Soil water retention curve determined by gamma-ray

beam attenuation

Luiz F. Pires*, Osny O. S. Bacchi, Klaus Reichardt

Laboratory of Soil Physics, Center for Nuclear Energy in Agriculture, USP. C.P. 96,

C.E.P. 13.400-970 Piracicaba, SP, Brazil

Received 30 December 2003; received in revised form 4 June 2004; accepted 10 June 2004

Abstract

The soil water retention curve relates the soil water matric potential (cm) and the soil water content (u). When no significant

changes occur in soil structure, the water retention curve can be considered as a soil physical characteristic. This article presents

a new procedure for soil water retention curve evaluation using gamma-ray beam attenuation as an auxiliary technique for u

determination. The radioactive source used in the experiment was 241Am, and the detector was a 300 � 300 NaI(Tl) scintillation

crystal coupled to a photomultiplier tube. The proposed procedure avoids the need of frequent sample manipulation as in the case

of the conventional method. The water content can be continuously monitored inside the chamber allowing a more precise

judgment of the equilibrium. The time required for the retention curve determination can be significantly reduced in comparison

with the traditional method. Therefore, the new procedure presents many advantages in relation to the traditional method and in

that it can be routinely used for soil water retention curve determination.

# 2004 Elsevier B.V. All rights reserved.

Keywords: Soil water retention curve; Gamma attenuation; Gamma radiation

www.elsevier.com/locate/still

Soil & Tillage Research 82 (2005) 89–97

1. Introduction

The soil water retention curve is a soil physical

characteristic expressed by the relationship between

the soil water matric potential (Cm) and the respective

water content (u). For more than 50 years, the method

that has mostly been used to obtain the soil water

retention curve is the traditional method of pressure

* Corresponding author. Tel.: +55 19 3429 4600x4712;

fax: +55 19 3429 4610.

E-mail address: lfpires@cena.usp.br (L.F. Pires).

0167-1987/$ – see front matter # 2004 Elsevier B.V. All rights reserved

doi:10.1016/j.still.2004.06.003

chambers (Richards, 1941; Richards and Fireman,

1943). Some other methods can also be mentioned,

e.g. centrifuges (Centurion et al., 1997), tensiometers

(Perroux et al., 1982) and suction tables (Jamison,

1958).

The traditional pressure chamber method involves

the establishment of a series of equilibria between the

water in the soil sample and the water at chosen

potentials (Klute, 1986). The hydraulic contact

between the water of the soil sample and the water

at the reference potential is made through a porous

plate or membrane. After pressure application, at each

.

L.F. Pires et al. / Soil & Tillage Research 82 (2005) 89–9790

equilibrium, the soil water content is determined

through gravimetry.

Since the idealization of the method, few improve-

ments were introduced despite the fact that some

practical problems still remain, e.g. (1) the difficulty

of a correct judgement of equilibrium (Bacchi et al.,

1998; Centurion et al., 1997); (2) the risk of changes in

soil structure and water retention characteristics of the

sample, due to its frequent manipulation during u

measurements at each chosen potential (Moraes et al.,

1993); and (3) the long time required for the whole

process, mainly due to sample weighing and re-

saturation (also affected by hysteresis) after each

equilibrium (Williams et al., 1992).

Bacchi et al. (1998), in a theoretical approach,

proposed the utilization of the gamma beam attenua-

tion technique as an auxiliary tool, associated to the

traditional pressure chambers, to obtain the water

retention curve. The gamma-ray attenuation technique

permits simultaneous nondestructive determinations

of soil bulk density and soil water content, and offers

many advantages in relation to the corresponding

conventional methods (Jalbert and Dane, 2001; Dane

et al., 1992; Ferraz and Mansell, 1979; Olesen, 1973;

De Swart and Groenevelt, 1971; Reichardt, 1965; van

Bavel, 1959).

The procedure idealized by Bacchi et al. (1998)

includes an adaptation of the conventional pressure

chamber to permit the gamma-ray beam to pass

through the soil sample inside the chamber, allowing

for a continuous soil moisture monitoring during the

whole process of soil water retention measurements,

without the opening of the chamber for u measure-

ments at each step. This new improvement leads also

to a more precise judgement of equilibria, since soil

moisture is continuously monitored inside the

chamber. Sample manipulation is eliminated since

it is saturated only once at the beginning of the

process, minimizing the risk of modifications in

structure and, as a consequence, the time required for

the whole water retention curve establishment is

shortened.

The present paper presents practical results of

water retention curves measured through the gamma

attenuation technique, as described by Bacchi et al.

(1998), for two soils different in texture and makes a

comparative analysis of the results with water

retention data obtained conventionally.

2. Theory

2.1. Richards method

The traditional method of determining soil water

retention curves involves establishing a series of

equilibria of the water in the soil sample at known

potentials (Klute, 1986). The instrument for determin-

ing these curves is a steel pressure chamber, inside of

which is a porous plate saturated with water, at the

bottom continuously submitted to atmospheric pres-

sure, on which soil samples are disposed in a way to

obtain hydraulic contact between sample and porous

plate. With constant pressure applications to the

chamber, soil samples lose water through the plate

until equilibrium is reached. A control panel with

pressure valves and manometers allows constant

pressure outputs in the range 0–1.5 MPa.

Initially, soil samples are water-saturated by

soaking them for 24 h, placing them on a tray with

a water level just below the top of the soil cores. After

that, soil samples are transferred to the previously

saturated porous plate, being sure to obtain hydraulic

contact between them. The chamber is closed and a

desired air pressure P is applied to it, driving away the

soil water retained at pressures below P, until

equilibrium is obtained.

Therefore, at each equilibrium condition, the pressure

applied to the soil sample represents the value of the

matric potential for the respective water content u. After

each equilibrium, the chamber is opened; soil samples

are weighted, re-saturated and placed again to be

submitted to a new pressure application. For the last

pressure value, the sample is oven-dried to recalculate u

for all pressure steps. The relationship between the soil

water matric potential and each respective water content

(obtained by weighing) for different equilibrium

conditions define the water retention curve.

2.2. Gamma-ray attenuation

When a gamma-ray beam passes through a soil

sample of thickness x (cm), photons are transmitted

following the Beer–Lambert law (Wang et al., 1975).

For soil samples, considering the two phases, solid

material and water, this law can be written as follows:

I ¼ I0 exp ½�xðmsrs þ mwuÞ (1)

L.F. Pires et al. / Soil & Tillage Research 82 (2005) 89–97 91

where I and I0 are, respectively, the rates of the

emerging and the incident photon beams; ms and

mw (cm2 g�1), the soil and water mass attenuation

coefficients; rs (g cm�3), the soil bulk density; and u(cm3 cm�3), the soil water content.

For soils in which the bulk density remains constant

during soil water content changes, if ms, mw, rs and x

are known, it is possible to obtain u by the gamma-ray

attenuation technique, by solving Eq. (1) for u:

u ¼ 1

xmw

lnI0

I

� �� xmsrs

� �(2)

For the case of swelling soils, a double energy

gamma-ray attenuation system can be used to evaluate

u and rs, simultaneously, using a set of equations

(Stroosnijder and De Swart, 1974). In this case, after

each pressure application, it is possible to measure u

and rs, taking into account changes in rs due to soil

shrinking.

2.3. Statistical error by nuclear method

Through the error propagation (Eq. (3)), it is

possible to estimate the error associated to soil water

content evaluation:

du ¼ @u

@AdA

� �þ @u

@xdx

� �þ @u

@rs

drs

� �

þ @u

@mw

dmw

� �þ @u

@ms

dms

� �(3)

where A = ln(I/I0). In ideal conditions, the parameters

x, rs, mw and ms can be considered constants and the

soil water content variation due to these parameters

become zero. In real laboratory conditions, these

parameters can be minimized turning very small the

second, third, fourth and fifth terms on the right side of

Eq. (3). In this case, these soil water content variations

can be considered directly related to the uncertainty of

the radioactive decay process.

The error associated to the rates of photon beam

measurements is given byffiffiI

p. When the increases of I

are small, it is possible to obtain:

dI

Iffi 1ffiffi

Ip (4)

Therefore, changes in Eq. (4) cause variations in u

values. Solving the first partial derivative in Eq. (3), it

is possible to obtain the uncertainty of soil water

content when it is measured by the nuclear method:

du ¼ � 1

xmw

ffiffiI

p�

ffiffiffiffiI0

pffiffiffiffiffiffiI0I

p� �

(5)

This soil water content error represents the

minimum measurable interval du when using the

nuclear method, and consequently, the u measurement

intervals are limited by du, which can be minimized

according to the choices of soil sample, radioactive

source, collimators, the distance between source and

detector, etc.

3. Material and methods

Soil core samples were taken from a soil profile of

an Oxisol (soil 1) and a Rhodic Kandiudox (soil 2),

from an experimental field of ESALQ/USP, in

Piracicaba, State of Sao Paulo, Brazil (22840S;

478380W; 580 m above sea level).

Samples were collected using aluminum cylinders

3.0 cm high and 5.0 cm in diameter. After sample

collection, top and bottom of the samples were

trimmed flat. The wetting procedure to saturate the

samples consisted in soaking them using a tray with

the water level just below the top of the cylinders. This

procedure is made over a period of 1 or 2 days to allow

saturation of the soil and to avoid the presence of the

entrapped air bubbles. After the wetting procedure,

soil samples were placed in contact with the porous

plate inside a pressure chamber and air pressure was

applied.

Water retention curves were determined on the very

same samples by (i) the traditional method, using a

commercial low-pressure extraction vessel (CAT No.

1600 – Soil Moisture Equipment Co.) that supports

pressures up to 0.5 MPa with pressure intervals

between points of 0.1 MPa and (ii) using the gamma

monoenergetic beam technique (Eq. (2)) applied to a

projected and constructed pressure chamber, consist-

ing of an acrylic cylinder 15.3 cm high, 7.1 and

7.9 cm, internal and external diameters, respectively,

with a ceramic porous plate at the bottom (Fig. 1). The

pressure chamber was positioned between the source

and the detector with the gamma-ray beam always

crossing the center of the chamber and the soil sample

L.F. Pires et al. / Soil & Tillage Research 82 (2005) 89–9792

Fig. 1. Acrylic pressure chamber built to obtain the water retention

curves by the nuclear method. Inside the chamber it is possible to see

the aluminum cylinder containing the soil sample, and in the top of

the chamber, the system for pressure input.

Table 1

(Fig. 2). The monoenergetic beam was used to

evaluate soil water contents u, since the employed

soils have a rigid structure.

The gamma-ray source has an activity of 7.4 GBq

consisting of 241Am, with an energy peak of

59.54 keV. The detection system consists of a 300 �300 NaI(Tl) scintillation crystal, photomultiplier, high

voltage supply, amplifier, monochannel analyzer, and

a counter/timer. The counter is interfaced with a PC,

which allows an easy automation of data acquisition.

Fig. 2. Scheme of the gamma-ray beam attenuation system to

evaluate soil water retention curves.

Rectangular slit (1.0 cm high � 0.2 cm wide) and

circular (0.4 cm diameter) lead collimators were

placed near the source and the detector and were

adjusted and aligned in order to produce a vertical and

circular beam.

4. Results and discussion

Tables 1 and 2 present the soil physical and

chemical characteristics and the attenuation coeffi-

cients for water and the two soils.

The mass attenuation coefficients for soil and water

are in agreement with those found in the literature for

59.54 keV photons of 241Am (Stroosnijder and De

Swart, 1974; Ferraz and Mansell, 1979; Oliveira et al.,

1997; Vaz et al., 1999; Cunha e Silva et al., 2000).

The choice of an acrylic pressure chamber for the

determination of retention curves using the gamma

beam technique was due to the relatively low activity

of the available radioactive source, the wall chamber

attenuation, and the decrease of the intensity of the

photons following the inverse of the square distance. If

one uses the traditional steel pressure chamber, the

distance between the source and detector would be of

the order of 40 cm and using the acrylic pressure

chamber, this distance is reduced to 18 cm, allowing a

more intense gamma-ray beam reach the detector. The

traditional pressure chamber supports up to 40 soil

samples each time and our experimental acrylic

Physical and chemical soil characteristics of the 0–0.15 m layer of

the soils utilized in the experiment

Characteristic Soil 1 Soil 2

Sand (%) 77 36

Silt (%) 5 19

Clay (%) 18 45

Particle density (g cm�3) 2.473 2.942

Bulk density (g cm�3) 1.618 1.407

Porosity (%) 34.5 52.1

Saturated water content (cm3 cm�3)a 0.265 0.491

pH (in CaCl2) 3.9 5.0

Organic matter (g cm�3) 0.016 0.025

Calcium (molc m�3) 13.0 64.0

Magnesium (molc m�3) 4.0 18.0

Potassium (molc m�3) 2.6 4.3

a Saturated water content was obtained through the gamma-ray

beam attenuation method (Ferraz and Mansell, 1979).

L.F. Pires et al. / Soil & Tillage Research 82 (2005) 89–97 93

Table 2

Mass and linear attenuation coefficients for water and both soil types for the 59.54 keV gamma radiation

Sample Collimator m (cm�1) m/r (cm2 g�1) sm (cm2 g�1) CV (%)

Water Rectangular 0.19295 0.19295 0.00071 0.37

Soil 1 Rectangular 0.28561 0.25672 0.00103 0.40

Soil 2 Rectangular 0.48520 0.36341 0.00156 0.43

sm = Standard deviation; CV = coefficient of variation.

Table 3

Matric potential (cm), soil water content (u), standard deviation and coefficient of variation for each applied pressure, for both soils, and the two

methods

Soil 1 Soil 2

Traditional method

cm (MPa) uT (cm3 cm�3) suT (cm3 cm�3) CV (%) Number of curves uT (cm3 cm�3) suT (cm3 cm�3) CV (%) Number

of curves

0.020 0.1890 0.0054 2.9 13 0.3899 0.0113 2.9 10

0.040 0.1722 0.0060 3.5 13 0.3792 0.0095 2.5 10

0.060 0.1649 0.0058 3.5 13 0.3730 0.0114 3.1 10

0.080 0.1593 0.0058 3.7 13 0.3634 0.0127 3.5 10

0.100 0.1510 0.0046 3.0 13 0.3575 0.0101 2.8 10

Nuclear method

cm (MPa) uN (cm3 cm�3) suN (cm3 cm�3) CV (%) Number of curves uN (cm3 cm�3) suN (cm3 cm�3) CV (%) Number

of curves

0.000 0.2570 0.0189 7.4 6 0.4461 0.0364 7.6 6

0.025 0.1855 0.0065 3.5 6 0.4025a 0.0110 2.7 6

0.050 0.1717 0.0055 3.2 6 0.3851 0.0081 2.1 6

0.075 0.1625 0.0042 2.6 6 0.3708a 0.0087 2.4 6

0.100 0.1542 0.0068 4.4 6 0.3568 0.0084 2.4 6

su = Standard deviation.a Values calculated from theoretical adjustment.

1 The average soil water content in this case was obtained

through: u ¼ ðuPi þ uPiþ1Þ=2, where P represents air pressure. In

Fig. 5 was excluded the differences between pressures 0 and

0.025 MPa for all curves obtained by the nuclear method.

chamber operates with only one sample. This limitation,

however, can be surpassed by the development of a new

pressure chamber model and instrumentation of the

method. Table 3 and Figs. 3 and 4 show the results

concerning soil water contents for the different applied

pressures for both soils and methods.

The pressure interval, and consequent number of

points per curve for the nuclear method, was chosen in

order to have variations in u compatible with the

resolution of the method. Due to the fact that the

photon emission by a radioactive source is a statistical

process, the determination of u is related with the241Am photon emission per unit of time. Due to this,

there is a minimum measurable interval du (Eq. (5))

for the nuclear method, which has to be taken into

account when establishing pressure steps DP. This

explains the differences between the pressure steps

applied in the two methods, shown in Table 3. For the

case of soils 1 and 2, these average minimum intervals

du for the nuclear method were 0.0080 and

0.0103 cm3 cm�3, respectively. Fig. 5 shows results

of du for soil samples presented in Figs. 3 and 4.

Differences between each average soil water content1

value in y-axis (dash horizontal lines) represent the

minimum interval in which u can be evaluated with

guarantee. All Du values smaller than this interval

(average points in Fig. 5 with its respective Du values)

do not permit to identify if the variation obtained is

really due to the soil water content variation or due to

the uncertainty caused by the statistical process of

radioactive decay. Fig. 5 shows that soils 1 and 2

L.F. Pires et al. / Soil & Tillage Research 82 (2005) 89–9794

Fig. 3. (A) Soil water retention curves obtained by both, traditional and nuclear (rectangular slit collimator) methods for soil 1, (B) deviation

analyzes for the curve adjustments between the two methods, (C) soil water retention curves obtained by both, traditional and nuclear (circular

collimator) methods for soil 1, and (D) deviation analyzes for the curve adjustments between the two methods. Soil water contents represent the

mean of three values for each curve obtained (rectangular and circular collimators).

present, for rectangular collimators, an interval

between 0.050 and 0.075 MPa with Du smaller than

du. For soil 1, three curves with the same problem

were found and for soil 2 just one, showing that for soil

1 it is necessary to use larger number of soil samples in

order to have better soil water retention curve

evaluations using the nuclear method.

From Figs. 3 and 4, it is possible to compare the

results obtained by the two methods. Higher devia-

tions between the two methods for the two soils occur

for values of soil moisture near saturation. A possible

cause of this fact could be the variability between

samples or the process of soil sample saturation.

Variability of soil samples can explain this deviation

because samples utilized in water retention curve

measurements by two methods, although collected

near each other, were different. For soil saturation,

samples were submitted to the saturation process at

distinct days, and although the same procedure was

applied (EMBRAPA, 1998), differences in the

saturation level can occur during this process. These

differences can be reflected in the soil moisture values

near saturation. Higher deviations were found for soil

2 (Fig. 4). After the construction of the retention

curves, soil samples were destroyed, and it was

observed that the soil samples 2 presented some

fractures and small holes inside, which possibly

affected the soil moisture values obtained by the

nuclear method. This problem can be avoided with the

aid of the same gamma equipment, working as a

computed tomograph. In this way, it is possible to

obtain an image of the soil sample before performing

retention curves and then to choose the best soil

sample for the determinations.

The deviations between the two methods can also

be caused by small modifications in soil structure

during the determination of the retention curve,

mainly in the case of the traditional method, which

can affect the value of soil bulk density that is

considered constant in Eq. (2). However, for the water

potential range (0–0.1 MPa) utilized here to obtain the

retention curves, the possible changes in soil structure

that could affect soil bulk densities were smaller than

the possible errors caused by the statistics of the

L.F. Pires et al. / Soil & Tillage Research 82 (2005) 89–97 95

Fig. 4. (A) Soil water retention curves obtained by both, traditional and nuclear (rectangular slit collimator) methods for soil 2, (B) deviation

analyzes for the curve adjustments between the two methods, (C) soil water retention curves obtained by both, traditional and nuclear (circular

slit collimator) methods for soil 2, and (D) deviation analyzes for the curve adjustments between the two methods. Soil water contents represent

the mean of three values for each curve obtained (rectangular and circular collimators).

source radioactivity. It is important to have in mind

that the soil sample utilized to obtain the retention

curve by a traditional method is submitted to several

wetting and drying cycles, which can lead to changes

in its structure (Hussein and Adey, 1998) and affect the

water retention curves. For the proposed nuclear

method the soil sample is submitted just one time to

the wetting and drying, which represents another

advantage of this method.

Table 4 shows the van Genuchten parameters for

soil samples presented in Figs. 3 and 4. The program

SWRC (Soil Water Retention Curve) developed by

Dourado-Neto et al. (2002) was used for the van

Genuchten adjustment. Higher values of a and n for

the curves obtained by the traditional method for both

soils indicate that these curves present a larger slope

and are steeper than the curves obtained by the nuclear

method (for both collimators). The r2 coefficients

values demonstrate a very good adjustment of the

experimental data to the model. Using the van

Genuchten equation, it was possible to estimate the

u values at the field capacity (0.033 MPa) for the two

methods, and the results were 0.2014 (soil 1) and

0.3969 cm3 cm�3 (soil 2) for the traditional method,

and 0.1777 and 0.1813 cm3 cm�3 (soil 1) and 0.3927

and 0.4031 cm3 cm�3 (soil 2) for the nuclear method

using the rectangular and circular collimators,

respectively. Unfortunately, since it was applied

different intervals of matric potential to determine

the soil water retention curves by the two methods

(Table 3), it was not possible to make a statistical

evaluation of the retention curve data. However, the

two methods present one common matric potential

value (0.1 MPa) for which the Tukey statistical

method was applied. The test shows that there are

no statistical significant differences (at 5% probability

level) between the soil water contents at 0.1 MPa

evaluated by the two methods.

Regarding the judgment of the equilibrium condi-

tion, since the gamma-ray system is linked to a

computer, the proposed technique allows, through a

software specifically elaborated for data acquisition,

to obtain the right moment to change the chamber

pressure to a new desired value, leading to a reduction

L.F. Pires et al. / Soil & Tillage Research 82 (2005) 89–9796

Fig. 5. Resolution of the nuclear method for soils 1 (A) and (B), and soil 2 (C) and (D). du represents the minimum measurable interval by the

nuclear method obtained by Eq. (5) and Du indicates the differences of soil water contents between Pi and Pi+1 pressure values.

of the time required to obtain for the whole retention

curve. In the conventional method, it is not possible

to determine with precision the exact moment of

the equilibrium, which is defined empirically after

the water outflow stops. For the nuclear method, the

procedure adopted to define the exact moment of the

equilibrium was following the variations in the soil

Table 4

Water retention curve parameters obtained by the van Genuchten (1980)

Parameters Soil 1

TRADa NUCL Cb NUCL

a (cm�1) 0.0096 0.0055 0.0018

us (cm3 cm�3) 0.2398 0.2539 0.2591

ur (cm3 cm�3) 0 0 0

m 0.0719 0.3556 0.6292

n 2.0251 0.7655 0.3777

r2 0.990 0.999 0.992

a Traditional method.b Nuclear method: circular collimator.c Nuclear method: rectangular collimator.

moisture values every day. When u reached a constant

value for each specific potential value (Cm), this value

was recorded and a new pressure step was applied. The

times required for the whole retention curve determi-

nation, with four points, for the soils 1 and 2, were 12

and 32 days, respectively, by the nuclear method. In

the case of the traditional method, these times were 20

model for the soils 1 and 2 (Figs. 3 and 4)

Soil 2

Rc TRADa NUCL Cb NUCL Rc

0.0035 0.0001 0.0021

0.3931 0.4798 0.4539

0 0 0

0.0234 1.0833 0.2475

3.1126 0.5119 0.6261

0.990 0.992 0.998

L.F. Pires et al. / Soil & Tillage Research 82 (2005) 89–97 97

and 48 days. These results allow to conclude that the

nuclear method presents some advantages in relation

to the traditional method, like the higher accuracy in

the determination of time of equilibrium, and

reduction in the time required for the whole retention

curve determination because the soil sample in the

nuclear method is submitted one time to the wetting

and drying.

Acknowledgements

To FAPESP (Grant Nos. 00/05732-0 and 02/05066-5)

for financial support.

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