the displacement of very small soil samples in petroleum (Monnier et al., 1973), in water after coating the soil samples with paraffin (Lauritzen and Stewart, 1941; Lauritzen, 1948), or by saran

0.62

OB’ = a

E 3 - 9 o

0.6

VJ

z

I Q.....-,

l I

I I I I

z, KIN{ s c

I I

R, I N, 1 S b I I

I I l l

Watercontent 0 (kgkg) Fig. 1. An example of soil core shrinkage curve (a) obtained by contin-

uous measurement (Braudeau 1987). Dotted lines (b) and (c) are two possible adaptations of the three straight lines model of McGarry and Malafant (1987) on the continuous-measured curve; (b) is done in this paper and (c) was done by Tariq and Durnford (1993b). Shrinkage zones are: Z = zero, R = residual, N = normal, and S = structural, with subscript b or c corresponding with the two interpretations.

resin (Brasher et al., 1966; Reeve and Hall, 1978; Bronswijk, 1988,1991). In this way, recently, Tariq and Durnford (1993a) suggested an original method to determine soil bulk volume of clods in water by means of a flexible rubber membrane. The second approach consists of indirectly measuring volumetric change by measuring the physical dimensions of soil samples (Berndt and Coughlan, 1976; Towner, 1986; Braudeau, 1987; Wires et al., 1987; Hallaire, 1987,1991), assuming or not assuming isotropic shrinkage.

Direct measurement does not allow the continuous monitoring of shrinkage of soil samples, the shrinkage curve commonly consisting of 10 to 20 points for the full moisture range. However, one indirect method using displacement transducers allows not only automation of the measurement but also continuous and accurate measurement of shrinkage as the samples dry. Braudeau (1987) first proposed such an automatic measurement with an apparatus called the Retractomètre modified later by Braudeau and Boivin (1995). The method consists of monitoring the diameter of a cylindrical soil sample in the vertical direction during its drying. The shrinkage of low- swelling material could be measured by this method, but the issue of isotropic shrinkage was neglected (Hallaire, 1991). The new method we present takes into account this problem by using several laser captors to measure the diameter and height of soil samples (Costantini, 1997).

Parametric Models of the Shrinkage Curve Each of the five shrinkage zones in Fig. 1 may be modeled by

either linear or a nonlinear parametric equations parameters using the coordinates of the endpoints (O, A, B, C, D, S).

Four parametric models are presently available in the literature (Giraldez et al., 1983; McGarry and Malafant, 1987; Braudeau, 1988a; Tariq and Durnford, 1993b). They are presented in Fig. 2. These models do not describe exactly the same shrinkage zones but they are developed on the same principle: the linear zones are modeled by straight lines equations, and the curvilinear zones by exponential (Braudeau, 1988a) or polynomial (Giraldez et al., 1983; Tariq and Dum- ford, 1993b) parametric equations, the parameters being the coordinates of the endpoints of the zone.

In the two last models in Fig. 2, referred to as exponential ( X P ) and polynomial (PL) models, the curvilinear functions are chosen such that their derivatives at the endpoints are continuous and equal to the slopes of the adjacent linear zones (Appendix I, II). However, there are some noticeable differences between the two models. Tariq and Durnford (1993b) have taken some working hypotheses derived from the three straight lines (TSL) model of McGarry and Malafant (1987): (i) the normal shrinkage zone was assumed to have a slope equal to unity (ICbs = 1 dm3 kg-’), which restricted the application range of their model to clayey soils; (ii) the structural shrinkage was considered as a single zone from the saturation point to the onset of the basic shrinkage zone, corresponding with the swelling limit as defined by McGarry and Malafant (1987). Figures 1 and 2 show how the PL and the XP models are related to the TSL model of McGarry and Malafant (1987).

In the model suggested by Braudeau (1988a), the slope of the basic zone did not have a fixed value and the structural shrinkage range was divided into two zones, a curvilinear [D-Cl and a linear [S-Dl zone, only the latter corresponding with the structural shrinkage of the TSL model of McGarry and Malafant (1987) as shown in Fig. 1.

In order to compare the parametric curvilinear equations of the two models suggested by Braudeau (1988a) and Tariq and Durnford (1993b), the latter has been slightly modified

BRAUDEAU ET AL.: SOIL SHRINKAGE MEASUREMENT AND CHARACTERIZATION

Experimental curve (Braudeau 1987) 5 shrinkage phases recognized

A, B, C, D, transition pohts of the shrinkage mnes

Model of Giraldez and al. (1983)

2 shrinkage m e s modeled by one linear and one polynomial equation.

527

S RESIDUAL BASIC STRUCTURAL

Il

MS / Model of MacGarry and Malafant (1987)

3 shrinkage zones modeled by 3 straight lines. (TSL model) MS= maximum swelling limit

1:l AE

Ms Model of Braudeau (1988~)

and 2 exponential equations. ( X P model)

Model of Tariq and Dumford (1993) 4 shrinkage m e s modeled by 2

linear and 2 polynomial equations ( PL model)

5 shrinkage mnes modeled by 3 linear C

~-

sbrinl.

Fig. 2. Presentation of a typical continuously measured shrinkage curve and the four parametric models of soil shrinkage curves published in soil Iiteratnre.

to take into account the same five shrinkage zones and their endpoints (Fig. 3). The slopes of the three linear zones (residual, basic, and structural) are K,,, Kb, and K,,, respectively, and the corresponding end-points are (OA, vA); (OB, vB); (Oc, vc); (OD, vD); (Os, vs). The equations of the two models are given in Table 1, where variables are expressed in their re- duced form, O,, and v,,, defined for each curvilinear zone. Expla- nations are reported in Appendixes I and II.

We have to observe, in Table 1, that the number of parameters needed to describe the normalized curvilinear zones, [A-BI or [C-DI, is not the same for the two XP and PL models: two and three parameters, respectively. The reason why only two parameters (the slopes at the two endpoints) are necessary for the exponential equation of Braudeau to describe each normalized curvilinear zone, is that it expresses an equation of state, v(8), that obeys the Law of Correspond- ing States (Sposito and Giraldez, 1976). Thus, v(8) can be expressed in a form that is the same for all macroscopic analogous systems, soil organizations in our case. If variables are taken in their normalized form, parameters will be even in number and they will depend on only the conditions at the endpoints. The parametric polynomial equation Giraldez et al. (1983) proposed for expressing the residual shrinkage zone also obeys this law, so the two parametric equations could be called General Soil Volume Change equations. Appendix III shows the close similarities between the coefficients of these two general equations, the exponential equation being ex- panded to its polynomial form.

This property of the exponential model is expressed by the following relations between the parameters (cf. Appendix I, Eq. 31 and [5]) that do not exist with the PL model:

PAF! = (VA - VB)/(eA - 0,)

= {&,[exp(l) - 21 f KeV[exp(1) - 11 [31 These two equations allow us to relate the XP model to the TSL model by adding only two other parameters (one by curvilinear zone) to those of the three straight lines fitting the three classical linear zones, in order to have the same number of parameters in the two cases. The new chosen parameters were the y-axis distances between the intersection points of the straight lines and the experimental curve, MM' and NN'

0.1 0.12 0.14 0.16 0.18 0.2

Fig. 3. Representation of the straight lines model fitting the linear zones of the classical sigmoidal shrinkage curve. The v coordinates of N and M are the two needed parameters in addition to those of the three lines to calculate the parameters of the exponential model (the transition points A, B, C, D).

Water content (kgkg)


- $1 I I I I

d

II

G

(Fig. 3). The correspondence between the parameters of the two models is given by the following equations (calculations in Appendix IV).

8 D = 8Mc 4- 4.8 MMr/(&, - &);

Oc = 8 ~ 1 - 3.46 MM'/(&,, - &) [41

8 B = + 3.46 N"/(Kb, - Kre) [51

8,A, = ONt - 4.8 N"/(Kbs - Kre);

The straight lines parameters system can easily be obtained by linear regression on the linear zones of the shrinkage curve. Thus, it may be a good method for calculating the coordinates of the characteristic transition points defined by the XP model.

MATERIALS AND METHODS soils

Different types of soil widespread in the intertropical zone were used in this study. The samples were collected in Senegal. The name of the soils in the French taxonomy (Duchaufour, 1977) is used, and their corresponding names according to U.S. soil taxonomy (Soil Survey Staff, 1975) are given in paren- theses. We used a strongly desaturated fenallitic soil (Plinthu- stox) from Kolda in Haute-Casamance (Maignien, 1961; Chauvel, 1977); a leached ferruginous tropical soil (Plinthus- ta@ from Thysee Kaymor near Nioro du Rip (Bertrand, 1972); a Vertisol (Pellustert) and a weakly developed soil on alluvial deposits (Torrifluvents) from, respectively, the lower and upper part of the alluvial basin of Nianga-Podor (Valley of the Senegal River) (Colleuille, 1993; Coquet et al., 1996). They are referred to as Silty alluvial, Ferruginous, Ferrallitic soil, and Vertisol in the text and figures. Their main chemical and physical characteristics are given in Table 2.

Sampling and Samples Preparation In order to avoid problems related to the spatial variability

of the soil structure in situ, particularly the macroporosity variability, reconstituted soil samples were used. Soil samples were gently broken into small aggregates by passing through a 2-mm wire screen. Polyvinyl chloride rings (diameter 55 mm; height 35 mm) were then filled in a homogeneous way with aggregates smaller than 2 mm. The inside wall of the rings was covered with a polyethylene film for easier removal of the soil core. A weight of 0.5 kg was put on the soil samples during their capillary wetting on a porous ceramic plate (12 h). They were then equilibrated (48 h) at a matrix potential of -100 kPa using a pressure membrane apparatus before being smoothly compacted under a given pressure in order to reach the specific volume of the undisturbed soil (Table 2). This matrix potential has been related to a particular hydrostructural status of the soil, namely the soil friability point (Colleuille and Braudeau, 1996), at which it is possible to decrease soil interaggregate porosity without damage to the soil aggregates. Afterwards, they were turned out and then preserved in airtight plastic boxes in a cool room (seven repli- cations by type of soil). Before measurement of their shrinkage, the soil samples were slowly saturated by capillarity with deionized water (2-3 d). This operation was carried out under atmospheric pressure and without load, which allowed the complete saturation and swelling without disturbing the structure of the sample (Dickson et al., 1991).

Shrinkage Curve Measurement The experimental procedure consisted of the simultaneous

and continuous measurements of the height H , diameter D,

BRAUDEAU ET AL.: SOIL SHRINKAGE MEASUREMENT AND CHARACTERIZATION 529

Table 2. Main chemical and physical characteristics of the soil samples.

Soil name French classification Silt Dry bulk (U.S. taxonomy) Locality Horizon Depth Clay (<50pm) Sand CEC S/T density

Alluvial soils (Senegal River, Podor) m kg kg-' cmol kg-' %

Vertisol (Pellusterts) Lower part of

Weakly develop. soil Upper part of basin B 0.8 0.43 0.14 0.37 21.76 100 1.79

(Aquic torrifluvent) basin B 0.4 0.W ' 0.27 059 5.6 100 1.57 Ferrallitic-ferruginous tropical soils (Senegal)

Strongly desaturated ferrallitic soil

Leached ferruginous soil (Plinthustox) Plateau B 0.6 0.43 0.14 0.43 5.94 24 152

(PlinthustaIf) Plateau BA 0.3 0.19 0.21 0.60 3.91 36 1.42

and weight w, of an initially saturated soil core sample during water removal by evaporation. The measurements were determined in isothermal conditions (30 -C O S T ) , using a new version of the Rétractomètre (Costantini, 1997). The principle of this apparatus is given in Fig. 4. The vertical sensor is a laser spot that measures the height of the soil sample by triangulation (resolution 10 pm), and the two horizontal sensors give the diameter of the sample by measuring the parts not intercepted by the laser beams. The swing-plate was equipped with eight porous removable sample racks on which saturated soil samples were carefully put flat. Every 10 min the plate did a one-eighth turn and lowered to put down the sample rack on the pan of the digital balance (nominal precision 0.01 g). The experiment was stopped when the sample diameter remained constant during a minimum of 10 h. For the studied soil samples, the complete shrinkage lasted =2 to 3 d.

After the experiment, some measurements were done on each core in order to convert the data, into volume and water content, Ms and vf, where Ms is the mass of the oven-dried soil sample (lOSOC), and vf is the specific volume of the soil sample at the end of the experiment (dry bulk volume of soil sample per unit mass of solids, expressed in dm3 kg-'). vf = V f / M s where the final volume of the sample Vf was assessed by measuring the water displacement of the soil sample coated with paraffin wax using the Archimedes' principle.

In order to calculate the 1:l line, the specific volume of dry solids vs, (volume of solids per unit mass of dry solids, expressed in dm3 kg-') has been determined for each soil type using a water pycnometer.

Shrinkage Curve Calculation Taking the Anisotropy of Shrinkage into Account

Assuming an axial isotropy for the volume change process, the shrinkage curve V ( 0 ) was determined by the following equations:

where 0 is the gravimetric water content in (kg kg-'), and Df and Hf are the last data of diameter and height at the end of the shrinkage process.

Despite that the resolution of the sensors given by the manufacturer is the same for the vertical and horizontal sensors (10 pm), the measurement of the height of the soil samples was not as precise as the horizontal diameter of the sample because the core stopped at slightly a different location each time and the impact point of the laser beam was not exactly the same at each measure. Moreover, the variability of the

height measurement may be due to the movement (as shrinkage occurred) of the little reflector put on top of the soil samples. Therefore, the shrinkage curves have been determined from the diameter change data, using Eq. [8], with an exponent ß that has been smoothed after direct calculation from D and H data (Eq. [ll] and [13]).

According to Towner (1986):

v = V f (D1Df)ß Pl coming from

dvlv = a dHIH = ß dDlD = y dD'lD' [9] where a, ß, y are the coefficients of variation of H, D , D'.

ß depends on the anisotropy of the shrinkage between the height and the diameter of the soil core, and is not constant along the shrinkage. It is calculated as follows.

Assuming an axial isotropy of the soil cores (ß = y), and from the small strain theory (Towner, 1986):

dvlv = dHlH + 2dDID

ß = 2 + ßla = 2 + l1Ci

[lo1

1111

and combining Eq. [9] and [lo]

where Ci is defined as the coefficient of isotropy of the soil sample: Ci = a/ß. Ci may be easily calculated from experimental data by Eq.

[13] considering the following approximations:

T

perforated 1 Fig. 4. Rétractomètre for continuous shrinkage measurement of soil

core samples.


V/Vf = (HIHf)" = (D/Df)ß i121 Ci = a/ß [(D - Df)/Df]/[(H - Hf)/Hf] [13]

Ci is calculated at each point of the curve and then fitted by a three-order polynomial equation. It supplies a smooth variation of the exponent ß calculated by Eq. [ll].

Shrinkage Curve Adjustment and Characteristic Points Determination

The equations of the four soil shrinkage models given in Fig. 2 have as parameters the coordinates of the endpoints of the shrinkage zones these models consider. A fitting of these equations on the measured data leads to a determination of the parameters. As we considered all the linear and curvilinear shrinkage zones and their endpoints (or transition points), the only existing models it was possible to use for their determination were the X P and the PL (modified) models. Two ways are chosen to maximize the adjustment.

One consists of using the classic multidimensional simplex method (Nedler and Mead, 1965) that converges by progres- sive fitting to the best combination of parameters. The equations of the two models used are given in Table l. Note that 10 parameters are needed with the polynomial model, such as K,, Kbsr Ksi, OA, VA, OB, VB, Oc, JE, and VE, but only eight parameters with the exponential model (Kre, Kbs, ICst, 0 ~ , VA, OB, Oc, and OE) because of the two relations, Eq. [2] and [3].

The second way consists of using the relationships between the straight lines (SL) model, which fits the linear zones of the measured shrinkage curve, and the X P model. Therefore the six parameters (&, Ksi, vM,, ONr, and vNf) of the system of three lines, which may be obtained by a linear regression on the linear zones of the curve, plus the two parameters vM and vN read on the curve at eM, and ONf, allow us to calculate the corresponding eight parameters of Braudeau's model following Eq. [4] and [5].

Si@ alluvial soil 5 2 / 3 1 Ferruginous soil

H (mmq:: 5 7 ~ (mm) 56

53

28 1000 2000

10-

4 ::& 2

0. 1000 2000

The two fitting methods were tested with four soil types and their efficiency to determine the characteristic transition points of the shrinkage curve compared. Practically, seven samples by soil type were analyzed.

RESULTS AND DISCUSSION Shrinkage Curve Calculation

It was observed that the measured shrinkage data of unconfined reconstituted soil samples covered practically the complete moisture content range, i.e., from near the fully saturated and swollen state to the air-dry and fully shrunken state. The measurement was realized in a relatively short time (2 d for the kaolinitic materials, 3 d for Vertisols). The experimental data gave smooth shrinkage characteristic curves (600 measured points for the kaolinitic materials and 800 for Vertisols), without sharp change but exhibiting distinct linear and curvilinear zones of shrinkage that corresponded with different moisture ranges.

Figure 5 illustrates the steps of calculation of the shrinkage curve. For each soil type, a sample is taken as an example.

Untreated shrinkage data plotted as diameter D and height H against time are presented in Fig. 5a. The total change in D and H was very small, 5 mm for the Vertisol and 2 mm for the other samples. In all the cases, change in D was more marked and more regular than change in H. For the ferruginous soil, for example, the residual standard deviation limited to only the linear structural shrinkage zone (70 data points) was 6 X low6 m for the

Ferralliic soil Vertisol

29

28 I 53-27 1 O00 2000

3

2

1

O O 1000 2000

50

46 26

25 440 2000 4000

41

'0 2000 4000

0.99

0.95 0.9 I000 2000 1000 2000 O 1000 2000 O 2000 4000

Time (min) Fig. 5. The different calculation steps of the shrinkage curve for four selected soil samples: (a) untreated shrinkage data from the rétractomètre,

plotted as diameter D and height H against time; (b) plot of the coefficient of isotropy, C, Calculated and modeled over lime by means of a third-degree polynomial regression, and plot of the deducted exponent (ß), against time; (c) plot of the relative spec¡& volume v/vf against lime.


diameter and 25 X lob6 m for the height. Note that in Fig. 5a the relatively important shrinkage that occurred in a first shrinkage phase, before the structural one, for soils with low clay content (Ferruginous, Ferrallitic, and weakly developed soils). During this shrinkage phase process, the lower shrinkage of the height compared with that of the diameter may be due to the influence of gravity during the wetting procedure. Cores bear their own weight when they remain saturated for many days before being put into the Rétractomètre, so they do not swell upward as much as horizontally in diameter. Thereafter, shrinkage reflects this anistropy of swelling. Towner (1986) reported an analogous observation about shrinkage of clay cores that had been previously stressed in one direction.

For each type of soil Fig. 5b gives an example of the coefficient of isotropy Ci and the corresponding exponent. Ci has been calculated at each measure point by Eq. [13] and modeled over time by means of a third- degree polynomial regression. ß has then been directly calculated from Ci by Eq. [U]. Except for Ferrallitic soil, ß is smaller than three all along the shrinkage ranges, which confirms the anisotropy of shrinking and the more marked change in D than H.

Figure 5c shows shrinkage curves as relative specific volume v/vf plotted against time. This relative specific volume was calculated from Eq. [SI, with two different values of the exponent for comparison, ß calculated from data and equal to three, corresponding with an isotropic shrinkage. From these curves, it is possible to assess the error of not taking into account the anisotropy of the shrinkage by taking p = 3 as a hypothesis, as in the classical measurement. This error A(vp - v3)/vf is 4% at high moisture content for the ferruginous soil sample and decreased as v neared vf. That error is maxi- mal for Ci = = (i.e., H = constant during shrinkage) so ß = 2 Amax/vf = (Di/Df)3 - (Di/Df)z = (Dilof - l) , subscript i referring to the initial value. For cases in Fig. 5c, Amax/vf = 11 % for Vertisols and <5 % for the others.

.

0.7

h

2 E B m. 0.6

al

5 0.5

o u) u)

8 4 .- s o.77

0.75

0.73

0.71

0.69 O 0.1 0.2 0.3

The Continuous Shrinkage Curve The corresponding soil shrinkage curves, v = f(0), are

shown in Fig. 6. In accordance with the data published in the literature, the basic shape of these experimental shrinkage curves is sigmoidal (“S”-shaped curve). The curvilinear zone [C-Dl of the structural range, is often more important than the linear normal zone [B-Cl for the weakly swelling soils (Fig. 6). Moreover, for this kind of soil, a new shrinkage zone is observed at the higher moisture content, with shrinkage two to three times greater than shrinkage in the normal zone. Its slope nears 1 dm3 kg-’, showing a volumetric change approximately equal to the water loss. This behavior was attributed to a weak cohesion of the reconstituted soil structure and to the removal of the water spacing the fabric members (skeleton grains, soil aggregates) at high moisture range (Colleuille and Braudeau, 1996). Note that this shrinkage zone parallel to the saturated line, is >5 dm3 kg-’ apart from it. Therefore, a great amount of air (20-30%) remained in the soil sample though it behaved as if it were fully saturated. This fact is well known for this kind of soil for which a complete saturation is never reached in the field conditions. So we attributed the term pseudo-saturated to that shrinkage zone (Fig. 6).

With these results, it is obvious that the slope Kbs of the basic shrinkage (O, < 0 < O,) may differ greatly from the unity and may be very small, as was observed for the weakly swelling soils. This property was interpreted as the idluence of structure by Bruand and Prost (1987) and Braudeau (1988a, 1988b), who assumed that Kbs = dv/dv, with vp being the massic volume of the clayey matrix contained within the soil structure.

Determination of the Characteristic Transition Points

The X P model of Braudeau (1988a) and PL model of Tariq and Durnford (1993b) were first tested on their

0.3

I 0

0.1 o2 0.64

””- I C I

Water content (kgkg) Fig. 6. Experimental and modeled shrinkage curves of the four selected soil samples of Fig. 5. Localization of the characteristic transition points

A, B, C, D, E, and F have been performed by the straight lines fitting method including the new pseudo-saturated zone [E-GI.

SOIL, SCI. SOC. AM. J., VOL. 63, MAY-JUNE 1999

ability to fit the data using the simplex method. Table 3 shows that there was no difference between the results derived from the PL and X P models; the fitting of the two models led to the same average value of the parameters and the residual variance concerning the whole curve was not higher than at each test. These results confirm that only two parameters instead of three are sufficient to determine the curvilinear zones in their normalized form, which consequently justifies Eq. [2] and [3] of the X P model and then, the relations Eq. [4] and [5] setting the correspondence between the shrinkage transition points and the straight lines system parameters.

The SL model has been then used as a simple method for determining all the transition points of the shrinkage curve, not only those of the residual and structural curvilinear zones, but also the new points E and F of the pseudo-saturated shrinkage zone (Fig. 6). The intersection point of the two lines fitting [D-E] and [F-GI zones was named L' and the corresponding point of the curve L. Equations relating LL' to the E and F points were analogous to Eq. [5] concerning the residual zone [A-BI. The fits were excellent with a standard deviation always near the results given in Table 3 show that, except the determination of the new transition points, there is no marked difference with the previous results obtained by the simplex method. Figure 6 shows the adjustment of the XP model obtained by this straight lines method on the four selected soil samples of the Fig. 5. Experi- mental and modeled curves are superposed and are not easily distinguished. Localization of the characteristic transition points A, B, C, D, E, and F in Fig. 6 have also been performed by the straight lines fitting method including the new pseudo-saturated zone [E-GI. The fact that a same exponential equation described well the three curvilinear zones of the shrinkage curve leads us to think that it was a similar hydrostructural physical process which presided over these three shrinkage phases.

CONCLUSION In this study we have shown that in order to determine

accurately the different shrinkage phases and characteristic transition points of a soil sample, the shrinkage curve sample has to be measured continuously by displacement transducers. New forms of shrinkage curves have been described with this method and some con- cepts of the shrinkage of soil organizations should be discussed in the future. In particular, the fact that soils with low clay content, which in the past were considered as nonswelling soils, have a clear shrinkage curve with seven easily identified linear and curvilinear zones. Then, we showed how parametric models of the shrinkage curve adjusted to the measured data by the simplex method allowed us to maximize the localization of the phase transition points. A study of models of soil shrinkage curves available in the literature led us to suggest a fitting method based on the exponential model given by Braudeau (1988a, 1988b) and its relation with the straight lines system fitted on the linear zones of the


curve. This suggested method more easily determines the characteristic transition points of all of the different phases of the soil shrinkage behavior with good repro- ducibility. These results allow us to consider the shrinkage curve, like the soil water potential curve, as a characteristic of the hydro structural functioning of soil.

APPENDIX I The Exponential Model

The linear ranges of the shrinkage curve (Fig. 1) are modeled by straight lines:

V, = e, where

in between Os and 8, (structural range)

and K,,, the slope of the residual range (0, 5 O ) , instead of K,, in Eq. [Al]:

pAB=---- VA - YB - Kbs(e - 2) + Kre e A - OB e - 1

and

v, = ~

v - VA

VB - V A

[A61 - &(een - e, - 1) + K, (2.718 e, - e e n + 1) -

0.718 Kbs + K r e The total number of parameters used in these equations are

KI,. The five relations between the slopes K,,, Kbs, K,,, PAB, Pa and the other parameters decrease the number of parameters necessary to describe the whole curve to 9 (including point S).

14: (OS, vS), (OD, VD), (OC, VC), (OB, VB), (OA, VA), (vo), Kst, Kbs,

between O , and OB (basic range)

8 - 0 A v - VA e, = ~ and v, = ~

e A Yo - VA

between OA and O = O (if v, # vA)

the following equations given by Braudeau (1988a). The curvilinear ranges [C-Dl and [A-BI are described by

For [C-Dl

where

By integration of Eq. [Al] between C and D:

- vD - &,(een - e, - 1) + K,,(ee, - een + 1) ~- OC - OD e - 1

[A21 that leads to the following relations when v = vc

VC - VD - Kbs(e - 2) + Kst P C D = ~ - oc - e - 1

then, combining Eq. [A21 and [A3],

v, = ~

v - VD

VC - VD

For the range [A-BI, similar equations are obtained with taking

APPENDIX I t

The Polynomial Model Using the reasoning of Tariq and Durnford (1993b) for the

structural zone [C-DI, we calculate the coefficients of the third-degree polyno@aI equation of the fitted curve that passed by the points C and D, of which the derivatives are determined in these points.

Written in their normalized form between C and D, the variables are:

The boundaries conditions are:

e, = O; v, = O; dvlde = Kst 8, = 1; v, = 1; dvlde = Kh [AS]

hence

ao = O u1 + u2 + u3 = 1

al = &(Oc - e D ) / ( e - 0,) = K s t l P c D

al + 202 + 3 a 3 = ~ 4 9 1 giving:

K s t 8, + ( 3 p C D - Kbs - 2Kst) e’, + (Kbs + Kst - 2pCD) el [A101 v, =

PCD where PcD = (vc - vD)/(Oc - O,) is not determined

In the same way for [A-B] range:

534

~~ - ~~~

SOIL SCI. SOC. AM. J., VOL. 63, MAY-JUNE 1999

In this polynomial model, the two parameters P A B and Pm are not related to the slopes KSI, Kbs or K,, so there are two parameters more than in the previous model.

APPENDIX III Comparison between the Equations Suggested by

Giraldez et al. (l983), Braudeau (l988a), Tariq and Durnford (1993b), for the Shrinkage Range AB

Expanding the exponential Eq. [A41 gives:

e, + ose; Kbs - KI, ( 1.718Kre v, = 0.718Kbs + Kre Kbs - KI,

+ 0.i66e: + ... + < e + .. e’ 1. i By substituting PAB in the polynomial Eq. [All] by its value in the exponential model (Eq. [A5]) P A B = 0.418Kbs + 0.582K1,, we obtain:

Kbs - KIe ( 1.718Kre v, = e n 0.718Kbs + Kre Kbs + Kre

+ 0.4368; + 0.282e; 1 ~ 1 3 1

It is then possible to compare these expressions with the polynomial expression given by Giraldez et al. (1983) by taking K,, = 0 and KbS = 1

v, = 0.6950; + 0.23683, + ... (Braudeau, 1988a) v, = 0.60se; + 0.392e;

(Tariq and Durnford, 1993b) (Giraldez et al., 1983) v, = 0.89~1: + o.io4e:

~ 4 1

APPENDIX IV Relation between the Three Straight Line Model

(McGarry and Malafant 1987) and the Exponential Model (Braudeau 1988a)

As an example, we consider the case of the structural shrinkage zone [C-DI. Each fo the curvilinear zones [A-B] and [C-D] were calculated with five parameters instead of six owing to Eq. [A31 and [A51 whichrelate the parameters among them. Therefore, knowing the five following parameters (cf. Fig. 3): the slopes (&,, K,,), the intersection point M’ (ci‘, ß‘) of the two straight lines that fit to the linear zones [B-Cl and [DS], and the corresponding point M of the shrinkage curve (01 = ci’, ß), it may be calculated the C and D points as follow:

The straight line equations are:

(y - ß’)/(x - (Y’) = K,, and

(y - ß’)/(x - (Y’) = Kbs ~4151 The C, D, and M’ points are related by the following expression:

Hence, after simplification and using Eq. [A3]:

e,(M‘) = ((Y’ - eD)/(ec - 8,) = l/(e - 1) = 0.582

~ 1 7 1 Otherwise, from Eq. [A16], by dividing each term by Pm = (vc - VD)/(& - OD)? vn(M’) = (8’ - VD)/(VC - VD) = @,(M‘) K,JPCD that gives by using Eq. [3]

KSt

0.718Kbs + Ks, v,(M’) =

The value of v,(M) is determined using 8, = On (M‘) = 0.582 in Eq. [A4]:

~ 1 9 1 ß - VD - 0.208Kbs + 0.792K,t

VC - VD v,(M) = ___ -

0.718Kbs + Kst The Eq. [A3], [A17], [Als], and [A191 represent a system of four equations with four unknown variables. Using El81 and [19] yields

ve - VD = (ß - ß‘)/[vn(M) - vn(M’)]

thus the values of vc and vD:

and

Combining [A3], [A20], and [A171 yields eD and Oc:

4211

3.46(ß‘ - ß) Kbs - Kst

and Oc = a’ -

ACKNOWLEDGMENTS We gratefully acknowledge program “Jachère et Biodiver-

sité,” contract TS3-CT93-0220 (DG lZHSMU), and its Coordi- nator in Senegal, Dr. C. Floret, who initiated this work and supported the first essays in Senegal. We thank the Soil Direc- torate (Ministry for Agriculture, Tunis) and the Director, Dr. A. Mtimet, for contributing to the installation of this new methodology in his laboratory, and thus allowing the comple- tion of this work.

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New device and method for soil shrinkage curve measurement